OpenVDB: PotentialFlow.h Source File

OpenVDB 7.0.0

PotentialFlow.h
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1 // Copyright Contributors to the OpenVDB Project
2 // SPDX-License-Identifier: MPL-2.0
3
9
10 #ifndef OPENVDB_TOOLS_POTENTIAL_FLOW_HAS_BEEN_INCLUDED
11 #define OPENVDB_TOOLS_POTENTIAL_FLOW_HAS_BEEN_INCLUDED
12
13 #include <openvdb/openvdb.h>
14
15 #include "GridOperators.h"
16 #include "GridTransformer.h"
17 #include "Mask.h" // interiorMask
18 #include "Morphology.h" // dilateVoxels, erodeVoxels
19 #include "PoissonSolver.h"
20
21
22 namespace openvdb {
23 OPENVDB_USE_VERSION_NAMESPACE
24 namespace OPENVDB_VERSION_NAME {
25 namespace tools {
26
28 template<typename VecGridT>
29 struct VectorToScalarGrid {
30 using Type =
31 typename VecGridT::template ValueConverter<typename VecGridT::ValueType::value_type>::Type;
32 using Ptr = typename Type::Ptr;
33 using ConstPtr = typename Type::ConstPtr;
34 };
35
36
42 template<typename GridT, typename MaskT = typename GridT::template ValueConverter<ValueMask>::Type>
43 inline typename MaskT::Ptr
44 createPotentialFlowMask(const GridT& grid, int dilation = 5);
45
46
56 template<typename Vec3T, typename GridT, typename MaskT>
57 inline typename GridT::template ValueConverter<Vec3T>::Type::Ptr
58 createPotentialFlowNeumannVelocities(const GridT& collider, const MaskT& domain,
59 const typename GridT::template ValueConverter<Vec3T>::Type::ConstPtr boundaryVelocity,
60 const Vec3T& backgroundVelocity);
61
62
74 template<typename Vec3GridT, typename MaskT, typename InterrupterT = util::NullInterrupter>
75 inline typename VectorToScalarGrid<Vec3GridT>::Ptr
76 computeScalarPotential(const MaskT& domain, const Vec3GridT& neumann, math::pcg::State& state,
77 InterrupterT* interrupter = nullptr);
78
79
86 template<typename Vec3GridT>
87 inline typename Vec3GridT::Ptr
88 computePotentialFlow(const typename VectorToScalarGrid<Vec3GridT>::Type& potential,
89 const Vec3GridT& neumann,
90 const typename Vec3GridT::ValueType backgroundVelocity =
91 zeroVal<typename Vec3GridT::TreeType::ValueType>());
92
93
95
96
97 namespace potential_flow_internal {
98
99
101 // helper function for retrieving a mask that comprises the outer-most layer of voxels
102 template<typename GridT>
103 inline typename GridT::TreeType::template ValueConverter<ValueMask>::Type::Ptr
104 extractOuterVoxelMask(GridT& inGrid)
105 {
106 using MaskTreeT = typename GridT::TreeType::template ValueConverter<ValueMask>::Type;
107 typename MaskTreeT::Ptr interiorMask(new MaskTreeT(inGrid.tree(), false, TopologyCopy()));
108 typename MaskTreeT::Ptr boundaryMask(new MaskTreeT(inGrid.tree(), false, TopologyCopy()));
109
110 erodeVoxels(*interiorMask, 1, NN_FACE);
111 boundaryMask->topologyDifference(*interiorMask);
112 return boundaryMask;
113 }
114
115
116 // computes Neumann velocities through sampling the gradient and velocities
117 template<typename Vec3GridT, typename GradientT>
118 struct ComputeNeumannVelocityOp
119 {
120 using ValueT = typename Vec3GridT::ValueType;
121 using VelocityAccessor = typename Vec3GridT::ConstAccessor;
122 using VelocitySamplerT = GridSampler<
123 typename Vec3GridT::ConstAccessor, BoxSampler>;
124 using GradientValueT = typename GradientT::TreeType::ValueType;
125
126 ComputeNeumannVelocityOp( const GradientT& gradient,
127 const Vec3GridT& velocity,
128 const ValueT& backgroundVelocity)
129 : mGradient(gradient)
130 , mVelocity(&velocity)
131 , mBackgroundVelocity(backgroundVelocity) { }
132
133 ComputeNeumannVelocityOp( const GradientT& gradient,
134 const ValueT& backgroundVelocity)
135 : mGradient(gradient)
136 , mBackgroundVelocity(backgroundVelocity) { }
137
138 void operator()(typename Vec3GridT::TreeType::LeafNodeType& leaf, size_t) const {
139 auto gradientAccessor = mGradient.getConstAccessor();
140
141 std::unique_ptr<VelocityAccessor> velocityAccessor;
142 std::unique_ptr<VelocitySamplerT> velocitySampler;
143 if (mVelocity) {
144 velocityAccessor.reset(new VelocityAccessor(mVelocity->getConstAccessor()));
145 velocitySampler.reset(new VelocitySamplerT(*velocityAccessor, mVelocity->transform()));
146 }
147
148 for (auto it = leaf.beginValueOn(); it; ++it) {
149 Coord ijk = it.getCoord();
150 auto gradient = gradientAccessor.getValue(ijk);
151 if (gradient.normalize()) {
152 const Vec3d xyz = mGradient.transform().indexToWorld(ijk);
153 const ValueT sampledVelocity = velocitySampler ?
