Fitting polynomial surfaces to triangular meshes with voronoi squared distance minimization

V. Nivoliers, D.M. Yan, B. Lévy
20th International Meshing Roundtable, pp. 601-618, (2011)

Fitting polynomial surfaces to triangular meshes with voronoi squared distance minimization

Keywords

Squared distance minimization, Centroidal Voronoi tessellation, Subdivision surface fitting

Abstract

​This paper introduces Voronoi squared distance minimization (VSDM), an algorithm that fits a surface to an input mesh. VSDM minimizes an objective function that corresponds to a Voronoi-based approximation of the overall squared distance function between the surface and the input mesh (SDM). This objective function is a generalization of the one minimized by centroidal Voronoi tessellation, and can be minimized by a quasi-Newton solver. VSDM naturally adapts the orientation of the mesh elements to best approximate the input, without estimating any differential quantities. Therefore, it can be applied to triangle soups or surfaces with degenerate triangles, topological noise and sharp features. Applications of fitting quad meshes and polynomial surfaces to input triangular meshes are demonstrated.

Code

DOI: 10.1007/s00366-012-0291-9

Sources

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