GNURBS Surfaces On Arbitrary Polygon Control Grid

Generalized non-uniform rational B-splines (GNURBS) is a novel geometric modeling method that extends non-uniform rational B-splines to handle any topological control net. The existing GNURBS method only supports fully quadrilateral control nets and requires identical node spacing on opposite edges of each face, resulting in limited modeling capability. This article extends the GNURBS method to handle polygonal control nets, where the knot intervals for the edges of the polygon can be different. The method first generate initial bicubic Bézier patches from control net through Bézier extraction operation. Then degree of some patches is elevated to biquintic, with G¹ continuity conditions defined for each C⁰ edge. Finally, the target surface is obtained by solving the constrained optimization problem in a stepwise manner. The experiment presents the surface generation results of multiple grid models. The zebra-stripe images demonstrate that the proposed method generates spline surfaces with global G¹ continuity from polygonal control nets.