Geometric continuity and compatibility conditions for 4-patch surfaces
Magazine article, 2010

When considering regularity of surfaces, it is its geometry that is of interest. Thus, the con- cept of geometric regularity or geometric continuity of a specific order is a relevant concept. In this paper we discuss necessary and sufficient conditions for a 4-patch surface to be geometrically continuous of order one and two or, in other words, being tangent plane continuous and curvature continuous respectively. The focus is on the regularity at the point where the four patches meet and the compatibility conditions that must appear in this case. In this article the compatibility conditions are proved to be independent of the patch parametrization, i.e., the compatibility con- ditions are universal. In the end of the paper these results are applied to a specific parametrization such as Bezier representation in order to generalize a 4-patch surface result by Sarraga.

Bezier patch

compatibility conditions

curvature continuity

4-patch surface

tangent plane continuity

Author

Bo Johansson

University of Gothenburg

Chalmers, Mathematical Sciences

arXiv:1009.0436

25-

Areas of Advance

Production

Subject Categories

Computational Mathematics

Roots

Basic sciences

More information

Created

10/8/2017