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Article
Open AccessOrthogonal ring patterns in the plane
We introduce orthogonal ring patterns consisting of pairs of concentric circles generalizing circle patterns. We show that orthogonal ring patterns are governed by the same equation as circle patterns. For eve...
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Article
Open AccessThe Ribaucour families of discrete R-congruences
While a generic smooth Ribaucour sphere congruence admits exactly two envelopes, a discrete R-congruence gives rise to a 2-parameter family of discrete envelo** surfaces. The main purpose of this paper is to...
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Article
Multi-Nets. Classification of Discrete and Smooth Surfaces with Characteristic Properties on Arbitrary Parameter Rectangles
We investigate the common underlying discrete structures for various smooth and discrete nets. The main idea is to impose the characteristic properties of the nets not only on elementary quadrilaterals but als...
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Chapter and Conference Paper
Surface Panelization Using Periodic Conformal Maps
We present a new method to obtain periodic conformal parameterizations of surfaces with cylinder topology and describe applications to architectural design and rationalization of surfaces. The method is based ...
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Article
Discretization of asymptotic line parametrizations using hyperboloid surface patches
Two-dimensional affine A-nets in \(3\) -space are quadrilateral meshes that discretize surfaces parametrized along asy...
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Chapter and Conference Paper
Quasiisothermic Mesh Layout
The quality of a quad-mesh depends on the shape of the individual quadrilaterals. The ideal shape from an architectural point of view is the planar square or rectangles with fixed aspect ratio. A parameterizat...
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Chapter and Conference Paper
Topology Optimisation of Regular and Irregular Elastic Gridshells by Means of a Non-linear Variational Method
Gridshells composed of elastically-bent profiles offer significant cost and time advantages during the production, transport and construction processes. Nevertheless, the sha** of the initially flat grid als...
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Article
Erratum zu: Polytope mit vielen Splits und ihre Sekundärfächer
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Article
Polytope mit vielen Splits und ihre Sekundärfächer
Konvexe Polytope, also konvexe Hüllen endlich vieler Punkte im euklidischen Raum, stehen an der Schnittstelle zwischen Geometrie und Kombinatorik. Ziel dieses Textes ist es, ein Ergebnis vorzuste...
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Chapter and Conference Paper
On the Materiality and Structural Behaviour of Highly-Elastic Gridshell Structures
Gridshell structures made of highly elastic materials provide significant advantages thanks to their cost-effective and rapid erection process, whereby the initially in-plane grid members are progressively ben...
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Article
Polyhedral surfaces in wedge products
We introduce the wedge product of two polytopes. The wedge product is described in terms of inequality systems, in terms of vertex coordinates as well as purely combinatorially, from the corresponding data of ...
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Article
Drawing polytopal graphs with polymake
This note wants to explain how to obtain meaningful pictures of (possibly high-dimensional) convex polytopes, triangulated manifolds, and other objects from the realm of geometric combinatorics such as tight s...
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Article
Zonotopes with Large 2D-Cuts
There are d-dimensional zonotopes with n zones for which a 2-dimensional central section has Ω(n d−1) vertices. For d=3, this was known, with examples provided ...
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Article
Neighborly cubical polytopes and spheres
We prove that the neighborly cubical polytopes studied by Günter M. Ziegler and the first named author [14] arise as a special case of the neighborly cubical spheres constructed by Babson, Billera and Chan [4]...
