منابع مشابه
Fixed Points and Stability of an Additive Functional Equation of n-Apollonius Type in C-Algebras
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Apollonius Solutions in Rd
Voronoi and related diagrams have technological applications, for example, in motion planning and surface reconstruction, and also find significant use in materials science, molecular biology, and crystallography. Apollonius diagrams arguably provide the most natural division of space for many materials and technology problems, but compared to Voronoi and power diagrams, their use has been limi...
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The Apollonius Circle Problem dates to Greek antiquity, circa 250 BC. Given three circles in the plane, find or construct a circle tangent to all three. This was generalized by replacing some circles with straight lines. Vieta [19] (or Viète) solved the problem using circle inversions before 1580. Two generations later, Descartes considered a special case in which all four circles are mutually ...
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We study the predicates involved in an efficient dynamic algorithm for computing the Apollonius diagram in the plane, also known as the additively weighted Voronoi diagram. We present a complete algorithmic analysis of these predicates, some of which are reduced to simpler and more easily computed primitives. This gives rise to an exact and efficient implementation of the algorithm, that handle...
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ژورنال
عنوان ژورنال: Tokyo Journal of Mathematics
سال: 2007
ISSN: 0387-3870
DOI: 10.3836/tjm/1184963650