154 velocitySampler->wsSample(xyz) : zeroVal<ValueT>();
155 auto velocity = sampledVelocity + mBackgroundVelocity;
156 auto value = gradient.dot(velocity) * gradient;
157 it.setValue(value);
158 }
159 else {
160 it.setValueOff();
161 }
162 }
163 }
164
165 private:
166 const GradientT& mGradient;
167 const Vec3GridT* mVelocity = nullptr;
168 const ValueT& mBackgroundVelocity;
169 }; // struct ComputeNeumannVelocityOp
170
171
172 // initalizes the boundary conditions for use in the Poisson Solver
173 template<typename Vec3GridT, typename MaskT>
174 struct SolveBoundaryOp
175 {
176 SolveBoundaryOp(const Vec3GridT& velGrid, const MaskT& domainGrid)
177 : mVoxelSize(domainGrid.voxelSize()[0])
178 , mVelGrid(velGrid)
179 , mDomainGrid(domainGrid)
180 { }
181
182 void operator()(const Coord& ijk, const Coord& neighbor,
183 double& source, double& diagonal) const {
184
185 typename Vec3GridT::ConstAccessor velGridAccessor = mVelGrid.getAccessor();
186 const Coord diff = (ijk - neighbor);
187
188 if (velGridAccessor.isValueOn(ijk)) { // Neumann
189 const typename Vec3GridT::ValueType& sampleVel = velGridAccessor.getValue(ijk);
190 source += mVoxelSize*diff[0]*sampleVel[0];
191 source += mVoxelSize*diff[1]*sampleVel[1];
192 source += mVoxelSize*diff[2]*sampleVel[2];
193 } else {
194 diagonal -= 1; // Zero Dirichlet
195 }
196
197 }
198
199 const double mVoxelSize;
200 const Vec3GridT& mVelGrid;
201 const MaskT& mDomainGrid;
202 }; // struct SolveBoundaryOp
203
204
205 } // namespace potential_flow_internal
206
207
209
210 template<typename GridT, typename MaskT>
211 inline typename MaskT::Ptr
212 createPotentialFlowMask(const GridT& grid, int dilation)
213 {
214 using MaskTreeT = typename MaskT::TreeType;
215
216 if (!grid.hasUniformVoxels()) {
217 OPENVDB_THROW(ValueError, "Transform must have uniform voxels for Potential Flow mask.");
218 }
219
220 // construct a new mask grid representing the interior region
221 auto interior = interiorMask(grid);
222
223 // create a new mask grid from the interior topology
224 typename MaskTreeT::Ptr maskTree(new MaskTreeT(interior->tree(), false, TopologyCopy()));
225 typename MaskT::Ptr mask = MaskT::create(maskTree);
226 mask->setTransform(grid.transform().copy());
227
228 dilateActiveValues(*maskTree, dilation, NN_FACE_EDGE);
229
230 // subtract the interior region from the mask to leave just the exterior narrow band
231 mask->tree().topologyDifference(interior->tree());
232
233 return mask;
234 }
235
236
237 template<typename Vec3T, typename GridT, typename MaskT>
238 typename GridT::template ValueConverter<Vec3T>::Type::Ptr createPotentialFlowNeumannVelocities(
239 const GridT& collider,
240 const MaskT& domain,
241 const typename GridT::template ValueConverter<Vec3T>::Type::ConstPtr boundaryVelocity,
242 const Vec3T& backgroundVelocity)
243 {
244 using Vec3GridT = typename GridT::template ValueConverter<Vec3T>::Type;
245 using TreeT = typename Vec3GridT::TreeType;
246 using ValueT = typename TreeT::ValueType;
247 using GradientT = typename ScalarToVectorConverter<GridT>::Type;
248
249 using potential_flow_internal::ComputeNeumannVelocityOp;
250
251 // this method requires the collider to be a level set to generate the gradient
252 // use the tools::topologyToLevelset() method if you need to convert a mask into a level set
253 if (collider.getGridClass() != GRID_LEVEL_SET ||
254 !std::is_floating_point<typename GridT::TreeType::ValueType>::value) {
255 OPENVDB_THROW(TypeError, "Potential Flow expecting the collider to be a level set.");
