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Open Asset Import Library (ASSIMP)
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/** @file  TriangulateProcess.cpp
 *  @brief Implementation of the post processing step to split up
 *    all faces with more than three indices into triangles.
 *
 *
 *  The triangulation algorithm will handle concave or convex polygons.
 *  Self-intersecting or non-planar polygons are not rejected, but
 *  they're probably not triangulated correctly.
 *
 * AI_BUILD_TRIANGULATE_COLOR_FACE_WINDING
 *   - generates vertex colors to represent the face winding order.
 *     the first vertex of a polygon becomes red, the last blue.
 */

#include "AssimpPCH.h"

#ifndef ASSIMP_BUILD_NO_TRIANGULATE_PROCESS
#include "TriangulateProcess.h"
#include "ProcessHelper.h"

//#define AI_BUILD_TRIANGULATE_COLOR_FACE_WINDING
using namespace Assimp;

// ------------------------------------------------------------------------------------------------
// Constructor to be privately used by Importer
TriangulateProcess::TriangulateProcess()
{
	// nothing to do here
}

// ------------------------------------------------------------------------------------------------
// Destructor, private as well
TriangulateProcess::~TriangulateProcess()
{
	// nothing to do here
}

// ------------------------------------------------------------------------------------------------
// Returns whether the processing step is present in the given flag field.
bool TriangulateProcess::IsActive( unsigned int pFlags) const
{
	return (pFlags & aiProcess_Triangulate) != 0;
}

// ------------------------------------------------------------------------------------------------
// Executes the post processing step on the given imported data.
void TriangulateProcess::Execute( aiScene* pScene)
{
	DefaultLogger::get()->debug("TriangulateProcess begin");

	bool bHas = false;
	for( unsigned int a = 0; a < pScene->mNumMeshes; a++)
	{
		if(	TriangulateMesh( pScene->mMeshes[a]))
			bHas = true;
	}
	if (bHas)DefaultLogger::get()->info ("TriangulateProcess finished. All polygons have been triangulated.");
	else     DefaultLogger::get()->debug("TriangulateProcess finished. There was nothing to be done.");
}

// ------------------------------------------------------------------------------------------------
// Test whether a point p2 is on the left side of the line formed by p0-p1 
inline bool OnLeftSideOfLine(const aiVector2D& p0, const aiVector2D& p1,const aiVector2D& p2)
{
	return ( (p1.x - p0.x) * (p2.y - p0.y) - (p2.x - p0.x) * (p1.y - p0.y) ) > 0;
}

// ------------------------------------------------------------------------------------------------
// Test whether a point is inside a given triangle in R2
inline bool PointInTriangle2D(const aiVector2D& p0, const aiVector2D& p1,const aiVector2D& p2, const aiVector2D& pp)
{
	// Point in triangle test using baryzentric coordinates
	const aiVector2D v0 = p1 - p0;
	const aiVector2D v1 = p2 - p0;
	const aiVector2D v2 = pp - p0;

	float dot00 = v0 * v0;
	float dot01 = v0 * v1;
	float dot02 = v0 * v2;
	float dot11 = v1 * v1;
	float dot12 = v1 * v2;

	const float invDenom = 1 / (dot00 * dot11 - dot01 * dot01);
	dot11 = (dot11 * dot02 - dot01 * dot12) * invDenom;
	dot00 = (dot00 * dot12 - dot01 * dot02) * invDenom;

	return (dot11 > 0) && (dot00 > 0) && (dot11 + dot00 < 1);
}

// ------------------------------------------------------------------------------------------------
// Triangulates the given mesh.
bool TriangulateProcess::TriangulateMesh( aiMesh* pMesh)
{
	// Now we have aiMesh::mPrimitiveTypes, so this is only here for test cases
	if (!pMesh->mPrimitiveTypes)	{
		bool bNeed = false;

		for( unsigned int a = 0; a < pMesh->mNumFaces; a++)	{
			const aiFace& face = pMesh->mFaces[a];

			if( face.mNumIndices != 3)	{
				bNeed = true;
			}
		}
		if (!bNeed)
			return false;
	}
	else if (!(pMesh->mPrimitiveTypes & aiPrimitiveType_POLYGON)) {
		return false;
	}

	// the output mesh will contain triangles, but no polys anymore
	pMesh->mPrimitiveTypes |= aiPrimitiveType_TRIANGLE;
	pMesh->mPrimitiveTypes &= ~aiPrimitiveType_POLYGON;

