My Math Forum calculate C position

 Geometry Geometry Math Forum

August 2nd, 2019, 09:37 AM   #1
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calculate C position

I need to calculate x and z of C

Here are the informations that I have:

-> P (xp, yp, zp)

-> C (xc, yc, zc) = (xc, yp + h, zc)

-> F (xf, yf, zf)

- C is given by the intersection of l and the circumference n

- l is the line that passes through F, m and n

* n is a circumference of radius r and center (xp, yp + h, zp) (in the plane xz)

* m is a line parallel to Y axis that passes through P

obs: l does not necessarily passes through the center of n as the drawing suggests.

If I'm not wrong, this only happens when yf = yc. In this case, there would be two intersections of l and n. If so, C is given by the one farthest from F.

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