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///////////////////////////////////////////////////////////////////////////
//
// Copyright (c) 2012-2018 DreamWorks Animation LLC
//
// All rights reserved. This software is distributed under the
// Mozilla Public License 2.0 ( http://www.mozilla.org/MPL/2.0/ )
//
// Redistributions of source code must retain the above copyright
// and license notice and the following restrictions and disclaimer.
//
// * Neither the name of DreamWorks Animation nor the names of
// its contributors may be used to endorse or promote products derived
// from this software without specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY INDIRECT, INCIDENTAL,
// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
// IN NO EVENT SHALL THE COPYRIGHT HOLDERS' AND CONTRIBUTORS' AGGREGATE
// LIABILITY FOR ALL CLAIMS REGARDLESS OF THEIR BASIS EXCEED US$250.00.
//
///////////////////////////////////////////////////////////////////////////
/// @file unittest/TestPotentialFlow.cc
#include <cppunit/extensions/HelperMacros.h>
#include <openvdb/openvdb.h>
#include <openvdb/tools/LevelSetSphere.h>
#include <openvdb/tools/PotentialFlow.h>
class TestPotentialFlow: public CppUnit::TestCase
{
public:
CPPUNIT_TEST_SUITE(TestPotentialFlow);
CPPUNIT_TEST(testMask);
CPPUNIT_TEST(testNeumannVelocities);
CPPUNIT_TEST(testUniformStream);
CPPUNIT_TEST(testFlowAroundSphere);
CPPUNIT_TEST_SUITE_END();
void testMask();
void testNeumannVelocities();
void testUniformStream();
void testFlowAroundSphere();
};
CPPUNIT_TEST_SUITE_REGISTRATION(TestPotentialFlow);
void
TestPotentialFlow::testMask()
{
using namespace openvdb;
const float radius = 1.5f;
const Vec3f center(0.0f, 0.0f, 0.0f);
const float voxelSize = 0.25f;
const float halfWidth = 3.0f;
FloatGrid::Ptr sphere =
tools::createLevelSetSphere<FloatGrid>(radius, center, voxelSize, halfWidth);
const int dilation = 5;
MaskGrid::Ptr mask = tools::createPotentialFlowMask(*sphere, dilation);
MaskGrid::Ptr defaultMask = tools::createPotentialFlowMask(*sphere);
CPPUNIT_ASSERT(*mask == *defaultMask);
auto acc = mask->getAccessor();
// the isosurface of this sphere is at y = 6
// this mask forms a band dilated outwards from the isosurface by 5 voxels
CPPUNIT_ASSERT(!acc.isValueOn(Coord(0, 5, 0)));
CPPUNIT_ASSERT(acc.isValueOn(Coord(0, 6, 0)));
CPPUNIT_ASSERT(acc.isValueOn(Coord(0, 10, 0)));
CPPUNIT_ASSERT(!acc.isValueOn(Coord(0, 11, 0)));
{ // error on non-uniform voxel size
FloatGrid::Ptr nonUniformSphere =
tools::createLevelSetSphere<FloatGrid>(radius, center, voxelSize, halfWidth);
math::Transform::Ptr nonUniformTransform(new math::Transform(
math::MapBase::Ptr(new math::ScaleMap(Vec3d(0.1, 0.2, 0.3)))));
nonUniformSphere->setTransform(nonUniformTransform);
CPPUNIT_ASSERT_THROW(tools::createPotentialFlowMask(*nonUniformSphere, dilation),
openvdb::ValueError);
}
// this is the minimum mask of one voxel either side of the isosurface
mask = tools::createPotentialFlowMask(*sphere, 2);
acc = mask->getAccessor();
