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 have been looking for this and I think I have a solution, for the case on which the box is axis-aligned (a fairly common case)

I believe that in that case you can calculate the distance like this:

function distance_aux(p, lower, upper)
  if p < lower then return lower - p end
  if p > upper then return p - upper end
  return min(p - lower, upper - p)
end

function distance(point, box)
  local dx = distance_aux(point.x, box.left, box.right)
  local dy = distance_aux(point.y, box.top, box.bottom)
  return sqrt(dx * dx + dy * dy)
end

This can be extended to z, of course.