assimp.assimp/code/IFCGeometry.cpp

/*
Open Asset Import Library (assimp)
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*/

/** @file  IFCGeometry.cpp
 *  @brief Geometry conversion and synthesis for IFC
 */

#include "AssimpPCH.h"

#ifndef ASSIMP_BUILD_NO_IFC_IMPORTER
#include "IFCUtil.h"
#include "PolyTools.h"
#include "ProcessHelper.h"

#include "../contrib/poly2tri/poly2tri/poly2tri.h"
#include "../contrib/clipper/clipper.hpp"

#include <iterator>

namespace Assimp {
	namespace IFC {

		using ClipperLib::ulong64;
		// XXX use full -+ range ...
		const ClipperLib::long64 max_ulong64 = 1518500249; // clipper.cpp / hiRange var

		//#define to_int64(p)  (static_cast<ulong64>( std::max( 0., std::min( static_cast<IfcFloat>((p)), 1.) ) * max_ulong64 ))
#define to_int64(p)  (static_cast<ulong64>(static_cast<IfcFloat>((p) ) * max_ulong64 ))
#define from_int64(p) (static_cast<IfcFloat>((p)) / max_ulong64)

// ------------------------------------------------------------------------------------------------
bool ProcessPolyloop(const IfcPolyLoop& loop, TempMesh& meshout, ConversionData& /*conv*/)
{
	size_t cnt = 0;
	BOOST_FOREACH(const IfcCartesianPoint& c, loop.Polygon) {
		IfcVector3 tmp;
		ConvertCartesianPoint(tmp,c);

		meshout.verts.push_back(tmp);
		++cnt;
	}

	meshout.vertcnt.push_back(cnt);

	// zero- or one- vertex polyloops simply ignored
	if (meshout.vertcnt.back() > 1) { 
		return true;
	}
	
	if (meshout.vertcnt.back()==1) {
		meshout.vertcnt.pop_back();
		meshout.verts.pop_back();
	}
	return false;
}

// ------------------------------------------------------------------------------------------------
void ComputePolygonNormals(const TempMesh& meshout, std::vector<IfcVector3>& normals, bool normalize = true, size_t ofs = 0) 
{
	size_t max_vcount = 0;
	std::vector<unsigned int>::const_iterator begin=meshout.vertcnt.begin()+ofs, end=meshout.vertcnt.end(),  iit;
	for(iit = begin; iit != end; ++iit) {
		max_vcount = std::max(max_vcount,static_cast<size_t>(*iit));
	}

	std::vector<IfcFloat> temp((max_vcount+2)*4);
	normals.reserve( normals.size() + meshout.vertcnt.size()-ofs );

	// `NewellNormal()` currently has a relatively strange interface and need to 
	// re-structure things a bit to meet them.
	size_t vidx = std::accumulate(meshout.vertcnt.begin(),begin,0);
	for(iit = begin; iit != end; vidx += *iit++) {
		if (!*iit) {
			normals.push_back(IfcVector3());
			continue;
		}
		for(size_t vofs = 0, cnt = 0; vofs < *iit; ++vofs) {
			const IfcVector3& v = meshout.verts[vidx+vofs];
			temp[cnt++] = v.x;
			temp[cnt++] = v.y;
			temp[cnt++] = v.z;
#ifdef _DEBUG
			temp[cnt] = std::numeric_limits<IfcFloat>::quiet_NaN();
#endif
			++cnt;
		}

		normals.push_back(IfcVector3());
		NewellNormal<4,4,4>(normals.back(),*iit,&temp[0],&temp[1],&temp[2]);
	}

	if(normalize) {
		BOOST_FOREACH(IfcVector3& n, normals) {
			n.Normalize();
		}
	}
}

// ------------------------------------------------------------------------------------------------
// Compute the normal of the last polygon in the given mesh
IfcVector3 ComputePolygonNormal(const TempMesh& inmesh, bool normalize = true) 
{
	size_t total = inmesh.vertcnt.back(), vidx = inmesh.verts.size() - total;
	std::vector<IfcFloat> temp((total+2)*3);
	for(size_t vofs = 0, cnt = 0; vofs < total; ++vofs) {
		const IfcVector3& v = inmesh.verts[vidx+vofs];
		temp[cnt++] = v.x;
		temp[cnt++] = v.y;
		temp[cnt++] = v.z;
	}
	IfcVector3 nor;
	NewellNormal<3,3,3>(nor,total,&temp[0],&temp[1],&temp[2]);
	return normalize ? nor.Normalize() : nor;
}

// ------------------------------------------------------------------------------------------------
void FixupFaceOrientation(TempMesh& result)
{
	const IfcVector3 vavg = result.Center();

	std::vector<IfcVector3> normals;
	ComputePolygonNormals(result,normals);

	size_t c = 0, ofs = 0;
	BOOST_FOREACH(unsigned int cnt, result.vertcnt) {
		if (cnt>2){
			const IfcVector3& thisvert = result.verts[c];
			if (normals[ofs]*(thisvert-vavg) < 0) {
				std::reverse(result.verts.begin()+c,result.verts.begin()+cnt+c);
			}
		}
		c += cnt;
		++ofs;
	}
}

// ------------------------------------------------------------------------------------------------
void RecursiveMergeBoundaries(TempMesh& final_result, const TempMesh& in, const TempMesh& boundary, std::vector<IfcVector3>& normals, const IfcVector3& nor_boundary)
{
	ai_assert(in.vertcnt.size() >= 1);
	ai_assert(boundary.vertcnt.size() == 1);
	std::vector<unsigned int>::const_iterator end = in.vertcnt.end(), begin=in.vertcnt.begin(), iit, best_iit;

	TempMesh out;

	// iterate through all other bounds and find the one for which the shortest connection
	// to the outer boundary is actually the shortest possible.
	size_t vidx = 0, best_vidx_start = 0;
	size_t best_ofs, best_outer = boundary.verts.size();
	IfcFloat best_dist = 1e10;
	for(std::vector<unsigned int>::const_iterator iit = begin; iit != end; vidx += *iit++) {
		
		for(size_t vofs = 0; vofs < *iit; ++vofs) {
			const IfcVector3& v = in.verts[vidx+vofs];

			for(size_t outer = 0; outer < boundary.verts.size(); ++outer) {
				const IfcVector3& o = boundary.verts[outer];
				const IfcFloat d = (o-v).SquareLength();

				if (d < best_dist) {
					best_dist = d;
					best_ofs = vofs;
					best_outer = outer;
					best_iit = iit;
					best_vidx_start = vidx;
				}
			}		
		}
	}

	ai_assert(best_outer != boundary.verts.size());


	// now that we collected all vertex connections to be added, build the output polygon
	const size_t cnt = boundary.verts.size() + *best_iit+2;
	out.verts.reserve(cnt);

	for(size_t outer = 0; outer < boundary.verts.size(); ++outer) {
		const IfcVector3& o = boundary.verts[outer];
		out.verts.push_back(o);

		if (outer == best_outer) {
			for(size_t i = best_ofs; i < *best_iit; ++i) {
				out.verts.push_back(in.verts[best_vidx_start + i]);
			}

			// we need the first vertex of the inner polygon twice as we return to the
			// outer loop through the very same connection through which we got there.
			for(size_t i = 0; i <= best_ofs; ++i) {
				out.verts.push_back(in.verts[best_vidx_start + i]);
			}

			// reverse face winding if the normal of the sub-polygon points in the
			// same direction as the normal of the outer polygonal boundary
			if (normals[std::distance(begin,best_iit)] * nor_boundary > 0) {
				std::reverse(out.verts.rbegin(),out.verts.rbegin()+*best_iit+1);
			}

			// also append a copy of the initial insertion point to be able to continue the outer polygon
			out.verts.push_back(o);
		}
	}
	out.vertcnt.push_back(cnt);
	ai_assert(out.verts.size() == cnt);

	if (in.vertcnt.size()-std::count(begin,end,0) > 1) {
		// Recursively apply the same algorithm if there are more boundaries to merge. The
		// current implementation is relatively inefficient, though.
		
