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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"`
`#include <openvdb/openvdb.h>`

Go to the source code of this file.

## Classes

struct | DirichletBoundaryOp< ValueType >
| Dirichlet boundary condition functor. More...

## Namespaces

namespace | openvdb
namespace | openvdb::v10_0
namespace | openvdb::v10_0::tools
namespace | openvdb::v10_0::tools::poisson

## Typedefs

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

## Functions

Low-level 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.
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.
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.
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, where b is a vector comprising the values of all of the active voxels in the input tree.
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, where b is a vector comprising the values of all of the active voxels in the input tree.
template<typename VIndexTreeType>
void | populateIndexTree (VIndexTreeType &)
| Overwrite each active voxel in the given scalar tree with a sequential index, starting from zero.
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.
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.
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.
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.
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.

## 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);
  openvdb::v10_0::math::Coord
  Signed (x, y, z) 32-bit integer coordinates.
  Definition Coord.h:25
  openvdb::v10_0::math::Coord::y
  Int32 y() const
  Definition Coord.h:131
  openvdb::v10_0::math::Coord::x
  Int32 x() const
  Definition Coord.h:130
  openvdb::v10_0::math::Coord::z
  Int32 z() const
  Definition Coord.h:132