Unifying Method for Computing the Circumcircles of Three Circles

Topics:
Mechanical and Industrial
Tags:
Computation,
Computing,
Engineering,
Generator
Source:
International Journal of CAD/CAM

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Overview: Given a set of three generator circles in a plane, we want to find a circumcircle of these generators. This problem is a part of well-known Apollonius' 10th Problem and is frequently encountered in various geometric computations such as the Voronoi diagram for circles. In addition, there can be several degenerate configurations of the generators. For example, there may not be any circumcircle, or there could be one or two circumcircle(s) depending on the generator configuration. Sometimes, a circumcircle itself may degenerate to a line. The presented algorithm is simple and the required computation is negligible.

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Format: PDF | Size: 375KB | Date: Feb 2003 | Pages: 10

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