منابع مشابه
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...
متن کاملConflict Management: Apollonius in airspace design
Conflict detection is the process by which potential collisions between aircraft are identified. Developing efficient detection methods is an engineering priority since the prevention of a mid-air collision is a major safety constraint for all airspace design. Proximity between two aircraft each flying with instantaneous uniform straight motion is re-examined. The Apollonius theorem for constru...
متن کاملAnother Solution of Apollonius Tenth Problem
We provide a new solution for the famous Apollonius Tenth Problem. The problem is to construct a circle tangent to three given circles in the plane. An equivalence between analytical and geometric approaches to the solution is explored. A new analytical solution for the problem is presented and a step by step geometrical interpretation of this solution is provided. We show that this interpretat...
متن کاملConic tangency equations and Apollonius problems in biochemistry and pharmacology
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 ...
متن کاملThe predicates of the Apollonius diagram: Algorithmic analysis and implementation
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: The Classical Review
سال: 1901
ISSN: 0009-840X,1464-3561
DOI: 10.1017/s0009840x00029991