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.. code:: c

    //------------------------------------------------------------------------------
    // Tutorial description:
    //
    // This tutorial shows how to interpolate surface limits at arbitrary
    // parametric locations using feature adaptive Far::PatchTables.
    //
    // The evaluation of the limit surface at arbitrary locations requires the
    // adaptive isolation of topological features. This process converts the
    // input polygonal control cage into a collection of bi-cubic patches.
    //
    // We can then evaluate the patches at random parametric locations and
    // obtain analytical positions and tangents on the limit surface.
    //
    // The results are dumped into a MEL script that draws 'streak' particle
    // systems that show the tangent and bi-tangent at the random samples locations.
    //

    #include <opensubdiv/far/topologyDescriptor.h>
    #include <opensubdiv/far/primvarRefiner.h>
    #include <opensubdiv/far/patchTableFactory.h>
    #include <opensubdiv/far/patchMap.h>
    #include <opensubdiv/far/ptexIndices.h>

    #include <cassert>
    #include <cstdio>
    #include <cstring>
    #include <cfloat>

    using namespace OpenSubdiv;

    // pyramid geometry from catmark_pyramid_crease0.h
    static int const g_nverts = 5;
    static float const g_verts[24] = { 0.0f,  0.0f, 2.0f,
                                       0.0f, -2.0f, 0.0f,
                                       2.0f,  0.0f, 0.0f,
                                       0.0f,  2.0f, 0.0f,
                                      -2.0f,  0.0f, 0.0f, };


    static int const g_vertsperface[5] = { 3, 3, 3, 3, 4 };

    static int const g_nfaces = 5;
    static int const g_faceverts[16] = { 0, 1, 2,
                                         0, 2, 3,
                                         0, 3, 4,
                                         0, 4, 1,
                                         4, 3, 2, 1 };

    static int const g_ncreases = 4;
    static int const g_creaseverts[8] = { 4, 3, 3, 2, 2, 1, 1, 4 };
    static float const g_creaseweights[4] = { 3.0f, 3.0f, 3.0f, 3.0f };

    // Creates a Far::TopologyRefiner from the pyramid shape above
    static Far::TopologyRefiner * createTopologyRefiner();

    //------------------------------------------------------------------------------
    // Vertex container implementation.
    //
    struct Vertex {

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

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

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

        float point[3];
    };

    //------------------------------------------------------------------------------
    // Limit frame container implementation -- this interface is not strictly
    // required but follows a similar pattern to Vertex.
    //
    struct LimitFrame {

        void Clear( void * =0 ) {
             point[0] =  point[1] =  point[2] = 0.0f;
            deriv1[0] = deriv1[1] = deriv1[2] = 0.0f;
            deriv2[0] = deriv2[1] = deriv2[2] = 0.0f;
        }

        void AddWithWeight(Vertex const & src,
            float weight, float d1Weight, float d2Weight) {

            point[0] += weight * src.point[0];
            point[1] += weight * src.point[1];
            point[2] += weight * src.point[2];

            deriv1[0] += d1Weight * src.point[0];
            deriv1[1] += d1Weight * src.point[1];
            deriv1[2] += d1Weight * src.point[2];

            deriv2[0] += d2Weight * src.point[0];
            deriv2[1] += d2Weight * src.point[1];
            deriv2[2] += d2Weight * src.point[2];
        }

        float point[3],
              deriv1[3],
              deriv2[3];
    };

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

        // Generate a FarTopologyRefiner (see far_tutorial_0 for details).
        Far::TopologyRefiner * refiner = createTopologyRefiner();

        // Adaptively refine the topology with an isolation level capped at 3
        // because the sharpest crease in the shape is 3.0f (in g_creaseweights[])
        int maxIsolation = 3;
        refiner->RefineAdaptive(
            Far::TopologyRefiner::AdaptiveOptions(maxIsolation));

        // Generate a set of Far::PatchTable that we will use to evaluate the
        // surface limit
        Far::PatchTableFactory::Options patchOptions;
        patchOptions.endCapType =
            Far::PatchTableFactory::Options::ENDCAP_GREGORY_BASIS;

        Far::PatchTable const * patchTable =
            Far::PatchTableFactory::Create(*refiner, patchOptions);

        // Compute the total number of points we need to evaluate patchtable.
        // we use local points around extraordinary features.
        int nRefinerVertices = refiner->GetNumVerticesTotal();
        int nLocalPoints = patchTable->GetNumLocalPoints();

        // Create a buffer to hold the position of the refined verts and
        // local points, then copy the coarse positions at the beginning.
        std::vector<Vertex> verts(nRefinerVertices + nLocalPoints);
        memcpy(&verts[0], g_verts, g_nverts*3*sizeof(float));

