|
Module |
|
|
Header |
/Engine/Plugins/Experimental/GeometryProcessing/Source/DynamicMesh/Public/Solvers/LaplacianMatrixAssembly.h |
|
Include |
#include "Solvers/LaplacianMatrixAssembly.h" |
namespace UE
{
namespace MeshDeformation
{
template<typename RealType>
void UE::MeshDeformation::ConstructCotangentLaplacian
(
const FDynamicMesh3 & DynamicMesh,
const FVertexLinearization & VertexMap,
UE::Solvers::TSparseMatrixAssembler< RealType > & LaplacianInterior,
UE::Solvers::TSparseMatrixAssembler< RealType > & LaplacianBoundary,
const bool bClampWeights
)
}
}
Construct a sparse matrix representation using a pre-multiplied cotangent-weighted Laplacian.
there is no reason to expect this to be a symmetric matrix. This computes the laplacian scaled by the average area A_ave: ie. LScaled = A_ave/(2A_i) ( Cot alpha_ij + Cot beta_ij )
The mesh itself is assumed to have N interior vertices, and M boundary vertices.
LaplacianInterior * Vector_InteriorVerts + LaplacianBoundary * Vector_BoundaryVerts = Full Laplacian applied to interior vertices.
|
Parameter |
Description |
|---|---|
|
DynamicMesh |
The triangle mesh |
|
VertexMap |
Additional arrays used to map between vertexID and offset in a linear array (i.e. the row). The vertices are ordered so that last M ( = VertexMap.NumBoundaryVerts() ) correspond to those on the boundary. |
|
LaplacianInterior |
On return, scaled laplacian operator that acts on the interior vertices: sparse N x N matrix |
|
LaplacianBoundary |
On return, scaled portion of the operator that acts on the boundary vertices: sparse N x M matrix |
|
bClampAreas |
Indicates if (A_ave / A_i) should be clamped to (0.5, 5) range. in practice this is desirable when creating the biharmonic operator, but not the mean curvature flow operator |