Re: tangent of a sphere

From: Hans-Bernhard Bröker <HBBroeker@xxxxxxxxxxx>
Date: Sun, 13 Apr 2008 23:40:42 +0200

whatazor wrote:

is there an optimized algorithm that allow me to calculate the tangent
point on a sphere, given

a sphere,
a point outside the sphere (the first point of the segment terminating
with the tangent point),
a plane (that intersects the sphere and contains the sphere center
and the segment initial point- tangent point),
a direction for choosing one of the two tangent points?

1) Restrict your problem to 2D by only considering the plane.
2) The problem is now to find a tangent to a circle through a point. The theorem of Thales makes that trivial: a circle around the point halfway between the original circle's center and the external point intersects the original circle in the tangent points.
3) Pick the one you wanted
4) Go back to 3D.

.

References:
- tangent of a sphere
  - From: whatazor

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