Thread: Line, sphere intersection.

Hi,

Ive been going over the analytical geo section of a 3d math primer for game development book and I am stuck on this question.

Calculate the intersection point(s), if any, between the line and the sphere.

Sphere: x^2 + y^2 + z^2 = 4
Line:
x = t
y = 2
z = 0

I know I need to get a quadratic to solve for t but I haven't been able to see exactly how to do this.

I have tried solving for t as you would with line, plane intersection and this obviously wasn't successful.

Thanks for any help or direction.

First, ponder on possible solutions. If the line fails to hit the sphere, there will be zero. If we pierce it, there will be two. If we just touch it, there will be only one.

Substitution? t^2 + 2^2 + 0^2 = 4

Then t^2 + 4 = 4

And t^2 = 0 ==> t = 0

Examine the point (0,2,0) -- Hmmmm. Only one?