Conic Approximation of Convolution Curve

Given two planar curves, a convolution curve is computed by applying vector sums to all pairs of curve points which have the same curve normal direction. The convolution curve can be used to compute Minkowski sum of two planar objects which is important in various geometric computations such as collision detection and font design. In this paper, we present an algorithm to generate a conic approximation of convolution curve computed from two conics. Conics play an important role in geometric design to represent primitive objects such as parabola, ellipse, and hyperbola. Our algorithm can be directly applied to compute the boundary of a Minkowski sum of two planar objects bounded by piecewise conics. We derive the necessary condition of cusp and describe the method of cusp detection. As an application, we demonstrate the piecewise conic approximation of the boundary of a Minkowski sum computed from two input curves.