Polyhedral vertex blending with setbacks using rational S-patches

Setbacks not only beautify the shape of polyhedral vertex blending, but also overcome the difficulties inherited from non-setback blending. However, stitching several tensor product Bézier surfaces, the existing approaches to setback vertex blending may cause twist compatibility problems and approximate solutions, especially when the vertex gathers more edges. This paper proposes a new algorithm, yielding an exact solution using a single rational S-patch. Although S-patch developers Loop and DeRose (1989), also investigated vertex blending (1990), they did not configure setback. In addition, the new algorithm reduces the depth of the S-patch and extends the edge blending surfaces to use rational Bézier representation, so that circular rounding can be made. Miscellaneous examples demonstrate that the method produces smooth and natural connecting shapes.