256 }
257
258 // empty grid if there are no velocities
259 if (backgroundVelocity == zeroVal<Vec3T>() &&
260 (!boundaryVelocity || boundaryVelocity->empty())) {
261 auto neumann = Vec3GridT::create();
262 neumann->setTransform(collider.transform().copy());
263 return neumann;
264 }
265
266 // extract the intersection between the collider and the domain
267 using MaskTreeT = typename GridT::TreeType::template ValueConverter<ValueMask>::Type;
268 typename MaskTreeT::Ptr boundary(new MaskTreeT(domain.tree(), false, TopologyCopy()));
269 boundary->topologyIntersection(collider.tree());
270
271 typename TreeT::Ptr neumannTree(new TreeT(*boundary, zeroVal<ValueT>(), TopologyCopy()));
272 neumannTree->voxelizeActiveTiles();
273
274 // compute the gradient from the collider
275 const typename GradientT::Ptr gradient = tools::gradient(collider);
276
277 typename tree::LeafManager<TreeT> leafManager(*neumannTree);
278
279 if (boundaryVelocity && !boundaryVelocity->empty()) {
280 ComputeNeumannVelocityOp<Vec3GridT, GradientT>
281 neumannOp(*gradient, *boundaryVelocity, backgroundVelocity);
282 leafManager.foreach(neumannOp, false);
283 }
284 else {
285 ComputeNeumannVelocityOp<Vec3GridT, GradientT>
286 neumannOp(*gradient, backgroundVelocity);
287 leafManager.foreach(neumannOp, false);
288 }
289
290 // prune any inactive values
291 tools::pruneInactive(*neumannTree);
292
293 typename Vec3GridT::Ptr neumann(Vec3GridT::create(neumannTree));
294 neumann->setTransform(collider.transform().copy());
295
296 return neumann;
297 }
298
299
300 template<typename Vec3GridT, typename MaskT, typename InterrupterT>
301 inline typename VectorToScalarGrid<Vec3GridT>::Ptr
302 computeScalarPotential(const MaskT& domain, const Vec3GridT& neumann,
303 math::pcg::State& state, InterrupterT* interrupter)
304 {
305 using ScalarT = typename Vec3GridT::ValueType::value_type;
306 using ScalarTreeT = typename Vec3GridT::TreeType::template ValueConverter<ScalarT>::Type;
307 using ScalarGridT = typename Vec3GridT::template ValueConverter<ScalarT>::Type;
308
309 using potential_flow_internal::SolveBoundaryOp;
310
311 // create the solution tree and activate using domain topology
312 ScalarTreeT solveTree(domain.tree(), zeroVal<ScalarT>(), TopologyCopy());
313 solveTree.voxelizeActiveTiles();
314
315 util::NullInterrupter nullInterrupt;
316 if (!interrupter) interrupter = &nullInterrupt;
317
318 // solve for scalar potential
319 SolveBoundaryOp<Vec3GridT, MaskT> solve(neumann, domain);
320 typename ScalarTreeT::Ptr potentialTree =
321 poisson::solveWithBoundaryConditions(solveTree, solve, state, *interrupter, true);
322
323 auto potential = ScalarGridT::create(potentialTree);
324 potential->setTransform(domain.transform().copy());
325
326 return potential;
327 }
328
329
330 template<typename Vec3GridT>
331 inline typename Vec3GridT::Ptr
332 computePotentialFlow(const typename VectorToScalarGrid<Vec3GridT>::Type& potential,
333 const Vec3GridT& neumann,
334 const typename Vec3GridT::ValueType backgroundVelocity)
335 {
336 using Vec3T = const typename Vec3GridT::ValueType;
337 using potential_flow_internal::extractOuterVoxelMask;
338
339 // The VDB gradient op uses the background grid value, which is zero by default, when
340 // computing the gradient at the boundary. This works at the zero-dirichlet boundaries, but
341 // give spurious values at Neumann ones as the potential should be non-zero there. To avoid
342 // the extra error, we just substitute the Neumann condition on the boundaries.
