Necessary and sufficient compatibility conditions for geometric regularity for an n-patch surface with n=3, 4 or 5

Preprint, 2013

When considering regularity of surfaces we are primarily interested in tangent plane continuity and curvature continuity respectively. We restrict ourselves to study funda- mental surfaces such as n -patch surfaces, i.e., n patches meeting at a common vertex point. The main problem here is to present necessary and sucient compatibility condi- tions for such a parameterized surface to be geometrically continuous of order one and two. In this article the compatibility conditions are proved to be independent of the patch parametrization. The number of patches, n , treated here is greater or equal to 3.