Conic Approximation of Convolution Curve

Given two planar curves, a convolution curve is com-puted by applying vector sums to all pairs of curve points which have the same curve normal direction. The convo-lution curve can be used to compute Minkowski sum of two planar objects which is important in various geometric com-putations such as collision detection and font design. In this paper, we present an algorithm to generate a conic ap-proximation of convolution curve computed from two con-ics. 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 com-pute the boundary of a Minkowski sum of two planar objects bounded by piecewise conics. We derive the necessary con-dition of cusp and describe the method of cusp detection. As an application, we demonstrate the piecewise conic ap-proximation of the boundary of a Minkowski sum computed from two input curves