The generation of circular arcs and conics by subdivision via averaging normal vectors

Abstract

We propose a nonlinear interpolatory curve subdivision based on averaging normal vectors, which can reproduce circular arcs when straight edges exist in the original control polygon and generate conics when initial control points are sampled uniformly. Corresponding proofs and examples are also given for verifying the correctness of this scheme.

Keywords:

• nonlinear subdivision
• circular arcs reproduction
• interpolation
• conics
• normal vectors

2000 AMS Subject Classification :

• 68T10

Acknowledgements

Project supported in part by NSFC grant 10871208 and Major Research Plan of NSFC (90715043).