		TempMesh temp;
		
		// drop the boundary that we just processed
		const size_t dist = std::distance(begin, best_iit);
		TempMesh remaining = in;
		remaining.vertcnt.erase(remaining.vertcnt.begin() + dist);
		remaining.verts.erase(remaining.verts.begin()+best_vidx_start,remaining.verts.begin()+best_vidx_start+*best_iit);

		normals.erase(normals.begin() + dist);
		RecursiveMergeBoundaries(temp,remaining,out,normals,nor_boundary);

		final_result.Append(temp);
	}
	else final_result.Append(out);
}

// ------------------------------------------------------------------------------------------------
void MergePolygonBoundaries(TempMesh& result, const TempMesh& inmesh, size_t master_bounds = -1) 
{
	// standard case - only one boundary, just copy it to the result vector
	if (inmesh.vertcnt.size() <= 1) {
		result.Append(inmesh);
		return;
	}

	result.vertcnt.reserve(inmesh.vertcnt.size()+result.vertcnt.size());

	// XXX get rid of the extra copy if possible
	TempMesh meshout = inmesh;

	// handle polygons with holes. Our built in triangulation won't handle them as is, but
	// the ear cutting algorithm is solid enough to deal with them if we join the inner
	// holes with the outer boundaries by dummy connections.
	IFCImporter::LogDebug("fixing polygon with holes for triangulation via ear-cutting");
	std::vector<unsigned int>::iterator outer_polygon = meshout.vertcnt.end(), begin=meshout.vertcnt.begin(), end=outer_polygon,  iit;

	// each hole results in two extra vertices
	result.verts.reserve(meshout.verts.size()+meshout.vertcnt.size()*2+result.verts.size());
	size_t outer_polygon_start = 0;

	// do not normalize 'normals', we need the original length for computing the polygon area
	std::vector<IfcVector3> normals;
	ComputePolygonNormals(meshout,normals,false);

	// see if one of the polygons is a IfcFaceOuterBound (in which case `master_bounds` is its index).
	// sadly we can't rely on it, the docs say 'At most one of the bounds shall be of the type IfcFaceOuterBound' 
	IfcFloat area_outer_polygon = 1e-10f;
	if (master_bounds != (size_t)-1) {
		outer_polygon = begin + master_bounds;
		outer_polygon_start = std::accumulate(begin,outer_polygon,0);
		area_outer_polygon = normals[master_bounds].SquareLength();
	}
	else {
		size_t vidx = 0;
		for(iit = begin; iit != meshout.vertcnt.end(); vidx += *iit++) {
			// find the polygon with the largest area, it must be the outer bound. 
			IfcVector3& n = normals[std::distance(begin,iit)];
			const IfcFloat area = n.SquareLength();
			if (area > area_outer_polygon) {
				area_outer_polygon = area;
				outer_polygon = iit;
				outer_polygon_start = vidx;
			}
		}
	}

	ai_assert(outer_polygon != meshout.vertcnt.end());	
	std::vector<IfcVector3>& in = meshout.verts;

	// skip over extremely small boundaries - this is a workaround to fix cases
	// in which the number of holes is so extremely large that the
	// triangulation code fails.
#define IFC_VERTICAL_HOLE_SIZE_THRESHOLD 0.000001f
	size_t vidx = 0, removed = 0, index = 0;
	const IfcFloat threshold = area_outer_polygon * IFC_VERTICAL_HOLE_SIZE_THRESHOLD;
	for(iit = begin; iit != end ;++index) {
		const IfcFloat sqlen = normals[index].SquareLength();
		if (sqlen < threshold) {
			std::vector<IfcVector3>::iterator inbase = in.begin()+vidx;
			in.erase(inbase,inbase+*iit);
			
			outer_polygon_start -= outer_polygon_start>vidx ? *iit : 0;
			*iit++ = 0;
			++removed;

			IFCImporter::LogDebug("skip small hole below threshold");
		}
		else {
			normals[index] /= sqrt(sqlen);
			vidx += *iit++;
		}
	}

	// see if one or more of the hole has a face that lies directly on an outer bound.
	// this happens for doors, for example.
	vidx = 0;
	for(iit = begin; ; vidx += *iit++) {
next_loop:
		if (iit == end) {
			break;
		}
		if (iit == outer_polygon) {
			continue;
		}

		for(size_t vofs = 0; vofs < *iit; ++vofs) {
			if (!*iit) {
				continue;
			}
			const size_t next = (vofs+1)%*iit;
			const IfcVector3& v = in[vidx+vofs], &vnext = in[vidx+next],&vd = (vnext-v).Normalize();

			for(size_t outer = 0; outer < *outer_polygon; ++outer) {
				const IfcVector3& o = in[outer_polygon_start+outer], &onext = in[outer_polygon_start+(outer+1)%*outer_polygon], &od = (onext-o).Normalize();

				if (fabs(vd * od) > 1.f-1e-6f && (onext-v).Normalize() * vd > 1.f-1e-6f && (onext-v)*(o-v) < 0) {
					IFCImporter::LogDebug("got an inner hole that lies partly on the outer polygonal boundary, merging them to a single contour");

					// in between outer and outer+1 insert all vertices of this loop, then drop the original altogether.
					std::vector<IfcVector3> tmp(*iit);

					const size_t start = (v-o).SquareLength() > (vnext-o).SquareLength() ? vofs :  next;
					std::vector<IfcVector3>::iterator inbase = in.begin()+vidx, it = std::copy(inbase+start, inbase+*iit,tmp.begin());
					std::copy(inbase, inbase+start,it);
					std::reverse(tmp.begin(),tmp.end());

					in.insert(in.begin()+outer_polygon_start+(outer+1)%*outer_polygon,tmp.begin(),tmp.end());
					vidx += outer_polygon_start<vidx ? *iit : 0;

					inbase = in.begin()+vidx;
					in.erase(inbase,inbase+*iit);

					outer_polygon_start -= outer_polygon_start>vidx ? *iit : 0;
					
					*outer_polygon += tmp.size();
					*iit++ = 0;
					++removed;
					goto next_loop;
				}
			}
		}
	}

	if ( meshout.vertcnt.size() - removed <= 1) {
		result.Append(meshout);
		return;
	}

	// extract the outer boundary and move it to a separate mesh
	TempMesh boundary;
	boundary.vertcnt.resize(1,*outer_polygon);
	boundary.verts.resize(*outer_polygon);

	std::vector<IfcVector3>::iterator b = in.begin()+outer_polygon_start;
	std::copy(b,b+*outer_polygon,boundary.verts.begin());
	in.erase(b,b+*outer_polygon);

	std::vector<IfcVector3>::iterator norit = normals.begin()+std::distance(meshout.vertcnt.begin(),outer_polygon);
	const IfcVector3 nor_boundary = *norit;
	normals.erase(norit);
	meshout.vertcnt.erase(outer_polygon);

	// keep merging the closest inner boundary with the outer boundary until no more boundaries are left
	RecursiveMergeBoundaries(result,meshout,boundary,normals,nor_boundary);
}


// ------------------------------------------------------------------------------------------------
void ProcessConnectedFaceSet(const IfcConnectedFaceSet& fset, TempMesh& result, ConversionData& conv)
{
	BOOST_FOREACH(const IfcFace& face, fset.CfsFaces) {

		// size_t ob = -1, cnt = 0;
		TempMesh meshout;
		BOOST_FOREACH(const IfcFaceBound& bound, face.Bounds) {
			
			// XXX implement proper merging for polygonal loops
			if(const IfcPolyLoop* const polyloop = bound.Bound->ToPtr<IfcPolyLoop>()) {
				if(ProcessPolyloop(*polyloop, meshout,conv)) {

					//if(bound.ToPtr<IfcFaceOuterBound>()) {
					//	ob = cnt;
					//}
					//++cnt;

				}
			}
			else {
				IFCImporter::LogWarn("skipping unknown IfcFaceBound entity, type is " + bound.Bound->GetClassName());
				continue;
			}

			/*if(!IsTrue(bound.Orientation)) {
				size_t c = 0;
				BOOST_FOREACH(unsigned int& c, meshout.vertcnt) {
					std::reverse(result.verts.begin() + cnt,result.verts.begin() + cnt + c);
					cnt += c;
				}
			}*/

		}
		MergePolygonBoundaries(result,meshout);
	}
}



// ------------------------------------------------------------------------------------------------
void ProcessRevolvedAreaSolid(const IfcRevolvedAreaSolid& solid, TempMesh& result, ConversionData& conv)
{
	TempMesh meshout;

	// first read the profile description
	if(!ProcessProfile(*solid.SweptArea,meshout,conv) || meshout.verts.size()<=1) {
		return;
	}

	IfcVector3 axis, pos;
	ConvertAxisPlacement(axis,pos,solid.Axis);

	IfcMatrix4 tb0,tb1;
	IfcMatrix4::Translation(pos,tb0);
	IfcMatrix4::Translation(-pos,tb1);

	const std::vector<IfcVector3>& in = meshout.verts;
	const size_t size=in.size();
	
	bool has_area = solid.SweptArea->ProfileType == "AREA" && size>2;
	const IfcFloat max_angle = solid.Angle*conv.angle_scale;
	if(fabs(max_angle) < 1e-3) {
		if(has_area) {
			result = meshout;
		}
		return;
	}

	const unsigned int cnt_segments = std::max(2u,static_cast<unsigned int>(16 * fabs(max_angle)/AI_MATH_HALF_PI_F));
	const IfcFloat delta = max_angle/cnt_segments;

	has_area = has_area && fabs(max_angle) < AI_MATH_TWO_PI_F*0.99;
	
	result.verts.reserve(size*((cnt_segments+1)*4+(has_area?2:0)));
	result.vertcnt.reserve(size*cnt_segments+2);

	IfcMatrix4 rot;
	rot = tb0 * IfcMatrix4::Rotation(delta,axis,rot) * tb1;

	size_t base = 0;
	std::vector<IfcVector3>& out = result.verts;