CPPUNIT_ASSERT(!acc.isValueOn(Coord(0, 5, 0)));
CPPUNIT_ASSERT(acc.isValueOn(Coord(0, 6, 0)));
CPPUNIT_ASSERT(acc.isValueOn(Coord(0, 7, 0)));
CPPUNIT_ASSERT(!acc.isValueOn(Coord(0, 8, 0)));
// these should all produce the same masks as the dilation value is clamped
MaskGrid::Ptr negativeMask = tools::createPotentialFlowMask(*sphere, -1);
MaskGrid::Ptr zeroMask = tools::createPotentialFlowMask(*sphere, 0);
MaskGrid::Ptr oneMask = tools::createPotentialFlowMask(*sphere, 1);
CPPUNIT_ASSERT(*negativeMask == *mask);
CPPUNIT_ASSERT(*zeroMask == *mask);
CPPUNIT_ASSERT(*oneMask == *mask);
}
void
TestPotentialFlow::testNeumannVelocities()
{
using namespace openvdb;
const float radius = 1.5f;
const Vec3f center(0.0f, 0.0f, 0.0f);
const float voxelSize = 0.25f;
const float halfWidth = 3.0f;
FloatGrid::Ptr sphere =
tools::createLevelSetSphere<FloatGrid>(radius, center, voxelSize, halfWidth);
MaskGrid::Ptr domain = tools::createPotentialFlowMask(*sphere);
{
// test identical potential from a wind velocity supplied through grid or background value
Vec3d windVelocityValue(0, 0, 10);
Vec3dTree::Ptr windTree(new Vec3dTree(sphere->tree(), zeroVal<Vec3d>(), TopologyCopy()));
dilateVoxels(*windTree, 2, tools::NN_FACE_EDGE_VERTEX);
windTree->voxelizeActiveTiles();
for (auto leaf = windTree->beginLeaf(); leaf; ++leaf) {
for (auto iter = leaf->beginValueOn(); iter; ++iter) {
iter.setValue(windVelocityValue);
}
}
Vec3dGrid::Ptr windGrid(Vec3dGrid::create(windTree));
windGrid->setTransform(sphere->transform().copy());
auto windPotentialFromGrid = tools::createPotentialFlowNeumannVelocities(
*sphere, *domain, windGrid, Vec3d(0));
CPPUNIT_ASSERT_EQUAL(windPotentialFromGrid->transform(), sphere->transform());
auto windPotentialFromBackground = tools::createPotentialFlowNeumannVelocities(
*sphere, *domain, Vec3dGrid::Ptr(), windVelocityValue);
auto accessor = windPotentialFromGrid->getConstAccessor();
auto accessor2 = windPotentialFromBackground->getConstAccessor();
CPPUNIT_ASSERT_EQUAL(windPotentialFromGrid->activeVoxelCount(),
windPotentialFromBackground->activeVoxelCount());
for (auto leaf = windPotentialFromGrid->tree().cbeginLeaf(); leaf; ++leaf) {
for (auto iter = leaf->cbeginValueOn(); iter; ++iter) {
CPPUNIT_ASSERT_EQUAL(accessor.isValueOn(iter.getCoord()),
accessor2.isValueOn(iter.getCoord()));
CPPUNIT_ASSERT_EQUAL(accessor.getValue(iter.getCoord()),
accessor2.getValue(iter.getCoord()));
}
}
// test potential from a wind velocity supplied through grid background value
Vec3dTree::Ptr emptyWindTree(
new Vec3dTree(sphere->tree(), windVelocityValue, TopologyCopy()));
Vec3dGrid::Ptr emptyWindGrid(Vec3dGrid::create(emptyWindTree));
emptyWindGrid->setTransform(sphere->transform().copy());
auto windPotentialFromGridBackground = tools::createPotentialFlowNeumannVelocities(
*sphere, *domain, emptyWindGrid, Vec3d(0));
CPPUNIT_ASSERT_EQUAL(windPotentialFromGridBackground->transform(), sphere->transform());
accessor = windPotentialFromGridBackground->getConstAccessor();
accessor2 = windPotentialFromBackground->getConstAccessor();
