diff --git a/src/ifcgeom/mapping/IfcAxis2PlacementLinear.cpp b/src/ifcgeom/mapping/IfcAxis2PlacementLinear.cpp
index 836a6391f8..212ca144b7 100644
--- a/src/ifcgeom/mapping/IfcAxis2PlacementLinear.cpp
+++ b/src/ifcgeom/mapping/IfcAxis2PlacementLinear.cpp
@@ -29,34 +29,26 @@ taxonomy::ptr mapping::map_impl(const IfcSchema::IfcAxis2PlacementLinear* inst)
         Logger::Error(std::runtime_error("Location must be IfcPointByDistanceExpression for IfcAxis2PlacementLinear"));
     }
 
-    Eigen::Vector3d o, axis(0, 0, 1), refDirection;
-
     taxonomy::matrix4::ptr m = taxonomy::cast<taxonomy::matrix4>(map(inst->Location()));
-    o = m->components().col(3).head<3>();
+    Eigen::Vector3d o = m->components().col(3).head<3>();
 
     // From 8.9.3.4 IfcAxis2PlacementLinear there are 4 cases that need to be considered
     // 1) Axis is given but not RefDirection
     // 2) RefDirection is given but not Axis
     // 3) Neither Axis or RefDirection are provided
     // 4) Both Axis and RefDirection are provided
+    // When Axis or RefDirection are not provided explicitly in the IfcAxis2PlacementLinear,
+    // they are taken from the context of curve by evaluating the Location, which is an IfcPointByDistanceExpression on a curve.
+    // The curve tangent is used as RefDirection and the curve normal is used as Axis.
 
     const bool hasAxis = inst->Axis() != nullptr;
     const bool hasRef = inst->RefDirection() != nullptr;
 
-    /*
-    if (hasAxis != hasRef) {
-		Logger::Warning("Axis and RefDirection should be specified together", inst);
-	}
-	*/
-
+    Eigen::Vector3d axis, refDirection;
     if (hasAxis && !hasRef) {
         taxonomy::direction3::ptr a = taxonomy::cast<taxonomy::direction3>(map(inst->Axis()));
         axis = *a->components_;
-
         refDirection = m->components().col(0).head<3>(); // RefDirection is the curve tangent when omitted
-        // refDirection is not necessarily orthogonal to axis.
-        // axis.cross(refDirection) gives y. y.cross(axis) gives x=refDirection
-        refDirection = axis.cross(refDirection).cross(axis);
     } else if (!hasAxis && hasRef) {
         taxonomy::direction3::ptr r = taxonomy::cast<taxonomy::direction3>(map(inst->RefDirection()));
         refDirection = *r->components_;
@@ -67,13 +59,10 @@ taxonomy::ptr mapping::map_impl(const IfcSchema::IfcAxis2PlacementLinear* inst)
     } else {
         taxonomy::direction3::ptr a = taxonomy::cast<taxonomy::direction3>(map(inst->Axis()));
         axis = *a->components_;
-
         taxonomy::direction3::ptr r = taxonomy::cast<taxonomy::direction3>(map(inst->RefDirection()));
         refDirection = *r->components_;
-        refDirection = axis.cross(refDirection).cross(axis); // refDirection needs to be orthogonal to axis
     }
 
-    // axis and refDirection need to be orthogonal
     return taxonomy::make<taxonomy::matrix4>(o, axis, refDirection);
 }
 
diff --git a/src/ifcgeom/taxonomy.h b/src/ifcgeom/taxonomy.h
index c1162eebb0..7a9a4325ca 100644
--- a/src/ifcgeom/taxonomy.h
+++ b/src/ifcgeom/taxonomy.h
@@ -277,20 +277,40 @@ typedef item const* ptr;
 			struct IFC_GEOM_API matrix4 : public item, public eigen_base<Eigen::Matrix4d> {
 			private:
 				void init(const Eigen::Vector3d& o, const Eigen::Vector3d& z, const Eigen::Vector3d& x) {
-					auto Z = z.normalized();
-					auto Y = Z.cross(x).normalized();
-					auto X = Y.cross(Z);
-					components_ = new Eigen::Matrix4d;
-					(*components_) <<
-						X(0), Y(0), Z(0), o(0),
-						X(1), Y(1), Z(1), o(1),
-						X(2), Y(2), Z(2), o(2),
-						0, 0, 0, 1.;
-					if (is_identity()) {
-						// @todo detect this earlier to save us the heapalloc.
-						delete components_;
-						components_ = nullptr;
-						tag = IDENTITY;
+                  auto valid_and_non_zero_extent = [](const Eigen::Vector3d&v,double eps = 1.e-9) {
+							 return v.allFinite() && v.squaredNorm() > eps*eps;
+                    };
+
+					// check z and x are valid vectors
+					if (!valid_and_non_zero_extent(z) || !valid_and_non_zero_extent(x)) {
+                  throw std::runtime_error("Invalid during for matrix4 construction");   
+					}
+
+					auto Z = z.normalized(); // ensure Z is a unit vector
+					auto Y = Z.cross(x); // Y is orthogonal to x and Z
+
+					// make sure Y is a valid vector
+					if (!valid_and_non_zero_extent(Y)) {
+						throw std::runtime_error("Parallel or degenerate matrix4 construction");
+               }
+
+					Y.normalize(); // ensure Y is a unit vector
+					auto X = Y.cross(Z); // X is orthogonal to Y and Z, and a unit vector
+
+					// check if this is going to be an identity matrix
+					double eps = 1.e-9;
+					if (X.isApprox(Eigen::Vector3d(1., 0., 0.), eps) &&
+ 						 Y.isApprox(Eigen::Vector3d(0., 1., 0.), eps) &&
+						 Z.isApprox(Eigen::Vector3d(0., 0., 1.), eps) &&
+						 o.isApprox(Eigen::Vector3d(0., 0., 0.), eps)) // in the full 4x4 matrix, this will be (0,0,0,1)
+					{
+                  tag = IDENTITY;
+					} else {
+                  components_ = new Eigen::Matrix4d;
+                  (*components_) << X(0), Y(0), Z(0), o(0),
+												X(1), Y(1), Z(1), o(1),
+												X(2), Y(2), Z(2), o(2),
+												0, 0, 0, 1.;
 					}
 				}
 			public: