1. Constrained Interpolation with Biarcs
- Author
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Liu, Xuzheng, Sun, Jiaguang, Zheng, Guo-Qin, Yong, Junhai, School of Software (THSS), Tsinghua University [Beijing] (THU), cgcad, Thss, Tsinghua University [Beijing], Computer Aided Design (CAD ), Laboratoire Franco-Chinois d'Informatique, d'Automatique et de Mathématiques Appliquées (LIAMA), Centre de Coopération Internationale en Recherche Agronomique pour le Développement (Cirad)-Institut National de la Recherche Agronomique (INRA)-Chinese Academy of Sciences [Changchun Branch] (CAS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institute of Automation - Chinese Academy of Sciences-Centre National de la Recherche Scientifique (CNRS)-Centre de Coopération Internationale en Recherche Agronomique pour le Développement (Cirad)-Institut National de la Recherche Agronomique (INRA)-Chinese Academy of Sciences [Changchun Branch] (CAS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institute of Automation - Chinese Academy of Sciences-Centre National de la Recherche Scientifique (CNRS)-Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria), and Tsinghua, Thss
- Subjects
const rained interpolation ,biarc ,[INFO.INFO-GR] Computer Science [cs]/Graphics [cs.GR] ,MathematicsofComputing_NUMERICALANALYSIS ,[INFO.INFO-IA]Computer Science [cs]/Computer Aided Engineering ,[INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR] ,st raight line const raint - Abstract
National audience; An algorithm to construct biarcs that not only match the interpolation requirement of the point positions and tangent vectors but also lie on one side of the constraint line is proposed. For C-type biarc interpolation with the line constraint , firstly twelve inequalities in total are provided according to different position relationships between the constraint line and the interpolation requirement. These inequalities are used to check if biarcs lie on one side of the constraint line. If there exist many biarcs satisfying both the interpolation requirement and the line constraint , the optimal biarc can be obtained by solving a minimum problem. Otherwise , one extra point is added to make it possible to obtain biarcs. For S-type biarc interpolation with the line constraint , some results are also listed.
- Published
- 2007