期刊
GRAPHICAL MODELS
卷 76, 期 -, 页码 312-320出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.gmod.2014.04.001
关键词
Rational Bezier curve; Self-intersection; Injectivity; Control polygon
资金
- National Natural Science Foundation of China-China [11271060]
- Fundamental Research of Civil Aircraft-China [MJ-F-2012-04]
- Fundamental Research Funds for the Central Universities-China [DUT14YQ111]
Rational Bezier curves provide a curve fitting tool and are widely used in Computer Aided Geometric Design, Computer Aided Design and Geometric Modeling. The injectivity (one-to-one property) of rational Bezier curve as a mapping function is equivalent to the curve without self-intersections. We present a geometric condition on the control polygon which is equivalent to the injectivity of rational Bezier curve with this control polygon for all possible choices of weights. The proof is based on the degree elevation and toric degeneration of rational Bezier curve. (C) 2014 Elsevier Inc. All rights reserved.
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