Adjustable Bézier Curves with Simple Geometric Continuity Conditions

Abstract

This paper aims to simplify the continuity conditions of Bézier curves. For this purpose, a special family of Bézier curves with three parameters, to be called adjustable Bézier curves, is constructed. They have the same structure as the quartic Bézier curves. The newly constructed curves possess some of the basic properties of Bézier curves, such as the convex hull property, symmetry, geometric invariance, etc., and they have shape adjustability. Moreover, under the geometric continuity of order 1 (G 1 ) conditions of the usual Bézier curves, the adjustable Bézier curves can reach geometric continuity of order k (G k ); here, k is one of the parameters of the newly constructed curves. The recursive evaluation algorithm of the new curves is provided. We also discuss how to construct the adjustable Bézier curves with a given tangent polygon. Numerical examples illustrate the correctness and validity of the proposed method.

Aplicación De Las Curvas De Bézier en La Generación De Una Señal Eléctrica

“…Por otro lado, las curvas de Bézier han sido implementadas en diferentes aplicaciones por ejemplo, Aumann (2003) presenta un algoritmo para generar superficies manipulables de grado y configuración arbitraria (Marin & Jaimez, 2008), Montés (2008) utilizó las curvas para calcular, en tiempo real, trayectorias curvas en robots móviles autónomos (Montés, Herraez, Armesto, & Tornero, 2008). Asimismo, existen autores que trabajan con las curvas de Bézier para la generación de figuras geométricas y planificación de trayectorias (Cai & Wang, 2009;Fougerolle, Lanquetin, Neveu, & Lauthelier, 2008;Marin & Jaimez, 2008;Marsh, 2006;Yan, 2006).…”

Geometric Modeling of C-Bézier Curve and Surface with Shape Parameters

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Geometric Modeling of Novel Generalized Hybrid Trigonometric Bézier-Like Curve with Shape Parameters and Its Applications

“…He considered the planner segmented Bézier curves and B-spline curves to present their parametric and geometric continuities. Yan [8] presented a particular family of Bézier curves with three different shape parameters, which are also known as adjustable Bézier curves. Those curves have same shape and structure like the traditional quartic Bézier curve.…”