CPPUNIT_ASSERT_EQUAL(windPotentialFromGridBackground->activeVoxelCount(),
windPotentialFromBackground->activeVoxelCount());
for (auto leaf = windPotentialFromGridBackground->tree().cbeginLeaf(); leaf; ++leaf) {
for (auto iter = leaf->cbeginValueOn(); iter; ++iter) {
CPPUNIT_ASSERT_EQUAL(accessor.isValueOn(iter.getCoord()),
accessor2.isValueOn(iter.getCoord()));
CPPUNIT_ASSERT_EQUAL(accessor.getValue(iter.getCoord()),
accessor2.getValue(iter.getCoord()));
}
}
// test potential values are double when applying wind velocity
// through grid and background values
auto windPotentialFromBoth = tools::createPotentialFlowNeumannVelocities(
*sphere, *domain, windGrid, windVelocityValue);
tools::prune(windPotentialFromBoth->tree(), Vec3d(1e-3));
tools::prune(windPotentialFromBackground->tree(), Vec3d(1e-3));
accessor = windPotentialFromBoth->getConstAccessor();
accessor2 = windPotentialFromBackground->getConstAccessor();
for (auto leaf = windPotentialFromBoth->tree().cbeginLeaf(); leaf; ++leaf) {
for (auto iter = leaf->cbeginValueOn(); iter; ++iter) {
CPPUNIT_ASSERT_EQUAL(accessor.isValueOn(iter.getCoord()),
accessor2.isValueOn(iter.getCoord()));
CPPUNIT_ASSERT_EQUAL(accessor.getValue(iter.getCoord()),
accessor2.getValue(iter.getCoord()) * 2);
}
}
CPPUNIT_ASSERT(*windPotentialFromBoth == *windPotentialFromBackground);
}
Vec3dGrid::Ptr zeroVelocity = Vec3dGrid::create(Vec3d(0));
{ // error if grid is not a levelset
FloatGrid::Ptr nonLevelSetSphere =
tools::createLevelSetSphere<FloatGrid>(radius, center, voxelSize, halfWidth);
nonLevelSetSphere->setGridClass(GRID_FOG_VOLUME);
CPPUNIT_ASSERT_THROW(tools::createPotentialFlowNeumannVelocities(
*nonLevelSetSphere, *domain, zeroVelocity, Vec3d(5)), openvdb::TypeError);
}
{ // accept double level set grid
DoubleGrid::Ptr doubleSphere =
tools::createLevelSetSphere<DoubleGrid>(radius, center, voxelSize, halfWidth);
CPPUNIT_ASSERT_NO_THROW(tools::createPotentialFlowNeumannVelocities(
*doubleSphere, *domain, zeroVelocity, Vec3d(5)));
}
{ // zero boundary velocities and background velocity
Vec3d zeroVelocityValue(zeroVal<Vec3d>());
auto neumannVelocities = tools::createPotentialFlowNeumannVelocities(
*sphere, *domain, zeroVelocity, zeroVelocityValue);
CPPUNIT_ASSERT_EQUAL(neumannVelocities->activeVoxelCount(), Index64(0));
}
}
void
TestPotentialFlow::testUniformStream()
{
// this unit test checks the scalar potential and velocity flow field
// for a uniform stream which consists of a 100x100x100 cube of
// neumann voxels with constant velocity (0, 0, 1)
using namespace openvdb;
auto transform = math::Transform::createLinearTransform(1.0);
auto mask = MaskGrid::create(false);
mask->setTransform(transform);
auto maskAccessor = mask->getAccessor();
auto neumann = Vec3dGrid::create(Vec3d(0));
auto neumannAccessor = neumann->getAccessor();
for (int i = -50; i < 50; i++) {
for (int j = -50; j < 50; j++) {
for (int k = -50; k < 50; k++) {
Coord ijk(i, j, k);
maskAccessor.setValueOn(ijk, true);
neumannAccessor.setValueOn(ijk, Vec3d(0, 0, 1));
