Surface Flattening Based on Constraint Global Optimization

Abstract

In this paper, the problem of generating a planar development of arbitrary three-dimensional surfaces is addressed. A new method based on a global optimization process under constraints is proposed. In this method an initial planar development is derived which is refined in order to satisfy certain criteria and constraints. The refinement is formulated as a global minimization problem. Using the proposed technique it is not required to predetermine a mapping from the three-dimensional surface to the plane in order to generate the planar development and it is possible to control the local accuracy in the derived planar development. Indicative applications are presented to illustrate the effectiveness of the proposed technique.