Derousseau's Generalization of the Malfatti circles

Barycentric Coordinates


Jump
[Guy]
[Lob & Richmond]
(0**)
(1**)
(2**)
(3**)

\[\begin{aligned}A^{\prime} &= \left(\dfrac{2\left(1+\cos\dfrac{\beta}{2}\right)\left(1+\cos\dfrac{\gamma}{2}\right)}{1+\cos\dfrac{\alpha}{2}}-1\right){\sin{\alpha}}:{\sin{\beta}}:{\sin{\gamma}}\\B^{\prime} &= {\sin{\alpha}}:\left(\dfrac{2\left(1+\cos\dfrac{\alpha}{2}\right)\left(1+\cos\dfrac{\gamma}{2}\right)}{1+\cos\dfrac{\beta}{2}}-1\right){\sin{\beta}}:{\sin{\gamma}}\\C^{\prime} &= {\sin{\alpha}}:{\sin{\beta}}:\left(\dfrac{2\left(1+\cos\dfrac{\alpha}{2}\right)\left(1+\cos\dfrac{\beta}{2}\right)}{1+\cos\dfrac{\gamma}{2}}-1\right){\sin{\gamma}}\end{aligned}\]
Guy L & R \(\alpha\) \(\beta\) \(\gamma\)
0 (000) \(A\) \(B\) \(C\)
1 (002) \(-A\) \(-B\) \(2\pi-C\)
2 (020) \(-A\) \(2\pi-B\) \(-C\)
3 (022) \(A\) \(2\pi+B\) \(2\pi+C\)
4 (200) \(2\pi-A\) \(-B\) \(-C\)
5 (202) \(2\pi+A\) \(B\) \(2\pi+C\)
6 (220) \(2\pi+A\) \(2\pi+B\) \(C\)
7 (222) \(2\pi-A\) \(2\pi-B\) \(2\pi-C\)
0a (011) \(-A\) \(\pi-B\) \(\pi-C\)
1a (013) \(A\) \(\pi+B\) \(3\pi+C\)
2a (031) \(A\) \(3\pi+B\) \(\pi+C\)
3a (033) \(-A\) \(3\pi-B\) \(3\pi-C\)
4a (211) \(2\pi+A\) \(\pi+B\) \(\pi+C\)
5a (213) \(2\pi-A\) \(\pi-B\) \(3\pi-C\)
6a (231) \(2\pi-A\) \(3\pi-B\) \(\pi-C\)
7a (233) \(2\pi+A\) \(3\pi+B\) \(3\pi+C\)
0b (101) \(\pi-A\) \(-B\) \(\pi-C\)
1b (103) \(\pi+A\) \(B\) \(3\pi+C\)
2b (121) \(\pi+A\) \(2\pi+B\) \(\pi+C\)
3b (123) \(\pi-A\) \(2\pi-B\) \(3\pi-C\)
4b (301) \(3\pi+A\) \(B\) \(\pi+C\)
5b (303) \(3\pi-A\) \(-B\) \(3\pi-C\)
6b (321) \(3\pi-A\) \(2\pi-B\) \(\pi-C\)
7b (323) \(3\pi+A\) \(2\pi+B\) \(3\pi+C\)
0c (110) \(\pi-A\) \(\pi-B\) \(-C\)
1c (112) \(\pi+A\) \(\pi+B\) \(2\pi+C\)
2c (130) \(\pi+A\) \(3\pi+B\) \(C\)
3c (132) \(\pi-A\) \(3\pi-B\) \(2\pi-C\)
4c (310) \(3\pi+A\) \(\pi+B\) \(C\)
5c (312) \(3\pi-A\) \(\pi-B\) \(2\pi-C\)
6c (330) \(3\pi-A\) \(3\pi-B\) \(-C\)
7c (332) \(3\pi+A\) \(3\pi+B\) \(2\pi+C\)

Hiroyasu Kamo