如何获取Python多边形内的网格点坐标？

Question

我要输入一个多边形的4个顶点的坐标，指定多边形的边（等分）的点数，目标是生成一个矩阵，里面有网格点的坐标多边形。

下图可以更好地解释我的目标：

所以在那种情况下，我将输入点 (P) 的坐标并指定我希望网格为 3 x 2。输出将是一个 3 x 2 矩阵，其坐标 (x,y) 为网格点数 (N).

我已经搜索了很多，但仍然找不到方法，老实说，我对 Python 一点经验都没有。我发现结合使用 numpy 的 meshgrid 和 matplotlib.path 的 contains_points 在多边形内创建网格，但我不知道如何获取网格点的坐标。我看到 shapely 在类似这样的问题中被大量使用，但同样，我没有这方面的经验，所以一些帮助将不胜感激！

提前谢谢大家！

Answer 1

为了解释这个方法，我们分为三个步骤：

找到 4 边形每边的刻度线
找到网格线
找到网格线的交点

def det(a, b):
    return a[0] * b[1] - a[1] * b[0]

ticks = []
A = (1, 2)  # wlog., suppose the polygon is ABCD;
B = (3, 2)
C = (3, 4)
D = (1, 4)
polygon = [A, B, C, D]
n = 3  # number of parts on each side of the grid

# we first find ticks on each side of the polygon
for j in range(4):  # because we are talking about 4-gons
    temp_ticks = []
    for i in range(n-1):
        t = (i+1)*(1/n)
        Ex = polygon[j][0] * (1-t) + polygon[(j+1) % 4][0] * t
        Ey = polygon[j][1] * (1-t) + polygon[(j+1) % 4][1] * t
        temp_ticks.append((Ex, Ey))
    if j < 2:
        ticks.append(temp_ticks)
    else: # because you are moving backward in this part
        temp_ticks.reverse()
        ticks.append(temp_ticks)

# then we find lines of the grid
h_lines = []
v_lines = []
for i in range(n-1):
    h_lines.append((ticks[0][i], ticks[2][i]))
    v_lines.append((ticks[1][i], ticks[3][i]))
        
# then we find the intersection of grid lines
for i in range(len(h_lines)):
    for j in range(len(v_lines)):
        line1 = h_lines[i]
        line2 = v_lines[j]
        xdiff = (line1[0][0] - line1[1][0], line2[0][0] - line2[1][0])
        ydiff = (line1[0][1] - line1[1][1], line2[0][1] - line2[1][1])
        div = det(xdiff, ydiff)
        if div == 0:
            raise Exception('lines do not intersect')

        d = (det(*line1), det(*line2))
        x = det(d, xdiff) / div
        y = det(d, ydiff) / div
        print(x,y) # this is an intersection point that you want

注：求交点部分代码来自here

如何获取Python多边形内的网格点坐标？

How to get the coordinates of grid points inside a polygon in Python?

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shapely