Transfinite surface interpolation over irregular [formula omitted]-sided domains

Abstract

Transfinite surface interpolation is a classic topic of computer-aided geometric design (CAGD), and many non-quadrilateral schemes are known. Surfaces defined solely by means of their boundary curves and cross-tangent functions are needed, for example, in three-dimensional curve network-based design, and to fill complex irregular holes such as in vertex blending. This paper deals with interpolating so-called tangential ribbons. Former schemes are enhanced and extended in order to minimize shape artifacts and to provide a more natural patch interior. The proposed representation is based on irregular convex domains that correspond to the lengths and orientations of the boundary curves. The mapping of the individual ribbons within the n-sided domain is calculated by focused parameterization methods that ensure a balanced orientation related to the center of the domain and avoid parametric shearing. Distance-based blending functions ensure that modifying or inserting a small edge will have only a local effect over the n-sided patch. Constructions to create one-sided or two-sided patches are also presented. Examples and open research topics conclude the paper.