diff --git a/src/ifcgeom/mapping/IfcAxis2PlacementLinear.cpp b/src/ifcgeom/mapping/IfcAxis2PlacementLinear.cpp
index f86f59ac98..b11b61b46b 100644
--- a/src/ifcgeom/mapping/IfcAxis2PlacementLinear.cpp
+++ b/src/ifcgeom/mapping/IfcAxis2PlacementLinear.cpp
@@ -29,8 +29,10 @@ 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()));
-    Eigen::Vector3d o = m->components().col(3).head<3>();
+    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
@@ -38,12 +40,43 @@ taxonomy::ptr mapping::map_impl(const IfcSchema::IfcAxis2PlacementLinear* inst)
     // 3) Neither Axis or RefDirection are provided
     // 4) Both Axis and RefDirection are provided
 
-    Eigen::Vector3d z = inst->Axis() ? *taxonomy::cast<taxonomy::direction3>(map(inst->Axis()))->components_ : Eigen::Vector3d(0,0,1); // Axis is (0,0,1) when omitted
-    Eigen::Vector3d rd = inst->RefDirection() ? *taxonomy::cast<taxonomy::direction3>(map(inst->RefDirection()))->components_ : m->components().col(0).head<3>(); // RefDirection is the curve tangent when omitted
-    Eigen::Vector3d y = z.cross(rd);
-    Eigen::Vector3d x = y.cross(z);
+    const bool hasAxis = inst->Axis() != nullptr;
+    const bool hasRef = inst->RefDirection() != nullptr;
 
-    return taxonomy::make<taxonomy::matrix4>(o, z, x);
+    /*
+    if (hasAxis != hasRef) {
+		Logger::Warning("Axis and RefDirection should be specified together", inst);
+	}
+	*/
+
+    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_;
+        Eigen::Vector3d up(0, 0, 1);
+        axis = refDirection.cross(up.cross(refDirection));
+    } else if (!hasAxis && !hasRef) {
+        refDirection = m->components().col(0).head<3>(); // RefDirection is the curve tangent when omitted
+        Eigen::Vector3d up(0, 0, 1);
+        axis = refDirection.cross(up.cross(refDirection));
+    } 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);
 }
 
 #endif