	// dummy data to simplify later processing
	for(size_t i = 0; i < size; ++i) {
		out.insert(out.end(),4,in[i]);
	}

	for(unsigned int seg = 0; seg < cnt_segments; ++seg) {
		for(size_t i = 0; i < size; ++i) {
			const size_t next = (i+1)%size;

			result.vertcnt.push_back(4);
			const IfcVector3& base_0 = out[base+i*4+3],base_1 = out[base+next*4+3];

			out.push_back(base_0);
			out.push_back(base_1);
			out.push_back(rot*base_1);
			out.push_back(rot*base_0);
		}
		base += size*4;
	}

	out.erase(out.begin(),out.begin()+size*4);

	if(has_area) {
		// leave the triangulation of the profile area to the ear cutting 
		// implementation in aiProcess_Triangulate - for now we just
		// feed in two huge polygons.
		base -= size*8;
		for(size_t i = size; i--; ) {
			out.push_back(out[base+i*4+3]);
		}
		for(size_t i = 0; i < size; ++i ) {
			out.push_back(out[i*4]);
		}
		result.vertcnt.push_back(size);
		result.vertcnt.push_back(size);
	}

	IfcMatrix4 trafo;
	ConvertAxisPlacement(trafo, solid.Position);
	
	result.Transform(trafo);
	IFCImporter::LogDebug("generate mesh procedurally by radial extrusion (IfcRevolvedAreaSolid)");
}



// ------------------------------------------------------------------------------------------------
void ProcessSweptDiskSolid(const IfcSweptDiskSolid solid, TempMesh& result, ConversionData& conv)
{
	const Curve* const curve = Curve::Convert(*solid.Directrix, conv);
	if(!curve) {
		IFCImporter::LogError("failed to convert Directrix curve (IfcSweptDiskSolid)");
		return;
	}

	const std::vector<IfcVector3>& in = result.verts;
	const size_t size=in.size();

	const unsigned int cnt_segments = 16;
	const IfcFloat deltaAngle = AI_MATH_TWO_PI/cnt_segments;

	const size_t samples = curve->EstimateSampleCount(solid.StartParam,solid.EndParam);

	result.verts.reserve(cnt_segments * samples * 4);
	result.vertcnt.reserve((cnt_segments - 1) * samples);

	std::vector<IfcVector3> points;
	points.reserve(cnt_segments * samples);

	TempMesh temp;
	curve->SampleDiscrete(temp,solid.StartParam,solid.EndParam);
	const std::vector<IfcVector3>& curve_points = temp.verts;

	if(curve_points.empty()) {
		IFCImporter::LogWarn("curve evaluation yielded no points (IfcSweptDiskSolid)");
		return;
	}

	IfcVector3 current = curve_points[0];
	IfcVector3 previous = current;
	IfcVector3 next;

	IfcVector3 startvec;
	startvec.x = 1.0f;
	startvec.y = 1.0f;
	startvec.z = 1.0f;

	unsigned int last_dir = 0;

	// generate circles at the sweep positions
	for(size_t i = 0; i < samples; ++i) {

		if(i != samples - 1) {
			next = curve_points[i + 1];
		}

		// get a direction vector reflecting the approximate curvature (i.e. tangent)
		IfcVector3 d = (current-previous) + (next-previous);
	
		d.Normalize();

		// figure out an arbitrary point q so that (p-q) * d = 0,
		// try to maximize ||(p-q)|| * ||(p_last-q_last)|| 
		IfcVector3 q;
		bool take_any = false;

		for (unsigned int i = 0; i < 2; ++i, take_any = true) {
			if ((last_dir == 0 || take_any) && abs(d.x) > 1e-6) {
				q.y = startvec.y;
				q.z = startvec.z;
				q.x = -(d.y * q.y + d.z * q.z) / d.x;
				last_dir = 0;
				break;
			}
			else if ((last_dir == 1 || take_any) && abs(d.y) > 1e-6) {
				q.x = startvec.x;
				q.z = startvec.z;
				q.y = -(d.x * q.x + d.z * q.z) / d.y;
				last_dir = 1;
				break;
			}
			else if ((last_dir == 2 && abs(d.z) > 1e-6) || take_any) { 
				q.y = startvec.y;
				q.x = startvec.x;
				q.z = -(d.y * q.y + d.x * q.x) / d.z;
				last_dir = 2;
				break;
			}
		}

		q *= solid.Radius / q.Length();
		startvec = q;

		// generate a rotation matrix to rotate q around d
		IfcMatrix4 rot;
		IfcMatrix4::Rotation(deltaAngle,d,rot);

		for (unsigned int seg = 0; seg < cnt_segments; ++seg, q *= rot ) {
			points.push_back(q + current);	
		}

		previous = current;
		current = next;
	}

	// make quads
	for(size_t i = 0; i < samples - 1; ++i) {

		const aiVector3D& this_start = points[ i * cnt_segments ];

		// locate corresponding point on next sample ring
		unsigned int best_pair_offset = 0;
		float best_distance_squared = 1e10f;
		for (unsigned int seg = 0; seg < cnt_segments; ++seg) {
			const aiVector3D& p = points[ (i+1) * cnt_segments + seg];
			const float l = (p-this_start).SquareLength();

			if(l < best_distance_squared) {
				best_pair_offset = seg;
				best_distance_squared = l;
			}
		}

		for (unsigned int seg = 0; seg < cnt_segments; ++seg) {

			result.verts.push_back(points[ i * cnt_segments + (seg % cnt_segments)]);
			result.verts.push_back(points[ i * cnt_segments + (seg + 1) % cnt_segments]);
			result.verts.push_back(points[ (i+1) * cnt_segments + ((seg + 1 + best_pair_offset) % cnt_segments)]);
			result.verts.push_back(points[ (i+1) * cnt_segments + ((seg + best_pair_offset) % cnt_segments)]);

			IfcVector3& v1 = *(result.verts.end()-1);
			IfcVector3& v2 = *(result.verts.end()-2);
			IfcVector3& v3 = *(result.verts.end()-3);
			IfcVector3& v4 = *(result.verts.end()-4);

			if (((v4-v3) ^ (v4-v1)) * (v4 - curve_points[i]) < 0.0f) {			
				std::swap(v4, v1);
				std::swap(v3, v2);
			} 

			result.vertcnt.push_back(4);
		}
	}

	IFCImporter::LogDebug("generate mesh procedurally by sweeping a disk along a curve (IfcSweptDiskSolid)");
}

// ------------------------------------------------------------------------------------------------
IfcMatrix3 DerivePlaneCoordinateSpace(const TempMesh& curmesh) {

	const std::vector<IfcVector3>& out = curmesh.verts;
	IfcMatrix3 m;

	const size_t s = out.size();
	assert(curmesh.vertcnt.size() == 1 && curmesh.vertcnt.back() == s);

	const IfcVector3 any_point = out[s-1];
	IfcVector3 nor; 

	// The input polygon is arbitrarily shaped, so we might need some tries
	// until we find a suitable normal (and it does not even need to be
	// right in all cases, Newell's algorithm would be the correct one ... ).
	size_t base = s-curmesh.vertcnt.back(), i, j;
	for (i = base; i < s-1; ++i) {
		for (j = i+1; j < s; ++j) {
			nor = -((out[i]-any_point)^(out[j]-any_point));
			if(fabs(nor.Length()) > 1e-8f) {
				goto out;
			}
		}
	}

	assert(0);

out:

	nor.Normalize();

	IfcVector3 r = (out[i]-any_point);
	r.Normalize();

	// reconstruct orthonormal basis
	IfcVector3 u = r ^ nor;
	u.Normalize();

	m.a1 = r.x;
	m.a2 = r.y;
	m.a3 = r.z;

	m.b1 = u.x;
	m.b2 = u.y;
	m.b3 = u.z;

	m.c1 = nor.x;
	m.c2 = nor.y;
	m.c3 = nor.z;

	return m;
}

// ------------------------------------------------------------------------------------------------
bool TryAddOpenings_Poly2Tri(const std::vector<TempOpening>& openings,const std::vector<IfcVector3>& nors, TempMesh& curmesh)
{
	std::vector<IfcVector3>& out = curmesh.verts;

	bool result = false;

	// Try to derive a solid base plane within the current surface for use as 
	// working coordinate system. 
	const IfcMatrix3& m = DerivePlaneCoordinateSpace(curmesh);
	const IfcMatrix3 minv = IfcMatrix3(m).Inverse();
	const IfcVector3& nor = IfcVector3(m.c1, m.c2, m.c3);

	IfcFloat coord = -1;

	std::vector<IfcVector2> contour_flat;
	contour_flat.reserve(out.size());

	IfcVector2 vmin, vmax;
	MinMaxChooser<IfcVector2>()(vmin, vmax);
	
	// Move all points into the new coordinate system, collecting min/max verts on the way
	BOOST_FOREACH(IfcVector3& x, out) {
		const IfcVector3 vv = m * x;

		// keep Z offset in the plane coordinate system. Ignoring precision issues
		// (which  are present, of course), this should be the same value for
		// all polygon vertices (assuming the polygon is planar).


