diff --git a/src/ifcgeom/mapping/IfcCurveSegment.cpp b/src/ifcgeom/mapping/IfcCurveSegment.cpp
index bfe8a191ca..1ca2e1b56f 100644
--- a/src/ifcgeom/mapping/IfcCurveSegment.cpp
+++ b/src/ifcgeom/mapping/IfcCurveSegment.cpp
@@ -448,14 +448,17 @@ class curve_segment_evaluator {
 
     // defines the parent_curve_fn_ functor for cant segments.
     void set_cant_spiral_function(std::function<double(double)> Superelevation, std::function<double(double)> SuperelevationSlope, std::function<double(double)> Cant) {
-        auto dy = (*curve_segment_placement_)(1, 2); // placement dy
-        auto dz = (*curve_segment_placement_)(2, 2); // placement dz
+        // compute start cross slope angle, measured relative to (0,0,1)
+        auto dy = (*curve_segment_placement_)(1, 2); // Axis.dy
+        auto dz = (*curve_segment_placement_)(2, 2); // Axis.dz
         auto start_angle = atan2(dz, dy);
 
+        // compute end cross slope angle, measured relative to (0,0,1)
         dy = (next_segment_placement_.has_value() ? (*next_segment_placement_)(1, 2) : 0.0);
         dz = (next_segment_placement_.has_value() ? (*next_segment_placement_)(2, 2) : 1.0);
         auto end_angle = atan2(dz, dy);
 
+        // angular change of railhead cross slope over the length of the segment
         auto delta_angle = end_angle - start_angle;
         auto start_cant = Cant(0.0 /*start_*/);
         auto end_cant = Cant(/* start_ + */ length_);
@@ -529,7 +532,7 @@ class curve_segment_evaluator {
         if (segment_type_ == ST_CANT) {
             boost::optional<std::function<double(double)>> super, slope;
             std::tie(super, slope) = get_superelevation_functions();
-            auto cant = [A, L](double t) -> double { return A ? L * A * t / fabs(pow(A, 3)) : 0.0; };
+            auto cant = [A, L](double t) -> double { return A ? L * L * A * t / fabs(pow(A, 3)) : 0.0; };
 
             if (!super.has_value()) {
                 super = cant;
@@ -579,9 +582,9 @@ class curve_segment_evaluator {
             std::tie(super, slope) = get_superelevation_functions();
             
             auto cant = [constant_term, cosine_term, L](double t) -> double {
-                auto a0 = constant_term.has_value() ? L / constant_term.value() : 0.0;
-                auto a1 = (L / cosine_term) * cos(PI * t / L);
-                return a0 + a1;
+                auto a0 = constant_term.has_value() ? 1 / constant_term.value() : 0.0;
+                auto a1 = (1 / cosine_term) * cos(PI * t / L);
+                return L*L*(a0 + a1);
             };
 
             if (!super.has_value()) {
@@ -627,7 +630,7 @@ class curve_segment_evaluator {
         if (segment_type_ == ST_HORIZONTAL) {
             auto theta = [constant_term, linear_term, sine_term, L](double t) -> double {
                 auto a0 = constant_term.has_value() ? t / constant_term.value() : 0.0;
-                auto a1 = linear_term.has_value() ? sign(linear_term.value()) * pow(t / linear_term.value(), 2.0) / 2.0 : 0.0;
+                auto a1 = linear_term.has_value() ? (linear_term.value() / fabs(linear_term.value())) * pow(t / linear_term.value(), 2.0) / 2.0 : 0.0;
                 auto a2 = -1.0 * (L / (2 * PI * sine_term)) * (cos(2 * PI * t / L) - 1.0);
                 return a0 + a1 + a2;
             };
@@ -635,7 +638,7 @@ class curve_segment_evaluator {
             auto fn_y = [theta](double t) -> double { return sin(theta(t)); };
             auto curvature = [constant_term, linear_term, sine_term, L](double t) -> double {
                 auto a0 = constant_term.has_value() ? L / constant_term.value() : 0.0;
-                auto a1 = linear_term.has_value() ? sign(linear_term.value()) * pow(L / linear_term.value(), 2.0)*(t/L) : 0.0;
+                auto a1 = linear_term.has_value() ? (linear_term.value() / fabs(linear_term.value())) * pow(L / linear_term.value(), 2.0) * (t / L) : 0.0;
                 auto a2 = (L / sine_term) * sin(2 * PI * t / L);
                 return a0 + a1 + a2;
             };
@@ -646,10 +649,10 @@ class curve_segment_evaluator {
             std::tie(super, slope) = get_superelevation_functions();
             
             auto cant = [constant_term, linear_term, sine_term, L](double t) -> double {
-               auto a0 = constant_term.has_value() ? L / constant_term.value() : 0.0;
-               auto a1 = linear_term.has_value() ? sign(linear_term.value()) * pow(L / linear_term.value(), 2.0) * (t / L) : 0.0;
-               auto a2 = (L / sine_term) * sin(2 * PI * t / L);
-               return a0 + a1 + a2;
+               auto a0 = constant_term.has_value() ? 1 / constant_term.value() : 0.0;
+               auto a1 = linear_term.has_value() ? (linear_term.value()/fabs(linear_term.value())) * pow(1 / linear_term.value(), 2.0) * t : 0.0;
+               auto a2 = (1 / sine_term) * sin(2 * PI * t / L);
+               return L*L*(a0 + a1 + a2);
             };
 
             if (!super.has_value()) {
@@ -681,14 +684,14 @@ class curve_segment_evaluator {
 
     void polynomial_spiral(boost::optional<double> A0, boost::optional<double> A1, boost::optional<double> A2, boost::optional<double> A3, boost::optional<double> A4, boost::optional<double> A5, boost::optional<double> A6, boost::optional<double> A7) {
         auto theta = [A0, A1, A2, A3, A4, A5, A6, A7, start = start_ * length_unit_, lu = length_unit_](double t) -> double {
-            auto a0 = A0.has_value() ? t / (A0.value() * lu) : 0.0;
-            auto a1 = A1.has_value() ? A1.value() * lu * std::pow(t, 2) / (2 * fabs(std::pow(A1.value() * lu, 3))) : 0.0;
-            auto a2 = A2.has_value() ? std::pow(t, 3) / (3 * std::pow(A2.value() * lu, 3)) : 0.0;
-            auto a3 = A3.has_value() ? A3.value() * lu * std::pow(t, 4) / (4 * fabs(std::pow(A3.value() * lu, 5))) : 0.0;
-            auto a4 = A4.has_value() ? std::pow(t, 5) / (5 * std::pow(A4.value() * lu, 5)) : 0.0;
-            auto a5 = A5.has_value() ? A5.value() * lu * std::pow(t, 6) / (6 * fabs(std::pow(A5.value() * lu, 7))) : 0.0;
-            auto a6 = A6.has_value() ? std::pow(t, 7) / (7 * std::pow(A6.value() * lu, 7)) : 0.0;
-            auto a7 = A7.has_value() ? A7.value() * lu * std::pow(t, 8) / (8 * fabs(std::pow(A7.value() * lu, 9))) : 0.0;
+            auto a0 = A0.get_value_or(0.0) != 0.0 ? t / (A0.value() * lu) : 0.0;
+            auto a1 = A1.get_value_or(0.0) != 0.0 ? A1.value() * lu * std::pow(t, 2) / (2 * fabs(std::pow(A1.value() * lu, 3))) : 0.0;
+            auto a2 = A2.get_value_or(0.0) != 0.0 ? std::pow(t, 3) / (3 * std::pow(A2.value() * lu, 3)) : 0.0;
+            auto a3 = A3.get_value_or(0.0) != 0.0 ? A3.value() * lu * std::pow(t, 4) / (4 * fabs(std::pow(A3.value() * lu, 5))) : 0.0;
+            auto a4 = A4.get_value_or(0.0) != 0.0 ? std::pow(t, 5) / (5 * std::pow(A4.value() * lu, 5)) : 0.0;
+            auto a5 = A5.get_value_or(0.0) != 0.0 ? A5.value() * lu * std::pow(t, 6) / (6 * fabs(std::pow(A5.value() * lu, 7))) : 0.0;
+            auto a6 = A6.get_value_or(0.0) != 0.0 ? std::pow(t, 7) / (7 * std::pow(A6.value() * lu, 7)) : 0.0;
+            auto a7 = A7.get_value_or(0.0) != 0.0 ? A7.value() * lu * std::pow(t, 8) / (8 * fabs(std::pow(A7.value() * lu, 9))) : 0.0;
             return a0 + a1 + a2 + a3 + a4 + a5 + a6 + a7;
         };
 
@@ -699,14 +702,14 @@ class curve_segment_evaluator {
         // this is same as cant function in polynomial_cant_spiral
         auto curvature = [A0, A1, A2, A3, A4, A5, A6, A7, start = start_, L = length_, lu = length_unit_, length = length_](double t) -> double {
             t += start;
-            auto a0 = A0.has_value() ? 1 / (A0.value() * lu) : 0.0;
-            auto a1 = A1.has_value() ? A1.value() * lu * t / fabs(std::pow(A1.value() * lu, 3)) : 0.0;
-            auto a2 = A2.has_value() ? std::pow(t, 2) / std::pow(A2.value() * lu, 3) : 0.0;
-            auto a3 = A3.has_value() ? A3.value() * lu * std::pow(t, 3) / fabs(std::pow(A3.value() * lu, 5)) : 0.0;
-            auto a4 = A4.has_value() ? std::pow(t, 4) / std::pow(A4.value() * lu, 5) : 0.0;
-            auto a5 = A5.has_value() ? A5.value() * lu * std::pow(t, 5) / fabs(std::pow(A5.value() * lu, 7)) : 0.0;
-            auto a6 = A6.has_value() ? std::pow(t, 6) / std::pow(A6.value() * lu, 7) : 0.0;
-            auto a7 = A7.has_value() ? A7.value() * lu * std::pow(t, 7) / fabs(std::pow(A7.value() * lu, 9)) : 0.0;
+            auto a0 = A0.get_value_or(0.0) != 0.0 ? 1 / (A0.value() * lu) : 0.0;
+            auto a1 = A1.get_value_or(0.0) != 0.0 ? A1.value() * lu * t / fabs(std::pow(A1.value() * lu, 3)) : 0.0;
+            auto a2 = A2.get_value_or(0.0) != 0.0 ? std::pow(t, 2) / std::pow(A2.value() * lu, 3) : 0.0;
+            auto a3 = A3.get_value_or(0.0) != 0.0 ? A3.value() * lu * std::pow(t, 3) / fabs(std::pow(A3.value() * lu, 5)) : 0.0;
+            auto a4 = A4.get_value_or(0.0) != 0.0 ? std::pow(t, 4) / std::pow(A4.value() * lu, 5) : 0.0;
+            auto a5 = A5.get_value_or(0.0) != 0.0 ? A5.value() * lu * std::pow(t, 5) / fabs(std::pow(A5.value() * lu, 7)) : 0.0;
+            auto a6 = A6.get_value_or(0.0) != 0.0 ? std::pow(t, 6) / std::pow(A6.value() * lu, 7) : 0.0;
+            auto a7 = A7.get_value_or(0.0) != 0.0 ? A7.value() * lu * std::pow(t, 7) / fabs(std::pow(A7.value() * lu, 9)) : 0.0;
             return L * (a0 + a1 + a2 + a3 + a4 + a5 + a6 + a7);
         };
 
@@ -721,15 +724,15 @@ class curve_segment_evaluator {
 
         auto cant = [A0, A1, A2, A3, A4, A5, A6, A7, start = start_, L = length_, lu = length_unit_, length = length_](double t) -> double {
             t += start;
-            auto a0 = A0.has_value() ? 1 / (A0.value() * lu) : 0.0;
-            auto a1 = A1.has_value() ? A1.value() * lu * t / fabs(std::pow(A1.value() * lu, 3)) : 0.0;
-            auto a2 = A2.has_value() ? std::pow(t, 2) / std::pow(A2.value() * lu, 3) : 0.0;
-            auto a3 = A3.has_value() ? A3.value() * lu * std::pow(t, 3) / fabs(std::pow(A3.value() * lu, 5)) : 0.0;
-            auto a4 = A4.has_value() ? std::pow(t, 4) / std::pow(A4.value() * lu, 5) : 0.0;
-            auto a5 = A5.has_value() ? A5.value() * lu * std::pow(t, 5) / fabs(std::pow(A5.value() * lu, 7)) : 0.0;
-            auto a6 = A6.has_value() ? std::pow(t, 6) / std::pow(A6.value() * lu, 7) : 0.0;
-            auto a7 = A7.has_value() ? A7.value() * lu * std::pow(t, 7) / fabs(std::pow(A7.value() * lu, 9)) : 0.0;
-            return L * (a0 + a1 + a2 + a3 + a4 + a5 + a6 + a7);
+            auto a0 = A0.get_value_or(0.0) != 0.0 ? 1 / (A0.value() * lu) : 0.0;
+            auto a1 = A1.get_value_or(0.0) != 0.0 ? A1.value() * lu * t / fabs(std::pow(A1.value() * lu, 3)) : 0.0;
+            auto a2 = A2.get_value_or(0.0) != 0.0 ? std::pow(t, 2) / std::pow(A2.value() * lu, 3) : 0.0;
+            auto a3 = A3.get_value_or(0.0) != 0.0 ? A3.value() * lu * std::pow(t, 3) / fabs(std::pow(A3.value() * lu, 5)) : 0.0;
+            auto a4 = A4.get_value_or(0.0) != 0.0 ? std::pow(t, 4) / std::pow(A4.value() * lu, 5) : 0.0;
+            auto a5 = A5.get_value_or(0.0) != 0.0 ? A5.value() * lu * std::pow(t, 5) / fabs(std::pow(A5.value() * lu, 7)) : 0.0;
+            auto a6 = A6.get_value_or(0.0) != 0.0 ? std::pow(t, 6) / std::pow(A6.value() * lu, 7) : 0.0;
+            auto a7 = A7.get_value_or(0.0) != 0.0 ? A7.value() * lu * std::pow(t, 7) / fabs(std::pow(A7.value() * lu, 9)) : 0.0;
+            return L * L * (a0 + a1 + a2 + a3 + a4 + a5 + a6 + a7);
         };
 
         if (!super.has_value()) {
@@ -739,14 +742,14 @@ class curve_segment_evaluator {
         if (!slope.has_value()) {
             slope = [A1, A2, A3, A4, A5, A6, A7, start = start_, L = length_, lu = length_unit_, length = length_](double t) -> double {
                 t += start;
-                auto a1 = A1.has_value() ? A1.value() * lu / fabs(std::pow(A1.value() * lu, 3)) : 0.0;
-                auto a2 = A2.has_value() ? 2 * t / std::pow(A2.value() * lu, 3) : 0.0;
-                auto a3 = A3.has_value() ? 3 * A3.value() * lu * std::pow(t, 2) / fabs(std::pow(A3.value() * lu, 5)) : 0.0;
-                auto a4 = A4.has_value() ? 4 * std::pow(t, 3) / std::pow(A4.value() * lu, 5) : 0.0;
-                auto a5 = A5.has_value() ? 5 * A5.value() * lu * std::pow(t, 4) / fabs(std::pow(A5.value() * lu, 7)) : 0.0;
-                auto a6 = A6.has_value() ? 6 * std::pow(t, 5) / std::pow(A6.value() * lu, 7) : 0.0;
-                auto a7 = A7.has_value() ? 7 * A7.value() * lu * std::pow(t, 6) / fabs(std::pow(A7.value() * lu, 9)) : 0.0;
-                return L * (a1 + a2 + a3 + a4 + a5 + a6 + a7);
+                auto a1 = A1.get_value_or(0.0) != 0.0 ? A1.value() * lu / fabs(std::pow(A1.value() * lu, 3)) : 0.0;
+                auto a2 = A2.get_value_or(0.0) != 0.0 ? 2 * t / std::pow(A2.value() * lu, 3) : 0.0;
+                auto a3 = A3.get_value_or(0.0) != 0.0 ? 3 * A3.value() * lu * std::pow(t, 2) / fabs(std::pow(A3.value() * lu, 5)) : 0.0;
+                auto a4 = A4.get_value_or(0.0) != 0.0 ? 4 * std::pow(t, 3) / std::pow(A4.value() * lu, 5) : 0.0;
+                auto a5 = A5.get_value_or(0.0) != 0.0 ? 5 * A5.value() * lu * std::pow(t, 4) / fabs(std::pow(A5.value() * lu, 7)) : 0.0;
+                auto a6 = A6.get_value_or(0.0) != 0.0 ? 6 * std::pow(t, 5) / std::pow(A6.value() * lu, 7) : 0.0;
+                auto a7 = A7.get_value_or(0.0) != 0.0 ? 7 * A7.value() * lu * std::pow(t, 6) / fabs(std::pow(A7.value() * lu, 9)) : 0.0;
+                return L * L * (a1 + a2 + a3 + a4 + a5 + a6 + a7);
             };
         }
 
diff --git a/src/ifcopenshell-python/ifcopenshell/api/alignment/__init__.py b/src/ifcopenshell-python/ifcopenshell/api/alignment/__init__.py
index bb127bc568..ee3e6a451d 100644
--- a/src/ifcopenshell-python/ifcopenshell/api/alignment/__init__.py
+++ b/src/ifcopenshell-python/ifcopenshell/api/alignment/__init__.py
@@ -60,7 +60,6 @@ from .get_curve import get_curve
 from .get_parent_alignment import get_parent_alignment
 from .has_zero_length_segment import has_zero_length_segment
 from .map_alignment_segments import map_alignment_segments
-from .map_alignment_segment import map_alignment_segment
 from .map_alignment_horizontal_segment import map_alignment_horizontal_segment
 from .map_alignment_vertical_segment import map_alignment_vertical_segment
 from .map_alignment_cant_segment import map_alignment_cant_segment
@@ -91,7 +90,6 @@ __all__ = [
     "get_parent_alignment",
     "has_zero_length_segment",
     "map_alignment_segments",
-    "map_alignment_segment",
     "map_alignment_horizontal_segment",
     "map_alignment_vertical_segment",
     "map_alignment_cant_segment",
diff --git a/src/ifcopenshell-python/ifcopenshell/api/alignment/add_zero_length_segment.py b/src/ifcopenshell-python/ifcopenshell/api/alignment/add_zero_length_segment.py
index a161757213..968b681ede 100644
--- a/src/ifcopenshell-python/ifcopenshell/api/alignment/add_zero_length_segment.py
+++ b/src/ifcopenshell-python/ifcopenshell/api/alignment/add_zero_length_segment.py
@@ -45,6 +45,9 @@ def add_zero_length_segment(file: ifcopenshell.file, entity: entity_instance) ->
             f"Expected entity type to be one of {[_ for _ in expected_types]}, instead received '{entity.is_a()}"
         )
 
