In computer-aided design and manufacturing (CAD/M), rational hypersurfaces, such as hypersurfaces with rational parameterizations, have many desirable properties. However, convolution of two general rational hypersurfaces does not guarantee the existence of a rational parameterization for the resulting hypersurface. Given the wide use of convolutions in shape design, it is important to understand the necessary conditions under which guarantees can be provided. This paper provides some interesting and insightful answers.

The authors reveal a link between the aforementioned problem and the concept of Gröbner bases. Based on the relationship, they state the conditions on a rational hypersurface so that the convolution of this hypersurface with any rational hypersurface is still rational. They refer to this special class of hypersurfaces as GRC hypersurfaces, and provide a number of examples.

Researchers and engineers in the field of CAD/M are the main audience of this work. On the other hand, other fields such as robotics and computer graphics can also benefit. The paper is well written and relatively easy to follow--except the part on Gröbner bases, which requires knowledge from abstract algebra (including ring theory).