		// XXX this should be guarded, but we somehow need to pick a suitable
		// epsilon
		// if(coord != -1.0f) {
		//	assert(fabs(coord - vv.z) < 1e-3f);
		// }

		coord = vv.z;

		vmin = std::min(IfcVector2(vv.x, vv.y), vmin);
		vmax = std::max(IfcVector2(vv.x, vv.y), vmax);

		contour_flat.push_back(IfcVector2(vv.x,vv.y));
	}
		
	// With the current code in DerivePlaneCoordinateSpace, 
	// vmin,vmax should always be the 0...1 rectangle (+- numeric inaccuracies) 
	// but here we won't rely on this.

	vmax -= vmin;

	// If this happens then the projection must have been wrong.
	assert(vmax.Length());

	ClipperLib::ExPolygons clipped;
	ClipperLib::Polygons holes_union;


	IfcVector3 wall_extrusion;
	bool do_connections = false, first = true;

	try {

		ClipperLib::Clipper clipper_holes;
		size_t c = 0;

		BOOST_FOREACH(const TempOpening& t,openings) {
			const IfcVector3& outernor = nors[c++];
			const IfcFloat dot = nor * outernor;
			if (fabs(dot)<1.f-1e-6f) {
				continue;
			}

			const std::vector<IfcVector3>& va = t.profileMesh->verts;
			if(va.size() <= 2) {
				continue;	
			}
		
			std::vector<IfcVector2> contour;

			BOOST_FOREACH(const IfcVector3& xx, t.profileMesh->verts) {
				IfcVector3 vv = m *  xx, vv_extr = m * (xx + t.extrusionDir);
				
				const bool is_extruded_side = fabs(vv.z - coord) > fabs(vv_extr.z - coord);
				if (first) {
					first = false;
					if (dot > 0.f) {
						do_connections = true;
						wall_extrusion = t.extrusionDir;
						if (is_extruded_side) {
							wall_extrusion = - wall_extrusion;
						}
					}
				}

				// XXX should not be necessary - but it is. Why? For precision reasons?
				vv = is_extruded_side ? vv_extr : vv;
				contour.push_back(IfcVector2(vv.x,vv.y));
			}

			ClipperLib::Polygon hole;
			BOOST_FOREACH(IfcVector2& pip, contour) {
				pip.x  = (pip.x - vmin.x) / vmax.x;
				pip.y  = (pip.y - vmin.y) / vmax.y;

				hole.push_back(ClipperLib::IntPoint(  to_int64(pip.x), to_int64(pip.y) ));
			}

			if (!ClipperLib::Orientation(hole)) {
				std::reverse(hole.begin(), hole.end());
			//	assert(ClipperLib::Orientation(hole));
			}

			/*ClipperLib::Polygons pol_temp(1), pol_temp2(1);
			pol_temp[0] = hole;

			ClipperLib::OffsetPolygons(pol_temp,pol_temp2,5.0);
			hole = pol_temp2[0];*/

			clipper_holes.AddPolygon(hole,ClipperLib::ptSubject);
		}

		clipper_holes.Execute(ClipperLib::ctUnion,holes_union,
			ClipperLib::pftNonZero,
			ClipperLib::pftNonZero);

		if (holes_union.empty()) {
			return false;
		}

		// Now that we have the big union of all holes, subtract it from the outer contour
		// to obtain the final polygon to feed into the triangulator.
		{
			ClipperLib::Polygon poly;
			BOOST_FOREACH(IfcVector2& pip, contour_flat) {
				pip.x  = (pip.x - vmin.x) / vmax.x;
				pip.y  = (pip.y - vmin.y) / vmax.y;

				poly.push_back(ClipperLib::IntPoint( to_int64(pip.x), to_int64(pip.y) ));
			}

			if (ClipperLib::Orientation(poly)) {
				std::reverse(poly.begin(), poly.end());
			}
			clipper_holes.Clear();
			clipper_holes.AddPolygon(poly,ClipperLib::ptSubject);

			clipper_holes.AddPolygons(holes_union,ClipperLib::ptClip);
			clipper_holes.Execute(ClipperLib::ctDifference,clipped,
				ClipperLib::pftNonZero,
				ClipperLib::pftNonZero);
		}

	}
	catch (const char* sx) {
		IFCImporter::LogError("Ifc: error during polygon clipping, skipping openings for this face: (Clipper: " 
			+ std::string(sx) + ")");

		return false;
	}

	std::vector<IfcVector3> old_verts;
	std::vector<unsigned int> old_vertcnt;

	old_verts.swap(curmesh.verts);
	old_vertcnt.swap(curmesh.vertcnt);


	// add connection geometry to close the adjacent 'holes' for the openings
	// this should only be done from one side of the wall or the polygons 
	// would be emitted twice.
	if (false && do_connections) {

		std::vector<IfcVector3> tmpvec;
		BOOST_FOREACH(ClipperLib::Polygon& opening, holes_union) {

			assert(ClipperLib::Orientation(opening));

			tmpvec.clear();

			BOOST_FOREACH(ClipperLib::IntPoint& point, opening) {

				tmpvec.push_back( minv * IfcVector3(
					vmin.x + from_int64(point.X) * vmax.x, 
					vmin.y + from_int64(point.Y) * vmax.y,
					coord));
			}

			for(size_t i = 0, size = tmpvec.size(); i < size; ++i) {
				const size_t next = (i+1)%size;

				curmesh.vertcnt.push_back(4);

				const IfcVector3& in_world = tmpvec[i];
				const IfcVector3& next_world = tmpvec[next];

				// Assumptions: no 'partial' openings, wall thickness roughly the same across the wall
				curmesh.verts.push_back(in_world);
				curmesh.verts.push_back(in_world+wall_extrusion);
				curmesh.verts.push_back(next_world+wall_extrusion);
				curmesh.verts.push_back(next_world);
			}
		}
	}
	
	std::vector< std::vector<p2t::Point*> > contours;
	BOOST_FOREACH(ClipperLib::ExPolygon& clip, clipped) {
		
		contours.clear();

		// Build the outer polygon contour line for feeding into poly2tri
		std::vector<p2t::Point*> contour_points;
		BOOST_FOREACH(ClipperLib::IntPoint& point, clip.outer) {
			contour_points.push_back( new p2t::Point(from_int64(point.X), from_int64(point.Y)) );
		}

		p2t::CDT* cdt ;
		try {
			// Note: this relies on custom modifications in poly2tri to raise runtime_error's
			// instead if assertions. These failures are not debug only, they can actually
			// happen in production use if the input data is broken. An assertion would be
			// inappropriate.
			cdt = new p2t::CDT(contour_points);
		}
		catch(const std::exception& e) {
			IFCImporter::LogError("Ifc: error during polygon triangulation, skipping some openings: (poly2tri: " 
				+ std::string(e.what()) + ")");
			continue;
		}
		

		// Build the poly2tri inner contours for all holes we got from ClipperLib
		BOOST_FOREACH(ClipperLib::Polygon& opening, clip.holes) {
			
			contours.push_back(std::vector<p2t::Point*>());
			std::vector<p2t::Point*>& contour = contours.back();

			BOOST_FOREACH(ClipperLib::IntPoint& point, opening) {
				contour.push_back( new p2t::Point(from_int64(point.X), from_int64(point.Y)) );
			}

			cdt->AddHole(contour);
		}
		
		try {
			// Note: See above
			cdt->Triangulate();
		}
		catch(const std::exception& e) {
			IFCImporter::LogError("Ifc: error during polygon triangulation, skipping some openings: (poly2tri: " 
				+ std::string(e.what()) + ")");
			continue;
		}

		const std::vector<p2t::Triangle*>& tris = cdt->GetTriangles();

		// Collect the triangles we just produced
		BOOST_FOREACH(p2t::Triangle* tri, tris) {
			for(int i = 0; i < 3; ++i) {

				const IfcVector2& v = IfcVector2( 
					static_cast<IfcFloat>( tri->GetPoint(i)->x ), 
					static_cast<IfcFloat>( tri->GetPoint(i)->y )
				);

				assert(v.x <= 1.0 && v.x >= 0.0 && v.y <= 1.0 && v.y >= 0.0);
				const IfcVector3 v3 = minv * IfcVector3(vmin.x + v.x * vmax.x, vmin.y + v.y * vmax.y,coord) ; 

				curmesh.verts.push_back(v3);
			}
			curmesh.vertcnt.push_back(3);
		}

		result = true;
	}

	if (!result) {
		// revert -- it's a shame, but better than nothing
		curmesh.verts.insert(curmesh.verts.end(),old_verts.begin(), old_verts.end());
		curmesh.vertcnt.insert(curmesh.vertcnt.end(),old_vertcnt.begin(), old_vertcnt.end());

		IFCImporter::LogError("Ifc: revert, could not generate openings for this wall");
	}

	return result;
}

// ------------------------------------------------------------------------------------------------
struct DistanceSorter {

	DistanceSorter(const IfcVector3& base) : base(base) {}

	bool operator () (const TempOpening& a, const TempOpening& b) const {
		return (a.profileMesh->Center()-base).SquareLength() < (b.profileMesh->Center()-base).SquareLength();
	}

	IfcVector3 base;
};

// ------------------------------------------------------------------------------------------------
struct XYSorter {

	// sort first by X coordinates, then by Y coordinates
	bool operator () (const IfcVector2&a, const IfcVector2& b) const {
		if (a.x == b.x) {
			return a.y < b.y;
		}
		return a.x < b.x;
	}
};

typedef std::pair< IfcVector2, IfcVector2 > BoundingBox;
typedef std::map<IfcVector2,size_t,XYSorter> XYSortedField;


// ------------------------------------------------------------------------------------------------
void QuadrifyPart(const IfcVector2& pmin, const IfcVector2& pmax, XYSortedField& field, 
	const std::vector< BoundingBox >& bbs, 
	std::vector<IfcVector2>& out)
{
	if (!(pmin.x-pmax.x) || !(pmin.y-pmax.y)) {
		return;
	}

