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Fast Loop mesh subdivision

version (5.32 KB) by Dylan Muir
Subdivide a surface mesh, using Loop subdivision. Boundary- and shape-maintaining


Updated 16 Aug 2017

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Usage: [mfRefinedMesh, mnTriangulation] = LoopSubdivisionLimited( mfMeshPoints, mnTriangulation, fMinResolution, vbBoundaryEdges)

This function sub-divides surface meshes, using the Loop subdivision algorithm [1]. This algorithm is based on B-spline curve continuity, leading to good shape-maintaining smoothing of a surface. The algorithm attempts to leave the boundary of the surface essentially undistorted.
'mfMeshPoints' is an Nx3 matrix, each row of which ['x' 'y' 'z'] defines a point in three-dimensional space. 'mnTriangulation' is a Mx3 matrix, each row of which ['m' 'n' 'p'] defines a triangle existing on the surface, where 'm', 'n' and 'p' are indices into 'mfMeshPoints'.
'fMinResolution' defines the desired minimum length of an edge in the final subdivision. Edges shorter than 'fMinResolution' will not be divided further.

The optional argument 'vbBoundaryEdges' identifies which edges should be treated as boundary edges (and so should their locations should be attempted to be maintained by the algorithm). This argument will be calculated by the algortihm, if it is not supplied.

'mfRefinedMesh' will be a Px3 matrix, each row of which specifies a vertex in the subdivided mesh. 'mnTringulation' will be a Rx3 matrix, each row of which specifies a surface triangle in the subdivided mesh.

Algorithm from [1].

If you work out how to maintain the vertex and edge adjacency matrices through a full subdivision run, then great! That would speed up subsequent runs a great deal, since a lot of the time is spent computing the edge adjacency matrix...

[1] Loop, C 1987. "Smooth subdivision surfaces based on triangles." M.S. Mathematics thesis, University of Utah.

Cite As

Dylan Muir (2022). Fast Loop mesh subdivision (, MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2009a
Compatible with any release
Platform Compatibility
Windows macOS Linux

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