# far_tutorial_2_3.cpp

https://github.com/PixarAnimationStudios/OpenSubdiv/blob/release/tutorials/far/tutorial_2_3/far_tutorial_2_3.cpp

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    .. code:: c++

        //------------------------------------------------------------------------------
        // Tutorial description:
        //
        // NOTE: The following approaches are approximations to compute smooth normals,
        //       for highest fidelity patches should be used for positions and normals,
        //       which form the true limit surface.
        //
        // Building on tutorial 3, this example shows how to instantiate a simple mesh,
        // refine it uniformly, interpolate both 'vertex' and 'face-varying'
        // primvar data, and finally calculate approximated smooth normals.
        // The resulting interpolated data is output in 'obj' format.
        //
        // Currently, this tutorial supports 3 methods to approximate smooth normals:
        //
        //     CrossTriangle : Calculates smooth normals (accumulating per vertex) using
        //                     3 verts to generate 2 vectors. This approximation has
        //                     trouble when working with quads (which can be non-planar)
        //                     since it only takes into account half of each face.
        //
        //     CrossQuad     : Calculates smooth normals (accumulating per vertex)
        //                     but this time, instead of taking into account only 3 verts
        //                     it creates 2 vectors crossing the quad.
        //                     This approximation builds upon CrossTriangle but takes
        //                     into account the 4 verts of the face.
        //
        //     Limit         : Calculates the normals at the limit for each vert
        //                     at the last level of subdivision.
        //                     These are the true limit normals, however, in this example
        //                     they are used with verts that are not at the limit.
        //                     This can lead to new visual artifacts since the normals
        //                     and the positions don't match. Additionally, this approach
        //                     requires extra computation to calculate the limit normals.
        //                     For this reason, we strongly suggest using
        //                     limit positions with limit normals.
        //

        #include <opensubdiv/far/topologyDescriptor.h>
        #include <opensubdiv/far/primvarRefiner.h>

        #include <cstdio>

        //------------------------------------------------------------------------------
        // Math helpers.
        //
        //

        // Returns the normalized version of the input vector
        inline void
        normalize(float *n) {
            float rn = 1.0f/sqrtf(n[0]*n[0] + n[1]*n[1] + n[2]*n[2]);
            n[0] *= rn;
            n[1] *= rn;
            n[2] *= rn;
        }

        // Returns the cross product of \p v1 and \p v2.
        void cross(float const *v1, float const *v2, float* vOut)
        {
            vOut[0] = v1[1] * v2[2] - v1[2] * v2[1];
            vOut[1] = v1[2] * v2[0] - v1[0] * v2[2];
            vOut[2] = v1[0] * v2[1] - v1[1] * v2[0];
        }

        //------------------------------------------------------------------------------
        // Face-varying implementation.
        //
        //
        struct Vertex {

            // Minimal required interface ----------------------
            Vertex() {
                Clear();
            }

            Vertex(Vertex const & src) {
                position[0] = src.position[0];
                position[1] = src.position[1];
                position[2] = src.position[2];
            }

            void Clear() {
                position[0]=position[1]=position[2]=0.0f;
            }

            void AddWithWeight(Vertex const & src, float weight) {
                position[0]+=weight*src.position[0];
                position[1]+=weight*src.position[1];
                position[2]+=weight*src.position[2];
            }

            // Public interface ------------------------------------
            void SetPosition(float x, float y, float z) {
                position[0]=x;
                position[1]=y;
                position[2]=z;
            }

            const float * GetPosition() const {
                return position;
            }

            float position[3];
        };

        //------------------------------------------------------------------------------
        // Face-varying container implementation.
        //
        // We are using a uv texture layout as a 'face-varying' primtiive variable
        // attribute. Because face-varying data is specified 'per-face-per-vertex',
        // we cannot use the same container that we use for 'vertex' or 'varying'
        // data. We specify a new container, which only carries (u,v) coordinates.
        // Similarly to our 'Vertex' container, we add a minimaliztic interpolation
        // interface with a 'Clear()' and 'AddWithWeight()' methods.
        //
        struct FVarVertexUV {