	IfcFloat xs = 1e10, xe = 1e10;	
	bool found = false;

	// Search along the x-axis until we find an opening
	XYSortedField::iterator start = field.begin();
	for(; start != field.end(); ++start) {
		const BoundingBox& bb = bbs[(*start).second];
		if(bb.first.x >= pmax.x) {
			break;
		} 

		if (bb.second.x > pmin.x && bb.second.y > pmin.y && bb.first.y < pmax.y) {
			xs = bb.first.x;
			xe = bb.second.x;
			found = true;
			break;
		}
	}

	if (!found) {
		// the rectangle [pmin,pend] is opaque, fill it
		out.push_back(pmin);
		out.push_back(IfcVector2(pmin.x,pmax.y));
		out.push_back(pmax);
		out.push_back(IfcVector2(pmax.x,pmin.y));
		return;
	}

	xs = std::max(pmin.x,xs);
	xe = std::min(pmax.x,xe);

	// see if there's an offset to fill at the top of our quad
	if (xs - pmin.x) {
		out.push_back(pmin);
		out.push_back(IfcVector2(pmin.x,pmax.y));
		out.push_back(IfcVector2(xs,pmax.y));
		out.push_back(IfcVector2(xs,pmin.y));
	}

	// search along the y-axis for all openings that overlap xs and our quad
	IfcFloat ylast = pmin.y;
	found = false;
	for(; start != field.end(); ++start) {
		const BoundingBox& bb = bbs[(*start).second];
		if (bb.first.x > xs || bb.first.y >= pmax.y) {
			break;
		}

		if (bb.second.y > ylast) {

			found = true;
			const IfcFloat ys = std::max(bb.first.y,pmin.y), ye = std::min(bb.second.y,pmax.y);
			if (ys - ylast > 0.0f) {
				QuadrifyPart( IfcVector2(xs,ylast), IfcVector2(xe,ys) ,field,bbs,out);
			}

			// the following are the window vertices

			/*wnd.push_back(IfcVector2(xs,ys));
			wnd.push_back(IfcVector2(xs,ye));
			wnd.push_back(IfcVector2(xe,ye));
			wnd.push_back(IfcVector2(xe,ys));*/
			ylast = ye;
		}
	}
	if (!found) {
		// the rectangle [pmin,pend] is opaque, fill it
		out.push_back(IfcVector2(xs,pmin.y));
		out.push_back(IfcVector2(xs,pmax.y));
		out.push_back(IfcVector2(xe,pmax.y));
		out.push_back(IfcVector2(xe,pmin.y));
		return;
	}
	if (ylast < pmax.y) {
		QuadrifyPart( IfcVector2(xs,ylast), IfcVector2(xe,pmax.y) ,field,bbs,out);
	}

	// now for the whole rest
	if (pmax.x-xe) {
		QuadrifyPart(IfcVector2(xe,pmin.y), pmax ,field,bbs,out);
	}
}

// ------------------------------------------------------------------------------------------------
void InsertWindowContours(const std::vector< BoundingBox >& bbs,
	const std::vector< std::vector<IfcVector2> >& contours,
	const std::vector<TempOpening>& openings,
	const IfcMatrix3& minv,
	const IfcVector2& scale,
	const IfcVector2& offset,
	IfcFloat coord,
	TempMesh& curmesh)
{
	ai_assert(contours.size() == bbs.size());

	// fix windows - we need to insert the real, polygonal shapes into the quadratic holes that we have now
	for(size_t i = 0; i < contours.size();++i) {
		const BoundingBox& bb = bbs[i];
		const std::vector<IfcVector2>& contour = contours[i];

		// check if we need to do it at all - many windows just fit perfectly into their quadratic holes,
		// i.e. their contours *are* already their bounding boxes.
		if (contour.size() == 4) {
			std::set<IfcVector2,XYSorter> verts;
			for(size_t n = 0; n < 4; ++n) {
				verts.insert(contour[n]);
			}
			const std::set<IfcVector2,XYSorter>::const_iterator end = verts.end();
			if (verts.find(bb.first)!=end && verts.find(bb.second)!=end
				&& verts.find(IfcVector2(bb.first.x,bb.second.y))!=end 
				&& verts.find(IfcVector2(bb.second.x,bb.first.y))!=end 
				) {
					continue;
			}
		}

		const IfcFloat diag = (bb.first-bb.second).Length();
		const IfcFloat epsilon = diag/1000.f;

		// walk through all contour points and find those that lie on the BB corner
		size_t last_hit = -1, very_first_hit = -1;
		IfcVector2 edge;
		for(size_t n = 0, e=0, size = contour.size();; n=(n+1)%size, ++e) {

			// sanity checking
			if (e == size*2) {
				IFCImporter::LogError("encountered unexpected topology while generating window contour");
				break;
			}

			const IfcVector2& v = contour[n];

			bool hit = false;
			if (fabs(v.x-bb.first.x)<epsilon) {
				edge.x = bb.first.x;
				hit = true;
			}
			else if (fabs(v.x-bb.second.x)<epsilon) {
				edge.x = bb.second.x;
				hit = true;
			}

			if (fabs(v.y-bb.first.y)<epsilon) {
				edge.y = bb.first.y;
				hit = true;
			}
			else if (fabs(v.y-bb.second.y)<epsilon) {
				edge.y = bb.second.y;
				hit = true;
			}

			if (hit) {
				if (last_hit != (size_t)-1) {

					const size_t old = curmesh.verts.size();
					size_t cnt = last_hit > n ? size-(last_hit-n) : n-last_hit;
					for(size_t a = last_hit, e = 0; e <= cnt; a=(a+1)%size, ++e) {
						// hack: this is to fix cases where opening contours are self-intersecting.
						// Clipper doesn't produce such polygons, but as soon as we're back in
						// our brave new floating-point world, very small distances are consumed
						// by the maximum available precision, leading to self-intersecting
						// polygons. This fix makes concave windows fail even worse, but
						// anyway, fail is fail.
						if ((contour[a] - edge).SquareLength() > diag*diag*0.7) {
							continue;
						}
						const IfcVector3 v3 = minv * IfcVector3(offset.x + contour[a].x * scale.x, offset.y + contour[a].y * scale.y, coord);
						curmesh.verts.push_back(v3);
					}

					if (edge != contour[last_hit]) {

						IfcVector2 corner = edge;

						if (fabs(contour[last_hit].x-bb.first.x)<epsilon) {
							corner.x = bb.first.x;
						}
						else if (fabs(contour[last_hit].x-bb.second.x)<epsilon) {
							corner.x = bb.second.x;
						}

						if (fabs(contour[last_hit].y-bb.first.y)<epsilon) {
							corner.y = bb.first.y;
						}
						else if (fabs(contour[last_hit].y-bb.second.y)<epsilon) {
							corner.y = bb.second.y;
						}

						const IfcVector3 v3 = minv * IfcVector3(offset.x + corner.x * scale.x, offset.y + corner.y * scale.y,coord);
						curmesh.verts.push_back(v3);
					}
					else if (cnt == 1) {
						// avoid degenerate polygons (also known as lines or points)
						curmesh.verts.erase(curmesh.verts.begin()+old,curmesh.verts.end());
					}

					if (const size_t d = curmesh.verts.size()-old) {
						curmesh.vertcnt.push_back(d);
						std::reverse(curmesh.verts.rbegin(),curmesh.verts.rbegin()+d);
					}
					if (n == very_first_hit) {
						break;
					}
				}
				else {
					very_first_hit = n;
				}

				last_hit = n;
			}
		}
	}
}

// ------------------------------------------------------------------------------------------------
void MergeWindowContours (const std::vector<IfcVector2>& a, 
	const std::vector<IfcVector2>& b, 
	ClipperLib::ExPolygons& out) 
{
	ClipperLib::Clipper clipper;
	ClipperLib::Polygon clip;

	BOOST_FOREACH(const IfcVector2& pip, a) {
		clip.push_back(ClipperLib::IntPoint(  to_int64(pip.x), to_int64(pip.y) ));
	}

	if (ClipperLib::Orientation(clip)) {
		std::reverse(clip.begin(), clip.end());
	}

	clipper.AddPolygon(clip, ClipperLib::ptSubject);
	clip.clear();

	BOOST_FOREACH(const IfcVector2& pip, b) {
		clip.push_back(ClipperLib::IntPoint(  to_int64(pip.x), to_int64(pip.y) ));
	}

	if (ClipperLib::Orientation(clip)) {
		std::reverse(clip.begin(), clip.end());
	}

	clipper.AddPolygon(clip, ClipperLib::ptSubject);
	clipper.Execute(ClipperLib::ctUnion, out,ClipperLib::pftNonZero,ClipperLib::pftNonZero);
}

// ------------------------------------------------------------------------------------------------
void CleanupWindowContours(std::vector< std::vector<IfcVector2> >& contours)
{
	std::vector<IfcVector2> scratch;

	// use polyclipper to clean up window contours as well
	try {
		BOOST_FOREACH(std::vector<IfcVector2>& contour, contours) {
			ClipperLib::Polygon subject;
			ClipperLib::Clipper clipper;
			ClipperLib::ExPolygons clipped;

