Posted by dxli on Oct 28, 2014; 4:00pm
URL: https://forum.librecad.org/preparation-for-2-0-6-any-blocker-tp5710555p5710579.html

It works well here for me, after the commit in master branch:

https://github.com/LibreCAD/LibreCAD/commit/9c7f68ff1ccb3901b677bc9a7473ca43e6703289

The basic idea is to avoid using intersections from two hyperbola.

The new algorithm takes one hyperbola, say H(C, P1), and the perpendicular bisector line of P1 and P2, since any circle passing P1 and P2 must center on this bisector line.

Therefore, instead of using two hyperbolas, a hyperbola and a straight line are used. Reducing the original (quadratic quadratic) equation system to (quadratic, linear) system.

(Quadratic, linear) can be reduced to a single quadratic equation. while the (quadratic quadratic) equation system is reduced to a quartic equation in general.

A minor addition, I also draw centers of possible tangential circles in preview, and you can simply move mouse pointer to be close to one of them to select.