343 // Technically, we should allow for some tangential velocity, coming from the gradient of
344 // potential. However, considering the voxelized nature of our solve, a decent approximation
345 // to a tangential derivative isn't probably worth our time. Any tangential component will be
346 // found in the next interior ring of voxels.
347
348 auto gradient = tools::gradient(potential);
349
350 // apply Neumann values to the gradient
351
352 auto applyNeumann = [&gradient, &neumann] (
353 const MaskGrid::TreeType::LeafNodeType& leaf, size_t)
354 {
355 typename Vec3GridT::Accessor gradientAccessor = gradient->getAccessor();
356 typename Vec3GridT::ConstAccessor neumannAccessor = neumann.getAccessor();
357 for (auto it = leaf.beginValueOn(); it; ++it) {
358 const Coord ijk = it.getCoord();
359 typename Vec3GridT::ValueType value;
360 if (neumannAccessor.probeValue(ijk, value)) {
361 gradientAccessor.setValue(ijk, value);
362 }
363 }
364 };
365
366 const MaskGrid::TreeType::Ptr boundary = extractOuterVoxelMask(*gradient);
367 typename tree::LeafManager<const typename MaskGrid::TreeType> leafManager(*boundary);
368 leafManager.foreach(applyNeumann);
369
370 // apply the background value to the gradient if supplied
371
372 if (backgroundVelocity != zeroVal<Vec3T>()) {
373 auto applyBackgroundVelocity = [&backgroundVelocity] (
374 typename Vec3GridT::TreeType::LeafNodeType& leaf, size_t)
375 {
376 for (auto it = leaf.beginValueOn(); it; ++it) {
377 it.setValue(it.getValue() - backgroundVelocity);
378 }
379 };
380
381 typename tree::LeafManager<typename Vec3GridT::TreeType> leafManager2(gradient->tree());
382 leafManager2.foreach(applyBackgroundVelocity);
383 }
384
385 return gradient;
386 }
387
388
390
391 } // namespace tools
392 } // namespace OPENVDB_VERSION_NAME
393 } // namespace openvdb
394
395 #endif // OPENVDB_TOOLS_POTENTIAL_FLOW_HAS_BEEN_INCLUDED
openvdb::v7_0::math::pcg::State
Information about the state of a conjugate gradient solution.
Definition: ConjGradient.h:46
openvdb::v7_0::tools::VectorToScalarGrid::Type
typename VecGridT::template ValueConverter< typename VecGridT::ValueType::value_type >::Type Type
Definition: PotentialFlow.h:31
openvdb::v7_0::tools::VectorToScalarGrid
Metafunction to convert a vector-valued grid type to a scalar grid type.
Definition: PotentialFlow.h:29
openvdb::v7_0::tools::potential_flow_internal::SolveBoundaryOp::operator()
void operator()(const Coord &ijk, const Coord &neighbor, double &source, double &diagonal) const
Definition: PotentialFlow.h:182
openvdb::v7_0::tools::potential_flow_internal::SolveBoundaryOp::mVelGrid
const Vec3GridT & mVelGrid
Definition: PotentialFlow.h:200
openvdb::v7_0::tools::BoxSampler
Definition: Interpolation.h:119
openvdb::v7_0::tools::potential_flow_internal::SolveBoundaryOp
Definition: PotentialFlow.h:174
openvdb::v7_0::tools::computePotentialFlow
Vec3GridT::Ptr computePotentialFlow(const typename VectorToScalarGrid< Vec3GridT >::Type &potential, const Vec3GridT &neumann, const typename Vec3GridT::ValueType backgroundVelocity=zeroVal< typename Vec3GridT::TreeType::ValueType >())
Compute a vector Flow Field comprising the gradient of the potential with Neumann boundary conditions...
