技術標籤：acmpython多邊形幾何pythonacm

採用射線法就可以判斷一個點是否在多邊形內， 只需從點出發向右側水平做出一條射線，如果跟多邊形交點個數為奇數，則點在多邊形內，否則在多邊形外。看一張圖就可以看懂啦

圖片來自：https://www.jianshu.com/p/ba03c600a557

輸入：P點座標[px, py]

多邊形poly頂點座標[[x1, y1], [x2, y2], ..., [xn, yn]]

返回：True or False

首先，利用迴圈對多邊形每條邊做同樣對待。然後，判斷是否有跟點P水平右向的射線是否有交點，若有交點，flag就翻轉一次。

看程式：

def is_in_poly(p, poly):
    """

    :param p: [x, y]
    :param poly: [[], [], [], [], ...]
    :return:
    """
    px, py = p
    flag = False
    i = 0
    length = len(poly)
    j = length - 1
    while i < length:
        x1, y1 = poly[i]
        x2, y2 = poly[j]
        if (x1 == px and y1 == py) or (x2 == px and y2 == py):
            flag = True
            break
        if y1 < py <= y2 or y2 < py <= y1:
            x = x1 + (py - y1) * (x2 - x1) / (y2 - y1)
            if x == px:
                flag = True
                break
            elif x > px:
                # convert the flag
                flag = not flag
        j = i
        i += 1

    return flag

if __name__ == '__main__':
    point = [3, 3]
    poly = [[0, 0], [7, 3], [8, 8], [5, 5]]
    print(is_in_poly(point, poly))