Cyclide blending in solid modelling

The family of surfaces known as cyclides includes all the surfaces conventionally used in solid modelling — the plane, cylinder, cone, sphere and torus — together with various types of generalisation of the torus. In an earlier paper it was shown that cyclides can be used to give exact blends between pairs of other cyclide surfaces in several situations which frequently occur in engineering design. The present paper reviews this work, extends it by the use of a new theorem due to Sabin, and also shows how piecewise cyclide blending surfaces can give still greater generality. All the blends created are subject to the restriction that their boundaries must be circles lying on the surfaces being blended. Such blends occur surprisingly often in the design of real objects.