Fitting polynomial surfaces to triangular meshes with Voronoi Squared Distance Minimization

Handle URI:
http://hdl.handle.net/10754/564480
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 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.
KAUST Department:
Visual Computing Center (VCC)
Journal:
Proceedings of the 20th International Meshing Roundtable, IMR 2011
Conference/Event name:
20th International Meshing Roundtable, IMR 2011
Issue Date:
1-Dec-2011
DOI:
10.1007/978-3-642-24734-7-33
Type:
Conference Paper
ISBN:
9783642247330
Appears in Collections:
Conference Papers; 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.accessioned2015-08-04T07:02:04Zen
dc.date.available2015-08-04T07:02:04Zen
dc.date.issued2011-12-01en
dc.identifier.isbn9783642247330en
dc.identifier.doi10.1007/978-3-642-24734-7-33en
dc.identifier.urihttp://hdl.handle.net/10754/564480en
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 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.en
dc.titleFitting polynomial surfaces to triangular meshes with Voronoi Squared Distance Minimizationen
dc.typeConference Paperen
dc.contributor.departmentVisual Computing Center (VCC)en
dc.identifier.journalProceedings of the 20th International Meshing Roundtable, IMR 2011en
dc.conference.date23 October 2011 through 26 October 2011en
dc.conference.name20th International Meshing Roundtable, IMR 2011en
dc.conference.locationParisen
dc.contributor.institutionProject ALICE, Institut National de Recherche en Informatique et en Automatique (INRIA) Nancy Grand Est, LORIA, Franceen
dc.contributor.institutionInstitut National Polytechnique de Lorraine (INPL), Franceen
kaust.authorYan, Dongmingen
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