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Degree reduction of disk rational Bézier curves.
TL;DR: An algorithm for optimal multi-degree reduction of rational disk B\'ezier curve in the $L^{2}$ norm is presented and some numerical examples are shown to illustrate the correctness and the validity of theoretical reasoning.
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Abstract: How to quickly and stably realize the degree reduction of the rational Bezier curve is an open problem in CAGD. Based on the weighted least squares method and weighted sum method of multi-objective optimization, this paper transforms the degree reduction problem of the rational Bezier curve into a convex optimization problem and then uses quadratic programming to solve it. Prove that the solution is the minimum. Numerical experiments show that the method is fast and stable.
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References
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Multiobjective Optimization: Principles and Case Studies
Yann Collette,Patrick Siarry +1 more
- 08 Aug 2003
TL;DR: In this article, the authors discuss the principles of multiobjective optimization methods and the criteria for choice of a method, and evaluate the performance of methods and their performance measurement criteria.
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Algorithms for rational Bézier curves
TL;DR: A recursive algorithm for the evaluation of rational Bezier curves is presented; it consists of a construction that works with a constant cross ratio and is carried over to other algorithms.
173
Approximation by interval Bezier curves
TL;DR: The interval Bezier curve, which, unlike other curve and surface approximation schemes, can transfer a complete description of approximation errors between diverse CAD/CAM systems that impose fundamentally incompatible constraints on their canonical representation schemes, is described.
Robust interval algorithm for surface intersections
TL;DR: A robust algorithm for computing intersections of two planar interval polynomial curves that provides results with numerical certainty and verifiability and is extended to solve unbalanced systems.
111
Disk Be´zier curves
Qun Lin,Jon G. Rokne +1 more
TL;DR: In this paper, the authors defined disk Bezier curves, a centered form, their use in approximating a real curve, their envelope, and an approximation to the curves.
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