Improved Algebraic Algorithm On Point Projection For Bézier Curves

Xiao-Diao Chen; Yin Zhou; Zhenyu Shu; Hua Su; Jean-Claude Paul

inria-00202457, version 1

Improved Algebraic Algorithm On Point Projection For Bézier Curves

Xiao-Diao Chen^a^, 1, Yin Zhou ², Zhenyu Shu ², Hua Su ³, Jean-Claude Paul^a^, 1

Second International Multi-Symposiums on Computer and Computational Sciences (IMSCCS 2007) (2007) 421-424

Résumé : This paper presents an improved algebraic pruning method for point projection for Bézier curves. It first turns the point projection into a root finding problem, and provides a simple but easily overlooked method to avoid finding invalid roots which is obviously irrelative to the closest point. The continued fraction method and its expansion are utilized to strengthen its robustness. Since NURBS curves can be easily turned into B´ezier form, the new method also works with NURBS curves. Examples are presented to illustrate the efficiency and robustness of the new method.

a – INRIA
1 : CAD (CAD LIAMA INRIA Paris - Rocquencourt)
Centre de coopération internationale en recherche agronomique pour le développement [CIRAD] – CNRS – Institut national de la recherche agronomique (INRA) – Chinese Academy of Science (CAS) – Institute of Automation, Chinese Academy of Sciences – INRIA
2 : Ningbo Institute of Technology (NIT)
Zhejiang University
3 : Tsinghua University
Tsinghua University

inria-00202457, version 1
http://hal.inria.fr/inria-00202457
oai:hal.inria.fr:inria-00202457
Contributeur : Chine Publications Liama <>
Soumis le : Lundi 7 Janvier 2008, 09:28:42
Dernière modification le : Lundi 7 Janvier 2008, 09:31:31

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DOI : 10.1109/IMSCCS.2007.17

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