Shape Modeling ina Homogenized Geometric Paradigm

The author proposes replacing the conventional Euclidean processing with homogeneous processing, which is free from the ill effects of division and has the desirable properties of duality and protective invariance. The division operation negatively affects such properties as exactness, robustness, and generality in computer-aided design systems. The author mainly discusses two-types of geometric processing in the homogenized geometric paradigm, i.e., subdivision method in surface design and set operations in solid modeling