APPLICATIONS OF LAGUERRE GEOMETRY IN CAGD

We briefly introduce to the basics of Laguerre geometry and then show that this classical sphere geometry can be applied to solve various pr oblems in geometric design. In the present part, we focus on applicati ons of the cyclographic model of Laguerre geometry and the cyclographi c map. It relates the medial axis and Voronoi curves/surfaces to speci al surface/surface intersections and the corresponding trimming proced ures to hidden line removal. Rational canal surfaces are treated as cy clographic images of rational curves in R-4. This leads to a simple co ntrol structure for rational canal surfaces. Its practical use is demo nstrated at hand of modeling techniques with Dupin cyclides. (C) 1998 Elsevier Science B.V.