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Vertex Location Optimisation for Improved Remeshing

Authors: Yu-Kun Lai and Ralph R. Martin

DOI: 10.1016/j.gmod.2012.04.011

Abstract:

Remeshing aims to produce a more regular mesh from a given input mesh, while representing the original geometry as accurately as possible. Many existing remeshing methods focus on where to place new mesh vertices; these samples are placed exactly on the input mesh. However, considering the output mesh as a piecewise linear approximation of some geometry, this simple scheme leads to significant systematic error in non-planar regions. Here, we use parameterised meshes and the recent mathematical development of orthogonal approximation using Sobolev-type inner products to develop a novel sampling scheme which allows vertices to lie in space near the input surface, rather than exactly on it. The algorithm requires little extra computational effort and can be readily incorporated into many remeshing approaches. Experimental results show that on average, approximation error can be reduced by 40% with the same number of vertices.

Link to Paper

Authors

Prof. Ralph Martin

Prof. Ralph Martin

Polygon mesh processing including registration, noise removal, segmentation and surface fitting.