How to find the nearest point in the perimeter of a rectangle to a given point?

Question

This is a language-agnostic question. Given a rectangle's dimensions with l,t,w,h (left, top, width, height) and a point x,y, how do I find the nearest point on the perimeter of the rectangle to that point?

I have tried to resolve it in Lua, but any other language would do. So far this is my best effort:

local function nearest(x, a, b)
  if a <= x and x <= b then
    return x
  elseif math.abs(a - x) < math.abs(b - x) then
    return a
  else
    return b
  end
end

local function getNearestPointInPerimeter(l,t,w,h, x,y)
  return nearest(x, l, l+w), nearest(y, t, t+h)
end

This works for a point outside of the perimeter or in the perimeter itself. But for points inside of the perimeter it fails (it just returns x,y)

My gut tells me that the solution should be simple, but I don't seem to find it.

Answer 1

This time I'm trying to catch the minimum distance of the point toward any side of the rectangle.

local abs, min, max = math.abs, math.min, math.max

local function clamp(x, lower, upper)
  return max(lower, min(upper, x))
end

local function getNearestPointInPerimeter(l,t,w,h, x,y)
  local r, b = l+w, t+h

  x, y = clamp(x, l, r), clamp(y, t, b)

  local dl, dr, dt, db = abs(x-l), abs(x-r), abs(y-t), abs(y-b)
  local m = min(dl, dr, dt, db)

  if m == dt then return x, t end
  if m == db then return x, b end
  if m == dl then return l, y end
  return r, y
end