https://github.com/PixarAnimationStudios/OpenSubdiv/blob/release/tutorials/far/tutorial_5_1/far_tutorial_5_1.cpp

//------------------------------------------------------------------------------
// 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;

typedef double Real;

// pyramid geometry from catmark_pyramid_crease0.h
static int const g_nverts = 5;
static Real  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, Real weight) {
        point[0] += weight * src.point[0];
        point[1] += weight * src.point[1];
        point[2] += weight * src.point[2];
    }

    Real 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,
        Real weight, Real d1Weight, Real 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];
    }

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

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

    // Generate a Far::TopologyRefiner (see tutorial_1_1 for details).
    Far::TopologyRefiner * refiner = createTopologyRefiner();

    // Patches are constructed from adaptively refined faces, but the processes
    // of constructing the PatchTable and of applying adaptive refinement have
    // historically been separate.  Adaptive refinement is applied purely to
    // satisfy the needs of the desired PatchTable, so options associated with
    // adaptive refinement should be derived from those specified for the
    // PatchTable.  This is not a strict requirement, but it will avoid
    // problems arising from specifying/coordinating the two independently
    // (especially when dealing with face-varying patches).

    // Initialize options for the PatchTable:
    //
    // Choose patches adaptively refined to level 3 since the sharpest crease
    // in the shape is 3.0f (in g_creaseweights[]), and include the inf-sharp
    // crease option just to illustrate the need to syncronize options.
    //
    int maxPatchLevel = 3;

    Far::PatchTableFactory::Options patchOptions(maxPatchLevel);
    patchOptions.SetPatchPrecision<Real>();
    patchOptions.useInfSharpPatch = true;
    patchOptions.generateVaryingTables = false;
    patchOptions.endCapType =
        Far::PatchTableFactory::Options::ENDCAP_GREGORY_BASIS;

    // Initialize corresonding options for adaptive refinement:
    Far::TopologyRefiner::AdaptiveOptions adaptiveOptions(maxPatchLevel);

    bool assignAdaptiveOptionsExplicitly = false;
    if (assignAdaptiveOptionsExplicitly) {
        adaptiveOptions.useInfSharpPatch = true;
    } else {
        // Be sure patch options were intialized with the desired max level
        adaptiveOptions = patchOptions.GetRefineAdaptiveOptions();
    }
    assert(adaptiveOptions.useInfSharpPatch == patchOptions.useInfSharpPatch);

    // Apply adaptive refinement and construct the associated PatchTable to
    // evaluate the limit surface:
    refiner->RefineAdaptive(adaptiveOptions);

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

    // Compute the total number of points we need to evaluate the PatchTable.
    // Approximations at irregular or extraordinary features require the use
    // of additional points associated with the patches that are referred to
    // as "local points" (i.e. local to the PatchTable).
    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);
    std::memcpy(&verts[0], g_verts, g_nverts*3*sizeof(Real));

    // Adaptive refinement may result in fewer levels than the max specified.
    int nRefinedLevels = refiner->GetNumLevels();

    // Interpolate vertex primvar data : they are the control vertices
    // of the limit patches (see tutorial_1_1 for details)
    Far::PrimvarRefinerReal<Real> primvarRefiner(*refiner);

    Vertex * src = &verts[0];
    for (int level = 1; level < nRefinedLevels; ++level) {
        Vertex * dst = src + refiner->GetLevel(level-1).GetNumVertices();
        primvarRefiner.Interpolate(level, src, dst);
        src = dst;
    }

    // Evaluate local points from interpolated vertex primvars.
    if (nLocalPoints) {
        patchTable->GetLocalPointStencilTable<Real>()->UpdateValues(
            &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 nsamplesPerFace = 200,
        nfaces = ptexIndices.GetNumFaces();

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

    srand( static_cast<int>(2147483647) );

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

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

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

            Real s = (Real)rand()/(Real)RAND_MAX,
                 t = (Real)rand()/(Real)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) {
            Real 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) {
            Real 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) {
            Real 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) {
            Real 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");
    }

    delete refiner;
    delete patchTable;
    return EXIT_SUCCESS;
}

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

    return refiner;
}