TY - GEN

T1 - Fitting polynomial surfaces to triangular meshes with Voronoi Squared Distance Minimization

AU - Nivoliers, Vincent

AU - Yan, Dongming

AU - Lévy, Bruno L.

N1 - KAUST Repository Item: Exported on 2020-10-01

PY - 2011/12/1

Y1 - 2011/12/1

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/564480

UR - http://www.scopus.com/inward/record.url?scp=84878929026&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-24734-7-33

DO - 10.1007/978-3-642-24734-7-33

M3 - Conference contribution

SN - 9783642247330

SP - 601

EP - 617

BT - Proceedings of the 20th International Meshing Roundtable, IMR 2011

ER -