Abstract: 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.

Abstract: A method and apparatus for flattening a three-dimensional surface into a two-dimensional pattern piece extracts a three-dimensional mesh from the surface to define surface elements and maps these elements in groups to a flat plane where they are reassembled. The position of data points in the flat plane are recursively adjusted in order to cancel error and to provide an optimum solution. Tools are provided to the user to determine the correctness of the flattening process and to insert darts into, and make other modifications to, the resulting flat pattern in order to further optimize the result.