Oriented bounding surfaces with at most six common normals

We present a new type of oriented bounding surfaces, which is particularly well suited for shortest distance computations. The bounding surfaces are obtained by considering surfaces whose support functions are restrictions of quadratic polynomials to the unit sphere. We show that the common normals of two surfaces of this type - and hence their shortest distance - can be computed by solving a polynomial of degree six. This compares favorably with other existing bounding surfaces, such as quadric surfaces, where the computation of the common normals is known to lead to a polynomial of degree 24.