            // Minimal required interface ----------------------
            void Clear() {
                u=v=0.0f;
            }

            void AddWithWeight(FVarVertexUV const & src, float weight) {
                u += weight * src.u;
                v += weight * src.v;
            }

            // Basic 'uv' layout channel
            float u,v;
        };

        struct FVarVertexColor {

            // Minimal required interface ----------------------
            void Clear() {
                r=g=b=a=0.0f;
            }

            void AddWithWeight(FVarVertexColor const & src, float weight) {
                r += weight * src.r;
                g += weight * src.g;
                b += weight * src.b;
                a += weight * src.a;
            }

            // Basic 'color' layout channel
            float r,g,b,a;
        };

        //------------------------------------------------------------------------------
        // Cube geometry from catmark_cube.h

        // 'vertex' primitive variable data & topology
        static float g_verts[8][3] = {{ -0.5f, -0.5f,  0.5f },
                                      {  0.5f, -0.5f,  0.5f },
                                      { -0.5f,  0.5f,  0.5f },
                                      {  0.5f,  0.5f,  0.5f },
                                      { -0.5f,  0.5f, -0.5f },
                                      {  0.5f,  0.5f, -0.5f },
                                      { -0.5f, -0.5f, -0.5f },
                                      {  0.5f, -0.5f, -0.5f }};
        static int g_nverts = 8,
                   g_nfaces = 6;

        static int g_vertsperface[6] = { 4, 4, 4, 4, 4, 4 };

        static int g_vertIndices[24] = { 0, 1, 3, 2,
                                         2, 3, 5, 4,
                                         4, 5, 7, 6,
                                         6, 7, 1, 0,
                                         1, 7, 5, 3,
                                         6, 0, 2, 4  };

        // 'face-varying' primitive variable data & topology for UVs
        static float g_uvs[14][2] = {{ 0.375, 0.00 },
                                     { 0.625, 0.00 },
                                     { 0.375, 0.25 },
                                     { 0.625, 0.25 },
                                     { 0.375, 0.50 },
                                     { 0.625, 0.50 },
                                     { 0.375, 0.75 },
                                     { 0.625, 0.75 },
                                     { 0.375, 1.00 },
                                     { 0.625, 1.00 },
                                     { 0.875, 0.00 },
                                     { 0.875, 0.25 },
                                     { 0.125, 0.00 },
                                     { 0.125, 0.25 }};

        static int g_nuvs = 14;

        static int g_uvIndices[24] = {  0,  1,  3,  2,
                                        2,  3,  5,  4,
                                        4,  5,  7,  6,
                                        6,  7,  9,  8,
                                        1, 10, 11,  3,
                                       12,  0,  2, 13  };

        // 'face-varying' primitive variable data & topology for color
        static float g_colors[24][4] = {{1.0, 1.0, 1.0, 1.0},
                                        {1.0, 1.0, 1.0, 1.0},
                                        {1.0, 1.0, 1.0, 1.0},
                                        {1.0, 1.0, 1.0, 1.0},
                                        {1.0, 1.0, 1.0, 1.0},
                                        {1.0, 1.0, 1.0, 1.0},
                                        {1.0, 1.0, 1.0, 1.0},
                                        {1.0, 1.0, 1.0, 1.0},
                                        {1.0, 1.0, 1.0, 1.0},
                                        {1.0, 0.0, 0.0, 1.0},
                                        {1.0, 0.0, 0.0, 1.0},
                                        {1.0, 0.0, 0.0, 1.0},
                                        {1.0, 1.0, 1.0, 1.0},
                                        {1.0, 1.0, 1.0, 1.0},
                                        {1.0, 1.0, 1.0, 1.0},
                                        {1.0, 1.0, 1.0, 1.0},
                                        {1.0, 1.0, 1.0, 1.0},
                                        {1.0, 1.0, 1.0, 1.0},
                                        {1.0, 1.0, 1.0, 1.0},
                                        {1.0, 1.0, 1.0, 1.0},
                                        {1.0, 1.0, 1.0, 1.0},
                                        {1.0, 1.0, 1.0, 1.0},
                                        {1.0, 1.0, 1.0, 1.0},
                                        {1.0, 1.0, 1.0, 1.0}};

        static int g_ncolors = 24;

        static int g_colorIndices[24] = { 0,  3,  9,  6,
                                          7, 10, 15, 12,
                                         13, 16, 21, 18,
                                         19, 22,  4,  1,
                                          5, 23, 17, 11,
                                         20,  2,  8, 14 };

        using namespace OpenSubdiv;

