Intersection between two circles (3)
Given O1(x1,y1,z1), O2(x2,y2,z2), the center of the circles and r1 and r2,
their Radius
Given M(x,y,z) the intersection, then another way is ...
O1H = x
MH = h
0102 = d
H02 = d - x
(1) R12
= h2 + x2
(2) R22
= h2 + (d - x )2
= h2 + d2 -2dx +
x2
(2) - (1) R22
- R12 = d2
- 2dx
=> x = (d2
- R22 + R12)/2d
(1) h = +/- squareroot(R12
- x2)
M = O1 + O1
H +/- HM
Then O1H = x. O1O2/||O1O2||
then inverse -x and y of O1O2/||O1O2|| vector to get an orthogonal vector