How to find closest point on line?

Question

I have a point (A) and a vector (V) (suppose it's infinite length), and I want to find the closest point (B) on the line to my original point (A). What's the simplest expression using Unity Vector2's or Vector3's to get this?

Answer 1

Infinite length:

If you have line with infinite length with start and direction, calculate the dot product of the line direction then multiply it by the direction and add the starting point to it.

public Vector2 FindNearestPointOnLine(Vector2 origin, Vector2 direction, Vector2 point)
{
    direction.Normalize();
    Vector2 lhs = point - origin;

    float dotP = Vector2.Dot(lhs, direction);
    return origin + direction * dotP;
}

Finite length:

If you have line with finite length with start to end positions, get the heading the perform a projection from the starting point to the. Also, use Mathf.Clamp to clap it just in case the line is off.

public Vector2 FindNearestPointOnLine(Vector2 origin, Vector2 end, Vector2 point)
{
    //Get heading
    Vector2 heading = (end - origin);
    float magnitudeMax = heading.magnitude;
    heading.Normalize();

    //Do projection from the point but clamp it
    Vector2 lhs = point - origin;
    float dotP = Vector2.Dot(lhs, heading);
    dotP = Mathf.Clamp(dotP, 0f, magnitudeMax);
    return origin + heading * dotP;
}