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.