Question

我的多边形矢量格式如下(x1,y1,x2,y2, ...., xn,yn)。作为示例，请考虑此多边形数组： polyPoints = [3,5,7,8,9,5]

如何获得从这些点生成的多边形内的所有索引（或坐标）？

到目前为止，我看到的答案要求您先创建2D蒙版，然后才能获得多边形内的索引。

Answer 1

您可以使用scikit-image：

import numpy as np
from skimage.draw import polygon
points = [3,5,7,8,9,5]
r, c = polygon(points[1::2], points[::2])
print(r, c)

输出是：

[5 5 5 5 5 5 6 6 6 6 7 7] [3 4 5 6 7 8 5 6 7 8 6 7]

Answer 2

使用面具可能会尽可能高效。这是一些效率相当低的算法，但可能会被优化为接近掩码方法。这基本上是一个面具，但在线上。

方法是：

查找所有边线的方程式
查找边界框
对于边界框内的每个y（或x，取较小者），计算在该y处与水平线（y = yi）相交的边，并找到它们相交的x。
对于边界框内的每个x，找到x行右边的y = yi相交的边数。如果边数是奇数，则点（x，y）在多边形内。

它适用于简单的方形几何体。

import numpy as np

# taken from: https://stackoverflow.com/questions/20677795/how-do-i-compute-the-intersection-point-of-two-lines-in-python
def line(p1, p2):
    A = (p1[1] - p2[1])
    B = (p2[0] - p1[0])
    C = (p1[0]*p2[1] - p2[0]*p1[1])
    return A, B, -C


def intersection(L1, L2):
    D  = L1[0] * L2[1] - L1[1] * L2[0]
    Dx = L1[2] * L2[1] - L1[1] * L2[2]
    Dy = L1[0] * L2[2] - L1[2] * L2[0]
    if D != 0:
        x = Dx / D
        y = Dy / D
        return x,y
    else:
        return False


# polyPoints = np.array([0, 0, 4, 0,4, 4, 0, 4])
polyPoints = np.array([[3,5,7,8,9,5]])
polyPoints = polyPoints.reshape(-1, 2)
npoints = polyPoints.shape[0]
polyEgdes = []

for i in range(npoints):
    point1, point2 = polyPoints[i, :], polyPoints[(i+1) % npoints, :]
    polyEgdes.append(line(point1, point2))

# bounding box
boundingBox = np.vstack((polyPoints.min(axis=0), polyPoints.max(axis=0)))


inside_points = []

for y in range(boundingBox[0, 1], boundingBox[1, 1]):
    x_intersect = []
    for l in polyEgdes:
        # y_ins should be same as y
        insect_point = intersection(l, [0, y, 0])
        if insect_point:
            x_intersect.append(insect_point[0])

    x_intersect = np.array(x_intersect)
    for x in range(boundingBox[0, 0]+1, boundingBox[1, 0]-1):
        x_int_points = x_intersect[(x_intersect - x) >= 0]

        if len(x_int_points) % 2 == 1:
            inside_points.append((x, y))

print(inside_points)

numpy：获取多边形内的索引而不创建蒙版

2 个答案: