Transfinite surface interpolation with interior control

Ribbon-based transfinite surfaces

“…The same reasoning works for the derivative by v. Similarly (Várady et al, 2012). The first image is based on the right side of the polygon; the second on the small side at the top-right; and the third on the top side.…”

“…Inserting two-sided or even one-sided patches has also become important, in order to complete general topology curve networks, see e.g. ), Várady et al (2012. Initially, domains were regular polygons, but later non-convex polygons and domains with internal hole loops were also proposed (Kato, 1991;.…”

“…Recent developments of transfinite surfaces include Coons patches having geodesic boundaries (Farouki et al, 2009), and methods to adjust the shape interior of transfinite patches while retaining their boundaries (Várady et al, 2012).…”

“…It contains one 2-sided, two 3-sided, two 4-sided, one 5-sided and one 6-sided patch, all smoothly connected. For the 4-sided loops ordinary Coons patches were used, for the 2-sided a special formula shown in Várady et al (2012) was used, and the rest was represented by CR patches. The cross-derivative functions were extracted from the curve network, and the ribbons satisfy tangent plane constraints at the vertices.…”

Efficient C2 Continuous Surface Creation Technique Based on Ordinary Differential Equation

“…In contrast to the approaches based on trimmed surfaces and control polyhedra, in curved network-based design feature, curves can be directly created and edited in 3D. The method introduced by [8] focuses on special design techniques to adjust the interior of transfinite patches when further shape control is needed.…”