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/// @file unittest/TestPoissonSolver.cc
/// @authors D.J. Hill, Peter Cucka

#include <cppunit/extensions/HelperMacros.h>
#include <openvdb/openvdb.h>
#include <openvdb/Types.h>
//#include <openvdb/math/Math.h> // for math::isApproxEqual()
#include <openvdb/math/ConjGradient.h> // for JacobiPreconditioner
#include <openvdb/tools/Composite.h> // for csgDifference/Union/Intersection
#include <openvdb/tools/LevelSetSphere.h> // for tools::createLevelSetSphere()
#include <openvdb/tools/LevelSetUtil.h> // for tools::sdfToFogVolume()
#include <openvdb/tools/MeshToVolume.h> // for createLevelSetBox()
#include <openvdb/tools/Morphology.h> // for tools::erodeVoxels()
#include <openvdb/tools/PoissonSolver.h>
#include <boost/math/constants/constants.hpp> // for boost::math::constants::pi
#include <cmath>


class TestPoissonSolver: public CppUnit::TestCase
{
public:
    CPPUNIT_TEST_SUITE(TestPoissonSolver);
    CPPUNIT_TEST(testIndexTree);
    CPPUNIT_TEST(testTreeToVectorToTree);
    CPPUNIT_TEST(testLaplacian);
    CPPUNIT_TEST(testSolve);
    CPPUNIT_TEST(testSolveWithBoundaryConditions);
    CPPUNIT_TEST(testSolveWithSegmentedDomain);
    CPPUNIT_TEST_SUITE_END();

    void testIndexTree();
    void testTreeToVectorToTree();
    void testLaplacian();
    void testSolve();
    void testSolveWithBoundaryConditions();
    void testSolveWithSegmentedDomain();
};

CPPUNIT_TEST_SUITE_REGISTRATION(TestPoissonSolver);


////////////////////////////////////////


void
TestPoissonSolver::testIndexTree()
{
    using namespace openvdb;
    using tools::poisson::VIndex;

    using VIdxTree = FloatTree::ValueConverter<VIndex>::Type;
    using LeafNodeType = VIdxTree::LeafNodeType;

    VIdxTree tree;
    /// @todo populate tree
    tree::LeafManager<const VIdxTree> leafManager(tree);

    VIndex testOffset = 0;
    for (size_t n = 0, N = leafManager.leafCount(); n < N; ++n) {
        const LeafNodeType& leaf = leafManager.leaf(n);
        for (LeafNodeType::ValueOnCIter it = leaf.cbeginValueOn(); it; ++it, testOffset++) {
            CPPUNIT_ASSERT_EQUAL(testOffset, *it);
        }
    }

    //if (testOffset != VIndex(tree.activeVoxelCount())) {
    //    std::cout << "--Testing offsetmap - "
    //              << testOffset<<" != "
    //              << tree.activeVoxelCount()
    //              << " has active tile count "
    //              << tree.activeTileCount()<<std::endl;
    //}

    CPPUNIT_ASSERT_EQUAL(VIndex(tree.activeVoxelCount()), testOffset);
}


void
TestPoissonSolver::testTreeToVectorToTree()
{
    using namespace openvdb;
    using tools::poisson::VIndex;

    using VIdxTree = FloatTree::ValueConverter<VIndex>::Type;

    FloatGrid::Ptr sphere = tools::createLevelSetSphere<FloatGrid>(
        /*radius=*/10.f, /*center=*/Vec3f(0.f), /*voxelSize=*/0.25f);
    tools::sdfToFogVolume(*sphere);
    FloatTree& inputTree = sphere->tree();

    const Index64 numVoxels = inputTree.activeVoxelCount();

    // Generate an index tree.
    VIdxTree::Ptr indexTree = tools::poisson::createIndexTree(inputTree);
    CPPUNIT_ASSERT(bool(indexTree));

    // Copy the values of the active voxels of the tree into a vector.
    math::pcg::VectorS::Ptr vec =
        tools::poisson::createVectorFromTree<float>(inputTree, *indexTree);
    CPPUNIT_ASSERT_EQUAL(math::pcg::SizeType(numVoxels), vec->size());

    {
        // Convert the vector back to a tree.
        FloatTree::Ptr inputTreeCopy = tools::poisson::createTreeFromVector(
            *vec, *indexTree, /*bg=*/0.f);

