Computing the Minkowski sum of ruled surfaces

The boundary of the Minkowski sum of two geometric objects is part of the so-called convolution surface of the boundary surfaces of the two input objects. In most cases, convolution surfaces can be computed only by numerical algorithms. The present paper studies convolution surfaces of ruled surfaces. There, explicit parameterizations for the convolution surface can be derived. Moreover, we study the rational convolution surface of two rational ruled surfaces and the connection to rational parameterizations of offsets of rational ruled surfaces.