Find distance from Vector2 to nearest point in Rectangle

Question

I'm setting up collision detection and I have Walls which store their positions as rectangles. I need to figure out the distance from a Vector2 to the nearest side of a rectangle. If this was two Vector2's I could just do Vector2.Distance() but I can't find similar methods for Vector2s and Rectangles. Here is an image to illustrate what I need:

So the red dot would be my Vector2 and the blue would be my Rectagle, and I need to get the distance of the orange line. Once I have this I can check the distance for my collision detection.

Answer 1

For arbitrary shapes

The basic algorithm goes like this:

// Gets the distance from a point to a shape made of line segments.
float GetDistance(Shape shape, Vector2 point):
    min_dist = float.max;
    foreach LineSegment line in shape:
         dist = GetDistance(line, point);
         min_dist = min(min_dist, dist);
    return min_dist;

// Gets the distance from a line segment to a point
float GetDistance(LineSegment, Vector2 point):
   ...

The distance from a line segment to a point is also pretty easy to find.

For axis aligned rectangles

Axis aligned rectanges (ie, non-rotated) have the nice property that they're already rotated into the same coordinate frame as the point. This makes the problem a lot easier. Suppose the rectangle has the parameterization:

[min_x, min_y, max_x, max_y]

You can clamp to the nearest point in the rectangle, and find the distance to that point. The nearest point on the rectangle is given by:

nearest = [point.x, point.y];
if (point.x < min_x)
   nearest.x = min_x;
else if(point.x > max_x)
   nearest.x = max_x;

if(point.y < min_y)
    nearest.y = min_y;
else if(point.y > max_x)
    nearest.y = max_y;

And the distance is given by:

 (nearest - point).Length();