        // Check that voxel values were preserved.
        FloatGrid::ConstAccessor inputAcc = sphere->getConstAccessor();
        for (FloatTree::ValueOnCIter it = inputTreeCopy->cbeginValueOn(); it; ++it) {
            const Coord ijk = it.getCoord();
            //if (!math::isApproxEqual(*it, inputTree.getValue(ijk))) {
            //    std::cout << " value error " << *it << " "
            //        << inputTree.getValue(ijk) << std::endl;
            //}
            CPPUNIT_ASSERT_DOUBLES_EQUAL(inputAcc.getValue(ijk), *it, /*tolerance=*/1.0e-6);
        }
    }
}


void
TestPoissonSolver::testLaplacian()
{
    using namespace openvdb;
    using tools::poisson::VIndex;

    using VIdxTree = FloatTree::ValueConverter<VIndex>::Type;

    // For two different problem sizes, N = 8 and N = 20...
    for (int N = 8; N <= 20; N += 12) {
        // Construct an N x N x N volume in which the value of voxel (i, j, k)
        // is sin(i) * sin(j) * sin(k), using a voxel spacing of pi / N.
        const double delta = boost::math::constants::pi<double>() / N;
        FloatTree inputTree(/*background=*/0.f);
        Coord ijk(0);
        Int32 &i = ijk[0], &j = ijk[1], &k = ijk[2];
        for (i = 1; i < N; ++i) {
            for (j = 1; j < N; ++j) {
                for (k = 1; k < N; ++k) {
                    inputTree.setValue(ijk, static_cast<float>(
                        std::sin(delta * i) * std::sin(delta * j) * std::sin(delta * k)));
                }
            }
        }
        const Index64 numVoxels = inputTree.activeVoxelCount();

        // Generate an index tree.
        VIdxTree::Ptr indexTree = tools::poisson::createIndexTree(inputTree);
        CPPUNIT_ASSERT(bool(indexTree));

        // Copy the values of the active voxels of the tree into a vector.
        math::pcg::VectorS::Ptr source =
            tools::poisson::createVectorFromTree<float>(inputTree, *indexTree);
        CPPUNIT_ASSERT_EQUAL(math::pcg::SizeType(numVoxels), source->size());

        // Create a mask of the interior voxels of the source tree.
        BoolTree interiorMask(/*background=*/false);
        interiorMask.fill(CoordBBox(Coord(2), Coord(N-2)), /*value=*/true, /*active=*/true);

        // Compute the Laplacian of the source:
        //     D^2 sin(i) * sin(j) * sin(k) = -3 sin(i) * sin(j) * sin(k)
        tools::poisson::LaplacianMatrix::Ptr laplacian =
            tools::poisson::createISLaplacian(*indexTree, interiorMask, /*staggered=*/true);
        laplacian->scale(1.0 / (delta * delta)); // account for voxel spacing
        CPPUNIT_ASSERT_EQUAL(math::pcg::SizeType(numVoxels), laplacian->size());

        math::pcg::VectorS result(source->size());
        laplacian->vectorMultiply(*source, result);

        // Dividing the result by the source should produce a vector of uniform value -3.
        // Due to finite differencing, the actual ratio will be somewhat different, though.
        const math::pcg::VectorS& src = *source;
        const float expected = // compute the expected ratio using one of the corner voxels
            float((3.0 * src[1] - 6.0 * src[0]) / (delta * delta * src[0]));
        for (math::pcg::SizeType n = 0; n < result.size(); ++n) {
            result[n] /= src[n];
            CPPUNIT_ASSERT_DOUBLES_EQUAL(expected, result[n], /*tolerance=*/1.0e-4);
        }
    }
}


void
TestPoissonSolver::testSolve()
{
    using namespace openvdb;

    FloatGrid::Ptr sphere = tools::createLevelSetSphere<FloatGrid>(
        /*radius=*/10.f, /*center=*/Vec3f(0.f), /*voxelSize=*/0.25f);
    tools::sdfToFogVolume(*sphere);

    math::pcg::State result = math::pcg::terminationDefaults<float>();
    result.iterations = 100;
    result.relativeError = result.absoluteError = 1.0e-4;

    FloatTree::Ptr outTree = tools::poisson::solve(sphere->tree(), result);

