COMPUTATIONAL PROBLEMS IN COMPUTER-AIDED DESIGN AND MANUFACTURING OF RULED AND PARAMETRIC SURFACES (CAD/CAM)

This thesis deals with sculptured surface representation and computational methods for processing parametrically defined surfaces. The results are applied to NC machining of surfaces.; In the first part of the thesis, ruled surfaces which use lines rather than points as their fundamental building blocks are studied. In general, the shape of a ruled patch is controlled not only by the shape of its two boundary curves but also by the parametrization of the ruling. Based on this concept, new methods are developed for blending of ruled patches to construct composite ruled surfaces.; In the second part of the thesis, two computational problems for processing parametrically defined surfaces are investigated. One technique deals with contouring of parametric surfaces. The technique presented allows for optimal generation of planar contour lines. The second computational technique presented deals with construction of offset surfaces. An algorithm is presented that allows detection and removal of any closed loop(s) on the offset surface due to its self-intersection. Finally, machining of sculptured surfaces is explored. Methods are developed to calculate the optimal step length and cutter path separation.