UE::MeshDeformation::ConstructUniformLaplacian

Construct a sparse matrix representation of a uniform weighted Laplacian.

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MacOS
Linux

References

Module

DynamicMesh

Header

/Engine/Plugins/Experimental/GeometryProcessing/Source/DynamicMesh/Public/Solvers/LaplacianMatrixAssembly.h

Include

#include "Solvers/LaplacianMatrixAssembly.h"

Syntax

namespace UE
{
    namespace MeshDeformation
    {
        template<typename RealType>
        void UE::MeshDeformation::ConstructUniformLaplacian
        (
            const FDynamicMesh3 & DynamicMesh,
            const FVertexLinearization & VertexMap,
            UE::Solvers::TSparseMatrixAssembler< RealType > & LaplacianInterior,
            UE::Solvers::TSparseMatrixAssembler< RealType > & LaplacianBoundary
        )
    }
}

Remarks

Construct a sparse matrix representation of a uniform weighted Laplacian. The uniform weighted Laplacian is defined solely in terms of the connectivity of the mesh. Note, by construction this should be a symmetric matrix.

The mesh itself is assumed to have N interior vertices, and M boundary vertices.

Row i represents the Laplacian at vert_i, the non-zero entries correspond to the incident one-ring vertices vert_j.

L{ij} = 1 if vert_j is in the one-ring of vert_i L{ii} = -Sum{ L_{ij}, j != i}

LaplacianInterior * Vector_InteriorVerts + LaplacianBoundary * Vector_BoundaryVerts = Full Laplacian applied to interior vertices.

Implementations

Parameters

Parameter

Description

DynamicMesh

The triangle mesh

VertexMap

On return, 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, the laplacian operator that acts on the interior vertices: sparse N x N matrix

LaplacianBoundary

On return, the portion of the operator that acts on the boundary vertices: sparse N x M matrix

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