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The Convex Hull Construction for Compact Surfaces and the Dirichlet Polygon
Author(s) -
Näätänen M.,
Penner R. C.
Publication year - 1991
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/23.6.568
Subject(s) - quadrilateral , mathematics , convex hull , hull , minkowski space , dirichlet distribution , regular polygon , polygon (computer graphics) , convex set , combinatorics , pure mathematics , mathematical analysis , geometry , convex optimization , computer science , structural engineering , telecommunications , frame (networking) , finite element method , engineering , boundary value problem , marine engineering
We describe the construction of Dirichlet domains for a closed surface in terms of a convex hull construction in Minkowski space. The equations governing this construction are found to be analogues of Ptolemy's theorem on cyclic Euclidean quadrilaterals.