Overlap patches: a new scheme for interpolating curve networks with n-sided regions

Abstract A general scheme for defining n -sided surface patches is described. So-called ‘overlap patches’ are made up of n vertex patches, each interpolating positional and tangential data relating to one corner. In this paper bicubic vertex patches and improved bicubic vertex patches with Gregory terms are used. However, the overlap scheme can be generalized for other parametric surface patches as well. The scheme offers an extra degree of freedom to adjust the interior of an overlap patch. After presenting how overlapping works, the conditions for providing VC 1 continuity and tangential ‘compatibility’ with bicubics is discussed, together with three typical overlap parametrizations. The main features of overlap patches in comparison with other n -sided methods are also presented.

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