Extensions of Superquadrics

Abstract

The modeling capabilities of superquadrics can be enhanced with global and local deformations. Global deformations such as tapering, bending or twisting require just a few additional parameters in the superquadric equations. Local deformation, in general, overlay the original superquadric with a new parameterization grid which enables local change of shape. Therefore, local deformations are by its nature not tightly integrated with superquadrics and are in this book just discussed at the end of this chapter. Hyperquadrics, which include superquadrics as a special case, and are generated by taking hyperslices of high-dimensional algebraic hypersurfaces, are also described at the end of the chapter, as well as ratioquadrics which are very similar to superquadrics but have continuous first derivatives everywhere on the surface.