The virtues of cyclides in CAGD

Abstract This paper summarises the current state of research into the uses of cyclides in CAGD, gives an account of their virtues and limitations, and suggests directions for future work. Space only allows a cursory treatment of recent published research, and references are given throughout to original papers giving fuller details. The main message is that cyclides are surfaces with important virtues; they have low algebraic and parametric rational polynomial degree, and they have a simple geometric characterisation permitting their use in an intuitive way for the design of simple blends. However, they appear not to provide quite enough flexibility for free-form surface design, which prompts a search for appropriate generalisations with more degrees of freedom.