Definition: PotentialFlow.h:332
openvdb::v7_0::tools::NN_FACE
Definition: Morphology.h:60
openvdb::v7_0::tools::potential_flow_internal::ComputeNeumannVelocityOp
Definition: PotentialFlow.h:118
openvdb::v7_0::tree::LeafManager::foreach
void foreach(const LeafOp &op, bool threaded=true, size_t grainSize=1)
Threaded method that applies a user-supplied functor to each leaf node in the LeafManager.
Definition: LeafManager.h:496
openvdb::v7_0::tools::potential_flow_internal::SolveBoundaryOp::SolveBoundaryOp
SolveBoundaryOp(const Vec3GridT &velGrid, const MaskT &domainGrid)
Definition: PotentialFlow.h:176
openvdb::v7_0::math::Coord
Signed (x, y, z) 32-bit integer coordinates.
Definition: Coord.h:25
PoissonSolver.h
Solve Poisson's equation ∇2x = b for x, where b is a vector comprising the values of all of the act...
openvdb::v7_0::tools::erodeVoxels
void erodeVoxels(TreeType &tree, int iterations=1, NearestNeighbors nn=NN_FACE)
Topologically erode all leaf-level active voxels in the given tree.
Definition: Morphology.h:846
openvdb::v7_0::tools::potential_flow_internal::ComputeNeumannVelocityOp::ComputeNeumannVelocityOp
ComputeNeumannVelocityOp(const GradientT &gradient, const Vec3GridT &velocity, const ValueT &backgroundVelocity)
Definition: PotentialFlow.h:126
openvdb::v7_0::tools::potential_flow_internal::ComputeNeumannVelocityOp::operator()
void operator()(typename Vec3GridT::TreeType::LeafNodeType &leaf, size_t) const
Definition: PotentialFlow.h:138
openvdb::v7_0::tools::potential_flow_internal::SolveBoundaryOp::mVoxelSize
const double mVoxelSize
Definition: PotentialFlow.h:199
openvdb::v7_0::Grid::Ptr
SharedPtr< Grid > Ptr
Definition: Grid.h:574
openvdb::v7_0::tools::gradient
ScalarToVectorConverter< GridType >::Type::Ptr gradient(const GridType &grid, bool threaded, InterruptT *interrupt)
Compute the gradient of the given scalar grid.
Definition: GridOperators.h:996
openvdb::v7_0::tools::GridSampler
Class that provides the interface for continuous sampling of values in a tree.
Definition: Interpolation.h:283
openvdb::v7_0::tools::poisson::solveWithBoundaryConditions
TreeType::Ptr solveWithBoundaryConditions(const TreeType &, const BoundaryOp &, math::pcg::State &, Interrupter &, bool staggered=false)
Solve ∇2x = b for x with user-specified boundary conditions, where b is a vector comprising the val...
Definition: PoissonSolver.h:757
openvdb::v7_0::tools::ScalarToVectorConverter::Type
ScalarGridType::template ValueConverter< VectorValueT >::Type Type
Definition: GridOperators.h:41
openvdb::v7_0::math::Vec3d
Vec3< double > Vec3d
Definition: Vec3.h:662
openvdb::v7_0::util::NullInterrupter
Dummy NOOP interrupter class defining interface.
Definition: NullInterrupter.h:25
openvdb::v7_0::math::pcg::solve
State solve(const PositiveDefMatrix &A, const Vector< typename PositiveDefMatrix::ValueType > &b, Vector< typename PositiveDefMatrix::ValueType > &x, Preconditioner< typename PositiveDefMatrix::ValueType > &preconditioner, const State &termination=terminationDefaults< typename PositiveDefMatrix::ValueType >())
Solve Ax = b via the preconditioned conjugate gradient method.
Definition: ConjGradient.h:1612
GridOperators.h
Apply an operator to an input grid to produce an output grid with the same active voxel topology but ...
openvdb::v7_0::TypeError
Definition: Exceptions.h:64
openvdb::v7_0::tree::LeafManager
This class manages a linear array of pointers to a given tree's leaf nodes, as well as optional auxil...
Definition: LeafManager.h:82
openvdb::v7_0::TopologyCopy
Tag dispatch class that distinguishes topology copy constructors from deep copy constructors.
