Edge offset meshes in Laguerre geometry
H. Pottmann, P. Grohs, B. Blaschitz

"Adv. Comp. Math.", (2009), to appear.


A mesh M with planar faces is called an edge offset (EO) mesh if there exists a combinatorially equivalent mesh Md such that corresponding edges of M and Md lie on parallel lines of constant distance d. The edges emanating from a vertex of M lie on a right circular cone. Viewing M as set of these vertex cones, we show that the image of M under any Laguerre transformation is again an EO mesh. As a generalization of this result, it is proved that the cyclographic mapping transforms any EO mesh in a hyperplane of Minkowksi 4-space into a pair of Euclidean EO meshes. This result leads to a derivation of EO meshes which are discrete versions of Laguerre minimal surfaces. Laguerre minimal EO meshes can also be constructed directly from certain pairs of Koebe meshes with help of a discrete Laguerre geometric counterpart of the classical Christo el duality.


author = "H. Pottmann, P. Grohs, and B. Blaschitz",
title = "Edge offset meshes in Laguerre geometry",
journal = "Adv. Comp. Math.",
year = "2009",
note = "to appear",

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