			BOOST_FOREACH(const IfcVector2& pip, contour) {
				subject.push_back(ClipperLib::IntPoint(  to_int64(pip.x), to_int64(pip.y) ));
			}

			clipper.AddPolygon(subject,ClipperLib::ptSubject);
			clipper.Execute(ClipperLib::ctUnion,clipped,ClipperLib::pftNonZero,ClipperLib::pftNonZero);

			// this should yield only one polygon or something went wrong 
			if (clipped.size() != 1) {

				// empty polygon? drop the contour altogether
				if(clipped.empty()) {
					contour.clear();
					continue;
				}

				// else: take only the first ...
				IFCImporter::LogError("error during polygon clipping, window contour is not convex");
			}

			scratch.clear();
			BOOST_FOREACH(const ClipperLib::IntPoint& point, clipped[0].outer) {
				scratch.push_back( IfcVector2(from_int64(point.X), from_int64(point.Y)));
			}
			contour.swap(scratch);
		}
	}
	catch (const char* sx) {
		IFCImporter::LogError("error during polygon clipping, window shape may be wrong: (Clipper: " 
			+ std::string(sx) + ")");
	}
}

// ------------------------------------------------------------------------------------------------
void CleanupOuterContour(const std::vector<IfcVector2>& contour_flat, TempMesh& curmesh, 
	const IfcMatrix3& minv, 
	const IfcVector2& scale, 
	const IfcVector2& offset,
	IfcFloat coord,
	const std::vector<IfcVector2>& outflat)
{
	std::vector<IfcVector3> vold;
	std::vector<unsigned int> iold;

	vold.reserve(outflat.size());
	iold.reserve(outflat.size() / 4);

	// Fix the outer contour using polyclipper
	try {

		ClipperLib::Polygon subject;
		ClipperLib::Clipper clipper;
		ClipperLib::ExPolygons clipped;

		ClipperLib::Polygon clip;
		clip.reserve(contour_flat.size());
		BOOST_FOREACH(const IfcVector2& pip, contour_flat) {
			clip.push_back(ClipperLib::IntPoint(  to_int64(pip.x), to_int64(pip.y) ));
		}

		if (!ClipperLib::Orientation(clip)) {
			std::reverse(clip.begin(), clip.end());
		}

		// We need to run polyclipper on every single quad -- we can't run it one all
		// of them at once or it would merge them all together which would undo all
		// previous steps
		subject.reserve(4);
		size_t cnt = 0;
		BOOST_FOREACH(const IfcVector2& pip, outflat) {
			subject.push_back(ClipperLib::IntPoint(  to_int64(pip.x), to_int64(pip.y) ));
			if (!(++cnt % 4)) {
				if (!ClipperLib::Orientation(subject)) {
					std::reverse(subject.begin(), subject.end());
				}

				clipper.AddPolygon(subject,ClipperLib::ptSubject);
				clipper.AddPolygon(clip,ClipperLib::ptClip);

				clipper.Execute(ClipperLib::ctIntersection,clipped,ClipperLib::pftNonZero,ClipperLib::pftNonZero);

				BOOST_FOREACH(const ClipperLib::ExPolygon& ex, clipped) {
					iold.push_back(ex.outer.size());
					BOOST_FOREACH(const ClipperLib::IntPoint& point, ex.outer) {
						vold.push_back( minv * IfcVector3(
							offset.x + from_int64(point.X) * scale.x, 
							offset.y + from_int64(point.Y) * scale.y,
							coord));
					}
				}

				subject.clear();
				clipped.clear();
				clipper.Clear();
			}
		}

		assert(!(cnt % 4));
	}
	catch (const char* sx) {
		IFCImporter::LogError("Ifc: error during polygon clipping, wall contour line may be wrong: (Clipper: " 
			+ std::string(sx) + ")");

		iold.resize(outflat.size()/4,4);

		BOOST_FOREACH(const IfcVector2& vproj, outflat) {
			const IfcVector3 v3 = minv * IfcVector3(offset.x + vproj.x * scale.x, offset.y + vproj.y * scale.y,coord);
			vold.push_back(v3);
		}
	}

	// undo the projection, generate output quads
	std::swap(vold,curmesh.verts);
	std::swap(iold,curmesh.vertcnt);
}

// ------------------------------------------------------------------------------------------------
bool TryAddOpenings_Quadrulate(const std::vector<TempOpening>& openings,
	const std::vector<IfcVector3>& nors, 
	TempMesh& curmesh)
{
	std::vector<IfcVector3>& out = curmesh.verts;

	const IfcVector2 one_vec = IfcVector2(static_cast<IfcFloat>(1.0),static_cast<IfcFloat>(1.0));

	// Try to derive a solid base plane within the current surface for use as 
	// working coordinate system. 
	const IfcMatrix3& m = DerivePlaneCoordinateSpace(curmesh);
	const IfcMatrix3& minv = IfcMatrix3(m).Inverse();
	const IfcVector3& nor = IfcVector3(m.c1, m.c2, m.c3);

	IfcFloat coord = -1;

	std::vector<IfcVector2> contour_flat;
	contour_flat.reserve(out.size());

	IfcVector2 vmin, vmax;
	MinMaxChooser<IfcVector2>()(vmin, vmax);

	// Move all points into the new coordinate system, collecting min/max verts on the way
	BOOST_FOREACH(IfcVector3& x, out) {
		const IfcVector3& vv = m * x;
		// keep Z offset in the plane coordinate system. Ignoring precision issues
		// (which  are present, of course), this should be the same value for
		// all polygon vertices (assuming the polygon is planar).

		// XXX this should be guarded, but we somehow need to pick a suitable
		// epsilon
		// if(coord != -1.0f) {
		//	assert(fabs(coord - vv.z) < 1e-3f);
		// }
		coord = vv.z;
		vmin = std::min(IfcVector2(vv.x, vv.y), vmin);
		vmax = std::max(IfcVector2(vv.x, vv.y), vmax);

		contour_flat.push_back(IfcVector2(vv.x,vv.y));
	}

	// With the current code in DerivePlaneCoordinateSpace, 
	// vmin,vmax should always be the 0...1 rectangle (+- numeric inaccuracies) 
	// but here we really need this to be accurate, so normalize again.

	vmax -= vmin;
	BOOST_FOREACH(IfcVector2& vv, contour_flat) {
		vv.x  = (vv.x - vmin.x) / vmax.x;
		vv.y  = (vv.y - vmin.y) / vmax.y;

		// sanity rounding
		vv = std::max(vv,IfcVector2());
		vv = std::min(vv,one_vec);
	}

	// project all openings into the coordinate system defined by the p+sv*tu plane
	// and compute bounding boxes for them
	std::vector< BoundingBox > bbs;
	std::vector< std::vector<IfcVector2> > contours;

	size_t c = 0;
	BOOST_FOREACH(const TempOpening& t,openings) {
		std::vector<IfcVector3> profile_verts = t.profileMesh->verts;
		std::vector<unsigned int> profile_vertcnts = t.profileMesh->vertcnt;
		if(profile_verts.size() <= 2) {
			continue;	
		}

		IfcVector2 vpmin,vpmax;
		MinMaxChooser<IfcVector2>()(vpmin,vpmax);

		// the opening meshes are real 3D meshes so skip over all faces
		// clearly facing into the wrong direction.
		std::vector<IfcVector2> contour;
		for (size_t f = 0, vi_total = 0, fend = profile_vertcnts.size(); f < fend; ++f) {

			const IfcVector3& face_nor = ((profile_verts[vi_total+2] - profile_verts[vi_total]) ^
				(profile_verts[vi_total+1] - profile_verts[vi_total])).Normalize();

			const IfcFloat abs_dot_face_nor = abs(nor * face_nor);
			if (abs_dot_face_nor < 0.5) {
				vi_total += profile_vertcnts[f];
				continue;
			}

			for (unsigned int vi = 0, vend = profile_vertcnts[f]; vi < vend; ++vi, ++vi_total) {
				const IfcVector3& x = profile_verts[vi_total];

				const IfcVector3& v = m * x;
				IfcVector2 vv(v.x, v.y);

				// rescale
				vv.x  = (vv.x - vmin.x) / vmax.x;
				vv.y  = (vv.y - vmin.y) / vmax.y;

				vv = std::max(vv,IfcVector2());
				vv = std::min(vv,one_vec);

				vpmin = std::min(vpmin,vv);
				vpmax = std::max(vpmax,vv);

				contour.push_back(vv);
			}
		}

		if(contour.size() <= 2) {
			continue;
		}

		BoundingBox bb = BoundingBox(vpmin,vpmax);

		// see if this BB intersects any other, in which case we could not use the Quadrify()
		// algorithm and would revert to Poly2Tri only.
		for (std::vector<BoundingBox>::iterator it = bbs.begin(); it != bbs.end();) {
			const BoundingBox& ibb = *it;

			if (ibb.first.x < bb.second.x && ibb.second.x > bb.first.x &&
				ibb.first.y < bb.second.y && ibb.second.y > bb.second.x) {

				// take these two contours and try to merge them. If they overlap (which 
				// should not happen, but in fact happens-in-the-real-world [tm] ),
				// resume using a single contour and a single bounding box.
				const std::vector<IfcVector2>& other = contours[std::distance(bbs.begin(),it)];