+    if ifcopenshell.api.alignment.has_zero_length_segment(entity):
+        return  # do nothing if the entity already has a zero length segment
+
     if entity.is_a("IfcCompositeCurve"):
         last_segment = entity.Segments[-1]
         settings = ifcopenshell.geom.settings()
@@ -67,7 +70,7 @@ def add_zero_length_segment(file: ifcopenshell.file, entity: entity_instance) ->
         curve_segment = file.createIfcCurveSegment(
             Transition="DISCONTINUOUS",
             Placement=file.createIfcAxis2Placement2D(
-                Location=file.createIfcCartesianPoint(Coordinates=((x, y))),
+                Location=file.createIfcCartesianPoint(((x, y))),
                 RefDirection=file.createIfcDirection((dx, dy)),
             ),
             SegmentStart=file.createIfcLengthMeasure(0.0),
@@ -80,22 +83,72 @@ def add_zero_length_segment(file: ifcopenshell.file, entity: entity_instance) ->
             if 0 < len(rel.RelatedObjects):
                 last_segment = rel.RelatedObjects[-1]
                 if last_segment.is_a("IfcAlignmentSegment"):
-                    design_parameters = file.createIfcAlignmentHorizontalSegment(
-                        StartPoint=file.createIfcCartesianPoint(
-                            (0.0, 0.0)
-                        ),  # this is a little problematic. need to know the end point and tangent
-                        StartDirection=0.0,  # of the previous segment, which requires geometry mapping
-                        SegmentLength=0.0,
-                        PredefinedType="LINE",
-                    )
-                    segment = file.createIfcAlignmentSegment(
-                        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
-                    )
-                    ifcopenshell.api.nest.assign_object(
-                        file,
-                        related_objects=[
-                            segment,
-                        ],
-                        relating_object=entity,
-                    )
-                    break
+                    if entity.is_a("IfcAlignmentHorizontal"):
+                        design_parameters = file.createIfcAlignmentHorizontalSegment(
+                            StartPoint=file.createIfcCartesianPoint(
+                                (0.0, 0.0)
+                            ),  # this is a little problematic. need to know the end point and tangent
+                            StartDirection=0.0,  # of the previous segment, which requires geometry mapping
+                            SegmentLength=0.0,
+                            PredefinedType="LINE",
+                        )
+                        segment = file.createIfcAlignmentSegment(
+                            GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+                        )
+                        ifcopenshell.api.nest.assign_object(
+                            file,
+                            related_objects=[
+                                segment,
+                            ],
+                            relating_object=entity,
+                        )
+                        break
+                    elif entity.is_a("IfcAlignmentVertical"):
+                        design_parameters = file.createIfcAlignmentVerticalSegment(
+                            StartDistAlong=last_segment.DesignParameters.StartDistAlong
+                            + last_segment.DesignParameters.HorizontalLength,
+                            HorizontalLength=0.0,
+                            StartHeight=0.0,
+                            StartGradient=last_segment.DesignParameters.EndGradient,
+                            EndGradient=last_segment.DesignParameters.EndGradient,
+                            PredefinedType="CONSTANTGRADIENT",
+                        )
+                        segment = file.createIfcAlignmentSegment(
+                            GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+                        )
+                        ifcopenshell.api.nest.assign_object(
+                            file,
+                            related_objects=[
+                                segment,
+                            ],
+                            relating_object=entity,
+                        )
+                        break
+                    elif entity.is_a("IfcAlignmentCant"):
+                        design_parameters = file.createIfcAlignmentCantSegment(
+                            StartDistAlong=last_segment.DesignParameters.StartDistAlong
+                            + last_segment.DesignParameters.HorizontalLength,
+                            HorizontalLength=0.0,
+                            StartCantLeft=(
+                                last_segment.DesignParameters.EndCantLeft
+                                if last_segment.DesignParameters.EndCantLeft != None
+                                else last_segment.DesignParameters.StartCantLeft
+                            ),
+                            StartCantRight=(
+                                last_segment.DesignParameters.EndCantRight
+                                if last_segment.DesignParameters.EndCantRight != None
+                                else last_segment.DesignParameters.StartCantRight
+                            ),
+                            PredefinedType="CONSTANTCANT",
+                        )
+                        segment = file.createIfcAlignmentSegment(
+                            GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+                        )
+                        ifcopenshell.api.nest.assign_object(
+                            file,
+                            related_objects=[
+                                segment,
+                            ],
+                            relating_object=entity,
+                        )
+                        break
diff --git a/src/ifcopenshell-python/ifcopenshell/api/alignment/create_geometric_representation.py b/src/ifcopenshell-python/ifcopenshell/api/alignment/create_geometric_representation.py
index c15fac39a4..8f38d7b2b0 100644
--- a/src/ifcopenshell-python/ifcopenshell/api/alignment/create_geometric_representation.py
+++ b/src/ifcopenshell-python/ifcopenshell/api/alignment/create_geometric_representation.py
@@ -60,6 +60,7 @@ def create_geometric_representation(file: ifcopenshell.file, alignment: entity_i
     if len(layouts) == 1 and len(children) == 0:
         assert layouts[0].is_a("IfcAlignmentHorizontal")
         # Horizontal only - IFC CT 4.1.7.1.1.1
+        ifcopenshell.api.alignment.add_zero_length_segment(file, layouts[0])
         composite_curve = file.createIfcCompositeCurve()
         ifcopenshell.api.alignment.map_alignment_segments(file, layouts[0], composite_curve)
         representation = file.create_entity(
@@ -74,6 +75,8 @@ def create_geometric_representation(file: ifcopenshell.file, alignment: entity_i
         # Horizontal and Vertical - IFC CT 4.1.7.1.1.1
         assert layouts[0].is_a("IfcAlignmentHorizontal")
         assert layouts[1].is_a("IfcAlignmentVertical")
+        ifcopenshell.api.alignment.add_zero_length_segment(file, layouts[0])
+        ifcopenshell.api.alignment.add_zero_length_segment(file, layouts[1])
         composite_curve = file.createIfcCompositeCurve()
         ifcopenshell.api.alignment.map_alignment_segments(file, layouts[0], composite_curve)
         representation = file.create_entity(
@@ -100,6 +103,9 @@ def create_geometric_representation(file: ifcopenshell.file, alignment: entity_i
         assert layouts[0].is_a("IfcAlignmentHorizontal")
         assert layouts[1].is_a("IfcAlignmentVertical")
         assert layouts[2].is_a("IfcAlignmentCant")
+        ifcopenshell.api.alignment.add_zero_length_segment(file, layouts[0])
+        ifcopenshell.api.alignment.add_zero_length_segment(file, layouts[1])
+        ifcopenshell.api.alignment.add_zero_length_segment(file, layouts[2])
         composite_curve = file.createIfcCompositeCurve()
         ifcopenshell.api.alignment.map_alignment_segments(file, layouts[0], composite_curve)
         representation = file.create_entity(
@@ -126,6 +132,7 @@ def create_geometric_representation(file: ifcopenshell.file, alignment: entity_i
     else:
         # Reusing Horizontal - CT 4.1.4.4.1.2
         # Create a representation on the parent alignment
+        ifcopenshell.api.alignment.add_zero_length_segment(file, layouts[0])
         composite_curve = file.createIfcCompositeCurve()
         ifcopenshell.api.alignment.map_alignment_segments(file, layouts[0], composite_curve)
         representation = file.create_entity(
@@ -142,6 +149,7 @@ def create_geometric_representation(file: ifcopenshell.file, alignment: entity_i
         child_layouts = ifcopenshell.api.alignment.get_alignment_layouts(child_alignment)
         if len(child_layouts) == 1:
             assert child_layouts[0].is_a("IfcAlignmentVertical")
+            ifcopenshell.api.alignment.add_zero_length_segment(file, child_layouts[0])
             base_curve = ifcopenshell.api.alignment.get_basis_curve(alignment)
             gradient_curve = file.createIfcGradientCurve(BaseCurve=base_curve)
             ifcopenshell.api.alignment.map_alignment_segments(file, child_layouts[0], gradient_curve)
@@ -156,6 +164,8 @@ def create_geometric_representation(file: ifcopenshell.file, alignment: entity_i
         elif len(child_layouts) == 2:
             assert child_layouts[0].is_a("IfcAlignmentVertical")
             assert child_layouts[1].is_a("IfcAlignmentCant")
+            ifcopenshell.api.alignment.add_zero_length_segment(file, child_layouts[0])
+            ifcopenshell.api.alignment.add_zero_length_segment(file, child_layouts[1])
             base_curve = ifcopenshell.api.alignment.get_basis_curve(alignment)
             gradient_curve = file.createIfcGradientCurve(BaseCurve=base_curve)
             ifcopenshell.api.alignment.map_alignment_segments(file, child_layouts[0], gradient_curve)
diff --git a/src/ifcopenshell-python/ifcopenshell/api/alignment/map_alignment_cant_segment.py b/src/ifcopenshell-python/ifcopenshell/api/alignment/map_alignment_cant_segment.py
index b911fc6b45..cd87c30c69 100644
--- a/src/ifcopenshell-python/ifcopenshell/api/alignment/map_alignment_cant_segment.py
+++ b/src/ifcopenshell-python/ifcopenshell/api/alignment/map_alignment_cant_segment.py
@@ -20,38 +20,367 @@ import ifcopenshell
 from ifcopenshell import entity_instance
 from ifcopenshell.api.alignment import get_axis_subcontext
 from typing import Sequence
+import math
+
+def _get_axis(file: ifcopenshell.file, Ds: float, rail_head_distance: float) -> entity_instance:
+    Dy = rail_head_distance
+    Dz = 2 * Ds
+    D = math.sqrt(Dy * Dy + Dz * Dz)
+    return file.createIfcDirection((0.0, Dz / D, Dy / D))
 
 
-def _map_constant_cant(file: ifcopenshell.file, design_parameters: entity_instance) -> Sequence[entity_instance]:
-    raise NotImplementedError("CONSTANTCANT not implemented")
+def _map_constant_cant(
+    file: ifcopenshell.file, design_parameters: entity_instance, rail_head_distance: float
+) -> Sequence[entity_instance]:
+    dist_along = design_parameters.StartDistAlong
+    length = design_parameters.HorizontalLength
+    Dsl = design_parameters.StartCantLeft
+    Dsr = design_parameters.StartCantRight
+
+    Ds = 0.5 * (Dsl + Dsr)
+
+    transition = "DISCONTINUOUS"
+
+    parent_curve = file.createIfcLine(
+        Pnt=file.createIfcCartesianPoint((0.0, 0.0)),
+        Dir=file.createIfcVector(Orientation=file.createIfcDirection((1.0, 0.0)), Magnitude=1.0),
+    )
+
+    start_point = file.createIfcCartesianPoint((dist_along, Ds, 0.0))
+    start_direction = 0.0
+
+    curve_segment = file.createIfcCurveSegment(
+        Transition=transition,
+        Placement=file.createIfcAxis2Placement3D(
+            Location=start_point,
+            Axis=_get_axis(file, Ds, rail_head_distance),
+            RefDirection=file.createIfcDirection((math.cos(start_direction), math.sin(start_direction), 0.0)),
+        ),
+        SegmentStart=file.createIfcLengthMeasure(0.0),
+        SegmentLength=file.createIfcLengthMeasure(length),
+        ParentCurve=parent_curve,
+    )
+    return (curve_segment, None)
 
 
-def _map_linear_transition(file: ifcopenshell.file, design_parameters: entity_instance) -> Sequence[entity_instance]:
-    raise NotImplementedError("LINEARTRANSTION not implemented")
+def _map_linear_transition(
+    file: ifcopenshell.file, design_parameters: entity_instance, rail_head_distance: float
+) -> Sequence[entity_instance]:
+    dist_along = design_parameters.StartDistAlong
+    length = design_parameters.HorizontalLength
+    Dsl = design_parameters.StartCantLeft
+    Del = design_parameters.EndCantLeft
+    Dsr = design_parameters.StartCantRight
+    Der = design_parameters.EndCantRight
+
+    Ds = 0.5 * (Dsl + Dsr)
+    De = 0.5 * (Del + Der)
+    f = De - Ds
+
+    a0 = Ds  # constant term
+    a1 = f  # linear term
+
+    transition = "DISCONTINUOUS"
+
+    A0 = math.pow(length, 2.0 / 1.0) * math.pow(math.fabs(a0), -1.0 / 1.0) * (a0 / math.fabs(a0)) if a0 != 0.0 else 0.0
+    A1 = math.pow(length, 3.0 / 2.0) * math.pow(math.fabs(a1), -1.0 / 2.0) * (a1 / math.fabs(a1)) if a1 != 0.0 else 0.0
+
+    parent_curve_location = file.createIfcCartesianPoint((0.0, 0.0))
+    parent_curve = file.createIfcClothoid(
+        Position=file.createIfcAxis2Placement2D(
+            Location=parent_curve_location, RefDirection=file.createIfcDirection((1.0, 0.0))
+        ),
+        ClothoidConstant=A1,
+    )
+
+    start_point = file.createIfcCartesianPoint(
+        (dist_along, math.pow(length, 2.0 / 1.0) / A0 if A0 != 0.0 else 0.0, 0.0)
+    )
+    start_direction = math.atan(A1 * math.pow(length, 2.0 / 1.0) / math.fabs(math.pow(A1, 3.0 / 1.0)))
+
+    curve_segment = file.createIfcCurveSegment(
+        Transition=transition,
+        Placement=file.createIfcAxis2Placement3D(
+            Location=start_point,
+            Axis=_get_axis(file, Ds, rail_head_distance),
+            RefDirection=file.createIfcDirection((math.cos(start_direction), math.sin(start_direction), 0.0)),
+        ),
+        SegmentStart=file.createIfcLengthMeasure(0.0),
+        SegmentLength=file.createIfcLengthMeasure(length),
+        ParentCurve=parent_curve,
+    )
+    return (curve_segment, None)
 
