Paper
Generating Bézier Surfaces Based on 8th-order PDE
- Authors:
- Zongzheng Wang; Guojin Wang
- Abstract
- This paper presents a general 8th-order PDE method to generate Bezier surfaces from the boundary with position and tangent vector information. We extend the work on generating biharmonic Bézier surfaces by Monterde to generating Bézier surfaces based on a general 4th-order PDE. And further the results are extended to generate tetraharmonic Bézier surfaces by a general 8th-order PDE. The solution of the general 8th-order PDE is actually the extreme value of the corresponding 4th-order quadratic functional. Furthermore we deduce its complete solution, and provide the concrete algorithm. Finally, we demonstrate that the tetraharmonic Bézier surfaces and the Coons bicubic blending surfaces which have significant application values in CAD are the special cases of our results.
- Keywords
- Bézier surfaces; PDE surfaces; 4th-order quadratic functional; general 8th-order PDE
- StartPage
- 10
- EndPage
- 17
- Doi