# Rounded Crescent (lune) - geometry

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## Rounded Crescent (lune) - geometry

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## Re: Rounded Crescent (lune) - geometry

 In the general case, it becomes the "Problem of Apollonius": a circle tangent to three circles. Wikipedia and Wolfram Mathworld have good articles on it. Your problem is not well defined in that any number of circles can be drawn within your lune depending on how much rounding you want to do. The third circle is centered at one of the cusps and determines the amount of the round. I came up with an OpenSCAD function to solve the problem of Apollonius in the external tangents case here: https://www.thingiverse.com/thing:2360208You would need to adapt that to change some of the signs around for your problem. When investigating this, I did not find any treatments that worked out the math to an implementable solution.  This may be useful, along with a few minutes with pencil and paper: http://mathforum.org/mathimages/index.php/Problem_of_Apollonius-- Sent from: http://forum.openscad.org/_______________________________________________ OpenSCAD mailing list [hidden email] http://lists.openscad.org/mailman/listinfo/discuss_lists.openscad.org
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