POLYNOMIAL RATIONAL APPROXIMATION OF MINKOWSKI SUM BOUNDARY CURVES/

Given two planar curves, their convolution curve is defined as the set of all vector sums generated by all pairs of curve points which have the same curve normal direction. The Minkowski sum of two planar objec ts is closely related to the convolution curve of the two object bound ary curves. That is, the convolution curve is a superset of the Minkow ski sum boundary. By eliminating all redundant parts in the convolutio n curve, one can generate the Minkowski sum boundary. The Minkowski su m can be used in various important geometric computations, especially for collision detection among planar curved objects. Unfortunately, th e convolution curve of two rational curves is not rational, in general . Therefore, in practice, one needs to approximate the convolution cur ves with polynomial/rational curves. Conventional approximation method s of convolution curves typically use piecewise linear approximations, which is not acceptable in many CAD systems due to data proliferation . In this paper, we generalize conventional approximation techniques o f offset curves and develop several new methods for approximating conv olution curves. Moreover, we introduce efficient methods to estimate t he error in convolution curve approximation. This paper also discusses various other important issues in the boundary construction of the Mi nkowski sum. (C) 1998 Academic Press.