Definition: Types.h:681
openvdb::v7_0::tools::potential_flow_internal::ComputeNeumannVelocityOp::ComputeNeumannVelocityOp
ComputeNeumannVelocityOp(const GradientT &gradient, const ValueT &backgroundVelocity)
Definition: PotentialFlow.h:133
openvdb::v7_0::tools::potential_flow_internal::ComputeNeumannVelocityOp::GradientValueT
typename GradientT::TreeType::ValueType GradientValueT
Definition: PotentialFlow.h:124
Mask.h
Construct boolean mask grids from grids of arbitrary type.
openvdb::v7_0::tools::dilateActiveValues
void dilateActiveValues(TreeType &tree, int iterations=1, NearestNeighbors nn=NN_FACE, TilePolicy mode=PRESERVE_TILES)
Topologically dilate all active values (i.e. both voxels and tiles) in a tree using one of three near...
Definition: Morphology.h:1047
OPENVDB_USE_VERSION_NAMESPACE
#define OPENVDB_USE_VERSION_NAMESPACE
Definition: version.h:154
openvdb::v7_0::tools::potential_flow_internal::ComputeNeumannVelocityOp::VelocityAccessor
typename Vec3GridT::ConstAccessor VelocityAccessor
Definition: PotentialFlow.h:121
openvdb::v7_0::tools::potential_flow_internal::SolveBoundaryOp::mDomainGrid
const MaskT & mDomainGrid
Definition: PotentialFlow.h:201
openvdb::v7_0::tools::interiorMask
GridType::template ValueConverter< bool >::Type::Ptr interiorMask(const GridType &grid, const double isovalue=0.0)
Given an input grid of any type, return a new, boolean grid whose active voxel topology matches the i...
Definition: Mask.h:111
openvdb::v7_0::tools::VectorToScalarGrid::ConstPtr
typename Type::ConstPtr ConstPtr
Definition: PotentialFlow.h:33
GridTransformer.h
Morphology.h
Implementation of morphological dilation and erosion.
openvdb::v7_0::tools::potential_flow_internal::ComputeNeumannVelocityOp::ValueT
typename Vec3GridT::ValueType ValueT
Definition: PotentialFlow.h:120
OPENVDB_VERSION_NAME
#define OPENVDB_VERSION_NAME
The version namespace name for this library version.
Definition: version.h:102
openvdb::v7_0::ValueError
Definition: Exceptions.h:65
openvdb::v7_0::tools::VectorToScalarGrid::Ptr
typename Type::Ptr Ptr
Definition: PotentialFlow.h:32
openvdb::v7_0::GRID_LEVEL_SET
Definition: Types.h:454
openvdb::v7_0::tools::computeScalarPotential
VectorToScalarGrid< Vec3GridT >::Ptr computeScalarPotential(const MaskT &domain, const Vec3GridT &neumann, math::pcg::State &state, InterrupterT *interrupter=nullptr)
Compute the Potential on the domain using the Neumann boundary conditions on solid boundaries.
Definition: PotentialFlow.h:302
openvdb
Definition: Exceptions.h:13
openvdb::v7_0::tools::createPotentialFlowNeumannVelocities
GridT::template ValueConverter< Vec3T >::Type::Ptr createPotentialFlowNeumannVelocities(const GridT &collider, const MaskT &domain, const typename GridT::template ValueConverter< Vec3T >::Type::ConstPtr boundaryVelocity, const Vec3T &backgroundVelocity)
Create a Potential Flow velocities grid for the Neumann boundary.
Definition: PotentialFlow.h:238
openvdb::v7_0::tools::pruneInactive
void pruneInactive(TreeT &tree, bool threaded=true, size_t grainSize=1)
Reduce the memory footprint of a tree by replacing with background tiles any nodes whose values are a...
Definition: Prune.h:354
openvdb.h
OPENVDB_THROW
#define OPENVDB_THROW(exception, message)
Definition: Exceptions.h:82
openvdb::v7_0::tools::createPotentialFlowMask
MaskT::Ptr createPotentialFlowMask(const GridT &grid, int dilation=5)
Construct a mask for the Potential Flow domain.
Definition: PotentialFlow.h:212
openvdb::v7_0::tools::NN_FACE_EDGE
Definition: Morphology.h:60