$G^n$-continuous Connections Between Normal Ringed Surfaces

Erich Hartmann

Abstract:
A ringed surface is a surface generated by sweeping a circle with non constant radius along a curve. The ringed surface is called normal if the circles are contained in the normal planes of the curve. The paper introduces a method for constructing $G^n$-continuous transition surfaces between two given normal ringed surfaces based on a recent $G^n$-blending method for parametric curves. Various design parameters give user the possibility to manipulate the solution. An advantage of the method is that there is no need for calculation of derivatives of the given ringed surfaces. For special cases implicit $G^n$-connection surfaces of several cylinders/cones are given. The implicit method is based on results on functional splines and can be extended to pipe surfaces with parametrically defined directrices.

Keywords: $G^n$-continuity, $G^n$-blending, parametric blending curve, ringed surface, implicit blending surface, pipe surface,

Figure 1: $G^2$-connection of a) a pipe surface and a surface of revolution, b) 5 pipe surfaces c) 5 cylinders with coplanar axes and a cone d) 5 cylinders with parallel axes