ImFusion::MeshInterpolation Namespace Reference

Functions for interpolating scalar functions on mesh surfaces. More...

Detailed Description

Functions for interpolating scalar functions on mesh surfaces.

Enumerations
enum class	LaplaceInterpolationMethod { ZeroLaplaceAtUnknownPoints , MinimizeLaplaceAtAllPoints }
	Interpolation methods described in: [1] https://doi.org/10.1016/0021-9991(89)90103-4. More...

Functions
Eigen::MatrixXd	laplaceInterpolation (const Eigen::SparseMatrix< double > &laplacian, const std::vector< int > &idsKnown, const Eigen::MatrixXd &valuesKnown, LaplaceInterpolationMethod method)
	Interpolates values from the vertices with idsKnown to all vertices using one of the two methods described in https://doi.org/10.1016/0021-9991(89)90103-4.
Eigen::SparseMatrix< double >	laplaceInterpolationMatrix (const Eigen::SparseMatrix< double > &laplacian, const std::vector< int > &idsKnown, LaplaceInterpolationMethod method)
	Returns a sparse matrix that interpolates values from the vertices with idsKnown to all vertices using one of the two methods described in https://doi.org/10.1016/0021-9991(89)90103-4.

Enumeration Type Documentation

LaplaceInterpolationMethod

enum class LaplaceInterpolationMethod

strong

Interpolation methods described in: [1] https://doi.org/10.1016/0021-9991(89)90103-4.

Enumerator
ZeroLaplaceAtUnknownPoints	Method A in [1].
MinimizeLaplaceAtAllPoints	Method B in [1].

Function Documentation

laplaceInterpolation()

Eigen::MatrixXd laplaceInterpolation	(	const Eigen::SparseMatrix< double > &	laplacian,
		const std::vector< int > &	idsKnown,
		const Eigen::MatrixXd &	valuesKnown,
		LaplaceInterpolationMethod	method )

Interpolates values from the vertices with idsKnown to all vertices using one of the two methods described in https://doi.org/10.1016/0021-9991(89)90103-4.

laplacian must be the mesh's discrete Laplace operator. Returns an empty matrix on failure. This example shows how to use this function to interpolate vertex positions from known to all other vertices:

Mesh& mesh = ...;
std::vector<int> idsKnown = ...;
auto laplacian = MeshLaplacian(mesh).getLaplacian();
matX3 values = Eigen::Map<const mat3X>(mesh.verticesPointer()->data(), 3, mesh.numberOfVertices()).transpose();
matX3 valuesKnown = vertices(Eigen::Map<vecXi>(idsKnown.data(), idsKnown.size()), Eigen::all);
matX3 valuesInterp = laplaceInterpolation(laplacian, idsKnown, valuesKnown,
                                          LaplaceInterpolationMethod::ZeroLaplaceAtUnknownPoints);
mesh.beginUpdate();
for (int i = 0; i < valuesInterp.rows(); ++i)
    mesh.setVertex(i, valuesInterp.row(i));
mesh.computeVertexNormals();
mesh.endUpdate();

laplaceInterpolationMatrix()

Eigen::SparseMatrix< double > laplaceInterpolationMatrix	(	const Eigen::SparseMatrix< double > &	laplacian,
		const std::vector< int > &	idsKnown,
		LaplaceInterpolationMethod	method )

Returns a sparse matrix that interpolates values from the vertices with idsKnown to all vertices using one of the two methods described in https://doi.org/10.1016/0021-9991(89)90103-4.

laplacian must be the mesh's discrete Laplace operator. Returns an empty matrix on failure. This example shows how to use this function to interpolate vertex positions from known to all other vertices:

Mesh& mesh = ...;
std::vector<int> idsKnown = ...;
auto laplacian = MeshLaplacian(mesh).getLaplacian();
matX3 values = Eigen::Map<const mat3X>(mesh.verticesPointer()->data(), 3, mesh.numberOfVertices()).transpose();
matX3 valuesKnown = vertices(Eigen::Map<vecXi>(idsKnown.data(), idsKnown.size()), Eigen::all);
auto interpMat = laplaceInterpolationMatrix(laplacian, idsKnown,
                                            LaplaceInterpolationMethod::ZeroLaplaceAtUnknownPoints);
matX3 valuesInterp = interpMat * valuesKnown;
mesh.beginUpdate();
for (int i = 0; i < valuesInterp.rows(); ++i)
    mesh.setVertex(i, valuesInterp.row(i));
mesh.computeVertexNormals();
mesh.endUpdate();