Super-hyperbolic Distance Functions and Spherical Cross Product Functions: An Extended Model to Super-quadrics

Abstract

This paper presents two families of new functions for implicit surface modeling. The first family is superhyperbolic distance functions that can produce smooth deformable shapes bounded by some superhyperbolic surfaces, folded planes, square planes, or planes. The second family is spherical cross product functions that can generate an implicit sweep object. The latter can be viewed as an extended model to superquadrics, since not only parametric curves but also any implicit curve defined using a ray linear function can be used to perform a spherical cross product. Hence, it can generate a greater variety of shapes than superquadrics. Both functions have a number of advantages. They can be (1) parameterized, (2) further constructed to generate a complex object via set operations, (3) used as a field function for soft objects, and (4) applied to Blinn’s blobby model and F-rep. Besides, some theorems are proposed to help users identify whether a function or a spherical cross product function is suitable as a field function.