id: 05904990
dt: j
an: 05904990
au: Pottmann, Helmut; Grohs, Philipp; Blaschitz, Bernhard
ti: Edge offset meshes in Laguerre geometry.
so: Adv. Comput. Math. 33, No. 1, 45-73 (2010).
py: 2010
pu: Springer, Dordrecht
la: EN
cc: 
ut: discrete differential geometry; Laguerre geometry; edge offset mesh; koebe
    polyhedron; minimal surface; Laguerre minimal surface
ci: 
li: doi:10.1007/s10444-009-9119-6
ab: Summary: A mesh $\cal M$ with planar faces is called an edge offset (EO)
    mesh if there exists a combinatorially equivalent mesh $\cal M^d$ such
    that corresponding edges of $\cal M$ and $\cal M^d$ lie on parallel
    lines of constant distance $d$. The edges emanating from a vertex of
    $\cal M$ lie on a right circular cone. Viewing $\cal M$ as set of these
    vertex cones, we show that the image of $\cal M$ 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
    the help of a discrete Laguerre geometric counterpart of the classical
    Christoffel duality.
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