        // Approximation methods for smooth normal computations
        enum NormalApproximation
        {
            CrossTriangle,
            CrossQuad,
            Limit
        };

        //------------------------------------------------------------------------------
        int main(int argc, char ** argv) {

            const int maxlevel = 2;
            enum NormalApproximation normalApproximation = CrossTriangle;

            // Parsing command line parameters to see if the user wants to use a
            // specific method to calculate normals
            for (int i = 1; i < argc; ++i) {

                if (strstr(argv[i], "-limit")) {
                    normalApproximation = Limit;
                } else if (!strcmp(argv[i], "-crossquad")) {
                    normalApproximation = CrossQuad;
                } else if (!strcmp(argv[i], "-crosstriangle")) {
                    normalApproximation = CrossTriangle;
                } else {
                    printf("Parameters : \n");
                    printf("  -crosstriangle : use the cross product of vectors\n");
                    printf("                   generated from 3 verts (default).\n");
                    printf("  -crossquad     : use the cross product of vectors\n");
                    printf("                   generated from 4 verts.\n");
                    printf("  -limit         : use normals calculated from the limit.\n");
                    return 0;
                }
            }

            typedef Far::TopologyDescriptor Descriptor;
            Sdc::SchemeType type = OpenSubdiv::Sdc::SCHEME_CATMARK;
            Sdc::Options options;
            options.SetVtxBoundaryInterpolation(Sdc::Options::VTX_BOUNDARY_EDGE_ONLY);
            options.SetFVarLinearInterpolation(Sdc::Options::FVAR_LINEAR_NONE);

            // Populate a topology descriptor with our raw data
            Descriptor desc;
            desc.numVertices  = g_nverts;
            desc.numFaces     = g_nfaces;
            desc.numVertsPerFace = g_vertsperface;
            desc.vertIndicesPerFace  = g_vertIndices;

            // Create a face-varying channel descriptor
            const int numChannels  = 2;
            const int channelUV    = 0;
            const int channelColor = 1;
            Descriptor::FVarChannel channels[numChannels];
            channels[channelUV].numValues = g_nuvs;
            channels[channelUV].valueIndices = g_uvIndices;
            channels[channelColor].numValues = g_ncolors;
            channels[channelColor].valueIndices = g_colorIndices;

            // Add the channel topology to the main descriptor
            desc.numFVarChannels = numChannels;
            desc.fvarChannels = channels;

            // Instantiate a Far::TopologyRefiner from the descriptor
            Far::TopologyRefiner * refiner =
                Far::TopologyRefinerFactory<Descriptor>::Create(desc,
                    Far::TopologyRefinerFactory<Descriptor>::Options(type, options));

            // Uniformly refine the topolgy up to 'maxlevel'
            // note: fullTopologyInLastLevel must be true to work with face-varying data
            {
                Far::TopologyRefiner::UniformOptions refineOptions(maxlevel);
                refineOptions.fullTopologyInLastLevel = true;
                refiner->RefineUniform(refineOptions);
            }

            // Allocate and initialize the 'vertex' primvar data (see tutorial 2 for
            // more details).
            std::vector<Vertex> vbuffer(refiner->GetNumVerticesTotal());
            Vertex * verts = &vbuffer[0];
            for (int i=0; i<g_nverts; ++i) {
                verts[i].SetPosition(g_verts[i][0], g_verts[i][1], g_verts[i][2]);
            }

            // Allocate & initialize the first channel of 'face-varying' primvars (UVs)
            std::vector<FVarVertexUV> fvBufferUV(refiner->GetNumFVarValuesTotal(channelUV));
            FVarVertexUV * fvVertsUV = &fvBufferUV[0];
            for (int i=0; i<g_nuvs; ++i) {
                fvVertsUV[i].u = g_uvs[i][0];
                fvVertsUV[i].v = g_uvs[i][1];
            }

