File Exchange

## Fast Loop mesh subdivision

version 1.5.0.0 (5.32 KB) by
Subdivide a surface mesh, using Loop subdivision. Boundary- and shape-maintaining

Updated 16 Aug 2017

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].

*ROOM FOR IMPROVEMENT*
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...

References
[1] Loop, C 1987. "Smooth subdivision surfaces based on triangles." M.S. Mathematics thesis, University of Utah. http://research.microsoft.com/en-us/um/people/cloop/thesis.pdf

### Cite As

Dylan Muir (2020). Fast Loop mesh subdivision (https://www.mathworks.com/matlabcentral/fileexchange/32727-fast-loop-mesh-subdivision), MATLAB Central File Exchange. Retrieved .

Albert Pun

Exactly what I wanted

Dylan Muir

Alec Jacobson

This code uses for loops (parallelized with parfor) over the mesh elements. A much faster alternative avoiding for loops can be found here: https://github.com/alecjacobson/gptoolbox see `mesh/loop.m`

Anton Semechko

This function gets the job done a lot faster than another Loop subdivision function on FEX: http://www.mathworks.com/matlabcentral/fileexchange/24942-loop-subdivision . Great job Dylan!

Dylan Muir

Hi Naive, the vertex order depends on the underlying triangulation functions, which are not under my control.

naive

Hi Dylan,
This is a quite useful function. Thanks so much! However, when I plot the mfRefinedMesh, I feel that the vertices of a triangle are not always in the same order, either all in clockwise or counterclockwise, but I am not 100% percent sure. Am I right?

Dylan Muir

Hi Dun,

I would be happy to include your improvements if you send them to me; my email address is my last name at hifo.uzh.ch

Regards,
Dylan

Dun Kirk

Update:
After adding a few tricks, it takes only 0.861 seconds from 223 triangles to 228352 triangles (5x subdivisions).

Dun Kirk

Making use of the Matlab embedded data structure: TriRep could make this a lot faster. This function took 206.36 seconds subdividing 122 triangles to 124928 triangles (5 times subdivision). I did it in 2.2 seconds with TriRep.

Dylan Muir

Hi Jaroslaw,

The Loop subdivision algorithm provides mesh smoothing and refinement:
http://en.wikipedia.org/wiki/Loop_subdivision_surface

Certainly the original mesh points are not preserved. That's not how the algorithm works.

Regards,
Dylan

Jaroslaw Tuszynski

This function does not seem to work for me. The output mesh does not resemble much the input mesh. I was expecting that all the original points would be preserved, but that is not the case.