assimp/code/PostProcessing/TriangulateProcess.cpp

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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.
 *
 * DEBUG SWITCHES - do not enable any of them in release builds:
 *
 * 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.
 * AI_BUILD_TRIANGULATE_DEBUG_POLYS
 *   - dump all polygons and their triangulation sequences to
 *     a file
 */
#ifndef ASSIMP_BUILD_NO_TRIANGULATE_PROCESS

#include "PostProcessing/TriangulateProcess.h"
#include "PostProcessing/ProcessHelper.h"
#include "Common/PolyTools.h"

#include <memory>
#include <cstdint>

//#define AI_BUILD_TRIANGULATE_COLOR_FACE_WINDING
//#define AI_BUILD_TRIANGULATE_DEBUG_POLYS

#define POLY_GRID_Y 40
#define POLY_GRID_X 70
#define POLY_GRID_XPAD 20
#define POLY_OUTPUT_FILE "assimp_polygons_debug.txt"

using namespace Assimp;

namespace {

    /**
     * @brief Helper struct used to simplify NGON encoding functions.
     */
    struct NGONEncoder {
        NGONEncoder() : mLastNGONFirstIndex((unsigned int)-1) {}

        /**
         * @brief Encode the current triangle, and make sure it is recognized as a triangle.
         *
         * This method will rotate indices in tri if needed in order to avoid tri to be considered
         * part of the previous ngon. This method is to be used whenever you want to emit a real triangle,
         * and make sure it is seen as a triangle.
         *
         * @param tri Triangle to encode.
         */
        void ngonEncodeTriangle(aiFace * tri) {
            ai_assert(tri->mNumIndices == 3);

            // Rotate indices in new triangle to avoid ngon encoding false ngons
            // Otherwise, the new triangle would be considered part of the previous NGON.
            if (isConsideredSameAsLastNgon(tri)) {
                std::swap(tri->mIndices[0], tri->mIndices[2]);
                std::swap(tri->mIndices[1], tri->mIndices[2]);
            }

            mLastNGONFirstIndex = tri->mIndices[0];
        }

        /**
         * @brief Encode a quad (2 triangles) in ngon encoding, and make sure they are seen as a single ngon.
         *
         * @param tri1 First quad triangle
         * @param tri2 Second quad triangle
         *
         * @pre Triangles must be properly fanned from the most appropriate vertex.
         */
        void ngonEncodeQuad(aiFace *tri1, aiFace *tri2) {
            ai_assert(tri1->mNumIndices == 3);
            ai_assert(tri2->mNumIndices == 3);
            ai_assert(tri1->mIndices[0] == tri2->mIndices[0]);

            // If the selected fanning vertex is the same as the previously
            // emitted ngon, we use the opposite vertex which also happens to work
            // for tri-fanning a concave quad.
            // ref: https://github.com/assimp/assimp/pull/3695#issuecomment-805999760
            if (isConsideredSameAsLastNgon(tri1)) {
                // Right-rotate indices for tri1 (index 2 becomes the new fanning vertex)
                std::swap(tri1->mIndices[0], tri1->mIndices[2]);
                std::swap(tri1->mIndices[1], tri1->mIndices[2]);

                // Left-rotate indices for tri2 (index 2 becomes the new fanning vertex)
                std::swap(tri2->mIndices[1], tri2->mIndices[2]);
                std::swap(tri2->mIndices[0], tri2->mIndices[2]);

                ai_assert(tri1->mIndices[0] == tri2->mIndices[0]);
            }

            mLastNGONFirstIndex = tri1->mIndices[0];
        }

        /**
         * @brief Check whether this triangle would be considered part of the lastly emitted ngon or not.
         *
         * @param tri Current triangle.
         * @return true If used as is, this triangle will be part of last ngon.
         * @return false If used as is, this triangle is not considered part of the last ngon.
         */
        bool isConsideredSameAsLastNgon(const aiFace * tri) const {
            ai_assert(tri->mNumIndices == 3);
            return tri->mIndices[0] == mLastNGONFirstIndex;
        }

    private:
        unsigned int mLastNGONFirstIndex;
    };

}

// ------------------------------------------------------------------------------------------------
// 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) {
    ASSIMP_LOG_DEBUG("TriangulateProcess begin");

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

// ------------------------------------------------------------------------------------------------
// 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;
    }