				ClipperLib::ExPolygons poly;
				MergeWindowContours(contour, other, poly);

				if (poly.size() > 1) {
					IFCImporter::LogWarn("cannot use quadrify algorithm to generate wall openings due to "  
						"bounding box overlaps, using poly2tri fallback method");
					return TryAddOpenings_Poly2Tri(openings, nors, curmesh);
				}
				else if (poly.size() == 0) {
					IFCImporter::LogWarn("ignoring duplicate opening");
					contour.clear();
					break;
				}
				else {
					IFCImporter::LogDebug("merging overlapping openings, this should not happen");

					contour.clear();
					BOOST_FOREACH(const ClipperLib::IntPoint& point, poly[0].outer) {
						IfcVector2 vv = IfcVector2( from_int64(point.X), from_int64(point.Y));
						vv = std::max(vv,IfcVector2());
						vv = std::min(vv,one_vec);

						contour.push_back( vv );
					}

					bb.first = std::min(bb.first, ibb.first);
					bb.second = std::max(bb.second, ibb.second);

					contours.erase(contours.begin() + std::distance(bbs.begin(),it));
					it = bbs.erase(it);
					continue;
				}
			}
			++it;
		}

		if(!contour.empty()) {
			contours.push_back(contour);
			bbs.push_back(bb);
		}
	}

	if (bbs.empty()) {
		return false;
	}

	XYSortedField field;
	for (std::vector<BoundingBox>::iterator it = bbs.begin(); it != bbs.end(); ++it) {
		if (field.find((*it).first) != field.end()) {
			IFCImporter::LogWarn("constraint failure during generation of wall openings, results may be faulty");
		}
		field[(*it).first] = std::distance(bbs.begin(),it);
	}

	std::vector<IfcVector2> outflat;
	outflat.reserve(openings.size()*4);
	QuadrifyPart(IfcVector2(0.f,0.f),IfcVector2(1.f,1.f),field,bbs,outflat);
	ai_assert(!(outflat.size() % 4));

	CleanupOuterContour(contour_flat, curmesh, minv, vmax, vmin, coord, outflat);
	CleanupWindowContours(contours);
	InsertWindowContours(bbs,contours,openings, minv,vmax, vmin, coord, curmesh);

	return true;
}


// ------------------------------------------------------------------------------------------------
void ProcessExtrudedAreaSolid(const IfcExtrudedAreaSolid& solid, TempMesh& result, 
	ConversionData& conv)
{
	TempMesh meshout;
	
	// First read the profile description
	if(!ProcessProfile(*solid.SweptArea,meshout,conv) || meshout.verts.size()<=1) {
		return;
	}

	IfcVector3 dir;
	ConvertDirection(dir,solid.ExtrudedDirection);

	dir *= solid.Depth;

	// Outline: assuming that `meshout.verts` is now a list of vertex points forming 
	// the underlying profile, extrude along the given axis, forming new
	// triangles.
	
	std::vector<IfcVector3>& in = meshout.verts;
	const size_t size=in.size();

	const bool has_area = solid.SweptArea->ProfileType == "AREA" && size>2;
	if(solid.Depth < 1e-3) {
		if(has_area) {
			meshout = result;
		}
		return;
	}

	result.verts.reserve(size*(has_area?4:2));
	result.vertcnt.reserve(meshout.vertcnt.size()+2);

	// First step: transform all vertices into the target coordinate space
	IfcMatrix4 trafo;
	ConvertAxisPlacement(trafo, solid.Position);
	BOOST_FOREACH(IfcVector3& v,in) {
		v *= trafo;
	}
	
	IfcVector3 min = in[0];
	dir *= IfcMatrix3(trafo);

	std::vector<IfcVector3> nors;
	const bool openings = !!conv.apply_openings && conv.apply_openings->size();
	
	// Compute the normal vectors for all opening polygons as a prerequisite
	// to TryAddOpenings_Poly2Tri()
	// XXX this belongs into the aforementioned function
	if (openings) {

		if (!conv.settings.useCustomTriangulation) {	         
			// it is essential to apply the openings in the correct spatial order. The direction	 
			// doesn't matter, but we would screw up if we started with e.g. a door in between	 
			// two windows.	 
			std::sort(conv.apply_openings->begin(),conv.apply_openings->end(),
				DistanceSorter(min));	 
		}
	
		nors.reserve(conv.apply_openings->size());
		BOOST_FOREACH(TempOpening& t,*conv.apply_openings) {
			TempMesh& bounds = *t.profileMesh.get();
		
			if (bounds.verts.size() <= 2) {
				nors.push_back(IfcVector3());
				continue;
			}
			nors.push_back(((bounds.verts[2]-bounds.verts[0])^(bounds.verts[1]-bounds.verts[0]) ).Normalize());
		}
	}
	

	TempMesh temp;
	TempMesh& curmesh = openings ? temp : result;
	std::vector<IfcVector3>& out = curmesh.verts;
 
	size_t sides_with_openings = 0;
	for(size_t i = 0; i < size; ++i) {
		const size_t next = (i+1)%size;

		curmesh.vertcnt.push_back(4);
		
		out.push_back(in[i]);
		out.push_back(in[i]+dir);
		out.push_back(in[next]+dir);
		out.push_back(in[next]);

		if(openings) {
			if(TryAddOpenings_Quadrulate(*conv.apply_openings,nors,temp)) {
				++sides_with_openings;
			}
			
			result.Append(temp);
			temp.Clear();
		}
	}
	
	size_t sides_with_v_openings = 0;
	if(has_area) {

		for(size_t n = 0; n < 2; ++n) {
			for(size_t i = size; i--; ) {
				out.push_back(in[i]+(n?dir:IfcVector3()));
			}

			curmesh.vertcnt.push_back(size);
			if(openings && size > 2) {
				if(TryAddOpenings_Quadrulate(*conv.apply_openings,nors,temp)) {
					++sides_with_v_openings;
				}

				result.Append(temp);
				temp.Clear();
			}
		}
	}


	if(openings && ((sides_with_openings != 2 && sides_with_openings) || (sides_with_v_openings != 2 && sides_with_v_openings))) {
		IFCImporter::LogWarn("failed to resolve all openings, presumably their topology is not supported by Assimp");
	}

	IFCImporter::LogDebug("generate mesh procedurally by extrusion (IfcExtrudedAreaSolid)");
}



// ------------------------------------------------------------------------------------------------
void ProcessSweptAreaSolid(const IfcSweptAreaSolid& swept, TempMesh& meshout, 
	ConversionData& conv)
{
	if(const IfcExtrudedAreaSolid* const solid = swept.ToPtr<IfcExtrudedAreaSolid>()) {
		// Do we just collect openings for a parent element (i.e. a wall)? 
		// In this case we don't extrude the surface yet, just keep the profile and transform it correctly
		if(conv.collect_openings) {
			boost::shared_ptr<TempMesh> meshtmp(new TempMesh());
			ProcessExtrudedAreaSolid(*solid,*meshtmp,conv);

			/*
			ProcessProfile(swept.SweptArea,*meshtmp,conv);

			IfcMatrix4 m;
			ConvertAxisPlacement(m,solid->Position);
			meshtmp->Transform(m);

			IfcVector3 dir;
			ConvertDirection(dir,solid->ExtrudedDirection); */
			conv.collect_openings->push_back(TempOpening(solid,IfcVector3(0,0,0) 
				/* IfcMatrix3(m) * (dir*static_cast<IfcFloat>(solid->Depth)) */,meshtmp));
			return;
		}

		ProcessExtrudedAreaSolid(*solid,meshout,conv);
	}
	else if(const IfcRevolvedAreaSolid* const rev = swept.ToPtr<IfcRevolvedAreaSolid>()) {
		ProcessRevolvedAreaSolid(*rev,meshout,conv);
	}
	else {
		IFCImporter::LogWarn("skipping unknown IfcSweptAreaSolid entity, type is " + swept.GetClassName());
	}
}


// ------------------------------------------------------------------------------------------------
enum Intersect {
	Intersect_No,
	Intersect_LiesOnPlane,
	Intersect_Yes
};

// ------------------------------------------------------------------------------------------------
Intersect IntersectSegmentPlane(const IfcVector3& p,const IfcVector3& n, const IfcVector3& e0, 
	const IfcVector3& e1, 
	IfcVector3& out) 
{
	const IfcVector3 pdelta = e0 - p, seg = e1-e0;
	const IfcFloat dotOne = n*seg, dotTwo = -(n*pdelta);

	if (fabs(dotOne) < 1e-6) {
		return fabs(dotTwo) < 1e-6f ? Intersect_LiesOnPlane : Intersect_No;
	}

	const IfcFloat t = dotTwo/dotOne;
	// t must be in [0..1] if the intersection point is within the given segment
	if (t > 1.f || t < 0.f) {
		return Intersect_No;
	}
	out = e0+t*seg;
	return Intersect_Yes;
}

// ------------------------------------------------------------------------------------------------
void ProcessBoolean(const IfcBooleanResult& boolean, TempMesh& result, ConversionData& conv)
{
	if(const IfcBooleanResult* const clip = boolean.ToPtr<IfcBooleanResult>()) {
		if(clip->Operator != "DIFFERENCE") {
			IFCImporter::LogWarn("encountered unsupported boolean operator: " + (std::string)clip->Operator);
			return;
		}

