calculating distance between a point and a rectangular box (nearest point)

Question

is there a easy formula to calculate this? i\'ve been working on some math but i can only find a way to calculate the distance directed to the center of the box, not direct

Answer 1

I think you need to analyze cases; there's no single formula. It's easier to illustrate in two dimensions:

1          2          3
    +-------------+
    |             |
4   |      0      |   5
    |             |
    +-------------+
6          7          8

The edges of the box (extended) divide the outside into 9 regions. Region 0 (inside the box) is solved by computing the distance to each edge and taking the minimum. Every point in region 1 is closest to the top left vertex, and similarly for regions 3, 6, and 8. For regions 2, 4, 5, and 7, you need to find the distance from the point to the closest edge, which is a fairly simple problem. You can determine which region a point is in by classifying it with respect to each edge. (It's easier to see how to do this by directing the edges say, counter-clockwise.) This will also tell you if the point is inside the box.

In 3D, the logic is exactly the same except that you classify with respect to the six faces and you have more cases.

The problem is simpler if the edges of the box are parallel to the coordinate axes.