get closest point to a line?

Question

I'd like to have a straight forward C# function to get a closest point (from a point P) to a line-segment, AB. An abstract function may look like this. I've search through SO but not found a usable (by me) solution. public Point getClosestPointFromLine(Point A, Point B, Point P);

Answer 1

This becomes a little easier to solve when you realize that the line from P will be perpendicular to the line AB.

You can use a dot product to find the distance of a vector from the start of the line to P, 'projected' onto the original vector.

public Vector3 NearestPointOnLine(Vector3 startPoint, Vector3 endPoint, Vector3 pnt)

{

// make a Vector3 representing the line

Vector3 line = (endPoint - startPoint);

// get the length of line to use in clamping the result to be ON line

Vector3 len = line.magnitude;

// make the length of line equal 1

line.Normalize();

// make a vector from the start of line to pnt

Vector3 v = pnt - startPoint;

// using the Dot Product gives us the length v 'projected' onto line

float d = Vector3.Dot(v, line);

// clamping this value makes sure it doesn't accidentally run past 'end'

// if you want to allow results off the end of the line, leave this off.

d = Mathf.Clamp(d, 0f, len);

// return a vector along the original line d units

return startPoint + line * d;

}