		TempMesh meshout;
		const IfcHalfSpaceSolid* const hs = clip->SecondOperand->ResolveSelectPtr<IfcHalfSpaceSolid>(conv.db);
		if(!hs) {
			IFCImporter::LogError("expected IfcHalfSpaceSolid as second clipping operand");
			return;
		}

		const IfcPlane* const plane = hs->BaseSurface->ToPtr<IfcPlane>();
		if(!plane) {
			IFCImporter::LogError("expected IfcPlane as base surface for the IfcHalfSpaceSolid");
			return;
		}

		if(const IfcBooleanResult* const op0 = clip->FirstOperand->ResolveSelectPtr<IfcBooleanResult>(conv.db)) {
			ProcessBoolean(*op0,meshout,conv);
		}
		else if (const IfcSweptAreaSolid* const swept = clip->FirstOperand->ResolveSelectPtr<IfcSweptAreaSolid>(conv.db)) {
			ProcessSweptAreaSolid(*swept,meshout,conv);
		}
		else {
			IFCImporter::LogError("expected IfcSweptAreaSolid or IfcBooleanResult as first clipping operand");
			return;
		}

		// extract plane base position vector and normal vector
		IfcVector3 p,n(0.f,0.f,1.f);
		if (plane->Position->Axis) {
			ConvertDirection(n,plane->Position->Axis.Get());
		}
		ConvertCartesianPoint(p,plane->Position->Location);

		if(!IsTrue(hs->AgreementFlag)) {
			n *= -1.f;
		}

		// clip the current contents of `meshout` against the plane we obtained from the second operand
		const std::vector<IfcVector3>& in = meshout.verts;
		std::vector<IfcVector3>& outvert = result.verts;
		std::vector<unsigned int>::const_iterator begin=meshout.vertcnt.begin(), end=meshout.vertcnt.end(), iit;

		outvert.reserve(in.size());
		result.vertcnt.reserve(meshout.vertcnt.size());

		unsigned int vidx = 0;
		for(iit = begin; iit != end; vidx += *iit++) {

			unsigned int newcount = 0;
			for(unsigned int i = 0; i < *iit; ++i) {
				const IfcVector3& e0 = in[vidx+i], e1 = in[vidx+(i+1)%*iit];

				// does the next segment intersect the plane?
				IfcVector3 isectpos;
				const Intersect isect = IntersectSegmentPlane(p,n,e0,e1,isectpos);
				if (isect == Intersect_No || isect == Intersect_LiesOnPlane) {
					if ( (e0-p).Normalize()*n > 0 ) {
						outvert.push_back(e0);
						++newcount;
					}
				}
				else if (isect == Intersect_Yes) {
					if ( (e0-p).Normalize()*n > 0 ) {
						// e0 is on the right side, so keep it 
						outvert.push_back(e0);
						outvert.push_back(isectpos);
						newcount += 2;
					}
					else {
						// e0 is on the wrong side, so drop it and keep e1 instead
						outvert.push_back(isectpos);
						++newcount;
					}
				}
			}	

			if (!newcount) {
				continue;
			}

			IfcVector3 vmin,vmax;
			ArrayBounds(&*(outvert.end()-newcount),newcount,vmin,vmax);

			// filter our IfcFloat points - those may happen if a point lies
			// directly on the intersection line. However, due to IfcFloat
			// precision a bitwise comparison is not feasible to detect
			// this case.
			const IfcFloat epsilon = (vmax-vmin).SquareLength() / 1e6f;
			FuzzyVectorCompare fz(epsilon);

			std::vector<IfcVector3>::iterator e = std::unique( outvert.end()-newcount, outvert.end(), fz );
			if (e != outvert.end()) {
				newcount -= static_cast<unsigned int>(std::distance(e,outvert.end()));
				outvert.erase(e,outvert.end());
			}
			if (fz(*( outvert.end()-newcount),outvert.back())) {
				outvert.pop_back();
				--newcount;
			}
			if(newcount > 2) {
				result.vertcnt.push_back(newcount);
			}
			else while(newcount-->0)result.verts.pop_back();

		}
		IFCImporter::LogDebug("generating CSG geometry by plane clipping (IfcBooleanClippingResult)");
	}
	else {
		IFCImporter::LogWarn("skipping unknown IfcBooleanResult entity, type is " + boolean.GetClassName());
	}
}



// ------------------------------------------------------------------------------------------------
bool ProcessGeometricItem(const IfcRepresentationItem& geo, std::vector<unsigned int>& mesh_indices, 
	ConversionData& conv)
{
	bool fix_orientation = true;
	TempMesh meshtmp; 
	if(const IfcShellBasedSurfaceModel* shellmod = geo.ToPtr<IfcShellBasedSurfaceModel>()) {
		BOOST_FOREACH(boost::shared_ptr<const IfcShell> shell,shellmod->SbsmBoundary) {
			try {
				const EXPRESS::ENTITY& e = shell->To<ENTITY>();
				const IfcConnectedFaceSet& fs = conv.db.MustGetObject(e).To<IfcConnectedFaceSet>(); 

				ProcessConnectedFaceSet(fs,meshtmp,conv);
			}
			catch(std::bad_cast&) {
				IFCImporter::LogWarn("unexpected type error, IfcShell ought to inherit from IfcConnectedFaceSet");
			}
		}
	}
	else  if(const IfcConnectedFaceSet* fset = geo.ToPtr<IfcConnectedFaceSet>()) {
		ProcessConnectedFaceSet(*fset,meshtmp,conv);
	}	
	else  if(const IfcSweptAreaSolid* swept = geo.ToPtr<IfcSweptAreaSolid>()) {
		ProcessSweptAreaSolid(*swept,meshtmp,conv);
	}   
	else  if(const IfcSweptDiskSolid* disk = geo.ToPtr<IfcSweptDiskSolid>()) {
		ProcessSweptDiskSolid(*disk,meshtmp,conv);
		fix_orientation = false;
	}   
	else if(const IfcManifoldSolidBrep* brep = geo.ToPtr<IfcManifoldSolidBrep>()) {
		ProcessConnectedFaceSet(brep->Outer,meshtmp,conv);
	} 
	else if(const IfcFaceBasedSurfaceModel* surf = geo.ToPtr<IfcFaceBasedSurfaceModel>()) {
		BOOST_FOREACH(const IfcConnectedFaceSet& fc, surf->FbsmFaces) {
			ProcessConnectedFaceSet(fc,meshtmp,conv);
		}
	}  
	else  if(const IfcBooleanResult* boolean = geo.ToPtr<IfcBooleanResult>()) {
		ProcessBoolean(*boolean,meshtmp,conv);
	}
	else if(geo.ToPtr<IfcBoundingBox>()) {
		// silently skip over bounding boxes
		return false; 
	} 
	else {
		IFCImporter::LogWarn("skipping unknown IfcGeometricRepresentationItem entity, type is " + geo.GetClassName());
		return false;
	}

	meshtmp.RemoveAdjacentDuplicates();

	if(fix_orientation) {
		FixupFaceOrientation(meshtmp);
	}

	aiMesh* const mesh = meshtmp.ToMesh();
	if(mesh) {
		mesh->mMaterialIndex = ProcessMaterials(geo,conv);
		mesh_indices.push_back(conv.meshes.size());
		conv.meshes.push_back(mesh);
		return true;
	}
	return false;
}

// ------------------------------------------------------------------------------------------------
void AssignAddedMeshes(std::vector<unsigned int>& mesh_indices,aiNode* nd,
	ConversionData& /*conv*/)
{
	if (!mesh_indices.empty()) {

		// make unique
		std::sort(mesh_indices.begin(),mesh_indices.end());
		std::vector<unsigned int>::iterator it_end = std::unique(mesh_indices.begin(),mesh_indices.end());

		const size_t size = std::distance(mesh_indices.begin(),it_end);

		nd->mNumMeshes = size;
		nd->mMeshes = new unsigned int[nd->mNumMeshes];
		for(unsigned int i = 0; i < nd->mNumMeshes; ++i) {
			nd->mMeshes[i] = mesh_indices[i];
		}
	}
}

// ------------------------------------------------------------------------------------------------
bool TryQueryMeshCache(const IfcRepresentationItem& item, 
	std::vector<unsigned int>& mesh_indices, 
	ConversionData& conv) 
{
	ConversionData::MeshCache::const_iterator it = conv.cached_meshes.find(&item);
	if (it != conv.cached_meshes.end()) {
		std::copy((*it).second.begin(),(*it).second.end(),std::back_inserter(mesh_indices));
		return true;
	}
	return false;
}

// ------------------------------------------------------------------------------------------------
void PopulateMeshCache(const IfcRepresentationItem& item, 
	const std::vector<unsigned int>& mesh_indices, 
	ConversionData& conv)
{
	conv.cached_meshes[&item] = mesh_indices;
}

// ------------------------------------------------------------------------------------------------
bool ProcessRepresentationItem(const IfcRepresentationItem& item, 
	std::vector<unsigned int>& mesh_indices, 
	ConversionData& conv)
{
	if (!TryQueryMeshCache(item,mesh_indices,conv)) {
		if(ProcessGeometricItem(item,mesh_indices,conv)) {
			if(mesh_indices.size()) {
				PopulateMeshCache(item,mesh_indices,conv);
			}
		}
		else return false;
	}
	return true;
}

#undef to_int64
#undef from_int64
#undef from_int64_f

} // ! IFC
} // ! Assimp

#endif