	// Find out how many output faces we'll get
	unsigned int numOut = 0, max_out = 0;
	for( unsigned int a = 0; a < pMesh->mNumFaces; a++)	{
		aiFace& face = pMesh->mFaces[a];
		if( face.mNumIndices <= 3)
			numOut++;

		else {
			numOut += face.mNumIndices-2;
			max_out = std::max(max_out,face.mNumIndices);
		}
	}

	// Just another check whether aiMesh::mPrimitiveTypes is correct
	assert(numOut != pMesh->mNumFaces);

	aiVector3D* nor_out = NULL;
	if (!pMesh->mNormals && pMesh->mPrimitiveTypes == aiPrimitiveType_POLYGON) {
		nor_out = pMesh->mNormals = new aiVector3D[pMesh->mNumVertices];
	}

	aiFace* out = new aiFace[numOut], *curOut = out;
	std::vector<aiVector3D> temp_verts(max_out+2); /* temporary storage for vertices */

	// Apply vertex colors to represent the face winding?
#ifdef AI_BUILD_TRIANGULATE_COLOR_FACE_WINDING
	if (!pMesh->mColors[0])
		pMesh->mColors[0] = new aiColor4D[pMesh->mNumVertices];
	else
		new(pMesh->mColors[0]) aiColor4D[pMesh->mNumVertices];

	aiColor4D* clr = pMesh->mColors[0];
#endif

	// use boost::scoped_array to avoid slow std::vector<bool> specialiations
	boost::scoped_array<bool> done(new bool[max_out]); 
	for( unsigned int a = 0; a < pMesh->mNumFaces; a++)	{
		aiFace& face = pMesh->mFaces[a];

		unsigned int* idx = face.mIndices;
		int num = (int)face.mNumIndices, ear = 0, tmp, prev = num-1, next = 0, max = num;

		// Apply vertex colors to represent the face winding?
#ifdef AI_BUILD_TRIANGULATE_COLOR_FACE_WINDING
		for (unsigned int i = 0; i < face.mNumIndices; ++i) {
			aiColor4D& c = clr[idx[i]];
			c.r = (i+1) / (float)max;
			c.b = 1.f - c.r;
		}
#endif

		// if it's a simple primitive, just copy it
		if( face.mNumIndices <= 3)
		{
			aiFace& nface = *curOut++;
			nface.mNumIndices = face.mNumIndices;
			nface.mIndices    = face.mIndices;
		} 
		else
		{
			// A polygon with more than 3 vertices can be either concave or convex.
			// Usually everything we're getting is convex and we could easily
			// triangulate by trifanning. However, LightWave is probably the only
			// modeller making extensive use of highly concave monster polygons ...
			// so we need to apply the full 'ear cutting' algorithm.

			// RERQUIREMENT: polygon is expected to be simple and *nearly* planar.
			// We project it onto a plane to get 2d data. Working in R3 would
			// also be possible but it's more difficult to implement. 

			// Collect all vertices of of the polygon.
			aiVector3D* verts = pMesh->mVertices;
			for (tmp = 0; tmp < max; ++tmp)
				temp_verts[tmp] = verts[idx[tmp]];

			// Get newell normal of the polygon. Store it for future use if it's a polygon-only mesh
			aiVector3D n;
			NewellNormal<3,3,3>(n,max,&temp_verts.front().x,&temp_verts.front().y,&temp_verts.front().z);
			if (nor_out) {
				 for (tmp = 0; tmp < max; ++tmp)
					 nor_out[idx[tmp]] = n;
			}

			// Select largest normal coordinate to ignore for projection
			const float ax = (n.x>0 ? n.x : -n.x);    
			const float ay = (n.y>0 ? n.y : -n.y);   
			const float az = (n.z>0 ? n.z : -n.z);    

			unsigned int ac = 0, bc = 1; /* no z coord. projection to xy */
			float inv = n.z;
			if (ax > ay) {
				if (ax > az) { /* no x coord. projection to yz */
					ac = 1; bc = 2;
					inv = n.x;
				}
			}
			else if (ay > az) { /* no y coord. projection to zy */
				ac = 2; bc = 0;
				inv = n.y;
			}

