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Intersection formulae for the kernel of a cone

✍ Scribed by J. Cel

Publisher
Springer
Year
1991
Tongue
English
Weight
468 KB
Volume
39
Category
Article
ISSN
0046-5755

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✦ Synopsis

A subset S of Euclidean space is called a cone if it is the union of a set of halflines having the same endpoint called the apex of the cone, and the set of all such apices is denoted I~y ker R S and called the R-kernel or, when it does not lead to any confusion with the kernel of a starshaped set, simply the kernel of S. ker R S is shown to be the intersection of a family of flats passing through some selected boundary points of S. Three independent formulae of this type are established, respectively: for an arbitrary proper subset S, for S closed, and for S closed connected and nonconvex.

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On the intersection of a set of directio
On the intersection of a set of direction cones
✍ Kai Tang πŸ“‚ Article πŸ“… 1989 πŸ› Elsevier Science βš– 312 KB

A new method is suggested to compute the intersection of a set of direction cones encountered in the problem of passing a convex polyhedron through a window. The time requirement of this method is 0( nm), where n is the number of vertices of the polyhedron and m is the number of vertices of the wind