    CPPUNIT_ASSERT(result.success);
    CPPUNIT_ASSERT(result.iterations < 60);
}


////////////////////////////////////////


namespace {

struct BoundaryOp {
    void operator()(const openvdb::Coord& ijk, const openvdb::Coord& neighbor,
        double& source, double& diagonal) const
    {
        if (neighbor.x() == ijk.x() && neighbor.z() == ijk.z()) {
            // Workaround for spurious GCC 4.8 -Wstrict-overflow warning:
            const openvdb::Coord::ValueType dy = (ijk.y() - neighbor.y());
            if (dy > 0) source -= 1.0;
            else diagonal -= 1.0;
        }
    }
};


template<typename TreeType>
void
doTestSolveWithBoundaryConditions()
{
    using namespace openvdb;

    using ValueType = typename TreeType::ValueType;

    // Solve for the pressure in a cubic tank of liquid that is open at the top.
    // Boundary conditions are P = 0 at the top, dP/dy = -1 at the bottom
    // and dP/dx = 0 at the sides.
    //
    //               P = 0
    //              +------+ (N,-1,N)
    //             /|     /|
    //   (0,-1,0) +------+ |
    //            | |    | | dP/dx = 0
    //  dP/dx = 0 | +----|-+
    //            |/     |/
    // (0,-N-1,0) +------+ (N,-N-1,0)
    //           dP/dy = -1

    const int N = 9;
    const ValueType zero = zeroVal<ValueType>();
    const double epsilon = math::Delta<ValueType>::value();

    TreeType source(/*background=*/zero);
    source.fill(CoordBBox(Coord(0, -N-1, 0), Coord(N, -1, N)), /*value=*/zero);

    math::pcg::State state = math::pcg::terminationDefaults<ValueType>();
    state.iterations = 100;
    state.relativeError = state.absoluteError = epsilon;

    util::NullInterrupter interrupter;

    typename TreeType::Ptr solution = tools::poisson::solveWithBoundaryConditions(
        source, BoundaryOp(), state, interrupter, /*staggered=*/true);

    CPPUNIT_ASSERT(state.success);
    CPPUNIT_ASSERT(state.iterations < 60);

    // Verify that P = -y throughout the solution space.
    for (typename TreeType::ValueOnCIter it = solution->cbeginValueOn(); it; ++it) {
        CPPUNIT_ASSERT_DOUBLES_EQUAL(
            double(-it.getCoord().y()), double(*it), /*tolerance=*/10.0 * epsilon);
    }
}

} // unnamed namespace


void
TestPoissonSolver::testSolveWithBoundaryConditions()
{
    doTestSolveWithBoundaryConditions<openvdb::FloatTree>();
    doTestSolveWithBoundaryConditions<openvdb::DoubleTree>();
}


namespace {

openvdb::FloatGrid::Ptr
newCubeLS(
    const int outerLength, // in voxels
    const int innerLength, // in voxels
    const openvdb::Vec3I& centerIS, // in index space
    const float dx, // grid spacing
    bool openTop)
{
    using namespace openvdb;

    using BBox = math::BBox<Vec3f>;

    // World space dimensions and center for this box
    const float outerWS = dx * float(outerLength);
    const float innerWS = dx * float(innerLength);
    Vec3f centerWS(centerIS);
    centerWS *= dx;

    // Construct world space bounding boxes
    BBox outerBBox(
        Vec3f(-outerWS / 2, -outerWS / 2, -outerWS / 2),
        Vec3f( outerWS / 2,  outerWS / 2,  outerWS / 2));
    BBox innerBBox;
    if (openTop) {
        innerBBox = BBox(
            Vec3f(-innerWS / 2, -innerWS / 2, -innerWS / 2),
            Vec3f( innerWS / 2,  innerWS / 2,  outerWS));
    } else {
        innerBBox = BBox(
            Vec3f(-innerWS / 2, -innerWS / 2, -innerWS / 2),
            Vec3f( innerWS / 2,  innerWS / 2,  innerWS / 2));
    }
    outerBBox.translate(centerWS);
    innerBBox.translate(centerWS);

    math::Transform::Ptr xform = math::Transform::createLinearTransform(dx);
    FloatGrid::Ptr cubeLS = tools::createLevelSetBox<FloatGrid>(outerBBox, *xform);
    FloatGrid::Ptr inside = tools::createLevelSetBox<FloatGrid>(innerBBox, *xform);
    tools::csgDifference(*cubeLS, *inside);