            // Allocate & interpolate the 'face-varying' primvar data (colors)
            std::vector<FVarVertexColor> fvBufferColor(refiner->GetNumFVarValuesTotal(channelColor));
            FVarVertexColor * fvVertsColor = &fvBufferColor[0];
            for (int i=0; i<g_ncolors; ++i) {
                fvVertsColor[i].r = g_colors[i][0];
                fvVertsColor[i].g = g_colors[i][1];
                fvVertsColor[i].b = g_colors[i][2];
                fvVertsColor[i].a = g_colors[i][3];
            }

            // Interpolate both vertex and face-varying primvar data
            Far::PrimvarRefiner primvarRefiner(*refiner);
            Vertex *          srcVert = verts;
            FVarVertexUV *    srcFVarUV = fvVertsUV;
            FVarVertexColor * srcFVarColor = fvVertsColor;

            for (int level = 1; level <= maxlevel; ++level) {
                Vertex *     dstVert = srcVert + refiner->GetLevel(level-1).GetNumVertices();
                FVarVertexUV * dstFVarUV = srcFVarUV + refiner->GetLevel(level-1).GetNumFVarValues(channelUV);
                FVarVertexColor * dstFVarColor = srcFVarColor + refiner->GetLevel(level-1).GetNumFVarValues(channelColor);

                primvarRefiner.Interpolate(level, srcVert, dstVert);
                primvarRefiner.InterpolateFaceVarying(level, srcFVarUV, dstFVarUV, channelUV);
                primvarRefiner.InterpolateFaceVarying(level, srcFVarColor, dstFVarColor, channelColor);

                srcVert = dstVert;
                srcFVarUV = dstFVarUV;
                srcFVarColor = dstFVarColor;
            }

            // Approximate normals
            Far::TopologyLevel const & refLastLevel = refiner->GetLevel(maxlevel);
            int nverts = refLastLevel.GetNumVertices();
            int nfaces = refLastLevel.GetNumFaces();
            int firstOfLastVerts = refiner->GetNumVerticesTotal() - nverts;

            std::vector<Vertex> normals(nverts);

            // Different ways to approximate smooth normals
            //
            // For details check the description at the beginning of the file
            if (normalApproximation == Limit) {

                // Approximation using the normal at the limit with verts that are
                // not at the limit
                //
                // For details check the description at the beginning of the file

                std::vector<Vertex> fineLimitPos(nverts);
                std::vector<Vertex> fineDu(nverts);
                std::vector<Vertex> fineDv(nverts);

                primvarRefiner.Limit(&verts[firstOfLastVerts], fineLimitPos, fineDu, fineDv);

                for (int vert = 0; vert < nverts; ++vert) {
                    float const * du = fineDu[vert].GetPosition();
                    float const * dv = fineDv[vert].GetPosition();

                    float norm[3];
                    cross(du, dv, norm);
                    normals[vert].SetPosition(norm[0], norm[1], norm[2]);
                }

            } else if (normalApproximation == CrossQuad) {

                // Approximate smooth normals by accumulating normal vectors computed as
                // the cross product of two vectors generated by the 4 verts that
                // form each quad
                //
                // For details check the description at the beginning of the file

                for (int f = 0; f < nfaces; f++) {
                    Far::ConstIndexArray faceVertices = refLastLevel.GetFaceVertices(f);

                    // We will use the first three verts to calculate a normal
                    const float * v0 = verts[ firstOfLastVerts + faceVertices[0] ].GetPosition();
                    const float * v1 = verts[ firstOfLastVerts + faceVertices[1] ].GetPosition();
                    const float * v2 = verts[ firstOfLastVerts + faceVertices[2] ].GetPosition();
                    const float * v3 = verts[ firstOfLastVerts + faceVertices[3] ].GetPosition();

                    // Calculate the cross product between the vectors formed by v1-v0 and
                    // v2-v0, and then normalize the result
                    float normalCalculated [] = {0.0,0.0,0.0};
                    float a[3] = { v2[0]-v0[0], v2[1]-v0[1], v2[2]-v0[2] };
                    float b[3] = { v3[0]-v1[0], v3[1]-v1[1], v3[2]-v1[2] };
                    cross(a, b, normalCalculated);
                    normalize(normalCalculated);

