Partial derivatives of rational Bézier surfaces

1997 ◽  
Vol 14 (4) ◽  
pp. 377-381 ◽  
Author(s):  
Guo-Jin Wang ◽  
Thomas W. Sederberg ◽  
Takafumi Saito
Keyword(s):  
Partial Derivatives ◽  
Bézier Surfaces ◽  
Bezier Surfaces ◽  
Derivatives Of

scholarly journals Quantum (q, h)-Bézier surfaces based on bivariate (q, h)-blossoming

2019 ◽  
Vol 52 (1) ◽  
pp. 451-466
Author(s):  
Ilija Jegdić ◽  
Plamen Simeonov ◽  
Vasilis Zafiris
Keyword(s):  
Bernstein Polynomials ◽  
Property A ◽  
Bivariate Polynomials ◽  
Dual Functional ◽  
Bézier Surfaces ◽  
Subdivision Algorithm ◽  
Bezier Surfaces ◽  
Recursive Evaluation ◽  
Derivatives Of ◽  
Marsden Identity

AbstractWe introduce the (q, h)-blossom of bivariate polynomials, and we define the bivariate (q, h)-Bernstein polynomials and (q, h)-Bézier surfaces on rectangular domains using the tensor product. Using the (q, h)-blossom, we construct recursive evaluation algorithms for (q, h)-Bézier surfaces and we derive a dual functional property, a Marsden identity, and a number of other properties for bivariate (q, h)-Bernstein polynomials and (q, h)-Bézier surfaces. We develop a subdivision algorithm for (q, h)-Bézier surfaces with a geometric rate of convergence. Recursive evaluation algorithms for quantum (q, h)-partial derivatives of bivariate polynomials are also derived.

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