 
-def _map_helmert_curve(file: ifcopenshell.file, design_parameters: entity_instance) -> Sequence[entity_instance]:
-    raise NotImplementedError("HELMERTCURVE not implemented")
+def _map_helmert_curve(
+    file: ifcopenshell.file, design_parameters: entity_instance, rail_head_distance: float
+) -> Sequence[entity_instance]:
+    dist_along = design_parameters.StartDistAlong
+    length = design_parameters.HorizontalLength
+    Dsl = design_parameters.StartCantLeft
+    Del = design_parameters.EndCantLeft
+    Dsr = design_parameters.StartCantRight
+    Der = design_parameters.EndCantRight
+
+    Ds = Dsl + Dsr
+    De = Del + Der
+    f = De - Ds
+
+    transition = "DISCONTINUOUS"
+
+    # First half
+    a0_1 = 2.0 * Ds  # constant term
+    a1_1 = 0.0  # linear term
+    a2_1 = 4.0 * f  # quadratic term
+
+    A0_1 = (
+        math.pow(length, 2.0 / 1.0) * math.pow(math.fabs(a0_1), -1.0 / 1.0) * (a0_1 / math.fabs(a0_1))
+        if a0_1 != 0.0
+        else 0.0
+    )
+    A1_1 = (
+        math.pow(length, 3.0 / 2.0) * math.pow(math.fabs(a1_1), -1.0 / 2.0) * (a1_1 / math.fabs(a1_1))
+        if a1_1 != 0.0
+        else 0.0
+    )
+    A2_1 = (
+        math.pow(length, 4.0 / 3.0) * math.pow(math.fabs(a2_1), -1.0 / 3.0) * (a2_1 / math.fabs(a2_1))
+        if a2_1 != 0.0
+        else 0.0
+    )
+
+    parent_curve_1 = file.createIfcSecondOrderPolynomialSpiral(
+        Position=file.createIfcAxis2Placement2D(
+            Location=file.createIfcCartesianPoint((0.0, 0.0)), RefDirection=file.createIfcDirection((1.0, 0.0))
+        ),
+        QuadraticTerm=A2_1,
+        LinearTerm=A1_1 if A1_1 != 0.0 else None,
+        ConstantTerm=A0_1 if A0_1 != 0.0 else None,
+    )
+
+    start_point_1 = file.createIfcCartesianPoint((dist_along, Ds / 2.0, 0.0))
+    start_direction_1 = 0.0
+
+    curve_segment_1 = file.createIfcCurveSegment(
+        Transition=transition,
+        Placement=file.createIfcAxis2Placement3D(
+            Location=start_point_1,
+            Axis=_get_axis(file, Ds / 2.0, rail_head_distance),
+            RefDirection=file.createIfcDirection((math.cos(start_direction_1), math.sin(start_direction_1), 0.0)),
+        ),
+        SegmentStart=file.createIfcLengthMeasure(0.0),
+        SegmentLength=file.createIfcLengthMeasure(length / 2.0),
+        ParentCurve=parent_curve_1,
+    )
+
+    # Second half
+
+    a0_2 = -2.0 * f + 2.0 * Ds  # constant term
+    a1_2 = 8.0 * f  # linear term
+    a2_2 = -4.0 * f  # quadratic term
+
+    A0_2 = (
+        math.pow(length, 2.0 / 1.0) * math.pow(math.fabs(a0_2), -1.0 / 1.0) * (a0_2 / math.fabs(a0_2))
+        if a0_2 != 0.0
+        else 0.0
+    )
+    A1_2 = (
+        math.pow(length, 3.0 / 2.0) * math.pow(math.fabs(a1_2), -1.0 / 2.0) * (a1_2 / math.fabs(a1_2))
+        if a1_2 != 0.0
+        else 0.0
+    )
+    A2_2 = (
+        math.pow(length, 4.0 / 3.0) * math.pow(math.fabs(a2_2), -1.0 / 3.0) * (a2_2 / math.fabs(a2_2))
+        if a2_2 != 0.0
+        else 0.0
+    )
+
+    parent_curve_2 = file.createIfcSecondOrderPolynomialSpiral(
+        Position=file.createIfcAxis2Placement2D(
+            Location=file.createIfcCartesianPoint((0.0, 0.0)), RefDirection=file.createIfcDirection((1.0, 0.0))
+        ),
+        QuadraticTerm=A2_2,
+        LinearTerm=A1_2 if A1_2 != 0.0 else None,
+        ConstantTerm=A0_2 if A0_2 != 0.0 else None,
+    )
+
+    start_point_2 = file.createIfcCartesianPoint((dist_along + length / 2.0, Ds / 2.0 + f / 4.0, 0.0))
+    slope = math.pow(length / 2.0, 2.0) * (2.0 * (length / 2.0) / pow(A2_1, 3.0))
+    start_direction_2 = math.atan(slope)
+
+    curve_segment_2 = file.createIfcCurveSegment(
+        Transition=transition,
+        Placement=file.createIfcAxis2Placement3D(
+            Location=start_point_2,
+            Axis=_get_axis(file, (Ds + De) / 4.0, rail_head_distance),
+            RefDirection=file.createIfcDirection((math.cos(start_direction_2), math.sin(start_direction_2), 0.0)),
+        ),
+        SegmentStart=file.createIfcLengthMeasure(length / 2.0),
+        SegmentLength=file.createIfcLengthMeasure(length / 2.0),
+        ParentCurve=parent_curve_2,
+    )
+
+    return (curve_segment_1, curve_segment_2)
 
 
-def _map_bloss_curve(file: ifcopenshell.file, design_parameters: entity_instance) -> Sequence[entity_instance]:
-    raise NotImplementedError("BLOSSCURVE not implemented")
+def _map_bloss_curve(
+    file: ifcopenshell.file, design_parameters: entity_instance, rail_head_distance: float
+) -> Sequence[entity_instance]:
+    dist_along = design_parameters.StartDistAlong
+    length = design_parameters.HorizontalLength
+    Dsl = design_parameters.StartCantLeft
+    Del = design_parameters.EndCantLeft
+    Dsr = design_parameters.StartCantRight
+    Der = design_parameters.EndCantRight
+
+    Ds = 0.5 * (Dsl + Dsr)
+    De = 0.5 * (Del + Der)
+    f = De - Ds
+
+    a0 = Ds  # constant term
+    a1 = 0.0  # linear term
+    a2 = 3.0 * f  # quadratic term
+    a3 = -2.0 * f  # cubic term
+
+    transition = "DISCONTINUOUS"
+
+    A0 = math.pow(length, 2.0 / 1.0) * math.pow(math.fabs(a0), -1.0 / 1.0) * (a0 / math.fabs(a0)) if a0 != 0.0 else 0.0
+    A1 = math.pow(length, 3.0 / 2.0) * math.pow(math.fabs(a1), -1.0 / 2.0) * (a1 / math.fabs(a1)) if a1 != 0.0 else 0.0
+    A2 = math.pow(length, 4.0 / 3.0) * math.pow(math.fabs(a2), -1.0 / 3.0) * (a2 / math.fabs(a2)) if a2 != 0.0 else 0.0
+    A3 = math.pow(length, 5.0 / 4.0) * math.pow(math.fabs(a3), -1.0 / 4.0) * (a3 / math.fabs(a3)) if a3 != 0.0 else 0.0
+
+    parent_curve = file.createIfcThirdOrderPolynomialSpiral(
+        Position=file.createIfcAxis2Placement2D(
+            Location=file.createIfcCartesianPoint((0.0, 0.0)), RefDirection=file.createIfcDirection((1.0, 0.0))
+        ),
+        CubicTerm=A3,
+        QuadraticTerm=A2 if A2 != 0.0 else None,
+        LinearTerm=A1 if A1 != 0.0 else None,
+        ConstantTerm=A0 if A0 != 0.0 else None,
+    )
+
+    start_point = file.createIfcCartesianPoint((dist_along, Ds, 0.0))
+    start_direction = 0.0
+
+    curve_segment = file.createIfcCurveSegment(
+        Transition=transition,
+        Placement=file.createIfcAxis2Placement3D(
+            Location=start_point,
+            Axis=_get_axis(file, Ds, rail_head_distance),
+            RefDirection=file.createIfcDirection((math.cos(start_direction), math.sin(start_direction), 0.0)),
+        ),
+        SegmentStart=file.createIfcLengthMeasure(0.0),
+        SegmentLength=file.createIfcLengthMeasure(length),
+        ParentCurve=parent_curve,
+    )
+    return (curve_segment, None)
 
 
-def _map_cosine_curve(file: ifcopenshell.file, design_parameters: entity_instance) -> Sequence[entity_instance]:
-    raise NotImplementedError("COSINECURVE not implemented")
+def _map_cosine_curve(
+    file: ifcopenshell.file, design_parameters: entity_instance, rail_head_distance: float
+) -> Sequence[entity_instance]:
+    dist_along = design_parameters.StartDistAlong
+    length = design_parameters.HorizontalLength
+    Dsl = design_parameters.StartCantLeft
+    Del = design_parameters.EndCantLeft
+    Dsr = design_parameters.StartCantRight
+    Der = design_parameters.EndCantRight
+
+    Ds = 0.5 * (Dsl + Dsr)
+    De = 0.5 * (Del + Der)
+    f = De - Ds
+
+    a0 = Ds + 0.5 * f  # constant term
+    a1 = -0.5 * f  # cosine term
+
+    A0 = math.pow(length, 2.0) * math.pow(math.fabs(a0), -1.0 / 1.0) * (a0 / math.fabs(a0)) if a0 != 0.0 else 0.0
+    A1 = math.pow(length, 2.0) * math.pow(math.fabs(a1), -1.0 / 1.0) * (a1 / math.fabs(a1)) if a1 != 0.0 else 0.0
+
+    transition = "DISCONTINUOUS"
+
+    parent_curve = file.createIfcCosineSpiral(
+        Position=file.createIfcAxis2Placement2D(
+            Location=file.createIfcCartesianPoint((0.0, 0.0)), RefDirection=file.createIfcDirection((1.0, 0.0))
+        ),
+        CosineTerm=A1,
+        ConstantTerm=A0 if A0 != 0.0 else None,
+    )
+
+    start_point = file.createIfcCartesianPoint((dist_along, Ds, 0.0))
+    start_direction = 0.0
+
+    curve_segment = file.createIfcCurveSegment(
+        Transition=transition,
+        Placement=file.createIfcAxis2Placement3D(
+            Location=start_point,
+            Axis=_get_axis(file, Ds, rail_head_distance),
+            RefDirection=file.createIfcDirection((math.cos(start_direction), math.sin(start_direction), 0.0)),
+        ),
+        SegmentStart=file.createIfcLengthMeasure(0.0),
+        SegmentLength=file.createIfcLengthMeasure(length),
+        ParentCurve=parent_curve,
+    )
+    return (curve_segment, None)
 
 
-def _map_sine_curve(file: ifcopenshell.file, design_parameters: entity_instance) -> Sequence[entity_instance]:
-    raise NotImplementedError("SINECURVE not implemented")
+def _map_sine_curve(
+    file: ifcopenshell.file, design_parameters: entity_instance, rail_head_distance: float
+) -> Sequence[entity_instance]:
+    dist_along = design_parameters.StartDistAlong
+    length = design_parameters.HorizontalLength
+    Dsl = design_parameters.StartCantLeft
+    Del = design_parameters.EndCantLeft
+    Dsr = design_parameters.StartCantRight
+    Der = design_parameters.EndCantRight
+
+    Ds = 0.5 * (Dsl + Dsr)
+    De = 0.5 * (Del + Der)
+    f = De - Ds
+
+    a0 = Ds  # constant term
+    a1 = f  # linear term
+    a2 = -(1.0 / (2.0 * math.pi)) * f  # sine term
+
+    A0 = math.pow(length, 2.0) * math.pow(math.fabs(a0), -1.0 / 1.0) * (a0 / math.fabs(a0)) if a0 != 0.0 else 0.0
+    A1 = math.pow(length, 1.5) * math.pow(math.fabs(a1), -1.0 / 2.0) * (a1 / math.fabs(a1)) if a1 != 0.0 else 0.0
+    A2 = math.pow(length, 2.0) * math.pow(math.fabs(a2), -1.0 / 1.0) * (a2 / math.fabs(a2)) if a2 != 0.0 else 0.0
+
+    transition = "DISCONTINUOUS"
+
+    parent_curve = file.createIfcSineSpiral(
+        Position=file.createIfcAxis2Placement2D(
+            Location=file.createIfcCartesianPoint((0.0, 0.0)), RefDirection=file.createIfcDirection((1.0, 0.0))
+        ),
+        SineTerm=A2,
+        LinearTerm=A1 if A1 != 0 else None,
+        ConstantTerm=A0 if A0 != 0.0 else None,
+    )
+
+    start_point = file.createIfcCartesianPoint((dist_along, Ds, 0.0))
+    start_direction = 0.0
+
+    curve_segment = file.createIfcCurveSegment(
+        Transition=transition,
+        Placement=file.createIfcAxis2Placement3D(
+            Location=start_point,
+            Axis=_get_axis(file, Ds, rail_head_distance),
+            RefDirection=file.createIfcDirection((math.cos(start_direction), math.sin(start_direction), 0.0)),
+        ),
+        SegmentStart=file.createIfcLengthMeasure(0.0),
+        SegmentLength=file.createIfcLengthMeasure(length),
+        ParentCurve=parent_curve,
+    )
+    return (curve_segment, None)
 
 
-def _map_viennese_bend(file: ifcopenshell.file, design_parameters: entity_instance) -> Sequence[entity_instance]:
+def _map_viennese_bend(
+    file: ifcopenshell.file, design_parameters: entity_instance, rail_head_distance: float
+) -> Sequence[entity_instance]:
     raise NotImplementedError("VIENNESEBEND not implemented")
 
 
 def map_alignment_cant_segment(
-    file: ifcopenshell.file, design_parameters: entity_instance
+    file: ifcopenshell.file, segment: entity_instance, rail_head_distance: float
 ) -> Sequence[entity_instance]:
     """
     Creates IfcCurveSegment entities for the represention of the supplied IfcAlignmentCantSegment business logic entity instance.
@@ -59,25 +388,25 @@ def map_alignment_cant_segment(
 
     The IfcCurveSegment.Transition transition code is set to DISCONTINUOUS.
     """
-    expected_type = "IfcAlignmentCantSegment"
-    if not design_parameters.is_a(expected_type):
-        raise TypeError(f"Expected to see type '{expected_type}', instead received '{design_parameters.is_a()}'.")
+    expected_type = "IfcAlignmentSegment"
+    if not segment.is_a(expected_type):
+        raise TypeError(f"Expected to see type '{expected_type}', instead received '{segment.is_a()}'.")
 
-    match design_parameters.PredefinedType:
+    match segment.DesignParameters.PredefinedType:
         case "CONSTANTCANT":
-            result = _map_constant_cant(file, design_parameters)
+            result = _map_constant_cant(file, segment.DesignParameters, rail_head_distance)
         case "LINEARTRANSITION":
-            result = _map_linear_transition(file, design_parameters)
+            result = _map_linear_transition(file, segment.DesignParameters, rail_head_distance)
         case "HELMERTCURVE":
-            result = _map_helmert_curve(file, design_parameters)
+            result = _map_helmert_curve(file, segment.DesignParameters, rail_head_distance)
         case "BLOSSCURVE":
-            result = _map_bloss_curve(file, design_parameters)
+            result = _map_bloss_curve(file, segment.DesignParameters, rail_head_distance)
         case "COSINECURVE":
-            result = _map_cosine_curve(file, design_parameters)
+            result = _map_cosine_curve(file, segment.DesignParameters, rail_head_distance)
         case "SINECURVE":
-            result = _map_sine_curve(file, design_parameters)
+            result = _map_sine_curve(file, segment.DesignParameters, rail_head_distance)
         case "VIENNESEBEND":
-            result = _map_viennese_bend(file, design_parameters)
+            result = _map_viennese_bend(file, segment.DesignParameters, rail_head_distance)
         case _:
             raise TypeError("Unexpected predefined type")
 
diff --git a/src/ifcopenshell-python/ifcopenshell/api/alignment/map_alignment_horizontal_segment.py b/src/ifcopenshell-python/ifcopenshell/api/alignment/map_alignment_horizontal_segment.py
index bb86ea6bbb..a51fcd6808 100644
--- a/src/ifcopenshell-python/ifcopenshell/api/alignment/map_alignment_horizontal_segment.py
+++ b/src/ifcopenshell-python/ifcopenshell/api/alignment/map_alignment_horizontal_segment.py
@@ -401,38 +401,36 @@ def _map_viennese_bend(file: ifcopenshell.file, design_parameters: entity_instan
     raise NotImplementedError("VIENNESEBEND not implemented")
 
 
-def map_alignment_horizontal_segment(
-    file: ifcopenshell.file, design_parameters: entity_instance
-) -> Sequence[entity_instance]:
+def map_alignment_horizontal_segment(file: ifcopenshell.file, segment: entity_instance) -> Sequence[entity_instance]:
     """
     Creates IfcCurveSegment entities for the represention of the supplied IfcAlignmentHorizontalSegment business logic entity instance.
     A pair of entities is returned because a single business logic segment of type HELMERTCURVE maps to two representaiton entities.
 
     The IfcCurveSegment.Transition transition code is set to DISCONTINUOUS
     """
-    expected_type = "IfcAlignmentHorizontalSegment"
-    if not design_parameters.is_a(expected_type):
-        raise TypeError(f"Expected to see type '{expected_type}', instead received '{design_parameters.is_a()}'.")
+    expected_type = "IfcAlignmentSegment"
+    if not segment.is_a(expected_type):
+        raise TypeError(f"Expected to see type '{expected_type}', instead received '{segment.is_a()}'.")
 
