Blending and Joining Using Cyclides

Abstract

We consider the use of Dupin cyclides in geometric modeling. These are algebraic surfaces of degree four with interesting properties such as rational parametric forms and closure under offsets. We have been focusing on methods for expanding the geometric coverage of solid modelers, and the cyclide as a new primitive offers promise. In this paper, we briefly describe the cyclide and discuss in details two applications. The first is the modeling of blending surfaces, an important problem in geometric modeling. We outline methods to use various forms of the cyclide in variable-radius blending. Next, we consider the problem of automatic joining of pipes, and describe a general method rooted in the definition of a cyclide for its solution. Implemented examples are provided for both applications.