Given a Ray R: P(t)=P_orig + t*d
where R represent all the points that start to P_orig(a,b,c) and go in ‘d’ direction;
and given a sphere with center point Q (x,y,z) and the Radius lenght K
1) Find the vector from P_orig to Q:

V = Q – P_orig = [x-a,y-b,z-c]

2) find the lenght of V

||V||=sqrt((x-a)^2 + (y-b)^2 + (z-c)^2)

3) calculate il dot product beetwen vector V and vector d

V(dot)d = cos(theta)*||V||*||d|| = >
(V(dot)d)/(||V||*||d||) = cos(theta)

theta represent the angle beetwen d and V
4) Multiply cos(theta) by ||V|| the have the distance from Q to the ray

G= ||V||*cos(theta)

5) check: if the radius is equal less then the distance, there is a collision!

if (G<=K)
{
//Collision!
}

By Christian Ruggiero on 12.02.10 9:12 am | Permalink