diff --git a/src/ifcgeom/kernels/cgal/CgalConversionResult.cpp b/src/ifcgeom/kernels/cgal/CgalConversionResult.cpp
index fb26abeed4..0947129b57 100644
--- a/src/ifcgeom/kernels/cgal/CgalConversionResult.cpp
+++ b/src/ifcgeom/kernels/cgal/CgalConversionResult.cpp
@@ -19,8 +19,9 @@ using ifcopenshell::geometry::NumberEpeck;
 #define NumberType NumberEpeck
 #endif
 
-ifcopenshell::geometry::CgalShape::CgalShape(const cgal_shape_t & shape) {
+ifcopenshell::geometry::CgalShape::CgalShape(const cgal_shape_t & shape, bool convex) {
 	shape_ = shape;
+	convex_tag_ = convex;
 	if (shape.size_of_facets() != 1) {
 		// this is for handling the specical case of storing a single point in a polyhedron,
 		// @todo come up with a proper variant for storing lower dimensional entities
@@ -35,8 +36,10 @@ void ifcopenshell::geometry::CgalShape::to_poly() const {
 		shape_.emplace();
 
 		convert_to_polyhedron(*nef_, *shape_);
-		// @todo why is this necessary? we have the mark of the volumes?
-		CGAL::Polygon_mesh_processing::orient_to_bound_a_volume(*shape_);
+		if (shape_->size_of_vertices() > 0) {
+			// @todo why is this necessary? we have the mark of the volumes?
+			CGAL::Polygon_mesh_processing::orient_to_bound_a_volume(*shape_);
+		}
 		
 		// nef_->convert_to_polyhedron(*shape_);
 	}
@@ -44,8 +47,10 @@ void ifcopenshell::geometry::CgalShape::to_poly() const {
 
 void ifcopenshell::geometry::CgalShape::to_nef() const {
 	if (!nef_) {
-		if (CGAL::Polygon_mesh_processing::does_self_intersect(*shape_)) {
-			throw std::runtime_error("Self-intersections detected, unable to proceed");
+		if (!convex_tag_) {
+			if (CGAL::Polygon_mesh_processing::does_self_intersect(*shape_)) {
+				throw std::runtime_error("Self-intersections detected, unable to proceed");
+			}
 		}
 		nef_ = utils::create_nef_polyhedron(*shape_);
 	}
@@ -382,7 +387,7 @@ std::vector<ConversionResultShape*> ifcopenshell::geometry::CgalShape::convex_de
 			// directly, so for now we need to isolate the individual volumes.
 			CGAL::Polyhedron_3<Kernel_> P;
 			copy.convert_inner_shell_to_polyhedron(ci->shells_begin(), P);
-			result.push_back(new CgalShape(P));
+			result.push_back(new CgalShape(P, /*convex=*/ true));
 		}
 	}
 	return result;
@@ -394,7 +399,7 @@ ConversionResultShape* ifcopenshell::geometry::CgalShape::halfspaces()
 #ifdef IFOPSH_SIMPLE_KERNEL
 	throw std::runtime_error("Not implemented");
 #else
-	return new CgalShapeHalfSpaceDecomposition(nef());
+	return new CgalShapeHalfSpaceDecomposition(nef(), convex_tag_);
 #endif
 }
 
@@ -529,7 +534,7 @@ ConversionResultShape* ifcopenshell::geometry::CgalShape::moved(ifcopenshell::ge
 		}
 	}
 
-	return new CgalShape(s);
+	return new CgalShape(s, convex_tag_);
 }
 
 void ifcopenshell::geometry::CgalShape::map(OpaqueCoordinate<4>& from, OpaqueCoordinate<4>& to) {
diff --git a/src/ifcgeom/kernels/cgal/CgalConversionResult.h b/src/ifcgeom/kernels/cgal/CgalConversionResult.h
index d6c1148175..16f53aaf38 100644
--- a/src/ifcgeom/kernels/cgal/CgalConversionResult.h
+++ b/src/ifcgeom/kernels/cgal/CgalConversionResult.h
@@ -177,16 +177,18 @@ namespace ifcopenshell { namespace geometry {
 
 	class CgalShape : public IfcGeom::ConversionResultShape {
 	private:
+		bool convex_tag_ = false;
 		mutable boost::optional<cgal_shape_t> shape_;
 #ifndef IFOPSH_SIMPLE_KERNEL
 		mutable boost::optional<CGAL::Nef_polyhedron_3<Kernel_>> nef_;
 #endif
     public:
-		CgalShape(const cgal_shape_t& shape);
+		CgalShape(const cgal_shape_t& shape, bool convex = false);
 
 #ifndef IFOPSH_SIMPLE_KERNEL
-		CgalShape(const CGAL::Nef_polyhedron_3<Kernel_>& shape) {
+		CgalShape(const CGAL::Nef_polyhedron_3<Kernel_>& shape, bool convex = false) {
 			nef_ = shape;
+			convex_tag_ = convex;
 		}
 #endif
 
@@ -252,6 +254,9 @@ namespace ifcopenshell { namespace geometry {
 		virtual void map(OpaqueCoordinate<4>& from, OpaqueCoordinate<4>& to);
 		virtual void map(const std::vector<OpaqueCoordinate<4>>& from, const std::vector<OpaqueCoordinate<4>>& to);
 		virtual ConversionResultShape* moved(ifcopenshell::geometry::taxonomy::matrix4::ptr) const;
+
+		bool convex_tag() const { return convex_tag_; }
+		bool& convex_tag() { return convex_tag_; }
 	};
 
 #ifndef IFOPSH_SIMPLE_KERNEL
@@ -261,9 +266,12 @@ namespace ifcopenshell { namespace geometry {
 		std::list<CGAL::Plane_3<Kernel_>> planes_;
 
 	public:
-		CgalShapeHalfSpaceDecomposition(const CGAL::Nef_polyhedron_3<Kernel_>& shape) {
-			auto shape_copy = shape;
-			shape_ = std::move(build_halfspace_tree_decomposed(shape_copy, planes_));
+		CgalShapeHalfSpaceDecomposition(const CGAL::Nef_polyhedron_3<Kernel_>& shape, bool is_convex) {
+			if (is_convex) {
+				shape_ = std::move(build_halfspace_tree_is_decomposed(shape, planes_));
+			} else {
+				shape_ = std::move(build_halfspace_tree_decomposed(shape, planes_));
+			}
 		}
 
 		CgalShapeHalfSpaceDecomposition(const CGAL::Plane_3<Kernel_>& shape) {