Circle and Rectangle Overlapping

Description

Given a circle represented as (radius, x_center, y_center) and an axis-aligned rectangle represented as (x1, y1, x2, y2), where (x1, y1) are the coordinates of the bottom-left corner, and (x2, y2) are the coordinates of the top-right corner of the rectangle.

Return True if the circle and rectangle are overlapped otherwise return False.

In other words, check if there are any point (xi, yi) such that belongs to the circle and the rectangle at the same time.

 

Example 1:

Input: radius = 1, x_center = 0, y_center = 0, x1 = 1, y1 = -1, x2 = 3, y2 = 1
Output: true
Explanation: Circle and rectangle share the point (1,0) 

Example 2:

Input: radius = 1, x_center = 0, y_center = 0, x1 = -1, y1 = 0, x2 = 0, y2 = 1
Output: true

Example 3:

Input: radius = 1, x_center = 1, y_center = 1, x1 = -3, y1 = -3, x2 = 3, y2 = 3
Output: true

Example 4:

Input: radius = 1, x_center = 1, y_center = 1, x1 = 1, y1 = -3, x2 = 2, y2 = -1
Output: false

 

Constraints:

• 1 <= radius <= 2000
• -10^4 <= x_center, y_center, x1, y1, x2, y2 <= 10^4
• x1 < x2
• y1 < y2

Solution(javascript)

/* eslint-disable camelcase */
/** https://mathworld.wolfram.com/Circle-LineIntersection.html
 * 求直线与圆的焦点, 判断焦点是否在矩形内部是不可以的！！！例如扁长的矩形
 * @param {number} radius
 * @param {number} x_center
 * @param {number} y_center
 * @param {number} x1
 * @param {number} y1
 * @param {number} x2
 * @param {number} y2
 * @return {boolean}
 */

const checkOverlap = function (radius, x_center, y_center, x1, y1, x2, y2) {
  const closet = (val, min, max) => {
    if (val > max) {
      return max
    }
    if (val < min) {
      return min
    }
    return val
  }
  const disX = closet(x_center, x1, x2) - x_center
  const disY = closet(y_center, y1, y2) - y_center
  return (disX ** 2) + (disY ** 2) <= (radius ** 2)
}