Generalized Bernstein Polynomials and Bézier Curves: An Application of Umbral Calculus to Computer Aided Geometric Design

Authors:
Rudolf Winkel
Affiliations:
Institut für Reine und Angewandte Mathematik, RWTH Aachen, D-52056, Aachen, Germany
Venue:
Advances in Applied Mathematics
Year:
2001

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Abstract

The umbral calculus is used to generalize Bernstein polynomials and Bezier curves. This adds great geometric flexibility to these fundamental objects of computer aided geometric design while retaining their basic properties.