What are the faces of a convex polytope/polyhedron?
... need to define the notion of supporting hyperplanes. A hyperplane of contains if it is either with a ... supporting hyperplane. , and are called the vertices, edges, ridges and facets, respectively. The vertices ... faces geometrically. For this, we need to define the notion of supporting hyperplanes. A hyperplane of ... is either , itself or the intersection of with a supporting hyperplane. The faces of dimension 0 ...
ETH - Z
... this. Intersect the variety with a hyperplane. Then, study what happens to this intersection when the ... hyperplane moves in a parallel family. This allows one to understand the topology of the original variety, in ... . Lefschetz' approach goes like this. Intersect the variety with a hyperplane. Then, study what happens to ... this intersection when the hyperplane moves in a parallel family. This allows one to understand the ...
https://kyng.inf.ethz.ch/courses/AGAO20/lectures/lecture12_convex-d...
... part of this lecture introduces the concept of a separating hyperplane of two sets followed by a proof ... that for two closed, convex and disjoint sets a separating hyperplane always exists. This is a variant ... part of this lecture introduces the concept of a separating hyperplane of two sets followed by a proof ... that for two closed, convex and disjoint sets a separating hyperplane always exists. This is a variant ...
Computational issues – Automatic Control Laboratory | ETH Zurich
... number of polyhedra. Both approaches are based on the notion of cells and markings in hyperplane ... the algorithms can be extended to general PWA systems lacking the hyperplane arrangement (like PWA ... number of polyhedra. Both approaches are based on the notion of cells and markings in hyperplane ... the algorithms can be extended to general PWA systems lacking the hyperplane arrangement (like PWA ...
https://www.fernuni-hagen.de/MATHEMATIK/DMO/pubs/feu-dmo042-16.pdf
... sweep an ori- ented matroid of rank ≥ 4 with a hyperplane. The authors immedi- ately afterwards remark ... is not a loop, f is not a coloop and g 6= f . We call g the hyperplane at infinity and f the ... sweep an ori- ented matroid of rank ≥ 4 with a hyperplane. The authors immedi- ately afterwards remark ... is not a loop, f is not a coloop and g 6= f . We call g the hyperplane at infinity and f the ...
http://people.ee.ethz.ch/~myin/AWEC05_Yin.pdf
... on a transversal hyperplane of the orbit [1]. Let the state of the kite be x, and the nomi- nal ... periodic trajectory be {x⋆(τ) | τ ∈ [0, T)}. Define S(τ) as a hyperplane transversal to the orbit. The ... on a transversal hyperplane of the orbit [1]. Let the state of the kite be x, and the nomi- nal ... periodic trajectory be {x⋆(τ) | τ ∈ [0, T)}. Define S(τ) as a hyperplane transversal to the orbit. The ...
Is it possible to determine the Delaunay cell containing a given po...
... corresponding hyperplane and the half line . The LP formulation is therefore: While an optimal solution ... hull of . A certificate of unboundedness actually induces a hyperplane strongly separating from ... -vertical facet inequality such that the intersecion point of the corresponding hyperplane and the half line ... , i.e., not in the convex hull of . A certificate of unboundedness actually induces a hyperplane ...
https://www.fernuni-hagen.de/MATHEMATIK/DMO/pubs/feu-dmo018-09.pdf
... Diskrete Mathematik und Optimierung Winfried Hochsta¨ttler: A Hadwiger Conjecture for Hyperplane ... matroids, oriented matroids A Hadwiger Conjecture for Hyperplane Arrangements Winfried Hochsta¨ttler ... Diskrete Mathematik und Optimierung Winfried Hochsta¨ttler: A Hadwiger Conjecture for Hyperplane ... matroids, oriented matroids A Hadwiger Conjecture for Hyperplane Arrangements Winfried Hochsta¨ttler ...
Mingzhou Yin | ETH Zürich
... hyperplane selection in identification of local limit cycle dynamics (2022.7 - , Semester project with Kailai ... projects Transversal hyperplane selection in identification of local limit cycle dynamics (2022.7 ...
What is the vertex enumeration problem, and what is the facet enume...
... enumeration is called nondegenerate if there is no given points which are on a common hyperplane, and ... called nondegenerate if there is no given points which are on a common hyperplane, and degenerate ...
