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API > API/Plugins > API/Plugins/DynamicMesh > API/Plugins/DynamicMesh/Solvers > API/Plugins/DynamicMesh/Solvers/UE__MeshDeformation__ConstructCo-
References
| Module | DynamicMesh |
| Header | /Engine/Plugins/Runtime/GeometryProcessing/Source/DynamicMesh/Public/Solvers/LaplacianMatrixAssembly.h |
| Include | #include "Solvers/LaplacianMatrixAssembly.h" |
namespace UE
{
namespace MeshDeformation
{
template<typename RealType>
void UE&58;&58;MeshDeformation&58;&58;ConstructCotangentLaplacian
&40;
const FDynamicMesh3 & DynamicMesh,
const FVertexLinearization & VertexMap,
UE::Solvers::TSparseMatrixAssembler< RealType > & LaplacianInterior,
UE::Solvers::TSparseMatrixAssembler< RealType > & LaplacianBoundary,
const bool bClampWeights
&41;
}
}
Remarks
Construct a sparse matrix representation using a pre-multiplied cotangent-weighted Laplacian. NB: 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.
Parameters
| Name | 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 |