如何在矩形的周长中找到最接近给定点的点? [英] How to find the nearest point in the perimeter of a rectangle to a given point?

问题描述

这是一个与语言无关的问题.给定矩形的尺寸为l,t,w,h(左，顶部，宽度，高度)，并指定一个点x,y，如何找到矩形周长上与该点最近的点?

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?

我试图用Lua解决它，但是任何其他语言都可以.到目前为止，这是我的最大努力:

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

这适用于周边的外部点或周边的点.但是对于外围的内部点，它会失败(它只会返回x,y)

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)

我的直觉告诉我解决方案应该很简单，但我似乎找不到.

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

推荐答案

这一次，我试图捕捉该点朝向矩形任意边的最小距离.

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

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