                    // Accumulate that normal on all verts that are part of that face
                    for(int vInFace = 0; vInFace < faceVertices.size() ; vInFace++ ) {

                        int vertexIndex = faceVertices[vInFace];
                        normals[vertexIndex].position[0] += normalCalculated[0];
                        normals[vertexIndex].position[1] += normalCalculated[1];
                        normals[vertexIndex].position[2] += normalCalculated[2];
                    }
                }

            } else if (normalApproximation == CrossTriangle) {

                // Approximate smooth normals by accumulating normal vectors computed as
                // the cross product of two vectors generated by 3 verts of the quad
                //
                // For details check the description at the beginning of the file

                for (int f = 0; f < nfaces; f++) {
                    Far::ConstIndexArray faceVertices = refLastLevel.GetFaceVertices(f);

                    // We will use the first three verts to calculate a normal
                    const float * v0 = verts[ firstOfLastVerts + faceVertices[0] ].GetPosition();
                    const float * v1 = verts[ firstOfLastVerts + faceVertices[1] ].GetPosition();
                    const float * v2 = verts[ firstOfLastVerts + faceVertices[2] ].GetPosition();

                    // Calculate the cross product between the vectors formed by v1-v0 and
                    // v2-v0, and then normalize the result
                    float normalCalculated [] = {0.0,0.0,0.0};
                    float a[3] = { v1[0]-v0[0], v1[1]-v0[1], v1[2]-v0[2] };
                    float b[3] = { v2[0]-v0[0], v2[1]-v0[1], v2[2]-v0[2] };
                    cross(a, b, normalCalculated);
                    normalize(normalCalculated);

                    // Accumulate that normal on all verts that are part of that face
                    for(int vInFace = 0; vInFace < faceVertices.size() ; vInFace++ ) {

                        int vertexIndex = faceVertices[vInFace];
                        normals[vertexIndex].position[0] += normalCalculated[0];
                        normals[vertexIndex].position[1] += normalCalculated[1];
                        normals[vertexIndex].position[2] += normalCalculated[2];
                    }
                }
            }

            // Finally we just need to normalize the accumulated normals
            for (int vert = 0; vert < nverts; ++vert) {
                normalize(&normals[vert].position[0]);
            }

            { // Output OBJ of the highest level refined -----------

                // Print vertex positions
                for (int vert = 0; vert < nverts; ++vert) {
                    float const * pos = verts[firstOfLastVerts + vert].GetPosition();
                    printf("v %f %f %f\n", pos[0], pos[1], pos[2]);
                }

                // Print vertex normals
                for (int vert = 0; vert < nverts; ++vert) {
                    float const * pos = normals[vert].GetPosition();
                    printf("vn %f %f %f\n", pos[0], pos[1], pos[2]);
                }

                // Print uvs
                int nuvs   = refLastLevel.GetNumFVarValues(channelUV);
                int firstOfLastUvs = refiner->GetNumFVarValuesTotal(channelUV) - nuvs;
                for (int fvvert = 0; fvvert < nuvs; ++fvvert) {
                    FVarVertexUV const & uv = fvVertsUV[firstOfLastUvs + fvvert];
                    printf("vt %f %f\n", uv.u, uv.v);
                }

                // Print faces
                for (int face = 0; face < nfaces; ++face) {
                    Far::ConstIndexArray fverts = refLastLevel.GetFaceVertices(face);
                    Far::ConstIndexArray fuvs   = refLastLevel.GetFaceFVarValues(face, channelUV);

                    // all refined Catmark faces should be quads
                    assert(fverts.size()==4 && fuvs.size()==4);

                    printf("f ");
                    for (int vert=0; vert<fverts.size(); ++vert) {
                        // OBJ uses 1-based arrays...
                        printf("%d/%d/%d ", fverts[vert]+1, fuvs[vert]+1, fverts[vert]+1);
                    }
                    printf("\n");
                }
            }

            delete refiner;
            return EXIT_SUCCESS;
        }
        //------------------------------------------------------------------------------

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