Bézier curves and surfaces with shape parameters

Abstract

Bézier curves with n shape parameters and triangular Bézier surfaces with 3n(n+1)/2 shape parameters are presented in this paper. The geometric significance of the shape parameters and the geometric properties of these curves and surfaces are discussed. The shapes of the curves and the surfaces can be modified intuitively, foreseeably and precisely by changing the values of the shape parameters.

Keywords:

• Bézier curves
• triangular Bézier surfaces
• shape parameters
• basis functions
• geometric significance

2000 AMS Subject Classification: :

• 65D17
• 65D18
• 65U05

Acknowledgements

The authors thank the subject editor and the referees for several important comments and suggestions which improved the quality of the paper. This work is supported by NSFC under Grant 10571145.