Piecewise Developable Surface Approximation of General NURBS Surfaces, with Global Error Bounds

摘要

Developable surfaces possess qualities that are desirable in the manufacturing processes of CAD/CAM models. Specifically, models formed out of developable surfaces can be manufactured from planar sheets of material without distortion. This quality proves most useful when dealing with materials such as paper, leather or sheet metal, which cannot be easily stretched or deformed during production. In this work, we present a semi-automatic algorithm to form a piecewise developable surface approximation of a general NURBS surface. These developable surfaces are constructed as envelopes of the tangent planes along a set of curves on the input surface. Furthermore, the Hausdorff distance between the given surface and the approximating set of developables is globally bounded by a user-provided threshold.