Approximate convolution with pairs of cubic Bézier LN curves

In this paper we present an approximation method for the convolution of two planar curves using a pair of two cubic Bézier curves with linear normals (LN). We characterize the necessary and sufficient conditions for two compatible cubic Bézier LN curves to have the same linear normal map. Using this characterization, we obtain the cubic spline approximation of the convolution curve. As illustration, we apply our method to the approximation of a font where the letters are constructed as the Minkowski sum of two planar curves. We also present numerical results using our approximation method for offset curve and compare our method to previous results.