-    match design_parameters.PredefinedType:
+    match segment.DesignParameters.PredefinedType:
         case "LINE":
-            result = _map_line(file, design_parameters)
+            result = _map_line(file, segment.DesignParameters)
         case "CIRCULARARC":
-            result = _map_circular_arc(file, design_parameters)
+            result = _map_circular_arc(file, segment.DesignParameters)
         case "CLOTHOID":
-            result = _map_clothoid(file, design_parameters)
+            result = _map_clothoid(file, segment.DesignParameters)
         case "CUBIC":
-            result = _map_cubic(file, design_parameters)
+            result = _map_cubic(file, segment.DesignParameters)
         case "HELMERTCURVE":
-            result = _map_helmert_curve(file, design_parameters)
+            result = _map_helmert_curve(file, segment.DesignParameters)
         case "BLOSSCURVE":
-            result = _map_bloss_curve(file, design_parameters)
+            result = _map_bloss_curve(file, segment.DesignParameters)
         case "COSINECURVE":
-            result = _map_cosine_curve(file, design_parameters)
+            result = _map_cosine_curve(file, segment.DesignParameters)
         case "SINECURVE":
-            result = _map_sine_curve(file, design_parameters)
+            result = _map_sine_curve(file, segment.DesignParameters)
         case "VIENNESEBEND":
-            result = _map_viennese_bend(file, design_parameters)
+            result = _map_viennese_bend(file, segment.DesignParameters)
         case _:
             raise TypeError("Unexpected predefined type")
 
diff --git a/src/ifcopenshell-python/ifcopenshell/api/alignment/map_alignment_segment.py b/src/ifcopenshell-python/ifcopenshell/api/alignment/map_alignment_segment.py
deleted file mode 100644
index d7b05d5544..0000000000
--- a/src/ifcopenshell-python/ifcopenshell/api/alignment/map_alignment_segment.py
+++ /dev/null
@@ -1,47 +0,0 @@
-# IfcOpenShell - IFC toolkit and geometry engine
-# Copyright (C) 2025 Thomas Krijnen <thomas@aecgeeks.com>
-#
-# This file is part of IfcOpenShell.
-#
-# IfcOpenShell is free software: you can redistribute it and/or modify
-# it under the terms of the GNU Lesser General Public License as published by
-# the Free Software Foundation, either version 3 of the License, or
-# (at your option) any later version.
-#
-# IfcOpenShell is distributed in the hope that it will be useful,
-# but WITHOUT ANY WARRANTY; without even the implied warranty of
-# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
-# GNU Lesser General Public License for more details.
-#
-# You should have received a copy of the GNU Lesser General Public License
-# along with IfcOpenShell.  If not, see <http://www.gnu.org/licenses/>.
-
-import ifcopenshell
-import ifcopenshell.api
-from ifcopenshell import entity_instance
-from typing import Sequence
-
-
-def map_alignment_segment(file: ifcopenshell.file, segment: entity_instance) -> Sequence[entity_instance]:
-    """
-    Creates IfcCurveSegment entities for the represention of the supplied IfcAlignmentSegment business logic entity instance.
-    A pair of entities is returned because a single business logic segment of type HELMERTCURVE maps to two representaiton entities.
-
-    The IfcCurveSegment.Transition transition code is set to DISCONTINUOUS, except for the transition between helmert curve segments.
-
-    This function will evaluate the IfcAlignmentSegment.DesignParameters type and call the correct lower level mapping function.
-    """
-    expected_type = "IfcAlignmentSegment"
-    if not segment.is_a(expected_type):
-        raise TypeError(f"Expected to see type '{expected_type}', instead received '{segment.is_a()}'.")
-
-    if segment.DesignParameters.is_a("IfcAlignmentHorizontalSegment"):
-        return ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, segment.DesignParameters)
-    elif segment.DesignParameters.is_a("IfcAlignmentVerticalSegment"):
-        return ifcopenshell.api.alignment.map_alignment_vertical_segment(file, segment.DesignParameters)
-    elif segment.DesignParameters.is_a("IfcAlignmentCantSegment"):
-        return ifcopenshell.api.alignment.map_alignment_cant_segment(file, segment.DesignParameters)
-    else:
-        raise TypeError("Unexpected type for segment.DesignParameters")
-
-    return (None, None)
diff --git a/src/ifcopenshell-python/ifcopenshell/api/alignment/map_alignment_segments.py b/src/ifcopenshell-python/ifcopenshell/api/alignment/map_alignment_segments.py
index d9012d59ef..f4946751c1 100644
--- a/src/ifcopenshell-python/ifcopenshell/api/alignment/map_alignment_segments.py
+++ b/src/ifcopenshell-python/ifcopenshell/api/alignment/map_alignment_segments.py
@@ -56,7 +56,14 @@ def map_alignment_segments(
     for rel_nests in alignment.IsNestedBy:
         for layout in rel_nests.RelatedObjects:
             if layout.is_a("IfcLinearElement"):
-                mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, layout)
+                if alignment.is_a("IfcAlignmentHorizontal"):
+                    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, layout)
+                elif alignment.is_a("IfcAlignmentVertical"):
+                    mapped_segments = ifcopenshell.api.alignment.map_alignment_vertical_segment(file, layout)
+                elif alignment.is_a("IfcAlignmentCant"):
+                    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(
+                        file, layout, alignment.RailHeadDistance
+                    )
                 for mapped_segment in mapped_segments:
                     if mapped_segment:
                         ifcopenshell.api.alignment.add_segment_to_curve(file, mapped_segment, composite_curve)
diff --git a/src/ifcopenshell-python/ifcopenshell/api/alignment/map_alignment_vertical_segment.py b/src/ifcopenshell-python/ifcopenshell/api/alignment/map_alignment_vertical_segment.py
index 3e80f3c6f3..d02a389106 100644
--- a/src/ifcopenshell-python/ifcopenshell/api/alignment/map_alignment_vertical_segment.py
+++ b/src/ifcopenshell-python/ifcopenshell/api/alignment/map_alignment_vertical_segment.py
@@ -60,10 +60,7 @@ def _map_constant_gradient(file: ifcopenshell.file, design_parameters: entity_in
 
     parent_curve = file.create_entity(
         type="IfcLine",
-        Pnt=file.create_entity(
-            type="IfcCartesianPoint",
-            Coordinates=(0.0, 0.0),
-        ),
+        Pnt=file.createIfcCartesianPoint((0.0, 0.0)),
         Dir=file.create_entity(
             type="IfcVector",
             Orientation=file.create_entity(
@@ -78,12 +75,10 @@ def _map_constant_gradient(file: ifcopenshell.file, design_parameters: entity_in
     dy = math.sin(math.atan(start_gradient))
     curve_segment_length = horizontal_length / dx
 
-    curve_segment = file.create_entity(
-        type="IfcCurveSegment",
+    curve_segment = file.createIfcCurveSegment(
         Transition=transition,
-        Placement=file.create_entity(
-            type="IfcAxis2Placement2D",
-            Location=file.create_entity(type="IfcCartesianPoint", Coordinates=(start_distance_along, start_height)),
+        Placement=file.createIfcAxis2Placement2D(
+            Location=file.createIfcCartesianPoint((start_distance_along, start_height)),
             RefDirection=file.createIfcDirection((dx, dy)),
         ),
         SegmentStart=file.createIfcLengthMeasure(0.0),
@@ -110,7 +105,7 @@ def _map_parabolic_arc(file: ifcopenshell.file, design_parameters: entity_instan
         type="IfcPolynomialCurve",
         Position=file.create_entity(
             type="IfcAxis2Placement2D",
-            Location=file.create_entity(type="IfcCartesianPoint", Coordinates=(0.0, 0.0)),
+            Location=file.createIfcCartesianPoint((0.0, 0.0)),
             RefDirection=file.createIfcDirection(
                 (1.0, 0.0),
             ),
@@ -128,7 +123,7 @@ def _map_parabolic_arc(file: ifcopenshell.file, design_parameters: entity_instan
         Transition=transition,
         Placement=file.create_entity(
             type="IfcAxis2Placement2D",
-            Location=file.create_entity(type="IfcCartesianPoint", Coordinates=(start_distance_along, start_height)),
+            Location=file.createIfcCartesianPoint((start_distance_along, start_height)),
             RefDirection=file.createIfcDirection((dx, dy)),
         ),
         SegmentStart=file.createIfcLengthMeasure(0.0),
@@ -194,32 +189,30 @@ def _map_clothoid(file: ifcopenshell.file, design_parameters: entity_instance) -
     raise NotImplementedError("mapping for IfcVerticalSegment.CLOTHOID not implemented")
 
 
-def map_alignment_vertical_segment(
-    file: ifcopenshell.file, design_parameters: entity_instance
-) -> Sequence[entity_instance]:
+def map_alignment_vertical_segment(file: ifcopenshell.file, segment: entity_instance) -> Sequence[entity_instance]:
     """
     Creates IfcCurveSegment entities for the represention of the supplied IfcAlignmentVerticalSegment business logic entity instance.
     A pair of entities is returned for consistency with map_alignment_horizontal_segment and map_alignment_cant_segment.
 
     """
-    expected_type = "IfcAlignmentVerticalSegment"
-    if not design_parameters.is_a(expected_type):
-        raise TypeError(f"Expected to see type '{expected_type}', instead received '{design_parameters.is_a()}'.")
+    expected_type = "IfcAlignmentSegment"
+    if not segment.is_a(expected_type):
+        raise TypeError(f"Expected to see type '{expected_type}', instead received '{segment.is_a()}'.")
 
-    match design_parameters.PredefinedType:
+    match segment.DesignParameters.PredefinedType:
         case "CONSTANTGRADIENT":
-            result = _map_constant_gradient(file, design_parameters)
+            result = _map_constant_gradient(file, segment.DesignParameters)
 
         case "PARABOLICARC":
-            result = _map_parabolic_arc(file, design_parameters)
+            result = _map_parabolic_arc(file, segment.DesignParameters)
 
         case "CIRCULARARC":
-            result = _map_circular_arc(file, design_parameters)
+            result = _map_circular_arc(file, segment.DesignParameters)
 
         case "CLOTHOID":
-            result = _map_clothoid(file, design_parameters)
+            result = _map_clothoid(file, segment.DesignParameters)
 
         case _:
-            raise TypeError("Unexpected predefined type")
+            raise TypeError(f"Unexpected predefined type - got {segment.DesignParameters.PredefinedType}")
 
     return result
diff --git a/src/ifcopenshell-python/test/api/alignment/test_map_alignment_cant_segment.py b/src/ifcopenshell-python/test/api/alignment/test_map_alignment_cant_segment.py
index 755fe3e13c..3e938df6e5 100644
--- a/src/ifcopenshell-python/test/api/alignment/test_map_alignment_cant_segment.py
+++ b/src/ifcopenshell-python/test/api/alignment/test_map_alignment_cant_segment.py
@@ -21,6 +21,1639 @@ import ifcopenshell.api.alignment
 import ifcopenshell.api.context
 