}
}
}
openvdb::math::pcg::State state = math::pcg::terminationDefaults<float>();
state.iterations = 2000;
state.absoluteError = 1e-8;
auto potential = tools::computeScalarPotential(*mask, *neumann, state);
// check convergence
CPPUNIT_ASSERT(state.success);
CPPUNIT_ASSERT(state.iterations > 0 && state.iterations < 1000);
CPPUNIT_ASSERT(state.absoluteError < 1e-6);
CPPUNIT_ASSERT_EQUAL(potential->activeVoxelCount(), mask->activeVoxelCount());
// for uniform flow along the z-axis, the scalar potential should be equal to the z co-ordinate
for (auto leaf = potential->tree().cbeginLeaf(); leaf; ++leaf) {
for (auto iter = leaf->cbeginValueOn(); iter; ++iter) {
const double staggeredZ = iter.getCoord().z() + 0.5;
CPPUNIT_ASSERT(math::isApproxEqual(iter.getValue(), staggeredZ, /*tolerance*/0.1));
}
}
auto flow = tools::computePotentialFlow(*potential, *neumann);
CPPUNIT_ASSERT_EQUAL(flow->activeVoxelCount(), mask->activeVoxelCount());
// flow velocity should be equal to the input velocity (0, 0, 1)
for (auto leaf = flow->tree().cbeginLeaf(); leaf; ++leaf) {
for (auto iter = leaf->cbeginValueOn(); iter; ++iter) {
CPPUNIT_ASSERT(math::isApproxEqual(iter.getValue().x(), 0.0, /*tolerance*/1e-6));
CPPUNIT_ASSERT(math::isApproxEqual(iter.getValue().y(), 0.0, /*tolerance*/1e-6));
CPPUNIT_ASSERT(math::isApproxEqual(iter.getValue().z(), 1.0, /*tolerance*/1e-6));
}
}
}
void
TestPotentialFlow::testFlowAroundSphere()
{
using namespace openvdb;
const float radius = 1.5f;
const Vec3f center(0.0f, 0.0f, 0.0f);
const float voxelSize = 0.25f;
const float halfWidth = 3.0f;
const int dilation = 50;
FloatGrid::Ptr sphere =
tools::createLevelSetSphere<FloatGrid>(radius, center, voxelSize, halfWidth);
MaskGrid::Ptr domain = tools::createPotentialFlowMask(*sphere, dilation);
{ // compute potential flow for a global wind velocity around a sphere
Vec3f windVelocity(0, 0, 1);
Vec3fGrid::Ptr neumann = tools::createPotentialFlowNeumannVelocities(*sphere,
*domain, Vec3fGrid::Ptr(), windVelocity);
openvdb::math::pcg::State state = math::pcg::terminationDefaults<float>();
state.iterations = 2000;
state.absoluteError = 1e-8;
FloatGrid::Ptr potential = tools::computeScalarPotential(*domain, *neumann, state);
// compute a laplacian of the potential within the domain (excluding neumann voxels)
// and ensure it evaluates to zero
auto mask = BoolGrid::create(/*background=*/false);
mask->setTransform(potential->transform().copy());
mask->topologyUnion(*potential);
auto dilatedSphereMask = tools::interiorMask(*sphere);
tools::dilateActiveValues(dilatedSphereMask->tree(), 1);
mask->topologyDifference(*dilatedSphereMask);
FloatGrid::Ptr laplacian = tools::laplacian(*potential, *mask);
for (auto leaf = laplacian->tree().cbeginLeaf(); leaf; ++leaf) {
for (auto iter = leaf->cbeginValueOn(); iter; ++iter) {
CPPUNIT_ASSERT(math::isApproxEqual(iter.getValue(), 0.0f, /*tolerance*/1e-3f));
}
}
Vec3fGrid::Ptr flowVel = tools::computePotentialFlow(*potential, *neumann);
// compute the divergence of the flow velocity within the domain
