Blending and Joining Using Cyclides

We consider the use of cyclides in geometric modeling. These are algebraic surfaces of degree four with interesting properties such as rational parametric forms and closure under offsets. The incorporation of cyclides as primitives in solid modellers will increase their geometric coverage. In this paper, we describe the cyclide and discuss two applications of its use in computer aided design — modeling blending surfaces and the automatic joining of pipes. Implemented examples are also included.