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


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 = "Helmut Pottmann and Philipp Grohs and Bernhard Blaschitz",
        title = "Edge offset meshes in {L}aguerre geometry",
        journal = "Adv. Comp. Math.",
        year = 2010,
        volume = 33,
        pages = "45-73",
        url = "http://www.dmg.tuwien.ac.at/grohs/papers/eolag.pdf",
        doi = "http://dx.doi.org/10.1007/s10444-009-9119-6",

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