Find the closest point on a ray

Question

I've got a ray defined by P1 and P2, and then a target P3, and I want to find P4. How do I go about this? I've come to understand that I should use vector projection, but I can't get it to work. Any help? I'm using C# and XNA.

Answer 1

Closest distance point segment:

float SqDistPointSegment(Point a, Point b, Point c)
{
    Vector ab = b – a, ac = c – a, bc = c – b;
    float e = Dot(ac, ab);
    // Handle cases where c projects outside ab
    if (e <= 0.0f) return Dot(ac, ac);
    float f = Dot(ab, ab);
    if (e >= f) return Dot(bc, bc);
    // Handle cases where c projects onto ab
    return Dot(ac, ac) – e * e / f;
}

Source: Christer Ericson Real Time Collision Detection. You can find all kind of algorithms for this things in that book, take it, it is a must.

Anyways to see the distance of a point to vector is easy just do:

vector.normalize().dot(point);

It gives you the distance. The vector must be normalized.

With this distance you can multiply it for the normalized vector and added to the P1 to get P4. Then:

Vector rayDir = (P2 - P1).normalize();
P4 = P1 + rayDir.Dot(P3)*rayDir