Design and connection of parametric surfaces through given regular curves

Abstract

This study focused on the connections between two parametric surfaces through the given regular curves. Accordingly, we analyzed a C-0-continuous connected surface in terms of the marchingscale functions of these surfaces. It should be noted that, in general, differentiability along a common curve for a C-0-continuously connected surface is not guaranteed. To solve this problem, we introduced a C-1-continuous connection and proved its existence for such continuous connections. These connections are improved versions of the G(1)-connection of developable surfaces introduced by Paluszny. Moreover, we suggested applications to illustrate the C-1-continuous connection using Bezier curves and some marchingscale functions of the parametric surfaces.