December 2012
Intermediate to advanced
631 pages
13h 10m
English
Content preview from Graphics Gems III (IBM Version)
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IV.7
SOLVING THE PROBLEM OF APOLLONIUS AND OTHER RELATED PROBLEMS
Constantin A. Sevici, GTS, Chelmsford, Massachusetts
Publisher Summary
The classical problem of Apollonius is to find a circle that is tangent to three given circles. This chapter presents a computationally simple solution to two generalizations of the problem: (1) finding the circle that intersects three other circles at given angles and (2) finding the circle with a given radius that intersects two other circles at given angles. To solve the nonlinear system of equations, first the general solution of the linear subsystem is found, and then the nonlinear equation can be solved. The technique presented in the chapter can be used to solve analogous problems in higher dimensions. ...
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