Meshless Non-Parametric Shape Design of Piecewise Approximately Developable Surfaces Using Discretized Local Gauss Map

Abstract

A meshless and non-parametric approach is proposed for shape design of curved surfaces consisting of approximately developable surface patches. A local Gauss map is defined at the grid point of a surface, and its developability is evaluated based on the area of the local Gauss map. An optimization problem is formulated for minimizing the sum of square areas of the local Gauss map at the grid points of the surface with specified boundary shape. Internal boundaries between the approximately developable surface patches are generated by relaxing the developability at the selected grid points. The effectiveness of the proposed method for generating various shapes of piecewise approximately developable surface is demonstrated in the numerical examples.