 
+def _BlossCurve_100_0_300_1000_1_Meter(file):
+    design_parameters = file.createIfcAlignmentCantSegment(
+        StartDistAlong=0.0,
+        HorizontalLength=100.0,
+        StartCantLeft=0.0,
+        EndCantLeft=0.0,
+        StartCantRight=0.16,
+        EndCantRight=0.0,
+        PredefinedType="BLOSSCURVE",
+    )
+
+    alignment_segment = file.createIfcAlignmentSegment(
+        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+    )
+
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(file, alignment_segment, 1.5)
+    mapped_segment = mapped_segments[0]
+    assert len(mapped_segments) == 2
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((0.0, 0.08, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0, 0.0))
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(100.0)
+    assert mapped_segment.ParentCurve.is_a("IfcThirdOrderPolynomialSpiral")
+    assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Position.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.CubicTerm == pytest.approx(500.00000000000017)
+    assert mapped_segment.ParentCurve.QuadraticTerm == pytest.approx(-746.9007910928623)
+    assert mapped_segment.ParentCurve.LinearTerm == pytest.approx(None)
+    assert mapped_segment.ParentCurve.ConstantTerm == pytest.approx(125000.0)
+
+
+def _BlossCurve_100_0__300__1000_1_Meter(file):
+    design_parameters = file.createIfcAlignmentCantSegment(
+        StartDistAlong=0.0,
+        HorizontalLength=100.0,
+        StartCantLeft=0.16,
+        EndCantLeft=0.0,
+        StartCantRight=0.0,
+        EndCantRight=0.0,
+        PredefinedType="BLOSSCURVE",
+    )
+
+    alignment_segment = file.createIfcAlignmentSegment(
+        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+    )
+
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(file, alignment_segment, 1.5)
+    mapped_segment = mapped_segments[0]
+    assert len(mapped_segments) == 2
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((0.0, 0.08, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0, 0.0))
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(100.0)
+    assert mapped_segment.ParentCurve.is_a("IfcThirdOrderPolynomialSpiral")
+    assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Position.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.CubicTerm == pytest.approx(500.00000000000017)
+    assert mapped_segment.ParentCurve.QuadraticTerm == pytest.approx(-746.9007910928623)
+    assert mapped_segment.ParentCurve.LinearTerm == pytest.approx(None)
+    assert mapped_segment.ParentCurve.ConstantTerm == pytest.approx(125000.0)
+
+
+def _BlossCurve_100_0_300_inf_1_Meter(file):
+    design_parameters = file.createIfcAlignmentCantSegment(
+        StartDistAlong=0.0,
+        HorizontalLength=100.0,
+        StartCantLeft=0.0,
+        EndCantLeft=0.0,
+        StartCantRight=0.16,
+        EndCantRight=0.0,
+        PredefinedType="BLOSSCURVE",
+    )
+
+    alignment_segment = file.createIfcAlignmentSegment(
+        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+    )
+
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(file, alignment_segment, 1.5)
+    mapped_segment = mapped_segments[0]
+    assert len(mapped_segments) == 2
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((0.0, 0.08, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0, 0.0))
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(100.0)
+    assert mapped_segment.ParentCurve.is_a("IfcThirdOrderPolynomialSpiral")
+    assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Position.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.CubicTerm == pytest.approx(500.00000000000017)
+    assert mapped_segment.ParentCurve.QuadraticTerm == pytest.approx(-746.9007910928623)
+    assert mapped_segment.ParentCurve.LinearTerm == pytest.approx(None)
+    assert mapped_segment.ParentCurve.ConstantTerm == pytest.approx(125000.0)
+
+
+def _BlossCurve_100_0__300__inf_1_Meter(file):
+    design_parameters = file.createIfcAlignmentCantSegment(
+        StartDistAlong=0.0,
+        HorizontalLength=100.0,
+        StartCantLeft=0.16,
+        EndCantLeft=0.0,
+        StartCantRight=0.0,
+        EndCantRight=0.0,
+        PredefinedType="BLOSSCURVE",
+    )
+
+    alignment_segment = file.createIfcAlignmentSegment(
+        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+    )
+
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(file, alignment_segment, 1.5)
+    mapped_segment = mapped_segments[0]
+    assert len(mapped_segments) == 2
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((0.0, 0.08, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0, 0.0))
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(100.0)
+    assert mapped_segment.ParentCurve.is_a("IfcThirdOrderPolynomialSpiral")
+    assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Position.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.CubicTerm == pytest.approx(500.00000000000017)
+    assert mapped_segment.ParentCurve.QuadraticTerm == pytest.approx(-746.9007910928623)
+    assert mapped_segment.ParentCurve.LinearTerm == pytest.approx(None)
+    assert mapped_segment.ParentCurve.ConstantTerm == pytest.approx(125000.0)
+
+
+def _BlossCurve_100_0_1000_300_1_Meter(file):
+    design_parameters = file.createIfcAlignmentCantSegment(
+        StartDistAlong=0.0,
+        HorizontalLength=100.0,
+        StartCantLeft=0.0,
+        EndCantLeft=0.0,
+        StartCantRight=0.0,
+        EndCantRight=0.16,
+        PredefinedType="BLOSSCURVE",
+    )
+
+    alignment_segment = file.createIfcAlignmentSegment(
+        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+    )
+
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(file, alignment_segment, 1.5)
+    mapped_segment = mapped_segments[0]
+    assert len(mapped_segments) == 2
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((0.0, 0.0, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0, 0.0))
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(100.0)
+    assert mapped_segment.ParentCurve.is_a("IfcThirdOrderPolynomialSpiral")
+    assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Position.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.CubicTerm == pytest.approx(-500.00000000000017)
+    assert mapped_segment.ParentCurve.QuadraticTerm == pytest.approx(746.9007910928623)
+    assert mapped_segment.ParentCurve.LinearTerm == pytest.approx(None)
+    assert mapped_segment.ParentCurve.ConstantTerm == pytest.approx(None)
+
+
+def _BlossCurve_100_0__1000__300_1_Meter(file):
+    design_parameters = file.createIfcAlignmentCantSegment(
+        StartDistAlong=0.0,
+        HorizontalLength=100.0,
+        StartCantLeft=0.0,
+        EndCantLeft=0.16,
+        StartCantRight=0.0,
+        EndCantRight=0.0,
+        PredefinedType="BLOSSCURVE",
+    )
+
+    alignment_segment = file.createIfcAlignmentSegment(
+        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+    )
+
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(file, alignment_segment, 1.5)
+    mapped_segment = mapped_segments[0]
+    assert len(mapped_segments) == 2
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((0.0, 0.0, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0, 0.0))
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(100.0)
+    assert mapped_segment.ParentCurve.is_a("IfcThirdOrderPolynomialSpiral")
+    assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Position.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.CubicTerm == pytest.approx(-500.00000000000017)
+    assert mapped_segment.ParentCurve.QuadraticTerm == pytest.approx(746.9007910928623)
+    assert mapped_segment.ParentCurve.LinearTerm == pytest.approx(None)
+    assert mapped_segment.ParentCurve.ConstantTerm == pytest.approx(None)
+
+
+def _BlossCurve_100_0_inf_300_1_Meter(file):
+    design_parameters = file.createIfcAlignmentCantSegment(
+        StartDistAlong=0.0,
+        HorizontalLength=100.0,
+        StartCantLeft=0.0,
+        EndCantLeft=0.0,
+        StartCantRight=0.0,
+        EndCantRight=0.16,
+        PredefinedType="BLOSSCURVE",
+    )
+
+    alignment_segment = file.createIfcAlignmentSegment(
+        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+    )
+
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(file, alignment_segment, 1.5)
+    mapped_segment = mapped_segments[0]
+    assert len(mapped_segments) == 2
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((0.0, 0.0, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0, 0.0))
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(100.0)
+    assert mapped_segment.ParentCurve.is_a("IfcThirdOrderPolynomialSpiral")
+    assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Position.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.CubicTerm == pytest.approx(-500.00000000000017)
+    assert mapped_segment.ParentCurve.QuadraticTerm == pytest.approx(746.9007910928623)
+    assert mapped_segment.ParentCurve.LinearTerm == pytest.approx(None)
+    assert mapped_segment.ParentCurve.ConstantTerm == pytest.approx(None)
+
+
+def _BlossCurve_100_0__inf__300_1_Meter(file):
+    design_parameters = file.createIfcAlignmentCantSegment(
+        StartDistAlong=0.0,
+        HorizontalLength=100.0,
+        StartCantLeft=0.0,
+        EndCantLeft=0.16,
+        StartCantRight=0.0,
+        EndCantRight=0.0,
+        PredefinedType="BLOSSCURVE",
+    )
+
+    alignment_segment = file.createIfcAlignmentSegment(
+        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+    )
+
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(file, alignment_segment, 1.5)
+    mapped_segment = mapped_segments[0]
+    assert len(mapped_segments) == 2
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((0.0, 0.0, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0, 0.0))
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(100.0)
+    assert mapped_segment.ParentCurve.is_a("IfcThirdOrderPolynomialSpiral")
+    assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Position.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.CubicTerm == pytest.approx(-500.00000000000017)
+    assert mapped_segment.ParentCurve.QuadraticTerm == pytest.approx(746.9007910928623)
+    assert mapped_segment.ParentCurve.LinearTerm == pytest.approx(None)
+    assert mapped_segment.ParentCurve.ConstantTerm == pytest.approx(None)
+
+
+def _ConstantCant_100_0_300_1000_1_Meter(file):
+    design_parameters = file.createIfcAlignmentCantSegment(
+        StartDistAlong=0.0,
+        HorizontalLength=100.0,
+        StartCantLeft=0.0,
+        EndCantLeft=0.0,
+        StartCantRight=0.16,
+        EndCantRight=0.0,
+        PredefinedType="CONSTANTCANT",
+    )
+
+    alignment_segment = file.createIfcAlignmentSegment(
+        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+    )
+
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(file, alignment_segment, 1.5)
+    mapped_segment = mapped_segments[0]
+    assert len(mapped_segments) == 2
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((0.0, 0.08, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0, 0.0))
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(100.0)
+    assert mapped_segment.ParentCurve.is_a("IfcLine")
+    assert mapped_segment.ParentCurve.Pnt.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Dir.Orientation.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.Dir.Magnitude == pytest.approx(1.0)
+
+
+def _ConstantCant_100_0__300__1000_1_Meter(file):
+    design_parameters = file.createIfcAlignmentCantSegment(
+        StartDistAlong=0.0,
+        HorizontalLength=100.0,
+        StartCantLeft=0.16,
+        EndCantLeft=0.0,
+        StartCantRight=0.0,
+        EndCantRight=0.0,
+        PredefinedType="CONSTANTCANT",
+    )
+
+    alignment_segment = file.createIfcAlignmentSegment(
+        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+    )
+
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(file, alignment_segment, 1.5)
+    mapped_segment = mapped_segments[0]
+    assert len(mapped_segments) == 2
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((0.0, 0.08, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0, 0.0))
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(100.0)
+    assert mapped_segment.ParentCurve.is_a("IfcLine")
+    assert mapped_segment.ParentCurve.Pnt.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Dir.Orientation.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.Dir.Magnitude == pytest.approx(1.0)
+
+
+def _ConstantCant_100_0_300_inf_1_Meter(file):
+    design_parameters = file.createIfcAlignmentCantSegment(
+        StartDistAlong=0.0,
+        HorizontalLength=100.0,
+        StartCantLeft=0.0,
+        EndCantLeft=0.0,
+        StartCantRight=0.16,
+        EndCantRight=0.0,
+        PredefinedType="CONSTANTCANT",
+    )
+
+    alignment_segment = file.createIfcAlignmentSegment(
+        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+    )
+
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(file, alignment_segment, 1.5)
+    mapped_segment = mapped_segments[0]
+    assert len(mapped_segments) == 2
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((0.0, 0.08, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0, 0.0))
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(100.0)
+    assert mapped_segment.ParentCurve.is_a("IfcLine")
+    assert mapped_segment.ParentCurve.Pnt.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Dir.Orientation.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.Dir.Magnitude == pytest.approx(1.0)
+
+
+def _ConstantCant_100_0__300__inf_1_Meter(file):
+    design_parameters = file.createIfcAlignmentCantSegment(
+        StartDistAlong=0.0,
+        HorizontalLength=100.0,
+        StartCantLeft=0.16,
+        EndCantLeft=0.0,
+        StartCantRight=0.0,
+        EndCantRight=0.0,
+        PredefinedType="CONSTANTCANT",
+    )
+
+    alignment_segment = file.createIfcAlignmentSegment(
+        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+    )
+
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(file, alignment_segment, 1.5)
+    mapped_segment = mapped_segments[0]
+    assert len(mapped_segments) == 2
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((0.0, 0.08, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0, 0.0))
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(100.0)
+    assert mapped_segment.ParentCurve.is_a("IfcLine")
+    assert mapped_segment.ParentCurve.Pnt.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Dir.Orientation.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.Dir.Magnitude == pytest.approx(1.0)
+
+
+def _ConstantCant_100_0_1000_300_1_Meter(file):
+    design_parameters = file.createIfcAlignmentCantSegment(
+        StartDistAlong=0.0,
+        HorizontalLength=100.0,
+        StartCantLeft=0.0,
+        EndCantLeft=0.0,
+        StartCantRight=0.0,
+        EndCantRight=0.16,
+        PredefinedType="CONSTANTCANT",
+    )
+
+    alignment_segment = file.createIfcAlignmentSegment(
+        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+    )
+
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(file, alignment_segment, 1.5)
+    mapped_segment = mapped_segments[0]
+    assert len(mapped_segments) == 2
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((0.0, 0.0, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0, 0.0))
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(100.0)
+    assert mapped_segment.ParentCurve.is_a("IfcLine")
+    assert mapped_segment.ParentCurve.Pnt.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Dir.Orientation.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.Dir.Magnitude == pytest.approx(1.0)
+
+
+def _ConstantCant_100_0__1000__300_1_Meter(file):
+    design_parameters = file.createIfcAlignmentCantSegment(
+        StartDistAlong=0.0,
+        HorizontalLength=100.0,
+        StartCantLeft=0.0,
+        EndCantLeft=0.16,
+        StartCantRight=0.0,
+        EndCantRight=0.0,
+        PredefinedType="CONSTANTCANT",
+    )
+
+    alignment_segment = file.createIfcAlignmentSegment(
+        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+    )
+
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(file, alignment_segment, 1.5)
+    mapped_segment = mapped_segments[0]
+    assert len(mapped_segments) == 2
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((0.0, 0.0, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0, 0.0))
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(100.0)
+    assert mapped_segment.ParentCurve.is_a("IfcLine")
+    assert mapped_segment.ParentCurve.Pnt.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Dir.Orientation.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.Dir.Magnitude == pytest.approx(1.0)
+
+
+def _ConstantCant_100_0_inf_300_1_Meter(file):
+    design_parameters = file.createIfcAlignmentCantSegment(
+        StartDistAlong=0.0,
+        HorizontalLength=100.0,
+        StartCantLeft=0.0,
+        EndCantLeft=0.0,
+        StartCantRight=0.0,
+        EndCantRight=0.16,
+        PredefinedType="CONSTANTCANT",
+    )
+
+    alignment_segment = file.createIfcAlignmentSegment(
+        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+    )
+
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(file, alignment_segment, 1.5)
+    mapped_segment = mapped_segments[0]
+    assert len(mapped_segments) == 2
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((0.0, 0.0, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0, 0.0))
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(100.0)
+    assert mapped_segment.ParentCurve.is_a("IfcLine")
+    assert mapped_segment.ParentCurve.Pnt.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Dir.Orientation.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.Dir.Magnitude == pytest.approx(1.0)
+
+
+def _ConstantCant_100_0__inf__300_1_Meter(file):
+    design_parameters = file.createIfcAlignmentCantSegment(
+        StartDistAlong=0.0,
+        HorizontalLength=100.0,
+        StartCantLeft=0.0,
+        EndCantLeft=0.16,
+        StartCantRight=0.0,
+        EndCantRight=0.0,
+        PredefinedType="CONSTANTCANT",
+    )
+
+    alignment_segment = file.createIfcAlignmentSegment(
+        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+    )
+
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(file, alignment_segment, 1.5)
+    mapped_segment = mapped_segments[0]
+    assert len(mapped_segments) == 2
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((0.0, 0.0, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0, 0.0))
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(100.0)
+    assert mapped_segment.ParentCurve.is_a("IfcLine")
+    assert mapped_segment.ParentCurve.Pnt.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Dir.Orientation.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.Dir.Magnitude == pytest.approx(1.0)
+
+
+def _CosineCurve_100_0_300_1000_1_Meter(file):
+    design_parameters = file.createIfcAlignmentCantSegment(
+        StartDistAlong=0.0,
+        HorizontalLength=100.0,
+        StartCantLeft=0.0,
+        EndCantLeft=0.0,
+        StartCantRight=0.16,
+        EndCantRight=0.0,
+        PredefinedType="COSINECURVE",
+    )
+
+    alignment_segment = file.createIfcAlignmentSegment(
+        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+    )
+
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(file, alignment_segment, 1.5)
+    mapped_segment = mapped_segments[0]
+    assert len(mapped_segments) == 2
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((0.0, 0.08, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0, 0.0))
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(100.0)
+    assert mapped_segment.ParentCurve.is_a("IfcCosineSpiral")
+    assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Position.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.CosineTerm == pytest.approx(250000.0)
+    assert mapped_segment.ParentCurve.ConstantTerm == pytest.approx(250000.0)
+
+
+def _CosineCurve_100_0__300__1000_1_Meter(file):
+    design_parameters = file.createIfcAlignmentCantSegment(
+        StartDistAlong=0.0,
+        HorizontalLength=100.0,
+        StartCantLeft=0.16,
+        EndCantLeft=0.0,
+        StartCantRight=0.0,
+        EndCantRight=0.0,
+        PredefinedType="COSINECURVE",
+    )
+
+    alignment_segment = file.createIfcAlignmentSegment(
+        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+    )
+
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(file, alignment_segment, 1.5)
+    mapped_segment = mapped_segments[0]
+    assert len(mapped_segments) == 2
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((0.0, 0.08, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0, 0.0))
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(100.0)
+    assert mapped_segment.ParentCurve.is_a("IfcCosineSpiral")
+    assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Position.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.CosineTerm == pytest.approx(250000.0)
+    assert mapped_segment.ParentCurve.ConstantTerm == pytest.approx(250000.0)
+
+
+def _CosineCurve_100_0_300_inf_1_Meter(file):
+    design_parameters = file.createIfcAlignmentCantSegment(
+        StartDistAlong=0.0,
+        HorizontalLength=100.0,