    return cubeLS;
}


class LSBoundaryOp
{
public:
    LSBoundaryOp(const openvdb::FloatTree& lsTree): mLS(&lsTree) {}
    LSBoundaryOp(const LSBoundaryOp& other): mLS(other.mLS) {}

    void operator()(const openvdb::Coord& ijk, const openvdb::Coord& neighbor,
        double& source, double& diagonal) const
    {
        // Doing nothing is equivalent to imposing dP/dn = 0 boundary condition

        if (neighbor.x() == ijk.x() && neighbor.y() == ijk.y()) { // on top or bottom
            if (mLS->getValue(neighbor) <= 0.f) {
                // closed boundary
                source -= 1.0;
            } else {
                // open boundary
                diagonal -= 1.0;
            }
        }
    }

private:
    const openvdb::FloatTree* mLS;
};

} // unnamed namespace


void
TestPoissonSolver::testSolveWithSegmentedDomain()
{
    // In fluid simulations, incompressibility is enforced by the pressure, which is
    // computed as a solution of a Poisson equation.  Often, procedural animation
    // of objects (e.g., characters) interacting with liquid will result in boundary
    // conditions that describe multiple disjoint regions: regions of free surface flow
    // and regions of trapped fluid.  It is this second type of region for which
    // there may be no consistent pressure (e.g., a shrinking watertight region
    // filled with incompressible liquid).
    //
    // This unit test demonstrates how to use a level set and topological tools
    // to separate the well-posed problem of a liquid with a free surface
    // from the possibly ill-posed problem of fully enclosed liquid regions.
    //
    // For simplicity's sake, the physical boundaries are idealized as three
    // non-overlapping cubes, one with an open top and two that are fully closed.
    // All three contain incompressible liquid (x), and one of the closed cubes
    // will be partially filled so that two of the liquid regions have a free surface
    // (Dirichlet boundary condition on one side) while the totally filled cube
    // would have no free surface (Neumann boundary conditions on all sides).
    //                              ________________        ________________
    //      __            __       |   __________   |      |   __________   |
    //     |  |x x x x x |  |      |  |          |  |      |  |x x x x x |  |
    //     |  |x x x x x |  |      |  |x x x x x |  |      |  |x x x x x |  |
    //     |  |x x x x x |  |      |  |x x x x x |  |      |  |x x x x x |  |
    //     |   ——————————   |      |   ——————————   |      |   ——————————   |
    //     |________________|      |________________|      |________________|
    //
    // The first two regions are clearly well-posed, while the third region
    // may have no solution (or multiple solutions).
    // -D.J.Hill

    using namespace openvdb;

    using PreconditionerType =
        math::pcg::IncompleteCholeskyPreconditioner<tools::poisson::LaplacianMatrix>;

    // Grid spacing
    const float dx = 0.05f;

    // Construct the solid boundaries in a single grid.
    FloatGrid::Ptr solidBoundary;
    {
        // Create three non-overlapping cubes.
        const int outerDim = 41;
        const int innerDim = 31;
        FloatGrid::Ptr
            openDomain = newCubeLS(outerDim, innerDim, /*ctr=*/Vec3I(0, 0, 0), dx, /*open=*/true),
            closedDomain0 = newCubeLS(outerDim, innerDim, /*ctr=*/Vec3I(60, 0, 0), dx, false),
            closedDomain1 = newCubeLS(outerDim, innerDim, /*ctr=*/Vec3I(120, 0, 0), dx, false);

        // Union all three cubes into one grid.
        tools::csgUnion(*openDomain, *closedDomain0);
        tools::csgUnion(*openDomain, *closedDomain1);

        // Strictly speaking the solidBoundary level set should be rebuilt
        // (with tools::levelSetRebuild()) after the csgUnions to insure a proper
        // signed distance field, but we will forgo the rebuild in this example.
        solidBoundary = openDomain;
    }

    // Generate the source for the Poisson solver.
    // For a liquid simulation this will be the divergence of the velocity field
    // and will coincide with the liquid location.
    //
    // We activate by hand cells in distinct solution regions.

