Approximate convolution with pairs of cubic Bézier LN curves Original Research Article

In this paper we present an approximation method for the convolution of two planar curves using pairs of compatible cubic Bézier curves with linear normals (LN). We characterize the necessary and sufficient conditions for two compatible cubic Bézier LN curves with the same linear normal map to exist. 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 curves and compare our method to previous results.