			// Swap projection axes to take the negated projection vector into account
			if (inv < 0.f) {
				std::swap(ac,bc);
			}

			for (tmp =0; tmp < max; ++tmp) {
				temp_verts[tmp].x = verts[idx[tmp]][ac];
				temp_verts[tmp].y = verts[idx[tmp]][bc];
				done[tmp] = false;	
			}

			//
			// FIXME: currently this is the slow O(kn) variant with a worst case
			// complexity of O(n^2) (I think). Can be done in O(n).
			while (num > 3)	{

				// Find the next ear of the polygon
				int num_found = 0;
				for (ear = next;;prev = ear,ear = next) {
				
					// break after we looped two times without a positive match
					for (next=ear+1;done[(next>max-1?next=0:next)];++next);
					if (next < ear) {
						if (++num_found == 2)
							break;
					}
					const aiVector2D* pnt1 = (const aiVector2D*)&temp_verts[ear], 
						*pnt0 = (const aiVector2D*)&temp_verts[prev], 
						*pnt2 = (const aiVector2D*)&temp_verts[next];
			
					// Must be a convex point. Assuming ccw winding, it must be on the right of the line between p-1 and p+1.
					if (OnLeftSideOfLine (*pnt0,*pnt2,*pnt1))
						continue;

					// and no other point may be contained in this triangle
					for ( tmp = 0; tmp < max; ++tmp) {

						// We need to compare the actual values because it's possible that multiple indexes in 
						// the polygon are refering to the same position. concave_polygon.obj is a sample
						//
						// FIXME: Use 'epsiloned' comparisons instead? Due to numeric inaccuracies in
						// PointInTriangle() I'm guessing that it's actually possible to construct
						// input data that would cause us to end up with no ears. The problem is,
						// which epsilon? If we chose a too large value, we'd get wrong results
						const aiVector2D& vtmp = * ((aiVector2D*) &temp_verts[tmp] ); 
						if ( vtmp != *pnt1 && vtmp != *pnt2 && vtmp != *pnt0 && PointInTriangle2D(*pnt0,*pnt1,*pnt2,vtmp))
							break;		

					}
					if (tmp != max)
						continue;
							
					// this vertex is an ear
					break;
				}
				if (num_found == 2) {

					// Due to the 'two ear theorem', every simple polygon with more than three points must
					// have 2 'ears'. Here's definitely someting wrong ... but we don't give up yet.
					//

					// Instead we're continuting with the standard trifanning algorithm which we'd
					// use if we had only convex polygons. That's life.
					DefaultLogger::get()->error("Failed to triangulate polygon (no ear found). Probably not a simple polygon?");

					curOut -= (max-num); /* undo all previous work */
					for (tmp = 0; tmp < max-2; ++tmp) {
						aiFace& nface = *curOut++;

						nface.mNumIndices = 3;
						if (!nface.mIndices)
							nface.mIndices = new unsigned int[3];

						nface.mIndices[0] = idx[0];
						nface.mIndices[1] = idx[tmp+1];
						nface.mIndices[2] = idx[tmp+2];
					}
					num = 0;
					break;
				}

				aiFace& nface = *curOut++;
				nface.mNumIndices = 3;

				if (!nface.mIndices)
					nface.mIndices = new unsigned int[3];

				// setup indices for the new triangle ...
				nface.mIndices[0] = idx[prev];
				nface.mIndices[1] = idx[ear];
				nface.mIndices[2] = idx[next];

				// exclude the ear from most further processing
				done[ear] = true;
				--num;
			}
			if (num > 0) {
				// We have three indices forming the last 'ear' remaining. Collect them.
				aiFace& nface = *curOut++;
				nface.mNumIndices = 3;
				nface.mIndices = face.mIndices;

				for (tmp = 0; done[tmp]; ++tmp);
				idx[0] = idx[tmp];

				for (++tmp; done[tmp]; ++tmp);
				idx[1] = idx[tmp];

				for (++tmp; done[tmp]; ++tmp);
				idx[2] = idx[tmp];
			}
		}
		face.mIndices = NULL; /* prevent unintended deletion of our awesome results. would be a pity */
	}

	// kill the old faces
	delete [] pMesh->mFaces;

	// ... and store the new ones
	pMesh->mFaces    = out;
	pMesh->mNumFaces = (unsigned int)(curOut-out); /* not necessarily equal to numOut */
	return true;
}

#endif // !! ASSIMP_BUILD_NO_TRIANGULATE_PROCESS