    // Find out how many output faces we'll get
    uint32_t numOut = 0, max_out = 0;
    bool get_normals = true;
    for( unsigned int a = 0; a < pMesh->mNumFaces; a++) {
        aiFace& face = pMesh->mFaces[a];
        if (face.mNumIndices <= 4) {
            get_normals = false;
        }
        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
    if (numOut == pMesh->mNumFaces) {
        ASSIMP_LOG_ERROR( "Invalidation detected in the number of indices: does not fit to the primitive type." );
        return false;
    }
    
    aiVector3D *nor_out = nullptr;

    // if we don't have normals yet, but expect them to be a cheap side
    // product of triangulation anyway, allocate storage for them.
    if (!pMesh->mNormals && get_normals) {
        // XXX need a mechanism to inform the GenVertexNormals process to treat these normals as preprocessed per-face normals
    //  nor_out = pMesh->mNormals = new aiVector3D[pMesh->mNumVertices];
    }

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

    // The mesh becomes NGON encoded now, during the triangulation process.
    pMesh->mPrimitiveTypes |= aiPrimitiveType_NGONEncodingFlag;

    aiFace* out = new aiFace[numOut](), *curOut = out;
    std::vector<aiVector3D> temp_verts3d(max_out+2); /* temporary storage for vertices */
    std::vector<aiVector2D> temp_verts(max_out+2);

    NGONEncoder ngonEncoder;

    // 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

#ifdef AI_BUILD_TRIANGULATE_DEBUG_POLYS
    FILE* fout = fopen(POLY_OUTPUT_FILE,"a");
#endif

    const aiVector3D* verts = pMesh->mVertices;

    // use std::unique_ptr to avoid slow std::vector<bool> specialiations
    std::unique_ptr<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

        aiFace* const last_face = curOut;

        // if it's a simple point,line or triangle: just copy it
        if( face.mNumIndices <= 3)
        {
            aiFace& nface = *curOut++;
            nface.mNumIndices = face.mNumIndices;
            nface.mIndices    = face.mIndices;
            face.mIndices = nullptr;

            // points and lines don't require ngon encoding (and are not supported either!)
            if (nface.mNumIndices == 3) ngonEncoder.ngonEncodeTriangle(&nface);

            continue;
        }
        // optimized code for quadrilaterals
        else if ( face.mNumIndices == 4) {

            // quads can have at maximum one concave vertex. Determine
            // this vertex (if it exists) and start tri-fanning from
            // it.
            unsigned int start_vertex = 0;
            for (unsigned int i = 0; i < 4; ++i) {
                const aiVector3D& v0 = verts[face.mIndices[(i+3) % 4]];
                const aiVector3D& v1 = verts[face.mIndices[(i+2) % 4]];
                const aiVector3D& v2 = verts[face.mIndices[(i+1) % 4]];

                const aiVector3D& v = verts[face.mIndices[i]];

                aiVector3D left = (v0-v);
                aiVector3D diag = (v1-v);
                aiVector3D right = (v2-v);

                left.Normalize();
                diag.Normalize();
                right.Normalize();

                const float angle = std::acos(left*diag) + std::acos(right*diag);
                if (angle > AI_MATH_PI_F) {
                    // this is the concave point
                    start_vertex = i;
                    break;
                }
            }

            const unsigned int temp[] = {face.mIndices[0], face.mIndices[1], face.mIndices[2], face.mIndices[3]};

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

            nface.mIndices[0] = temp[start_vertex];
            nface.mIndices[1] = temp[(start_vertex + 1) % 4];
            nface.mIndices[2] = temp[(start_vertex + 2) % 4];

            aiFace& sface = *curOut++;
            sface.mNumIndices = 3;
            sface.mIndices = new unsigned int[3];

            sface.mIndices[0] = temp[start_vertex];
            sface.mIndices[1] = temp[(start_vertex + 2) % 4];
            sface.mIndices[2] = temp[(start_vertex + 3) % 4];

            // prevent double deletion of the indices field
            face.mIndices = nullptr;

            ngonEncoder.ngonEncodeQuad(&nface, &sface);

            continue;
        }
        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 tri-fanning. However, LightWave is probably the only
            // modeling suite to make extensive use of highly concave, monster polygons ...
            // so we need to apply the full 'ear cutting' algorithm to get it right.

            // REQUIREMENT: polygon is expected to be simple and *nearly* planar.
            // We project it onto a plane to get a 2d triangle.

