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I've two spheres in cartesian space: $(x_1, y_1, z_1, r_1)$ and $(x_2, y_2, z_2, r_2)$.

They don't intersect each other.

I want to calculate the conical frustum tangent to these two spheres.

In particular, I need to find the center point and the radius of bases of conical frustum.

How can I do it?

EDIT:

My problem is represented in this image (che 2D equivalent one).

I need to find red segments, that in the 3D space problem are circles. In order to find these I need to know (always in 3D) the center and the radius of red shapes, that always in 3D are conical frustum bases.

enter image description here

Jepessen
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  • There are many frusta tangent to both spheres (a quick mental exercise suggests four degrees of freedom). Are there any additional conditions you want to impose? – Travis Willse Oct 31 '14 at 16:16
  • I've edited the problem. Pleas check it. – Jepessen Oct 31 '14 at 16:34
  • This is a variation on the problem of finding the common (external) tangents to two circles; you might be able to adapt the solution given here: http://math.stackexchange.com/questions/211538/common-tangent-to-two-circles – Travis Willse Oct 31 '14 at 17:15
  • Ok I'll check it. Thanks. – Jepessen Nov 03 '14 at 09:38

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