A generalized Malfatti problem

作者：Chiang, Ching-Shoei; Hoffmann, Christoph M.^*; Rosen, Paul

来源：Computational Geometry-Theory and Applications, 2012, 45(8): 425-435.

DOI：10.1016/j.comgeo.2010.06.005

• Malfatti's problem
• Circle packing
• Geometric constraint solving
• CPU programming

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 triangle's 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.

• 出版日期2012-10
• 单位苏州大学