        // Interpolate vertex primvar data : they are the control vertices
        // of the limit patches (see far_tutorial_0 for details)
        Vertex * src = &verts[0];
        for (int level = 1; level <= maxIsolation; ++level) {
            Vertex * dst = src + refiner->GetLevel(level-1).GetNumVertices();
            Far::PrimvarRefiner(*refiner).Interpolate(level, src, dst);
            src = dst;
        }

        // Evaluate local points from interpolated vertex primvars.
        patchTable->ComputeLocalPointValues(&verts[0], &verts[nRefinerVertices]);

        // Create a Far::PatchMap to help locating patches in the table
        Far::PatchMap patchmap(*patchTable);

        // Create a Far::PtexIndices to help find indices of ptex faces.
        Far::PtexIndices ptexIndices(*refiner);

        // Generate random samples on each ptex face
        int nsamples = 200,
            nfaces = ptexIndices.GetNumFaces();

        std::vector<LimitFrame> samples(nsamples * nfaces);

        srand( static_cast<int>(2147483647) );

        float pWeights[20], dsWeights[20], dtWeights[20];

        for (int face=0, count=0; face<nfaces; ++face) {

            for (int sample=0; sample<nsamples; ++sample, ++count) {

                float s = (float)rand()/(float)RAND_MAX,
                      t = (float)rand()/(float)RAND_MAX;

                // Locate the patch corresponding to the face ptex idx and (s,t)
                Far::PatchTable::PatchHandle const * handle =
                    patchmap.FindPatch(face, s, t);
                assert(handle);

                // Evaluate the patch weights, identify the CVs and compute the limit frame:
                patchTable->EvaluateBasis(*handle, s, t, pWeights, dsWeights, dtWeights);

                Far::ConstIndexArray cvs = patchTable->GetPatchVertices(*handle);

                LimitFrame & dst = samples[count];
                dst.Clear();
                for (int cv=0; cv < cvs.size(); ++cv) {
                    dst.AddWithWeight(verts[cvs[cv]], pWeights[cv], dsWeights[cv], dtWeights[cv]);
                }

            }
        }

        { // Visualization with Maya : print a MEL script that generates particles
          // at the location of the limit vertices

            int nsamples = (int)samples.size();

            printf("file -f -new;\n");

            // Output particle positions for the tangent
            printf("particle -n deriv1 ");
            for (int sample=0; sample<nsamples; ++sample) {
                float const * pos = samples[sample].point;
                printf("-p %f %f %f\n", pos[0], pos[1], pos[2]);
            }
            printf(";\n");
            // Set per-particle direction using the limit tangent (display as 'Streak')
            printf("setAttr \"deriv1.particleRenderType\" 6;\n");
            printf("setAttr \"deriv1.velocity\" -type \"vectorArray\" %d ",nsamples);
            for (int sample=0; sample<nsamples; ++sample) {
                float const * tan1 = samples[sample].deriv1;
                printf("%f %f %f\n", tan1[0], tan1[1], tan1[2]);
            }
            printf(";\n");

            // Output particle positions for the bi-tangent
            printf("particle -n deriv2 ");
            for (int sample=0; sample<nsamples; ++sample) {
                float const * pos = samples[sample].point;
                printf("-p %f %f %f\n", pos[0], pos[1], pos[2]);
            }
            printf(";\n");
            printf("setAttr \"deriv2.particleRenderType\" 6;\n");
            printf("setAttr \"deriv2.velocity\" -type \"vectorArray\" %d ",nsamples);
            for (int sample=0; sample<nsamples; ++sample) {
                float const * tan2 = samples[sample].deriv2;
                printf("%f %f %f\n", tan2[0], tan2[1], tan2[2]);
            }
            printf(";\n");

            // Exercise to the reader : cross tangent & bi-tangent for limit
            // surface normal...

            // Force Maya DAG update to see the result in the viewport
            printf("currentTime -edit `currentTime -q`;\n");
            printf("select deriv1Shape deriv2Shape;\n");
        }

    }

    //------------------------------------------------------------------------------
    static Far::TopologyRefiner *
    createTopologyRefiner() {


        typedef Far::TopologyDescriptor Descriptor;

        Sdc::SchemeType type = OpenSubdiv::Sdc::SCHEME_CATMARK;

        Sdc::Options options;
        options.SetVtxBoundaryInterpolation(Sdc::Options::VTX_BOUNDARY_EDGE_ONLY);

        Descriptor desc;
        desc.numVertices = g_nverts;
        desc.numFaces = g_nfaces;
        desc.numVertsPerFace = g_vertsperface;
        desc.vertIndicesPerFace = g_faceverts;
        desc.numCreases = g_ncreases;
        desc.creaseVertexIndexPairs = g_creaseverts;
        desc.creaseWeights = g_creaseweights;

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

        return refiner;
    }