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Sphere/Ray intersection?

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Can anyone tell me the math involved with finding the point on a sphere where a ray intersects it? Its easy enough with a tessalated sphere (plane/ray intersection) but I''m trying to find the exact point. Anyone?

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I hope I''m not mistaken, but here is what I think of your problem:

Lets''s say we have the sphere (xs,ys,zs) -center , r- radius
A point on the sphere (x,y,z) is defined by :
(x-xs)^2 + (y-ys)^2 + (z-zs)^2 = r^2 (1)

Now the ray should have a start point (x0,y0,z0) and a vector (xv,yv,zv)
A point on the ray (x,y,z) is defined by :
(x-x0) (y-y0) (z-z0)
----- = ------ = ------ (2)
xv yv zv

now, take a point on the ray with an arbitrary x and find y and z for it using the 2nd equation. Put them in the 1st equation and you should have a 2nd degree equation that you can solve to find the x of the intersection. Using (2) you now have y and z.
Hope this does it for you. Horia

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