+        StartCantLeft=0.0,
+        EndCantLeft=0.0,
+        StartCantRight=0.16,
+        EndCantRight=0.0,
+        PredefinedType="COSINECURVE",
+    )
+
+    alignment_segment = file.createIfcAlignmentSegment(
+        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+    )
+
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(file, alignment_segment, 1.5)
+    mapped_segment = mapped_segments[0]
+    assert len(mapped_segments) == 2
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((0.0, 0.08, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0, 0.0))
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(100.0)
+    assert mapped_segment.ParentCurve.is_a("IfcCosineSpiral")
+    assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Position.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.CosineTerm == pytest.approx(250000.0)
+    assert mapped_segment.ParentCurve.ConstantTerm == pytest.approx(250000.0)
+
+
+def _CosineCurve_100_0__300__inf_1_Meter(file):
+    design_parameters = file.createIfcAlignmentCantSegment(
+        StartDistAlong=0.0,
+        HorizontalLength=100.0,
+        StartCantLeft=0.16,
+        EndCantLeft=0.0,
+        StartCantRight=0.0,
+        EndCantRight=0.0,
+        PredefinedType="COSINECURVE",
+    )
+
+    alignment_segment = file.createIfcAlignmentSegment(
+        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+    )
+
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(file, alignment_segment, 1.5)
+    mapped_segment = mapped_segments[0]
+    assert len(mapped_segments) == 2
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((0.0, 0.08, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0, 0.0))
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(100.0)
+    assert mapped_segment.ParentCurve.is_a("IfcCosineSpiral")
+    assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Position.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.CosineTerm == pytest.approx(250000.0)
+    assert mapped_segment.ParentCurve.ConstantTerm == pytest.approx(250000.0)
+
+
+def _CosineCurve_100_0_1000_300_1_Meter(file):
+    design_parameters = file.createIfcAlignmentCantSegment(
+        StartDistAlong=0.0,
+        HorizontalLength=100.0,
+        StartCantLeft=0.0,
+        EndCantLeft=0.0,
+        StartCantRight=0.0,
+        EndCantRight=0.16,
+        PredefinedType="COSINECURVE",
+    )
+
+    alignment_segment = file.createIfcAlignmentSegment(
+        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+    )
+
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(file, alignment_segment, 1.5)
+    mapped_segment = mapped_segments[0]
+    assert len(mapped_segments) == 2
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((0.0, 0.0, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0, 0.0))
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(100.0)
+    assert mapped_segment.ParentCurve.is_a("IfcCosineSpiral")
+    assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Position.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.CosineTerm == pytest.approx(-250000.0)
+    assert mapped_segment.ParentCurve.ConstantTerm == pytest.approx(250000.0)
+
+
+def _CosineCurve_100_0__1000__300_1_Meter(file):
+    design_parameters = file.createIfcAlignmentCantSegment(
+        StartDistAlong=0.0,
+        HorizontalLength=100.0,
+        StartCantLeft=0.0,
+        EndCantLeft=0.16,
+        StartCantRight=0.0,
+        EndCantRight=0.0,
+        PredefinedType="COSINECURVE",
+    )
+
+    alignment_segment = file.createIfcAlignmentSegment(
+        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+    )
+
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(file, alignment_segment, 1.5)
+    mapped_segment = mapped_segments[0]
+    assert len(mapped_segments) == 2
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((0.0, 0.0, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0, 0.0))
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(100.0)
+    assert mapped_segment.ParentCurve.is_a("IfcCosineSpiral")
+    assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Position.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.CosineTerm == pytest.approx(-250000.0)
+    assert mapped_segment.ParentCurve.ConstantTerm == pytest.approx(250000.0)
+
+
+def _CosineCurve_100_0_inf_300_1_Meter(file):
+    design_parameters = file.createIfcAlignmentCantSegment(
+        StartDistAlong=0.0,
+        HorizontalLength=100.0,
+        StartCantLeft=0.0,
+        EndCantLeft=0.0,
+        StartCantRight=0.0,
+        EndCantRight=0.16,
+        PredefinedType="COSINECURVE",
+    )
+
+    alignment_segment = file.createIfcAlignmentSegment(
+        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+    )
+
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(file, alignment_segment, 1.5)
+    mapped_segment = mapped_segments[0]
+    assert len(mapped_segments) == 2
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((0.0, 0.0, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0, 0.0))
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(100.0)
+    assert mapped_segment.ParentCurve.is_a("IfcCosineSpiral")
+    assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Position.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.CosineTerm == pytest.approx(-250000.0)
+    assert mapped_segment.ParentCurve.ConstantTerm == pytest.approx(250000.0)
+
+
+def _CosineCurve_100_0__inf__300_1_Meter(file):
+    design_parameters = file.createIfcAlignmentCantSegment(
+        StartDistAlong=0.0,
+        HorizontalLength=100.0,
+        StartCantLeft=0.0,
+        EndCantLeft=0.16,
+        StartCantRight=0.0,
+        EndCantRight=0.0,
+        PredefinedType="COSINECURVE",
+    )
+
+    alignment_segment = file.createIfcAlignmentSegment(
+        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+    )
+
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(file, alignment_segment, 1.5)
+    mapped_segment = mapped_segments[0]
+    assert len(mapped_segments) == 2
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((0.0, 0.0, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0, 0.0))
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(100.0)
+    assert mapped_segment.ParentCurve.is_a("IfcCosineSpiral")
+    assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Position.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.CosineTerm == pytest.approx(-250000.0)
+    assert mapped_segment.ParentCurve.ConstantTerm == pytest.approx(250000.0)
+
+
+def _HelmertCurve_100_0_300_1000_1_Meter(file):
+    design_parameters = file.createIfcAlignmentCantSegment(
+        StartDistAlong=0.0,
+        HorizontalLength=100.0,
+        StartCantLeft=0.0,
+        EndCantLeft=0.0,
+        StartCantRight=0.16,
+        EndCantRight=0.0,
+        PredefinedType="HELMERTCURVE",
+    )
+
+    alignment_segment = file.createIfcAlignmentSegment(
+        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+    )
+
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(file, alignment_segment, 1.5)
+    mapped_segment = mapped_segments[0]
+    assert len(mapped_segments) == 2
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((0.0, 0.08, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0, 0.0))
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(50.0)
+    assert mapped_segment.ParentCurve.is_a("IfcSecondOrderPolynomialSpiral")
+    assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Position.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.QuadraticTerm == pytest.approx(-538.6086725079696)
+    assert mapped_segment.ParentCurve.LinearTerm == pytest.approx(None)
+    assert mapped_segment.ParentCurve.ConstantTerm == pytest.approx(31250.0)
+    mapped_segment = mapped_segments[1]
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((50.0, 0.04, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx(
+        (0.999998720000819, -0.00159999897600066, 0.0)
+    )
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(50.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(50.0)
+    assert mapped_segment.ParentCurve.is_a("IfcSecondOrderPolynomialSpiral")
+    assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Position.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.QuadraticTerm == pytest.approx(538.6086725079696)
+    assert mapped_segment.ParentCurve.LinearTerm == pytest.approx(-883.8834764831845)
+    assert mapped_segment.ParentCurve.ConstantTerm == pytest.approx(15625.0)
+
+
+def _HelmertCurve_100_0__300__1000_1_Meter(file):
+    design_parameters = file.createIfcAlignmentCantSegment(
+        StartDistAlong=0.0,
+        HorizontalLength=100.0,
+        StartCantLeft=0.16,
+        EndCantLeft=0.0,
+        StartCantRight=0.0,
+        EndCantRight=0.0,
+        PredefinedType="HELMERTCURVE",
+    )
+
+    alignment_segment = file.createIfcAlignmentSegment(
+        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+    )
+
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(file, alignment_segment, 1.5)
+    mapped_segment = mapped_segments[0]
+    assert len(mapped_segments) == 2
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((0.0, 0.08, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0, 0.0))
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(50.0)
+    assert mapped_segment.ParentCurve.is_a("IfcSecondOrderPolynomialSpiral")
+    assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Position.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.QuadraticTerm == pytest.approx(-538.6086725079696)
+    assert mapped_segment.ParentCurve.LinearTerm == pytest.approx(None)
+    assert mapped_segment.ParentCurve.ConstantTerm == pytest.approx(31250.0)
+    mapped_segment = mapped_segments[1]
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((50.0, 0.04, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx(
+        (0.999998720000819, -0.00159999897600066, 0.0)
+    )
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(50.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(50.0)
+    assert mapped_segment.ParentCurve.is_a("IfcSecondOrderPolynomialSpiral")
+    assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Position.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.QuadraticTerm == pytest.approx(538.6086725079696)
+    assert mapped_segment.ParentCurve.LinearTerm == pytest.approx(-883.8834764831845)
+    assert mapped_segment.ParentCurve.ConstantTerm == pytest.approx(15625.0)
+
+
+def _HelmertCurve_100_0_300_inf_1_Meter(file):
+    design_parameters = file.createIfcAlignmentCantSegment(
+        StartDistAlong=0.0,
+        HorizontalLength=100.0,
+        StartCantLeft=0.0,
+        EndCantLeft=0.0,
+        StartCantRight=0.16,
+        EndCantRight=0.0,
+        PredefinedType="HELMERTCURVE",
+    )
+
+    alignment_segment = file.createIfcAlignmentSegment(
+        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+    )
+
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(file, alignment_segment, 1.5)
+    mapped_segment = mapped_segments[0]
+    assert len(mapped_segments) == 2
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((0.0, 0.08, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0, 0.0))
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(50.0)
+    assert mapped_segment.ParentCurve.is_a("IfcSecondOrderPolynomialSpiral")
+    assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Position.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.QuadraticTerm == pytest.approx(-538.6086725079696)
+    assert mapped_segment.ParentCurve.LinearTerm == pytest.approx(None)
+    assert mapped_segment.ParentCurve.ConstantTerm == pytest.approx(31250.0)
+    mapped_segment = mapped_segments[1]
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((50.0, 0.04, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx(
+        (0.999998720000819, -0.00159999897600066, 0.0)
+    )
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(50.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(50.0)
+    assert mapped_segment.ParentCurve.is_a("IfcSecondOrderPolynomialSpiral")
+    assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Position.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.QuadraticTerm == pytest.approx(538.6086725079696)
+    assert mapped_segment.ParentCurve.LinearTerm == pytest.approx(-883.8834764831845)
+    assert mapped_segment.ParentCurve.ConstantTerm == pytest.approx(15625.0)
+
+
+def _HelmertCurve_100_0__300__inf_1_Meter(file):
+    design_parameters = file.createIfcAlignmentCantSegment(
+        StartDistAlong=0.0,
+        HorizontalLength=100.0,
+        StartCantLeft=0.16,
+        EndCantLeft=0.0,
+        StartCantRight=0.0,
+        EndCantRight=0.0,
+        PredefinedType="HELMERTCURVE",
+    )
+
+    alignment_segment = file.createIfcAlignmentSegment(
+        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+    )
+
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(file, alignment_segment, 1.5)
+    mapped_segment = mapped_segments[0]
+    assert len(mapped_segments) == 2
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((0.0, 0.08, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0, 0.0))
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(50.0)
+    assert mapped_segment.ParentCurve.is_a("IfcSecondOrderPolynomialSpiral")
+    assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Position.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.QuadraticTerm == pytest.approx(-538.6086725079696)
+    assert mapped_segment.ParentCurve.LinearTerm == pytest.approx(None)
+    assert mapped_segment.ParentCurve.ConstantTerm == pytest.approx(31250.0)
+    mapped_segment = mapped_segments[1]
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((50.0, 0.04, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx(
+        (0.999998720000819, -0.00159999897600066, 0.0)
+    )
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(50.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(50.0)
+    assert mapped_segment.ParentCurve.is_a("IfcSecondOrderPolynomialSpiral")
+    assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Position.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.QuadraticTerm == pytest.approx(538.6086725079696)
+    assert mapped_segment.ParentCurve.LinearTerm == pytest.approx(-883.8834764831845)
+    assert mapped_segment.ParentCurve.ConstantTerm == pytest.approx(15625.0)
+
+
+def _HelmertCurve_100_0_1000_300_1_Meter(file):
+    design_parameters = file.createIfcAlignmentCantSegment(
+        StartDistAlong=0.0,
+        HorizontalLength=100.0,
+        StartCantLeft=0.0,
+        EndCantLeft=0.0,
+        StartCantRight=0.0,
+        EndCantRight=0.16,
+        PredefinedType="HELMERTCURVE",
+    )
+
+    alignment_segment = file.createIfcAlignmentSegment(
+        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+    )
+
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(file, alignment_segment, 1.5)
+    mapped_segment = mapped_segments[0]
+    assert len(mapped_segments) == 2
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((0.0, 0.0, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0, 0.0))
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(50.0)
+    assert mapped_segment.ParentCurve.is_a("IfcSecondOrderPolynomialSpiral")
+    assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Position.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.QuadraticTerm == pytest.approx(538.6086725079696)
+    assert mapped_segment.ParentCurve.LinearTerm == pytest.approx(None)
+    assert mapped_segment.ParentCurve.ConstantTerm == pytest.approx(None)
+    mapped_segment = mapped_segments[1]
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((50.0, 0.04, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx(
+        (0.999998720000819, 0.00159999897600066, 0.0)
+    )
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(50.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(50.0)
+    assert mapped_segment.ParentCurve.is_a("IfcSecondOrderPolynomialSpiral")
+    assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Position.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.QuadraticTerm == pytest.approx(-538.6086725079696)
+    assert mapped_segment.ParentCurve.LinearTerm == pytest.approx(883.8834764831845)
+    assert mapped_segment.ParentCurve.ConstantTerm == pytest.approx(-31250.0)
+
+
+def _HelmertCurve_100_0__1000__300_1_Meter(file):
+    design_parameters = file.createIfcAlignmentCantSegment(
+        StartDistAlong=0.0,
+        HorizontalLength=100.0,
+        StartCantLeft=0.0,
+        EndCantLeft=0.16,
+        StartCantRight=0.0,
+        EndCantRight=0.0,
+        PredefinedType="HELMERTCURVE",
+    )
+
+    alignment_segment = file.createIfcAlignmentSegment(
+        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+    )
+
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(file, alignment_segment, 1.5)
+    mapped_segment = mapped_segments[0]
+    assert len(mapped_segments) == 2
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((0.0, 0.0, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0, 0.0))
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(50.0)
+    assert mapped_segment.ParentCurve.is_a("IfcSecondOrderPolynomialSpiral")
+    assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Position.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.QuadraticTerm == pytest.approx(538.6086725079696)
+    assert mapped_segment.ParentCurve.LinearTerm == pytest.approx(None)
+    assert mapped_segment.ParentCurve.ConstantTerm == pytest.approx(None)
+    mapped_segment = mapped_segments[1]
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((50.0, 0.04, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx(
+        (0.999998720000819, 0.00159999897600066, 0.0)
+    )
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(50.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(50.0)
+    assert mapped_segment.ParentCurve.is_a("IfcSecondOrderPolynomialSpiral")
+    assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Position.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.QuadraticTerm == pytest.approx(-538.6086725079696)
+    assert mapped_segment.ParentCurve.LinearTerm == pytest.approx(883.8834764831845)
+    assert mapped_segment.ParentCurve.ConstantTerm == pytest.approx(-31250.0)
+
+
+def _HelmertCurve_100_0_inf_300_1_Meter(file):
+    design_parameters = file.createIfcAlignmentCantSegment(
+        StartDistAlong=0.0,
+        HorizontalLength=100.0,
+        StartCantLeft=0.0,
+        EndCantLeft=0.0,
+        StartCantRight=0.0,
+        EndCantRight=0.16,
+        PredefinedType="HELMERTCURVE",
+    )
+
+    alignment_segment = file.createIfcAlignmentSegment(
+        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+    )
+
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(file, alignment_segment, 1.5)
+    mapped_segment = mapped_segments[0]
+    assert len(mapped_segments) == 2
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((0.0, 0.0, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0, 0.0))
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(50.0)
+    assert mapped_segment.ParentCurve.is_a("IfcSecondOrderPolynomialSpiral")
+    assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Position.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.QuadraticTerm == pytest.approx(538.6086725079696)
+    assert mapped_segment.ParentCurve.LinearTerm == pytest.approx(None)
+    assert mapped_segment.ParentCurve.ConstantTerm == pytest.approx(None)
+    mapped_segment = mapped_segments[1]
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((50.0, 0.04, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx(
+        (0.999998720000819, 0.00159999897600066, 0.0)
+    )
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(50.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(50.0)
+    assert mapped_segment.ParentCurve.is_a("IfcSecondOrderPolynomialSpiral")
+    assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Position.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.QuadraticTerm == pytest.approx(-538.6086725079696)
+    assert mapped_segment.ParentCurve.LinearTerm == pytest.approx(883.8834764831845)
+    assert mapped_segment.ParentCurve.ConstantTerm == pytest.approx(-31250.0)
+
+
+def _HelmertCurve_100_0__inf__300_1_Meter(file):
+    design_parameters = file.createIfcAlignmentCantSegment(
+        StartDistAlong=0.0,
+        HorizontalLength=100.0,
+        StartCantLeft=0.0,
+        EndCantLeft=0.16,
+        StartCantRight=0.0,
+        EndCantRight=0.0,
+        PredefinedType="HELMERTCURVE",
+    )
+
+    alignment_segment = file.createIfcAlignmentSegment(
+        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+    )
+
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(file, alignment_segment, 1.5)
+    mapped_segment = mapped_segments[0]
+    assert len(mapped_segments) == 2
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((0.0, 0.0, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0, 0.0))
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(50.0)
+    assert mapped_segment.ParentCurve.is_a("IfcSecondOrderPolynomialSpiral")
+    assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Position.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.QuadraticTerm == pytest.approx(538.6086725079696)
