Prescribing the length of rational Bézier curves

Autor:	John A. Roulier, Bruce Piper
Rok vydání:	1996
Předmět:	Convex curve Aerospace Engineering Bézier curve Rational function Computer Graphics and Computer-Aided Design Secant method Inflection point Modeling and Simulation Automotive Engineering Calculus Applied mathematics Convex function Parametric equation Arc length Mathematics
Zdroj:	Computer Aided Geometric Design. 13:23-43
ISSN:	0167-8396
Popis:	Theorems and corresponding algorithms are presented which produce a rational Bezier curve of a specified arc length subject to certain constraints. Extraneous inflection points are avoided. The problem is reduced to expressing the arc length as a function of a single variable. A general theorem from a previous paper of the authors is used which gives conditions under which the arc length function is convex or strictly convex. An algorithm to automatically choose the initial parameters for the secant method will produce a solution to this problem with performance comparable to the Newton-Raphson method. Theory and algorithms for rational parametric curves are presented. It is shown that in certain cases rational parametric curves of degree three can be used while polynomials of bounded degree cannot.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::d9aa0d071b873ab91468a6d64236d781 https://doi.org/10.1016/0167-8396(95)00005-4 Zobrazit plný text záznamu Full Text from ScienceDirect