Conformal Optimization Algorithm for Undevelopable Surfaces and its Application

In the industrial manufacturing process, most kinds of surfaces are processed by planar materials, but undevelopable surfaces are difficult develop to the plane. The approximation algorithms to develop a undevelopable surface is an important research topic in Computer Aided Geometric Design (CAGD). In this paper, we propose a new approximation algorithms based optimization algorithm. We guarantee the deformation vector make the minimum changes during the developing process. In the paper, some numerical example are given and the can illustrate the our method is effective.