Fitting polynomial surfaces to triangular meshes with Voronoi squared distance minimization

Handle URI:
http://hdl.handle.net/10754/564627
Title:
Fitting polynomial surfaces to triangular meshes with Voronoi squared distance minimization
Authors:
Nivoliers, Vincent; Yan, Dongming ( 0000-0003-2209-2404 ) ; Lévy, Bruno L.
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. © 2012 Springer-Verlag London.
KAUST Department:
Visual Computing Center (VCC)
Publisher:
Springer Science + Business Media
Journal:
Engineering with Computers
Issue Date:
6-Nov-2012
DOI:
10.1007/s00366-012-0291-9
Type:
Article
ISSN:
01770667
Sponsors:
The authors wish to thank Sylvain Lefebvre for a discussion (about an unrelated topic) that inspired this work, Rhaleb Zayer, Xavier Goaoc, Tamy Boubekeur, Yang Liu and Wenping Wang for many discussions, Loic Marechal, Marc Loriot and the AimAtShape repository for data. This project is partly supported by the European Research Council grant GOODSHAPE ERC-StG-205693 and ANR/NSFC (60625202,60911130368) Program (SHAN Project).
Appears in Collections:
Articles; Visual Computing Center (VCC)

Full metadata record

DC FieldValue Language
dc.contributor.authorNivoliers, Vincenten
dc.contributor.authorYan, Dongmingen
dc.contributor.authorLévy, Bruno L.en
dc.date.accessioned2015-08-04T07:05:28Zen
dc.date.available2015-08-04T07:05:28Zen
dc.date.issued2012-11-06en
dc.identifier.issn01770667en
dc.identifier.doi10.1007/s00366-012-0291-9en
dc.identifier.urihttp://hdl.handle.net/10754/564627en
dc.description.abstractThis 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. © 2012 Springer-Verlag London.en
dc.description.sponsorshipThe authors wish to thank Sylvain Lefebvre for a discussion (about an unrelated topic) that inspired this work, Rhaleb Zayer, Xavier Goaoc, Tamy Boubekeur, Yang Liu and Wenping Wang for many discussions, Loic Marechal, Marc Loriot and the AimAtShape repository for data. This project is partly supported by the European Research Council grant GOODSHAPE ERC-StG-205693 and ANR/NSFC (60625202,60911130368) Program (SHAN Project).en
dc.publisherSpringer Science + Business Mediaen
dc.subjectCentroidal Voronoi tessellationen
dc.subjectSquared distance minimizationen
dc.subjectSubdivision surface fittingen
dc.titleFitting polynomial surfaces to triangular meshes with Voronoi squared distance minimizationen
dc.typeArticleen
dc.contributor.departmentVisual Computing Center (VCC)en
dc.identifier.journalEngineering with Computersen
dc.contributor.institutionProject ALICE/Institut National de Recherche en Informatique et en Automatique Nancy Grand-Est, LORIA, Nancy, Franceen
dc.contributor.institutionInstitut National Polytechnique de Lorraine (INPL), Nancy, Franceen
kaust.authorYan, Dongmingen
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