182 citations · 549 across the 43 of their papers we have counts for
8 papers · 1 filter
Towards a Geometric Understanding of the 4-Dimensional Point Groups
Laith Rastanawi, Günter Rote
We classify the finite groups of orthogonal transformations in 4-space, and we study these groups from the viewpoint of their geometric action, using polar orbit polytopes. For one…
Area difference bounds for dissections of a square into an odd number of triangles
Jean-Philippe Labbé, Günter Rote, Günter M. Ziegler
Monsky's theorem from 1970 states that a square cannot be dissected into an odd number of triangles of the same area, but it does not give a lower bound for the area differences th…
Optimal Triangulation of Saddle Surfaces
Dror Atariah, Günter Rote, Mathijs Wintraecken
We consider the piecewise linear approximation of saddle functions of the form under the L-infinity error norm. We show that interpolating approximations are not…
Optimally solving a transportation problem using Voronoi diagrams
Darius Geiß, Rolf Klein, Rainer Penninger +1
We consider the following variant of the Monge-Kantorovich transportation problem. Let S be a finite set of point sites in d dimensions. A bounded set C in d-dimensional space is t…
Lines pinning lines
Boris Aronov, Otfried Cheong, Xavier Goaoc +1
A line g is a transversal to a family F of convex polytopes in 3-dimensional space if it intersects every member of F. If, in addition, g is an isolated point of the space of line…
On the maximum size of an anti-chain of linearly separable sets and convex pseudo-discs
Rom Pinchasi, Günter Rote
We show that the maximum cardinality of an anti-chain composed of intersections of a given set of n points in the plane with half-planes is close to quadratic in n. We approach thi…