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Geometric continuity and compatibility conditions for 4-patch surfaces

Bo Johansson (Institutionen för matematiska vetenskaper)
arXiv:1009.0436 p. 25. (2010)
[Artikel, övrig vetenskaplig]

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.

Nyckelord: 4-patch surface; tangent plane continuity; curvature continuity; compatibility conditions, Bezier patch

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Denna post skapades 2011-01-11.
CPL Pubid: 132947


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Institutionen för matematiska vetenskaperInstitutionen för matematiska vetenskaper (GU)


Tillämpad matematik
Numerisk analys

Chalmers infrastruktur