            // Collect all vertices of of the polygon.
            for (tmp = 0; tmp < max; ++tmp) {
                temp_verts3d[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_verts3d.front().x,&temp_verts3d.front().y,&temp_verts3d.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;
            }

#ifdef AI_BUILD_TRIANGULATE_DEBUG_POLYS
            // plot the plane onto which we mapped the polygon to a 2D ASCII pic
            aiVector2D bmin,bmax;
            ArrayBounds(&temp_verts[0],max,bmin,bmax);

            char grid[POLY_GRID_Y][POLY_GRID_X+POLY_GRID_XPAD];
            std::fill_n((char*)grid,POLY_GRID_Y*(POLY_GRID_X+POLY_GRID_XPAD),' ');

            for (int i =0; i < max; ++i) {
                const aiVector2D& v = (temp_verts[i] - bmin) / (bmax-bmin);
                const size_t x = static_cast<size_t>(v.x*(POLY_GRID_X-1)), y = static_cast<size_t>(v.y*(POLY_GRID_Y-1));
                char* loc = grid[y]+x;
                if (grid[y][x] != ' ') {
                    for(;*loc != ' '; ++loc);
                    *loc++ = '_';
                }
                *(loc+::ai_snprintf(loc, POLY_GRID_XPAD,"%i",i)) = ' ';
            }


            for(size_t y = 0; y < POLY_GRID_Y; ++y) {
                grid[y][POLY_GRID_X+POLY_GRID_XPAD-1] = '\0';
                fprintf(fout,"%s\n",grid[y]);
            }

            fprintf(fout,"\ntriangulation sequence: ");
#endif

            //
            // 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?next=0:next)];++next);
                    if (next < ear) {
                        if (++num_found == 2) {
                            break;
                        }
                    }
                    const aiVector2D* pnt1 = &temp_verts[ear],
                        *pnt0 = &temp_verts[prev],
                        *pnt2 = &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 (OnLeftSideOfLine2D(*pnt0,*pnt2,*pnt1) == 1) {
                        continue;
                    }

                    // Skip when three point is in a line
                    aiVector2D left = *pnt0 - *pnt1;
                    aiVector2D right = *pnt2 - *pnt1;

                    left.Normalize();
                    right.Normalize();
                    auto mul = left * right;

                    // if the angle is 0 or 180
                    if (std::abs(mul - 1.f) < ai_epsilon || std::abs(mul + 1.f) < ai_epsilon) {
                        // skip this ear
                        ASSIMP_LOG_WARN("Skip a ear, due to its angle is near 0 or 180.");
                        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 referring 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 = 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 something wrong ... but we don't give up yet.
                    //

                    // Instead we're continuing with the standard tri-fanning algorithm which we'd
                    // use if we had only convex polygons. That's life.
                    ASSIMP_LOG_ERROR("Failed to triangulate polygon (no ear found). Probably not a simple polygon?");

#ifdef AI_BUILD_TRIANGULATE_DEBUG_POLYS
                    fprintf(fout,"critical error here, no ear found! ");
#endif
                    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] = prev;
                nface.mIndices[1] = ear;
                nface.mIndices[2] = 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;
                if (!nface.mIndices) {
                    nface.mIndices = new unsigned int[3];
                }

                for (tmp = 0; done[tmp]; ++tmp);
                nface.mIndices[0] = tmp;

                for (++tmp; done[tmp]; ++tmp);
                nface.mIndices[1] = tmp;

                for (++tmp; done[tmp]; ++tmp);
                nface.mIndices[2] = tmp;

            }
        }

#ifdef AI_BUILD_TRIANGULATE_DEBUG_POLYS

        for(aiFace* f = last_face; f != curOut; ++f) {
            unsigned int* i = f->mIndices;
            fprintf(fout," (%i %i %i)",i[0],i[1],i[2]);
        }

        fprintf(fout,"\n*********************************************************************\n");
        fflush(fout);

#endif

        for(aiFace* f = last_face; f != curOut; ) {
            unsigned int* i = f->mIndices;

            i[0] = idx[i[0]];
            i[1] = idx[i[1]];
            i[2] = idx[i[2]];

            // IMPROVEMENT: Polygons are not supported yet by this ngon encoding + triangulation step.
            //              So we encode polygons as regular triangles. No way to reconstruct the original
            //              polygon in this case.
            ngonEncoder.ngonEncodeTriangle(f);
            ++f;
        }

        delete[] face.mIndices;
        face.mIndices = nullptr;
    }

#ifdef AI_BUILD_TRIANGULATE_DEBUG_POLYS
    fclose(fout);
#endif

    // 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