A New Bi-cubic Triangular Gregory Patch

A basic problem may be often encountered when people construct smooth surface that interpolates the given curve meshes. In general, object surface can be divided into triangular and quadrangular areas by the given curve meshes. The problem is that while the methods satisfy the continuity and interpolation requirements, they often fail to produce pleasing shapes, or in reverse to the condition. In this paper, we propose a new triangular Gregory patch which is a variant of quadrangular Gregory patch and Bezier triangle. It owns more simple mathematical formula and can make G¹ continuity more easily controlled.