scholarly journals Surface design by blending rational Bézier curves and surfaces

2014 ◽  
Author(s):  
Solehah Jamilah Ismail ◽  
Jamaludin Md. Ali
Keyword(s):  
Bezier Curves ◽  
Bézier Curves ◽  
Surface Design ◽  
Rational Bézier Curves ◽  
Curves And Surfaces

Evaluation of difference bounds for computing rational Bézier curves and surfaces

2004 ◽  
Vol 28 (4) ◽  
pp. 551-558 ◽  
Author(s):  
Wu Zhongke ◽  
Lin Feng ◽  
Seah Hock Soon ◽  
Chan Kai Yun
Keyword(s):  
Bezier Curves ◽  
Bézier Curves ◽  
Rational Bézier Curves ◽  
Curves And Surfaces

scholarly journals A Novel Generalization of Trigonometric Bézier Curve and Surface with Shape Parameters and Its Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-25 ◽  
Author(s):  
Sidra Maqsood ◽  
Muhammad Abbas ◽  
Gang Hu ◽  
Ahmad Lutfi Amri Ramli ◽  
Kenjiro T. Miura
Keyword(s):  
Basis Functions ◽  
Geometric Continuity ◽  
Shape Parameters ◽  
Bernstein Basis ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Surface Design ◽  
Curves And Surfaces ◽  
Bernstein Basis Functions ◽  
Parametric Continuity

Adopting a recurrence technique, generalized trigonometric basis (or GT-basis, for short) functions along with two shape parameters are formulated in this paper. These basis functions carry a lot of geometric features of classical Bernstein basis functions and maintain the shape of the curve and surface as well. The generalized trigonometric Bézier (or GT-Bézier, for short) curves and surfaces are defined on these basis functions and also analyze their geometric properties which are analogous to classical Bézier curves and surfaces. This analysis shows that the existence of shape parameters brings a convenience to adjust the shape of the curve and surface by simply modifying their values. These GT-Bézier curves meet the conditions required for parametric continuity (C0, C1, C2, and C3) as well as for geometric continuity (G0, G1, and G2). Furthermore, some curve and surface design applications have been discussed. The demonstrating examples clarify that the new curves and surfaces provide a flexible approach and mathematical sketch of Bézier curves and surfaces which make them a treasured way for the project of curve and surface modeling.

scholarly journals Monotonicity preserving representations of curves and surfaces

2016 ◽  
Vol 1 (2) ◽  
pp. 517-528 ◽  
Author(s):  
Jorge Delgado ◽  
Juan Manuel Peña
Keyword(s):  
Bezier Curves ◽  
Bézier Curves ◽  
Open Problems ◽  
Rational Bézier Curves ◽  
Curves And Surfaces ◽  
Bézier Surfaces ◽  
Bezier Surfaces ◽  
New Formula ◽  
Monotonicity Preserving

AbstractIn this paper we revisit the problem of monotonicity preservation of curves and surfaces and we provide some new proofs and open problems. In particular, we prove a new formula for the derivation of rational Bézier curves. We also deal with the rational monotonicity preservation of rational Bézier surfaces and a related conjecture is presented.

Sign in / Sign up

Export Citation Format

Share Document