    FloatTree source(/*background=*/0.f);

    // The source is active in the union of the following "liquid" regions:

    // Fill the open box.
    const int N = 15;
    CoordBBox liquidInOpenDomain(Coord(-N, -N, -N), Coord(N, N, N));
    source.fill(liquidInOpenDomain, 0.f);

    // Totally fill closed box 0.
    CoordBBox liquidInClosedDomain0(Coord(-N, -N, -N), Coord(N, N, N));
    liquidInClosedDomain0.translate(Coord(60, 0, 0));
    source.fill(liquidInClosedDomain0, 0.f);

    // Half fill closed box 1.
    CoordBBox liquidInClosedDomain1(Coord(-N, -N, -N), Coord(N, N, 0));
    liquidInClosedDomain1.translate(Coord(120, 0, 0));
    source.fill(liquidInClosedDomain1, 0.f);

    // Compute the number of voxels in the well-posed region of the source.
    const Index64 expectedWellPosedVolume =
        liquidInOpenDomain.volume() + liquidInClosedDomain1.volume();

    // Generate a mask that defines the solution domain.
    // Inactive values of the source map to false and active values map to true.
    const BoolTree totalSourceDomain(source, /*inactive=*/false, /*active=*/true, TopologyCopy());

    // Extract the "interior regions" from the solid boundary.
    // The result will correspond to the the walls of the boxes unioned with inside of the full box.
    const BoolTree::ConstPtr interiorMask = tools::extractEnclosedRegion(
        solidBoundary->tree(), /*isovalue=*/float(0), &totalSourceDomain);

    // Identify the well-posed part of the problem.
    BoolTree wellPosedDomain(source, /*inactive=*/false, /*active=*/true, TopologyCopy());
    wellPosedDomain.topologyDifference(*interiorMask);
    CPPUNIT_ASSERT_EQUAL(expectedWellPosedVolume, wellPosedDomain.activeVoxelCount());

    // Solve the well-posed Poisson equation.

    const double epsilon = math::Delta<float>::value();
    math::pcg::State state = math::pcg::terminationDefaults<float>();
    state.iterations = 200;
    state.relativeError = state.absoluteError = epsilon;

    util::NullInterrupter interrupter;

    // Define boundary conditions that are consistent with solution = 0
    // at the liquid/air boundary and with a linear response with depth.
    LSBoundaryOp boundaryOp(solidBoundary->tree());

    // Compute the solution
    FloatTree::Ptr wellPosedSolutionP =
        tools::poisson::solveWithBoundaryConditionsAndPreconditioner<PreconditionerType>(
            source, wellPosedDomain, boundaryOp, state, interrupter, /*staggered=*/true);

    CPPUNIT_ASSERT_EQUAL(expectedWellPosedVolume, wellPosedSolutionP->activeVoxelCount());
    CPPUNIT_ASSERT(state.success);
    CPPUNIT_ASSERT(state.iterations < 68);

    // Verify that the solution is linear with depth.
    for (FloatTree::ValueOnCIter it = wellPosedSolutionP->cbeginValueOn(); it; ++it) {
        Index32 depth;
        if (liquidInOpenDomain.isInside(it.getCoord())) {
            depth = 1 + liquidInOpenDomain.max().z() - it.getCoord().z();
        } else {
            depth = 1 + liquidInClosedDomain1.max().z() - it.getCoord().z();
        }
        CPPUNIT_ASSERT_DOUBLES_EQUAL(double(depth), double(*it), /*tolerance=*/10.0 * epsilon);
    }

#if 0
    // Optionally, one could attempt to compute the solution in the enclosed regions.
    {
        // Identify the potentially ill-posed part of the problem.
        BoolTree illPosedDomain(source, /*inactive=*/false, /*active=*/true, TopologyCopy());
        illPosedDomain.topologyIntersection(source);

        // Solve the Poisson equation in the two unconnected regions.
        FloatTree::Ptr illPosedSoln =
            tools::poisson::solveWithBoundaryConditionsAndPreconditioner<PreconditionerType>(
                source, illPosedDomain, LSBoundaryOp(*solidBoundary->tree()),
                state, interrupter, /*staggered=*/true);
    }
#endif
}

// Copyright (c) 2012-2017 DreamWorks Animation LLC
// All rights reserved. This software is distributed under the
// Mozilla Public License 2.0 ( http://www.mozilla.org/MPL/2.0/ )
