Article
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The Various Radii Circle Packing Problem in a Triangle
Version 1
: Received: 11 July 2024 / Approved: 11 July 2024 / Online: 12 July 2024 (09:41:54 CEST)
How to cite: Chiang, C.-S.; Chiang, Y.-T. The Various Radii Circle Packing Problem in a Triangle. Preprints 2024, 2024070931. https://doi.org/10.20944/preprints202407.0931.v1 Chiang, C.-S.; Chiang, Y.-T. The Various Radii Circle Packing Problem in a Triangle. Preprints 2024, 2024070931. https://doi.org/10.20944/preprints202407.0931.v1
Abstract
In the extended malfatti problem, the numbers of circles in the triangle are triangle numbers, because the tangency properties among the internal circles and 3 sides of the triangle have special type of structure. That is, the corner circle tangent to two sides of the triangle and two boundary circles, the boundary circles tangent to one side of the triangle and 4 other circles, and the inner circles always tangent to 6 other circles. The circles we find in extended general Malfatti’s problem has the property that the smallest radius and the largest radius for the circle has big difference. In this paper, we proposed algorithms to solve the problem that the tangency properties among circles and sides of triangle is not fixed, so that the number of circles in the triangle is not necessary a triangle numbers. The purpose of this change is try to find the radii of the circles in the triangle is within a small range.
Keywords
Malfatti’s problem; Geometric Constraint Solver; Computer Aided Geometric Design; Circle Packing line
Subject
Computer Science and Mathematics, Computational Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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