A Generalized Malfatti Problem
A Generalized Malfatti Problem |
Abstract
Malfatti’s problem, first published in 1803, is commonly understood to ask fitting three circles into a given triangle such that they are tangent to each other, externally, and such that each circle is tangent to a pair of the triangles sides. There are many solutions based on geometric constructions, as well as generalizations in which the triangle sides are assumed to be circle arcs. A generalization that asks to fit six circles into the triangle, tangent to each other and to the triangle sides, has been considered a good example of a problem that requires sophisticated numerical iteration to solve by computer. We analyze this problem and show how to solve it quickly.
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Citation
Ching-Shoei Chiang, Christoph M Hoffmann, and Paul Rosen. A Generalized Malfatti Problem. Computational Geometry: Theory and Applications, 2012.
Bibtex
@article{chiang2012generalized, title = {A Generalized Malfatti Problem}, author = {Chiang, Ching-Shoei and Hoffmann, Christoph M and Rosen, Paul}, journal = {Computational Geometry: Theory and Applications}, volume = {45}, pages = {425--435}, year = {2012}, keywords = {Malfatti's problem, circle packing, geometric constraint solving, GPU programming}, abstract = {Malfatti's problem, first published in 1803, is commonly understood to ask fitting three circles into a given triangle such that they are tangent to each other, externally, and such that each circle is tangent to a pair of the triangles sides. There are many solutions based on geometric constructions, as well as generalizations in which the triangle sides are assumed to be circle arcs. A generalization that asks to fit six circles into the triangle, tangent to each other and to the triangle sides, has been considered a good example of a problem that requires sophisticated numerical iteration to solve by computer. We analyze this problem and show how to solve it quickly.} }