Fitting polynomial surfaces to triangular meshes with Voronoi Squared Distance Minimization

Vincent Nivoliers, Dongming Yan, Bruno L. Lévy

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Scopus citations

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 Centroidal Voronoi Tesselation (CVT), and can be minimized by a quasi-Newton solver. VSDM naturally adapts the orientation of the mesh 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.
Original languageEnglish (US)
Title of host publicationProceedings of the 20th International Meshing Roundtable, IMR 2011
Pages601-617
Number of pages17
DOIs
StatePublished - Dec 1 2011

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