Algebraic solution for geometry from dimensional constraints
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
Solving geometric constraints by homotopy
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Fast computation of generalized Voronoi diagrams using graphics hardware
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Decomposition plans for geometric constraint systems, part I: performance measures for CAD
Journal of Symbolic Computation
Decomposition plans for geometric constraint problems, part II: new algorithms
Journal of Symbolic Computation
Computational Geometry: Theory and Applications
Revisiting variable radius circles in constructive geometric constraint solving
Computer Aided Geometric Design
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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.