// (excluding neumann voxels and exterior voxels)
// and ensure it evaluates to zero
tools::erodeVoxels(mask->tree(), 2, tools::NN_FACE);
FloatGrid::Ptr divergence = tools::divergence(*flowVel, *mask);
for (auto leaf = divergence->tree().cbeginLeaf(); leaf; ++leaf) {
for (auto iter = leaf->cbeginValueOn(); iter; ++iter) {
CPPUNIT_ASSERT(math::isApproxEqual(iter.getValue(), 0.0f, /*tolerance*/0.1f));
}
}
// check the background velocity has been applied correctly
Vec3fGrid::Ptr flowVelBackground =
tools::computePotentialFlow(*potential, *neumann, windVelocity);
CPPUNIT_ASSERT_EQUAL(flowVelBackground->activeVoxelCount(),
flowVelBackground->activeVoxelCount());
auto maskAccessor = mask->getConstAccessor();
auto accessor = flowVel->getConstAccessor();
auto accessor2 = flowVelBackground->getConstAccessor();
for (auto leaf = flowVelBackground->tree().cbeginLeaf(); leaf; ++leaf) {
for (auto iter = leaf->cbeginValueOn(); iter; ++iter) {
// ignore values near the neumann boundary
if (!maskAccessor.isValueOn(iter.getCoord())) continue;
const Vec3f value1 = accessor.getValue(iter.getCoord());
const Vec3f value2 = accessor2.getValue(iter.getCoord()) + windVelocity;
CPPUNIT_ASSERT(math::isApproxEqual(value1.x(), value2.x(), /*tolerance=*/1e-3f));
CPPUNIT_ASSERT(math::isApproxEqual(value1.y(), value2.y(), /*tolerance=*/1e-3f));
CPPUNIT_ASSERT(math::isApproxEqual(value1.z(), value2.z(), /*tolerance=*/1e-3f));
}
}
}
{ // check double-precision solve
DoubleGrid::Ptr sphereDouble =
tools::createLevelSetSphere<DoubleGrid>(radius, center, voxelSize, halfWidth);
Vec3d windVelocity(0, 0, 1);
Vec3dGrid::Ptr neumann = tools::createPotentialFlowNeumannVelocities(*sphereDouble,
*domain, Vec3dGrid::Ptr(), windVelocity);
openvdb::math::pcg::State state = math::pcg::terminationDefaults<float>();
state.iterations = 2000;
state.absoluteError = 1e-8;
DoubleGrid::Ptr potential = tools::computeScalarPotential(*domain, *neumann, state);
CPPUNIT_ASSERT(potential);
// compute a laplacian of the potential within the domain (excluding neumann voxels)
// and ensure it evaluates to zero
auto mask = BoolGrid::create(/*background=*/false);
mask->setTransform(potential->transform().copy());
mask->topologyUnion(*potential);
auto dilatedSphereMask = tools::interiorMask(*sphereDouble);
tools::dilateActiveValues(dilatedSphereMask->tree(), 1);
mask->topologyDifference(*dilatedSphereMask);
DoubleGrid::Ptr laplacian = tools::laplacian(*potential, *mask);
for (auto leaf = laplacian->tree().cbeginLeaf(); leaf; ++leaf) {
for (auto iter = leaf->cbeginValueOn(); iter; ++iter) {
CPPUNIT_ASSERT(math::isApproxEqual(iter.getValue(), 0.0, /*tolerance*/1e-5));
}
}
Vec3dGrid::Ptr flowVel = tools::computePotentialFlow(*potential, *neumann);
CPPUNIT_ASSERT(flowVel);
}
}
// Copyright (c) 2012-2018 DreamWorks Animation LLC
// All rights reserved. This software is distributed under the
// Mozilla Public License 2.0 ( http://www.mozilla.org/MPL/2.0/ )
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