Curvature continuous connections of cones and cylinders

Abstract

Dupin cyclides are used to obtain connections of cones and cylinders with continuous tangent planes. However, it is impossible to obtain connections with continuous principal curvatures in the same way. In the paper, curvature continuous connections are formed by using so-called normal ringed surfaces. Like cyclides, these surfaces are generated by a circle of variable radius sweeping through space. Further, the curve of the centres is perpendicular to the planes of the circles. A parametric representation of normal ringed surfaces is given which allows a simple algorithm to be developed for the construction of curvature continuous connections of cones and/or cylinders.