Computer-assisted design system for flattening a three- dimensional surface and for wrapping a flat shape to a three-dimensional surface

摘要

A computer-assisted design apparatus and method for flattening a three- dimensional surface region to a two-dimensional shape in a flat plane or for wrapping a two-dimensional shape to a three-dimensional surface region. A mesh is grown on the surface to be wrapped or unwrapped. The polygonal elements of the mesh are mapped to a growing surface, which is independent of the three-dimensional surface. The growing surface is rotated and translated in order to position the polygonal elements on the two-dimensional surface, for unwrapping, or adjacent to the three- dimensional surface, for wrapping. For unwrapping and flattening, the mesh is grown on the three-dimensional surface region to be unwrapped and flattened independent of the surface boundaries of the parametric spline patch surfaces joined together to form the three- dimensional surface region. In this manner, the resulting mesh spans the mathematical definition of the corresponding surfaces. For wrapping, the polygonal elements are mapped to the three-dimensional surface region and assembled independent of the surface boundaries of the plurality of parametric spline patch surfaces joined together to form the three- dimensional surface region to which the two-dimensional shape is wrapped.