OpenVDB 5.1.0

Classes | Namespaces | Macros | Typedefs
PoissonSolver.h File Reference

Solve Poisson's equation ∇2x = b for x, where b is a vector comprising the values of all of the active voxels in a grid. More...

`#include <openvdb/Types.h>`
`#include <openvdb/math/ConjGradient.h>`
`#include <openvdb/tree/LeafManager.h>`
`#include <openvdb/tree/Tree.h>`
`#include <openvdb/util/NullInterrupter.h>`
`#include "Morphology.h"`

Go to the source code of this file.

## Classes
struct | DirichletBoundaryOp< ValueType >
| Dirichlet boundary condition functor. More...
struct | LeafCountOp< LeafType >
| Functor for use with LeafManager::foreach() to populate an array with per-leaf active voxel counts. More...
struct | LeafIndexOp< LeafType >
| Functor for use with LeafManager::foreach() to populate active leaf voxels with sequential indices. More...
struct | CopyToVecOp< VectorValueType, SourceTreeType >
| Functor for use with LeafManager::foreach() to populate a vector with the values of a tree's active voxels. More...
struct | CopyFromVecOp< TreeValueType, VIndexTreeType, VectorValueType >
| Functor for use with LeafManager::foreach() to populate a tree with values from a vector. More...
struct | ISStaggeredLaplacianOp< BoolTreeType, BoundaryOp >
| Functor for use with LeafManager::foreach() to populate a sparse Laplacian matrix. More...
struct | ISLaplacianOp< VIdxTreeT, BoundaryOp >
| Functor for use with LeafManager::foreach() to populate a sparse Laplacian matrix. More...

## Namespaces
| openvdb
| openvdb::v5_1
| openvdb::v5_1::tools
| openvdb::v5_1::tools::poisson
| openvdb::v5_1::tools::poisson::internal

## Macros
#define | OPENVDB_TOOLS_POISSON_LAPLACIAN_STENCIL 2

## Typedefs
using | VIndex = Int32
using | LaplacianMatrix = math::pcg::SparseStencilMatrix< double, 7 >
| The type of a matrix used to represent a three-dimensional Laplacian operator. More...

## Functions
template<typename TreeType >
TreeType::Ptr | solve (const TreeType &, math::pcg::State &, bool staggered=false)
| Solve ∇2x = b for x, where b is a vector comprising the values of all of the active voxels in the input tree. More...
template<typename TreeType , typename Interrupter >
TreeType::Ptr | solve (const TreeType &, math::pcg::State &, Interrupter &, bool staggered=false)
| Solve ∇2x = b for x, where b is a vector comprising the values of all of the active voxels in the input tree. More...
template<typename TreeType , typename BoundaryOp , typename Interrupter >
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 values of all of the active voxels in the input tree or domain mask if provided. More...
template<typename PreconditionerType , typename TreeType , typename BoundaryOp , typename Interrupter >
TreeType::Ptr | solveWithBoundaryConditionsAndPreconditioner (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 values of all of the active voxels in the input tree or domain mask if provided. More...
template<typename PreconditionerType , typename TreeType , typename DomainTreeType , typename BoundaryOp , typename Interrupter >
TreeType::Ptr | solveWithBoundaryConditionsAndPreconditioner (const TreeType &, const DomainTreeType &, 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 values of all of the active voxels in the input tree or domain mask if provided. More...
Low-level functions
template<typename VIndexTreeType >
void | populateIndexTree (VIndexTreeType &)
| Overwrite each active voxel in the given scalar tree with a sequential index, starting from zero. More...
template<typename TreeType >
TreeType::template ValueConverter< VIndex >::Type::Ptr | createIndexTree (const TreeType &)
| Iterate over the active voxels of the input tree and for each one assign its index in the iteration sequence to the corresponding voxel of an integer-valued output tree. More...
template<typename VectorValueType , typename SourceTreeType >
math::pcg::Vector< VectorValueType >::Ptr | createVectorFromTree (const SourceTreeType &source, const typename SourceTreeType::template ValueConverter< VIndex >::Type &index)
| Return a vector of the active voxel values of the scalar-valued source tree. More...
template<typename TreeValueType , typename VIndexTreeType , typename VectorValueType >
VIndexTreeType::template ValueConverter< TreeValueType >::Type::Ptr | createTreeFromVector (const math::pcg::Vector< VectorValueType > &values, const VIndexTreeType &index, const TreeValueType &background)
| Return a tree with the same active voxel topology as the index tree but whose voxel values are taken from the the given vector. More...
template<typename BoolTreeType >
LaplacianMatrix::Ptr | createISLaplacian (const typename BoolTreeType::template ValueConverter< VIndex >::Type &vectorIndexTree, const BoolTreeType &interiorMask, bool staggered=false)
| Generate a sparse matrix of the index-space (Δx = 1) Laplacian operator using second-order finite differences. More...
template<typename BoolTreeType , typename BoundaryOp >
LaplacianMatrix::Ptr | createISLaplacianWithBoundaryConditions (const typename BoolTreeType::template ValueConverter< VIndex >::Type &vectorIndexTree, const BoolTreeType &interiorMask, const BoundaryOp &boundaryOp, typename math::pcg::Vector< LaplacianMatrix::ValueType > &source, bool staggered=false)
| Generate a sparse matrix of the index-space (Δx = 1) Laplacian operator with user-specified boundary conditions using second-order finite differences. More...

## Detailed Description

Solve Poisson's equation ∇2x = b for x, where b is a vector comprising the values of all of the active voxels in a grid.

Authors
  D.J. Hill, Peter Cucka

Example:
  Solve for the pressure in a cubic tank of liquid, assuming uniform boundary conditions:
  FloatTree source(/*background=*/0.0f);
  // Activate voxels to indicate that they contain liquid.
  source.fill(CoordBBox(Coord(0, -10, 0), Coord(10, 0, 10)), /*value=*/0.0f);
  math::pcg::State state = math::pcg::terminationDefaults<float>();
  FloatTree::Ptr solution = tools::poisson::solve(source, state);

Example:
  Solve for the pressure, P, in a cubic tank of liquid that is open at the top. Boundary conditions are P = 0 at the top, ∂P/∂y = −1 at the bottom and ∂P/∂x = 0 at the sides:

                     P = 0
                  +--------+ (N,0,N)
                 /|       /|
        (0,0,0) +--------+ |
                | |      | | dP/dx = 0
      dP/dx = 0 | +------|-+
                |/       |/
       (0,-N,0) +--------+ (N,-N,0)
                dP/dy = -1

  const int N = 10;
  DoubleTree source(/*background=*/0.0);
  // Activate voxels to indicate that they contain liquid.
  source.fill(CoordBBox(Coord(0, -N, 0), Coord(N, 0, N)), /*value=*/0.0);
  auto boundary = [](const openvdb::Coord& ijk, const openvdb::Coord& neighbor,
  double& source, double& diagonal)
  {
  if (neighbor.x() == ijk.x() && neighbor.z() == ijk.z()) {
  if (neighbor.y() < ijk.y()) source -= 1.0;
  else diagonal -= 1.0;
  }
  };
  math::pcg::State state = math::pcg::terminationDefaults<double>();
  util::NullInterrupter interrupter;
  DoubleTree::Ptr solution = tools::poisson::solveWithBoundaryConditions(
  source, boundary, state, interrupter);

## Macro Definition Documentation

## ◆ OPENVDB_TOOLS_POISSON_LAPLACIAN_STENCIL

#define OPENVDB_TOOLS_POISSON_LAPLACIAN_STENCIL 2