Optimal slicing of free-form surfaces

Many applications, such as contour machining, rapid prototyping, and reverse engineering by laser scanner or coordinate measuring machine, involve sampling of free-from surfaces along section cuts by a family of parallel planes with equidistant spacing and common normal N. To ensure that such planar sections provide faithful descriptions of the shape of a surface, it is desirable to choose the relative orientation that maximizes, over the entire surface, the minimum angle between N and the local surface normal n. We address this optimization problem by computing the (symmetrized) Gauss map for the surface, projecting it stereographically onto a plane, and invoking the medial axis transform for the complement of its image to identify the orientation N that is "most distant" from the symmetrized Gauss map boundary. Using a Gauss map algorithm described elsewhere, the method is implemented in the context of bicubic B

• Type: Journal
• Year: 2002
• Where: CAGD
• Authors: Tait S. Smith, Rida T. Farouki, Mohammad al-Kandari, Helmut Pottmann
• Keywords: CAGD 2002, Contour Machining, Gauss Map, Gauss Map Boundary