+    assert mapped_segment.ParentCurve.LinearTerm == pytest.approx(None)
+    assert mapped_segment.ParentCurve.ConstantTerm == pytest.approx(None)
+    mapped_segment = mapped_segments[1]
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((50.0, 0.04, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx(
+        (0.999998720000819, 0.00159999897600066, 0.0)
+    )
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(50.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(50.0)
+    assert mapped_segment.ParentCurve.is_a("IfcSecondOrderPolynomialSpiral")
+    assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Position.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.QuadraticTerm == pytest.approx(-538.6086725079696)
+    assert mapped_segment.ParentCurve.LinearTerm == pytest.approx(883.8834764831845)
+    assert mapped_segment.ParentCurve.ConstantTerm == pytest.approx(-31250.0)
+
+
+def _LinearTransition_100_0_300_1000_1_Meter(file):
+    design_parameters = file.createIfcAlignmentCantSegment(
+        StartDistAlong=0.0,
+        HorizontalLength=100.0,
+        StartCantLeft=0.0,
+        EndCantLeft=0.0,
+        StartCantRight=0.16,
+        EndCantRight=0.0,
+        PredefinedType="LINEARTRANSITION",
+    )
+
+    alignment_segment = file.createIfcAlignmentSegment(
+        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+    )
+
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(file, alignment_segment, 1.5)
+    mapped_segment = mapped_segments[0]
+    assert len(mapped_segments) == 2
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((0.0, 0.08, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx(
+        (0.999999680000154, -0.000799999744000123, 0.0)
+    )
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(100.0)
+    assert mapped_segment.ParentCurve.is_a("IfcClothoid")
+    assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Position.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.ClothoidConstant == pytest.approx(-3535.53390593274)
+
+
+def _LinearTransition_100_0__300__1000_1_Meter(file):
+    design_parameters = file.createIfcAlignmentCantSegment(
+        StartDistAlong=0.0,
+        HorizontalLength=100.0,
+        StartCantLeft=0.16,
+        EndCantLeft=0.0,
+        StartCantRight=0.0,
+        EndCantRight=0.0,
+        PredefinedType="LINEARTRANSITION",
+    )
+
+    alignment_segment = file.createIfcAlignmentSegment(
+        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+    )
+
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(file, alignment_segment, 1.5)
+    mapped_segment = mapped_segments[0]
+    assert len(mapped_segments) == 2
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((0.0, 0.08, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx(
+        (0.999999680000154, -0.000799999744000123, 0.0)
+    )
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(100.0)
+    assert mapped_segment.ParentCurve.is_a("IfcClothoid")
+    assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Position.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.ClothoidConstant == pytest.approx(-3535.53390593274)
+
+
+def _LinearTransition_100_0_300_inf_1_Meter(file):
+    design_parameters = file.createIfcAlignmentCantSegment(
+        StartDistAlong=0.0,
+        HorizontalLength=100.0,
+        StartCantLeft=0.0,
+        EndCantLeft=0.0,
+        StartCantRight=0.16,
+        EndCantRight=0.0,
+        PredefinedType="LINEARTRANSITION",
+    )
+
+    alignment_segment = file.createIfcAlignmentSegment(
+        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+    )
+
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(file, alignment_segment, 1.5)
+    mapped_segment = mapped_segments[0]
+    assert len(mapped_segments) == 2
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((0.0, 0.08, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx(
+        (0.999999680000154, -0.000799999744000123, 0.0)
+    )
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(100.0)
+    assert mapped_segment.ParentCurve.is_a("IfcClothoid")
+    assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Position.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.ClothoidConstant == pytest.approx(-3535.53390593274)
+
+
+def _LinearTransition_100_0__300__inf_1_Meter(file):
+    design_parameters = file.createIfcAlignmentCantSegment(
+        StartDistAlong=0.0,
+        HorizontalLength=100.0,
+        StartCantLeft=0.16,
+        EndCantLeft=0.0,
+        StartCantRight=0.0,
+        EndCantRight=0.0,
+        PredefinedType="LINEARTRANSITION",
+    )
+
+    alignment_segment = file.createIfcAlignmentSegment(
+        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+    )
+
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(file, alignment_segment, 1.5)
+    mapped_segment = mapped_segments[0]
+    assert len(mapped_segments) == 2
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((0.0, 0.08, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx(
+        (0.999999680000154, -0.000799999744000123, 0.0)
+    )
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(100.0)
+    assert mapped_segment.ParentCurve.is_a("IfcClothoid")
+    assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Position.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.ClothoidConstant == pytest.approx(-3535.53390593274)
+
+
+def _LinearTransition_100_0_1000_300_1_Meter(file):
+    design_parameters = file.createIfcAlignmentCantSegment(
+        StartDistAlong=0.0,
+        HorizontalLength=100.0,
+        StartCantLeft=0.0,
+        EndCantLeft=0.0,
+        StartCantRight=0.0,
+        EndCantRight=0.16,
+        PredefinedType="LINEARTRANSITION",
+    )
+
+    alignment_segment = file.createIfcAlignmentSegment(
+        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+    )
+
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(file, alignment_segment, 1.5)
+    mapped_segment = mapped_segments[0]
+    assert len(mapped_segments) == 2
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((0.0, 0.0, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx(
+        (0.999999680000154, 0.000799999744000123, 0.0)
+    )
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(100.0)
+    assert mapped_segment.ParentCurve.is_a("IfcClothoid")
+    assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Position.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.ClothoidConstant == pytest.approx(3535.53390593274)
+
+
+def _LinearTransition_100_0__1000__300_1_Meter(file):
+    design_parameters = file.createIfcAlignmentCantSegment(
+        StartDistAlong=0.0,
+        HorizontalLength=100.0,
+        StartCantLeft=0.0,
+        EndCantLeft=0.16,
+        StartCantRight=0.0,
+        EndCantRight=0.0,
+        PredefinedType="LINEARTRANSITION",
+    )
+
+    alignment_segment = file.createIfcAlignmentSegment(
+        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+    )
+
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(file, alignment_segment, 1.5)
+    mapped_segment = mapped_segments[0]
+    assert len(mapped_segments) == 2
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((0.0, 0.0, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx(
+        (0.999999680000154, 0.000799999744000123, 0.0)
+    )
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(100.0)
+    assert mapped_segment.ParentCurve.is_a("IfcClothoid")
+    assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Position.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.ClothoidConstant == pytest.approx(3535.53390593274)
+
+
+def _LinearTransition_100_0_inf_300_1_Meter(file):
+    design_parameters = file.createIfcAlignmentCantSegment(
+        StartDistAlong=0.0,
+        HorizontalLength=100.0,
+        StartCantLeft=0.0,
+        EndCantLeft=0.0,
+        StartCantRight=0.0,
+        EndCantRight=0.16,
+        PredefinedType="LINEARTRANSITION",
+    )
+
+    alignment_segment = file.createIfcAlignmentSegment(
+        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+    )
+
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(file, alignment_segment, 1.5)
+    mapped_segment = mapped_segments[0]
+    assert len(mapped_segments) == 2
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((0.0, 0.0, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx(
+        (0.999999680000154, 0.000799999744000123, 0.0)
+    )
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(100.0)
+    assert mapped_segment.ParentCurve.is_a("IfcClothoid")
+    assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Position.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.ClothoidConstant == pytest.approx(3535.53390593274)
+
+
+def _LinearTransition_100_0__inf__300_1_Meter(file):
+    design_parameters = file.createIfcAlignmentCantSegment(
+        StartDistAlong=0.0,
+        HorizontalLength=100.0,
+        StartCantLeft=0.0,
+        EndCantLeft=0.16,
+        StartCantRight=0.0,
+        EndCantRight=0.0,
+        PredefinedType="LINEARTRANSITION",
+    )
+
+    alignment_segment = file.createIfcAlignmentSegment(
+        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+    )
+
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(file, alignment_segment, 1.5)
+    mapped_segment = mapped_segments[0]
+    assert len(mapped_segments) == 2
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((0.0, 0.0, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx(
+        (0.999999680000154, 0.000799999744000123, 0.0)
+    )
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(100.0)
+    assert mapped_segment.ParentCurve.is_a("IfcClothoid")
+    assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Position.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.ClothoidConstant == pytest.approx(3535.53390593274)
+
+
+def _SineCurve_100_0_300_1000_1_Meter(file):
+    design_parameters = file.createIfcAlignmentCantSegment(
+        StartDistAlong=0.0,
+        HorizontalLength=100.0,
+        StartCantLeft=0.0,
+        EndCantLeft=0.0,
+        StartCantRight=0.16,
+        EndCantRight=0.0,
+        PredefinedType="SINECURVE",
+    )
+
+    alignment_segment = file.createIfcAlignmentSegment(
+        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+    )
+
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(file, alignment_segment, 1.5)
+    mapped_segment = mapped_segments[0]
+    assert len(mapped_segments) == 2
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((0.0, 0.08, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0, 0.0))
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(100.0)
+    assert mapped_segment.ParentCurve.is_a("IfcSineSpiral")
+    assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Position.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.SineTerm == pytest.approx(785398.163397448)
+    assert mapped_segment.ParentCurve.LinearTerm == pytest.approx(-3535.53390593274)
+    assert mapped_segment.ParentCurve.ConstantTerm == pytest.approx(125000.0)
+
+
+def _SineCurve_100_0__300__1000_1_Meter(file):
+    design_parameters = file.createIfcAlignmentCantSegment(
+        StartDistAlong=0.0,
+        HorizontalLength=100.0,
+        StartCantLeft=0.16,
+        EndCantLeft=0.0,
+        StartCantRight=0.0,
+        EndCantRight=0.0,
+        PredefinedType="SINECURVE",
+    )
+
+    alignment_segment = file.createIfcAlignmentSegment(
+        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+    )
+
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(file, alignment_segment, 1.5)
+    mapped_segment = mapped_segments[0]
+    assert len(mapped_segments) == 2
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((0.0, 0.08, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0, 0.0))
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(100.0)
+    assert mapped_segment.ParentCurve.is_a("IfcSineSpiral")
+    assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Position.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.SineTerm == pytest.approx(785398.163397448)
+    assert mapped_segment.ParentCurve.LinearTerm == pytest.approx(-3535.53390593274)
+    assert mapped_segment.ParentCurve.ConstantTerm == pytest.approx(125000.0)
+
+
+def _SineCurve_100_0_300_inf_1_Meter(file):
+    design_parameters = file.createIfcAlignmentCantSegment(
+        StartDistAlong=0.0,
+        HorizontalLength=100.0,
+        StartCantLeft=0.0,
+        EndCantLeft=0.0,
+        StartCantRight=0.16,
+        EndCantRight=0.0,
+        PredefinedType="SINECURVE",
+    )
+
+    alignment_segment = file.createIfcAlignmentSegment(
+        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+    )
+
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(file, alignment_segment, 1.5)
+    mapped_segment = mapped_segments[0]
+    assert len(mapped_segments) == 2
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((0.0, 0.08, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0, 0.0))
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(100.0)
+    assert mapped_segment.ParentCurve.is_a("IfcSineSpiral")
+    assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Position.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.SineTerm == pytest.approx(785398.163397448)
+    assert mapped_segment.ParentCurve.LinearTerm == pytest.approx(-3535.53390593274)
+    assert mapped_segment.ParentCurve.ConstantTerm == pytest.approx(125000.0)
+
+
+def _SineCurve_100_0__300__inf_1_Meter(file):
+    design_parameters = file.createIfcAlignmentCantSegment(
+        StartDistAlong=0.0,
+        HorizontalLength=100.0,
+        StartCantLeft=0.16,
+        EndCantLeft=0.0,
+        StartCantRight=0.0,
+        EndCantRight=0.0,
+        PredefinedType="SINECURVE",
+    )
+
+    alignment_segment = file.createIfcAlignmentSegment(
+        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+    )
+
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(file, alignment_segment, 1.5)
+    mapped_segment = mapped_segments[0]
+    assert len(mapped_segments) == 2
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((0.0, 0.08, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0, 0.0))
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(100.0)
+    assert mapped_segment.ParentCurve.is_a("IfcSineSpiral")
+    assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Position.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.SineTerm == pytest.approx(785398.163397448)
+    assert mapped_segment.ParentCurve.LinearTerm == pytest.approx(-3535.53390593274)
+    assert mapped_segment.ParentCurve.ConstantTerm == pytest.approx(125000.0)
+
+
+def _SineCurve_100_0_1000_300_1_Meter(file):
+    design_parameters = file.createIfcAlignmentCantSegment(
+        StartDistAlong=0.0,
+        HorizontalLength=100.0,
+        StartCantLeft=0.0,
+        EndCantLeft=0.16,
+        StartCantRight=0.0,
+        EndCantRight=0.0,
+        PredefinedType="SINECURVE",
+    )
+
+    alignment_segment = file.createIfcAlignmentSegment(
+        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+    )
+
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(file, alignment_segment, 1.5)
+    mapped_segment = mapped_segments[0]
+    assert len(mapped_segments) == 2
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((0.0, 0.0, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0, 0.0))
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(100.0)
+    assert mapped_segment.ParentCurve.is_a("IfcSineSpiral")
+    assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Position.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.SineTerm == pytest.approx(-785398.163397448)
+    assert mapped_segment.ParentCurve.LinearTerm == pytest.approx(3535.53390593274)
+    assert mapped_segment.ParentCurve.ConstantTerm == pytest.approx(None)
+
+
+def _SineCurve_100_0__1000__300_1_Meter(file):
+    design_parameters = file.createIfcAlignmentCantSegment(
+        StartDistAlong=0.0,
+        HorizontalLength=100.0,
+        StartCantLeft=0.0,
+        EndCantLeft=0.16,
+        StartCantRight=0.0,
+        EndCantRight=0.0,
+        PredefinedType="SINECURVE",
+    )
+
+    alignment_segment = file.createIfcAlignmentSegment(
+        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+    )
+
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(file, alignment_segment, 1.5)
+    mapped_segment = mapped_segments[0]
+    assert len(mapped_segments) == 2
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((0.0, 0.0, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0, 0.0))
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(100.0)
+    assert mapped_segment.ParentCurve.is_a("IfcSineSpiral")
+    assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Position.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.SineTerm == pytest.approx(-785398.163397448)
+    assert mapped_segment.ParentCurve.LinearTerm == pytest.approx(3535.53390593274)
+    assert mapped_segment.ParentCurve.ConstantTerm == pytest.approx(None)
+
+
+def _SineCurve_100_0_inf_300_1_Meter(file):
+    design_parameters = file.createIfcAlignmentCantSegment(
+        StartDistAlong=0.0,
+        HorizontalLength=100.0,
+        StartCantLeft=0.0,
+        EndCantLeft=0.0,
+        StartCantRight=0.0,
+        EndCantRight=0.16,
+        PredefinedType="SINECURVE",
+    )
+
+    alignment_segment = file.createIfcAlignmentSegment(
+        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+    )
+
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(file, alignment_segment, 1.5)
+    mapped_segment = mapped_segments[0]
+    assert len(mapped_segments) == 2
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((0.0, 0.0, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0, 0.0))
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(100.0)
+    assert mapped_segment.ParentCurve.is_a("IfcSineSpiral")
+    assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Position.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.SineTerm == pytest.approx(-785398.163397448)
+    assert mapped_segment.ParentCurve.LinearTerm == pytest.approx(3535.53390593274)
+    assert mapped_segment.ParentCurve.ConstantTerm == pytest.approx(None)
+
+
+def _SineCurve_100_0__inf__300_1_Meter(file):
+    design_parameters = file.createIfcAlignmentCantSegment(
+        StartDistAlong=0.0,
+        HorizontalLength=100.0,
+        StartCantLeft=0.0,
+        EndCantLeft=0.16,
+        StartCantRight=0.0,
+        EndCantRight=0.0,
+        PredefinedType="SINECURVE",
+    )
+
+    alignment_segment = file.createIfcAlignmentSegment(
+        GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
+    )
+
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_cant_segment(file, alignment_segment, 1.5)
+    mapped_segment = mapped_segments[0]
+    assert len(mapped_segments) == 2
+    assert "DISCONTINUOUS" == mapped_segment.Transition
+    assert mapped_segment.Placement.Location.Coordinates == pytest.approx((0.0, 0.0, 0.0))
+    assert mapped_segment.Placement.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0, 0.0))
+    assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(100.0)
+    assert mapped_segment.ParentCurve.is_a("IfcSineSpiral")
+    assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
+    assert mapped_segment.ParentCurve.Position.RefDirection.DirectionRatios == pytest.approx((1.0, 0.0))
+    assert mapped_segment.ParentCurve.SineTerm == pytest.approx(-785398.163397448)
+    assert mapped_segment.ParentCurve.LinearTerm == pytest.approx(3535.53390593274)
+    assert mapped_segment.ParentCurve.ConstantTerm == pytest.approx(None)
+
+
 def test_map_alignment_cant_segment():
     file = ifcopenshell.file(schema="IFC4X3_ADD2")
-    # create tests as the mapping functions are implemented
+    _BlossCurve_100_0_300_1000_1_Meter(file)
+    _BlossCurve_100_0__300__1000_1_Meter(file)
+    _BlossCurve_100_0_300_inf_1_Meter(file)
+    _BlossCurve_100_0__300__inf_1_Meter(file)
+    _BlossCurve_100_0_1000_300_1_Meter(file)
+    _BlossCurve_100_0__1000__300_1_Meter(file)
+    _BlossCurve_100_0_inf_300_1_Meter(file)
+    _BlossCurve_100_0__inf__300_1_Meter(file)
+    _ConstantCant_100_0_300_1000_1_Meter(file)
+    _ConstantCant_100_0__300__1000_1_Meter(file)
+    _ConstantCant_100_0_300_inf_1_Meter(file)
+    _ConstantCant_100_0__300__inf_1_Meter(file)
+    _ConstantCant_100_0_1000_300_1_Meter(file)
+    _ConstantCant_100_0__1000__300_1_Meter(file)
+    _ConstantCant_100_0_inf_300_1_Meter(file)
+    _ConstantCant_100_0__inf__300_1_Meter(file)
+    _CosineCurve_100_0_300_1000_1_Meter(file)
+    _CosineCurve_100_0__300__1000_1_Meter(file)
+    _CosineCurve_100_0_300_inf_1_Meter(file)
+    _CosineCurve_100_0__300__inf_1_Meter(file)
+    _CosineCurve_100_0_1000_300_1_Meter(file)
+    _CosineCurve_100_0__1000__300_1_Meter(file)
+    _CosineCurve_100_0_inf_300_1_Meter(file)
+    _CosineCurve_100_0__inf__300_1_Meter(file)
+    _HelmertCurve_100_0_300_1000_1_Meter(file)
+    _HelmertCurve_100_0__300__1000_1_Meter(file)
+    _HelmertCurve_100_0_300_inf_1_Meter(file)
+    _HelmertCurve_100_0__300__inf_1_Meter(file)
+    _HelmertCurve_100_0_1000_300_1_Meter(file)
+    _HelmertCurve_100_0__1000__300_1_Meter(file)
+    _HelmertCurve_100_0_inf_300_1_Meter(file)
