Implicit $G^n$-blending of Vertices

Erich Hartmann

Abstract:
Implicit vertex blending methods are introduced which generate pencils of surfaces $G^n$-continuous to three given surfaces. There are solutions for the three possible corners (suitcase-, house-, 3-beam-corner) between three transversally intersecting surfaces. The basic tools are functional splines (implicitly defined blending surfaces). Several examples show applications of functional splines and the implicit vertex blending. All implicit methods can be applied to more general surfaces, especially to parametricly defined surfaces, via the normalform of a surface.

Keywords: $G^n$-continuity, $G^n$-blending, implicit blending curves/surfaces, implicit blending, vertex blending, functional splines, setback blending

Figure: $G^2$ blending of a 3-beam corner between parametric surfaces