Trimming and Closure of Constrained Surfaces

We consider surfaces defined with the dimensionality paradigm as the natural projection of a 2-manifold in n-space into a subspace of three dimensions. Such surfaces can represent exactly many operations of interest in geometric modeling and its appfcations. We show that this class of surfaces is closed under the operations of offsetting, bisecting, and blending (using rolling-ball blends), and analyze the growth behavior of the number of variables needed. Furthermore, me present several techniques how to evaluate trimmed patches of Lhese surlaces and demonstrate the utility of these techniques. 'Work supported in part by ONR Contract NOO014-90-J-1590, by NSF Grant CDA 92-23502, and by NSF Grant ECD 88-03017. Trimming and Closure of Constrained Surfaces* Xiangping Chen Christoph M. Hoffmann Computer Science Department Purdue University West Lafayette, Ind. 47907