+    _HelmertCurve_100_0__inf__300_1_Meter(file)
+    _LinearTransition_100_0_300_1000_1_Meter(file)
+    _LinearTransition_100_0__300__1000_1_Meter(file)
+    _LinearTransition_100_0_300_inf_1_Meter(file)
+    _LinearTransition_100_0__300__inf_1_Meter(file)
+    _LinearTransition_100_0_1000_300_1_Meter(file)
+    _LinearTransition_100_0__1000__300_1_Meter(file)
+    _LinearTransition_100_0_inf_300_1_Meter(file)
+    _LinearTransition_100_0__inf__300_1_Meter(file)
+    _SineCurve_100_0_300_1000_1_Meter(file)
+    _SineCurve_100_0__300__1000_1_Meter(file)
+    _SineCurve_100_0_300_inf_1_Meter(file)
+    _SineCurve_100_0__300__inf_1_Meter(file)
+    _SineCurve_100_0_1000_300_1_Meter(file)
+    _SineCurve_100_0__1000__300_1_Meter(file)
+    _SineCurve_100_0_inf_300_1_Meter(file)
+    _SineCurve_100_0__inf__300_1_Meter(file)
+
+    # VIENESSE BEND NOT IMPLEMENTED
diff --git a/src/ifcopenshell-python/test/api/alignment/test_map_alignment_horizontal_segment.py b/src/ifcopenshell-python/test/api/alignment/test_map_alignment_horizontal_segment.py
index 0d8e55293d..bbe744e537 100644
--- a/src/ifcopenshell-python/test/api/alignment/test_map_alignment_horizontal_segment.py
+++ b/src/ifcopenshell-python/test/api/alignment/test_map_alignment_horizontal_segment.py
@@ -37,7 +37,7 @@ def _BlossCurve_100_0_300_1000_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -68,7 +68,7 @@ def _BlossCurve_100_0__300__1000_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -99,7 +99,7 @@ def _BlossCurve_100_0_300_inf_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -130,7 +130,7 @@ def _BlossCurve_100_0__300__inf_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -161,7 +161,7 @@ def _BlossCurve_100_0_1000_300_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -192,7 +192,7 @@ def _BlossCurve_100_0__1000__300_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -223,7 +223,7 @@ def _BlossCurve_100_0_inf_300_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -254,7 +254,7 @@ def _BlossCurve_100_0__inf__300_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -285,7 +285,7 @@ def _CircularArc_100_0_300_1000_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -313,7 +313,7 @@ def _CircularArc_100_0__300__1000_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -341,7 +341,7 @@ def _CircularArc_100_0_300_inf_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -369,7 +369,7 @@ def _CircularArc_100_0__300__inf_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -397,7 +397,7 @@ def _CircularArc_100_0_1000_300_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -425,7 +425,7 @@ def _CircularArc_100_0__1000__300_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -453,7 +453,7 @@ def _CircularArc_100_0_inf_300_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -481,7 +481,7 @@ def _CircularArc_100_0__inf__300_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -509,7 +509,7 @@ def _Clothoid_100_0_300_1000_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -537,7 +537,7 @@ def _Clothoid_100_0__300__1000_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -565,7 +565,7 @@ def _Clothoid_100_0_300_inf_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -593,7 +593,7 @@ def _Clothoid_100_0__300__inf_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -621,7 +621,7 @@ def _Clothoid_100_0_1000_300_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -649,7 +649,7 @@ def _Clothoid_100_0__1000__300_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -677,7 +677,7 @@ def _Clothoid_100_0_inf_300_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -705,7 +705,7 @@ def _Clothoid_100_0__inf__300_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -733,7 +733,7 @@ def _CosineCurve_100_0_300_1000_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -762,7 +762,7 @@ def _CosineCurve_100_0__300__1000_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -791,7 +791,7 @@ def _CosineCurve_100_0_300_inf_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -820,7 +820,7 @@ def _CosineCurve_100_0__300__inf_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -849,7 +849,7 @@ def _CosineCurve_100_0_1000_300_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -878,7 +878,7 @@ def _CosineCurve_100_0__1000__300_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -907,7 +907,7 @@ def _CosineCurve_100_0_inf_300_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -936,7 +936,7 @@ def _CosineCurve_100_0__inf__300_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -965,7 +965,7 @@ def _Cubic_100_0_300_1000_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -994,7 +994,7 @@ def _Cubic_100_0__300__1000_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -1023,7 +1023,7 @@ def _Cubic_100_0_300_inf_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -1052,7 +1052,7 @@ def _Cubic_100_0__300__inf_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -1081,7 +1081,7 @@ def _Cubic_100_0_1000_300_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -1110,7 +1110,7 @@ def _Cubic_100_0__1000__300_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -1139,7 +1139,7 @@ def _Cubic_100_0_inf_300_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -1168,7 +1168,7 @@ def _Cubic_100_0__inf__300_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -1197,7 +1197,7 @@ def _HelmertCurve_100_0_300_1000_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -1245,7 +1245,7 @@ def _HelmertCurve_100_0__300__1000_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -1293,7 +1293,7 @@ def _HelmertCurve_100_0_300_inf_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -1341,7 +1341,7 @@ def _HelmertCurve_100_0__300__inf_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -1389,7 +1389,7 @@ def _HelmertCurve_100_0_1000_300_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -1437,7 +1437,7 @@ def _HelmertCurve_100_0__1000__300_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -1485,7 +1485,7 @@ def _HelmertCurve_100_0_inf_300_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -1533,7 +1533,7 @@ def _HelmertCurve_100_0__inf__300_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -1581,7 +1581,7 @@ def _Line_100_0_300_1000_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -1609,7 +1609,7 @@ def _Line_100_0__300__1000_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -1637,7 +1637,7 @@ def _Line_100_0_300_inf_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -1665,7 +1665,7 @@ def _Line_100_0__300__inf_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -1693,7 +1693,7 @@ def _Line_100_0_1000_300_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -1721,7 +1721,7 @@ def _Line_100_0__1000__300_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -1749,7 +1749,7 @@ def _Line_100_0_inf_300_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -1777,7 +1777,7 @@ def _Line_100_0__inf__300_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -1805,7 +1805,7 @@ def _SineCurve_100_0_300_1000_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -1835,7 +1835,7 @@ def _SineCurve_100_0__300__1000_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -1865,7 +1865,7 @@ def _SineCurve_100_0_300_inf_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -1895,7 +1895,7 @@ def _SineCurve_100_0__300__inf_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -1925,7 +1925,7 @@ def _SineCurve_100_0_1000_300_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -1955,7 +1955,7 @@ def _SineCurve_100_0__1000__300_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -1985,7 +1985,7 @@ def _SineCurve_100_0_inf_300_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
@@ -2015,7 +2015,7 @@ def _SineCurve_100_0__inf__300_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_horizontal_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert "DISCONTINUOUS" == mapped_segment.Transition
diff --git a/src/ifcopenshell-python/test/api/alignment/test_map_alignment_segments.py b/src/ifcopenshell-python/test/api/alignment/test_map_alignment_segments.py
deleted file mode 100644
index 1c9d04bc24..0000000000
--- a/src/ifcopenshell-python/test/api/alignment/test_map_alignment_segments.py
+++ /dev/null
@@ -1,102 +0,0 @@
-# IfcOpenShell - IFC toolkit and geometry engine
-# Copyright (C) 2025 Thomas Krijnen <thomas@aecgeeks.com>
-#
-# This file is part of IfcOpenShell.
-#
-# IfcOpenShell is free software: you can redistribute it and/or modify
-# it under the terms of the GNU Lesser General Public License as published by
-# the Free Software Foundation, either version 3 of the License, or
-# (at your option) any later version.
-#
-# IfcOpenShell is distributed in the hope that it will be useful,
-# but WITHOUT ANY WARRANTY; without even the implied warranty of
-# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
-# GNU Lesser General Public License for more details.
-#
-# You should have received a copy of the GNU Lesser General Public License
-# along with IfcOpenShell.  If not, see <http://www.gnu.org/licenses/>.
-
-import pytest
-import ifcopenshell.api.alignment
-import ifcopenshell.api.context
-
-
-def test_map_alignment_horizontal_segment():
-    file = ifcopenshell.file(schema="IFC4X3_ADD2")
-    project = file.createIfcProject(Name="Test")
-    geometric_representation_context = ifcopenshell.api.context.add_context(file, context_type="Model")
-    axis_model_representation_subcontext = ifcopenshell.api.context.add_context(
-        file,
-        context_type="Model",
-        context_identifier="Axis",
-        target_view="MODEL_VIEW",
-        parent=geometric_representation_context,
-    )
-
-    coordinates = [(500.0, 2500.0), (3340.0, 660.0), (4340.0, 5000.0), (7600.0, 4560.0), (8480.0, 2010.0)]
-    radii = [(1000.0), (1250.0), (950.0)]
-    vpoints = [(0.0, 100.0), (2000.0, 135.0), (5000.0, 105.0), (7400.0, 153.0), (9800.0, 105.0), (12800.0, 90.0)]
-    lengths = [(1600.0), (1200.0), (2000.0), (800.0)]
-
-    alignment = ifcopenshell.api.alignment.create_alignment_by_pi_method(
-        file, "TestAlignment", coordinates, radii, vpoints, lengths
-    )
-
-    horizontal_alignment = alignment.IsNestedBy[0].RelatedObjects[0]
-    assert horizontal_alignment.is_a("IfcAlignmentHorizontal")
-
-    composite_curve = file.create_entity(
-        type="IfcCompositeCurve",
-        Segments=[],
-        SelfIntersect=False,
-    )
-
-    ifcopenshell.api.alignment.map_alignment_segments(file, horizontal_alignment, composite_curve)
-    assert len(composite_curve.Segments) == 8
-    assert composite_curve.Segments[0].ParentCurve.is_a("IfcLine")
-    assert composite_curve.Segments[0].Transition == "CONTSAMEGRADIENT"
-    assert composite_curve.Segments[1].ParentCurve.is_a("IfcCircle")
-    assert composite_curve.Segments[1].Transition == "CONTSAMEGRADIENT"
-    assert composite_curve.Segments[2].ParentCurve.is_a("IfcLine")
-    assert composite_curve.Segments[2].Transition == "CONTSAMEGRADIENT"
-    assert composite_curve.Segments[3].ParentCurve.is_a("IfcCircle")
-    assert composite_curve.Segments[3].Transition == "CONTSAMEGRADIENT"
-    assert composite_curve.Segments[4].ParentCurve.is_a("IfcLine")
-    assert composite_curve.Segments[4].Transition == "CONTSAMEGRADIENT"
-    assert composite_curve.Segments[5].ParentCurve.is_a("IfcCircle")
-    assert composite_curve.Segments[5].Transition == "CONTSAMEGRADIENT"
-    assert composite_curve.Segments[6].ParentCurve.is_a("IfcLine")
-    assert composite_curve.Segments[6].Transition == "CONTSAMEGRADIENTSAMECURVATURE"
-    assert composite_curve.Segments[7].ParentCurve.is_a("IfcLine")
-    assert composite_curve.Segments[7].Transition == "DISCONTINUOUS"
-
-    vertical_alignment = alignment.IsNestedBy[0].RelatedObjects[1]
-    assert vertical_alignment.is_a("IfcAlignmentVertical")
-
-    gradient_curve = file.create_entity(
-        type="IfcGradientCurve", Segments=[], SelfIntersect=False, BaseCurve=composite_curve, EndPoint=None
-    )
-
-    ifcopenshell.api.alignment.map_alignment_segments(file, vertical_alignment, gradient_curve)
-    assert len(gradient_curve.Segments) == 10
-
-    assert gradient_curve.Segments[0].ParentCurve.is_a("IfcLine")
-    assert gradient_curve.Segments[0].Transition == "CONTSAMEGRADIENT"
-    assert gradient_curve.Segments[1].ParentCurve.is_a("IfcPolynomialCurve")
-    assert gradient_curve.Segments[1].Transition == "CONTSAMEGRADIENT"
-    assert gradient_curve.Segments[2].ParentCurve.is_a("IfcLine")
-    assert gradient_curve.Segments[2].Transition == "CONTSAMEGRADIENT"
-    assert gradient_curve.Segments[3].ParentCurve.is_a("IfcPolynomialCurve")
-    assert gradient_curve.Segments[3].Transition == "CONTSAMEGRADIENT"
-    assert gradient_curve.Segments[4].ParentCurve.is_a("IfcLine")
-    assert gradient_curve.Segments[4].Transition == "CONTSAMEGRADIENT"
-    assert gradient_curve.Segments[5].ParentCurve.is_a("IfcPolynomialCurve")
-    assert gradient_curve.Segments[5].Transition == "CONTSAMEGRADIENT"
-    assert gradient_curve.Segments[6].ParentCurve.is_a("IfcLine")
-    assert gradient_curve.Segments[6].Transition == "CONTSAMEGRADIENT"
-    assert gradient_curve.Segments[7].ParentCurve.is_a("IfcPolynomialCurve")
-    assert gradient_curve.Segments[7].Transition == "CONTSAMEGRADIENT"
-    assert gradient_curve.Segments[8].ParentCurve.is_a("IfcLine")
-    assert gradient_curve.Segments[8].Transition == "CONTSAMEGRADIENTSAMECURVATURE"
-    assert gradient_curve.Segments[9].ParentCurve.is_a("IfcLine")
-    assert gradient_curve.Segments[9].Transition == "DISCONTINUOUS"
diff --git a/src/ifcopenshell-python/test/api/alignment/test_map_alignment_vertical_segment.py b/src/ifcopenshell-python/test/api/alignment/test_map_alignment_vertical_segment.py
index 867183d369..0d72fe6b83 100644
--- a/src/ifcopenshell-python/test/api/alignment/test_map_alignment_vertical_segment.py
+++ b/src/ifcopenshell-python/test/api/alignment/test_map_alignment_vertical_segment.py
@@ -37,7 +37,7 @@ def _CircularArc_100_0_10_0_0_0_0_5_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_vertical_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert mapped_segments[1] == None
@@ -66,7 +66,7 @@ def _CircularArc_100_0_10_0_0_0__0_5_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_vertical_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert mapped_segments[1] == None
@@ -97,7 +97,7 @@ def _CircularArc_100_0_10_0_0_5_0_0_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_vertical_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert mapped_segments[1] == None
@@ -128,7 +128,7 @@ def _CircularArc_100_0_10_0__0_5_0_0_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_vertical_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert mapped_segments[1] == None
@@ -159,7 +159,7 @@ def _CircularArc_100_0_10_0_0_5_1_0_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_vertical_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert mapped_segments[1] == None
@@ -192,7 +192,7 @@ def _CircularArc_100_0_10_0__0_5__1_0_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_vertical_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert mapped_segments[1] == None
@@ -225,7 +225,7 @@ def _CircularArc_100_0_10_0_1_0_0_5_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_vertical_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert mapped_segments[1] == None
@@ -258,7 +258,7 @@ def _CircularArc_100_0_10_0__1_0__0_5_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_vertical_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert mapped_segments[1] == None
@@ -291,7 +291,7 @@ def _ConstantGradient_100_0_10_0_0_0_0_5_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_vertical_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert mapped_segments[1] == None
@@ -320,7 +320,7 @@ def _ConstantGradient_100_0_10_0_0_0__0_5_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_vertical_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert mapped_segments[1] == None
@@ -349,7 +349,7 @@ def _ConstantGradient_100_0_10_0_0_5_0_0_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_vertical_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert mapped_segments[1] == None
@@ -380,7 +380,7 @@ def _ConstantGradient_100_0_10_0__0_5_0_0_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_vertical_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert mapped_segments[1] == None
@@ -411,7 +411,7 @@ def _ConstantGradient_100_0_10_0_0_5_1_0_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_vertical_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert mapped_segments[1] == None
@@ -442,7 +442,7 @@ def _ConstantGradient_100_0_10_0__0_5__1_0_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_vertical_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert mapped_segments[1] == None
@@ -473,7 +473,7 @@ def _ConstantGradient_100_0_10_0_1_0_0_5_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_vertical_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert mapped_segments[1] == None
@@ -504,7 +504,7 @@ def _ConstantGradient_100_0_10_0__1_0__0_5_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_vertical_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert mapped_segments[1] == None
@@ -535,7 +535,7 @@ def _ParabolicArc_100_0_10_0_0_0_0_5_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_vertical_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert mapped_segments[1] == None
@@ -564,7 +564,7 @@ def _ParabolicArc_100_0_10_0_0_0__0_5_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_vertical_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert mapped_segments[1] == None
@@ -593,7 +593,7 @@ def _ParabolicArc_100_0_10_0_0_5_0_0_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_vertical_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert mapped_segments[1] == None
@@ -624,7 +624,7 @@ def _ParabolicArc_100_0_10_0__0_5_0_0_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_vertical_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert mapped_segments[1] == None
@@ -655,7 +655,7 @@ def _ParabolicArc_100_0_10_0_0_5_1_0_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_vertical_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert mapped_segments[1] == None
@@ -665,7 +665,7 @@ def _ParabolicArc_100_0_10_0_0_5_1_0_1_Meter(file):
         (0.894427190999916, 0.447213595499958)
     )
     assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
-    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(125.53583325398947)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(125.53583299580873)
     assert mapped_segment.ParentCurve.is_a("IfcPolynomialCurve")
     assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
     assert mapped_segment.ParentCurve.CoefficientsX == pytest.approx((0.0, 1.0))
@@ -686,7 +686,7 @@ def _ParabolicArc_100_0_10_0__0_5__1_0_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_vertical_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert mapped_segments[1] == None
@@ -696,7 +696,7 @@ def _ParabolicArc_100_0_10_0__0_5__1_0_1_Meter(file):
         (0.894427190999916, -0.447213595499958)
     )
     assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
-    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(125.53583325398947)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(125.53583299580873)
     assert mapped_segment.ParentCurve.is_a("IfcPolynomialCurve")
     assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
     assert mapped_segment.ParentCurve.CoefficientsX == pytest.approx((0.0, 1.0))
@@ -717,7 +717,7 @@ def _ParabolicArc_100_0_10_0_1_0_0_5_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_vertical_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert mapped_segments[1] == None
@@ -727,7 +727,7 @@ def _ParabolicArc_100_0_10_0_1_0_0_5_1_Meter(file):
         (0.707106781186547, 0.707106781186547)
     )
     assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
-    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(125.53583325398947)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(125.53583299580873)
     assert mapped_segment.ParentCurve.is_a("IfcPolynomialCurve")
     assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
     assert mapped_segment.ParentCurve.CoefficientsX == pytest.approx((0.0, 1.0))
@@ -748,7 +748,7 @@ def _ParabolicArc_100_0_10_0__1_0__0_5_1_Meter(file):
         GlobalId=ifcopenshell.guid.new(), DesignParameters=design_parameters
     )
 
-    mapped_segments = ifcopenshell.api.alignment.map_alignment_segment(file, alignment_segment)
+    mapped_segments = ifcopenshell.api.alignment.map_alignment_vertical_segment(file, alignment_segment)
     mapped_segment = mapped_segments[0]
     assert len(mapped_segments) == 2
     assert mapped_segments[1] == None
@@ -758,7 +758,7 @@ def _ParabolicArc_100_0_10_0__1_0__0_5_1_Meter(file):
         (0.707106781186547, -0.707106781186547)
     )
     assert mapped_segment.SegmentStart.wrappedValue == pytest.approx(0.0)
-    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(125.53583325398947)
+    assert mapped_segment.SegmentLength.wrappedValue == pytest.approx(125.53583299580873)
     assert mapped_segment.ParentCurve.is_a("IfcPolynomialCurve")
     assert mapped_segment.ParentCurve.Position.Location.Coordinates == pytest.approx((0.0, 0.0))
     assert mapped_segment.ParentCurve.CoefficientsX == pytest.approx((0.0, 1.0))