A general framework for adding interior control to ribbon-based multi-sided surfaces

Ribbon-based multi-sided parametric patches represent a special group of free-form surfaces. While ribbons with boundary and cross-derivative constraints can sufficiently define patches, modifying their interior – in addition – may be required, as well.

We introduce a new technique to add interior control structures for Generalized B-spline (GBS) patches defined over multi-connected curved domains, where the sum of the blending functions produces a weight deficiency. A local parameterization and a parametric MAT (medial axis transform) structure is computed within the domain, which leads to a family of quad structures, called templates. We define blend functions by distributing weight deficiency amongst the vertices of the template and describe algorithms to locate related control points in 3D, yielding Template GBS patches that tightly approximate the input ribbons.

As a final step, a modified representation is created, called Hybrid GBS, that exactly interpolates the given input ribbons and inherits the interior control structure of an arbitrarily chosen Template GBS patch.