A Boundary-Blending Method for the Parametrization of 2D Surfaces With Highly Irregular Boundaries

Abstract

In this paper three methods are used to generate boundary-conformed parametrization of 2D surfaces. They include two conventional approaches, the Coons method and the Laplace method, and a new method, called “boundary-blending method.” In this new method, unidirectional 2D parametrization is achieved based on the geometric information of the given boundary curves. A dual offsetting procedure is adopted. The geometric properties considered for offsettings include position, curvature, and normal of the two facing parent curves. The algorithm contains two adjustable parameters that enable fine-tuning of this parametrization. This unidirectional process can be easily extended to bi-directional parametrization via superposition to include both boundary pairs. Examples show that this algorithm leads to reasonable smooth blending of the boundaries, and the dual process achieves seamless converging at the middle. It is more robust than the Coons method with regard to parametrization anomalies and relieves the relatively large uneven grid distribution problem experienced in the Laplace method. We believe that this method provides a useful alternative for the 2D boundary-conformed parametrization problems.