Fitting quad surfaces to complex shapes using Voronoi Squared distance minimization.

Vincent Nivoliers and Dong-Ming Yan and Bruno Levy. ( 2011 )
in: Proc. 31st Gocad Meeting, Nancy

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 Voronoibased 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 anisotropy of the surface to the input mesh, without estimating any differential quantities. Therefore it can be applied to triangle soups or surfaces with degenerate triangles, topological noise and sharp features. Applications to fitting quad meshes, triangle-based and quadrangle-based subdivision surfaces are demonstrated. The results are evaluated using standard metrics.

Download / Links

BibTeX Reference

@inproceedings{NivoliersGM2011,
 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 Voronoibased 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 anisotropy of the surface to the input mesh, without estimating any differential quantities. Therefore it can be applied to triangle soups or surfaces with degenerate triangles, topological noise and sharp features.
Applications to fitting quad meshes, triangle-based and quadrangle-based subdivision surfaces are demonstrated. The results are evaluated using standard metrics. },
 author = { Nivoliers, Vincent AND Yan, Dong-Ming AND Levy, Bruno },
 booktitle = { Proc. 31st Gocad Meeting, Nancy },
 title = { Fitting quad surfaces to complex shapes using Voronoi Squared distance minimization. },
 year = { 2011 }
}