python - 为什么 Shapely.Geometry 库的 symmetry_difference 和交集操作明显不一致？

Question

我在 python 脚本中使用 Shapely 来确定 LinearRings 之间的交集和二维多边形之间的对称差。我遇到了我认为的容忍问题，并且我在 Shapely 引用中找不到有关此事的任何信息。我现在将介绍迄今为止我所做的事情，以尝试确定正在发生的事情。

from shapely.geometry import LinearRing, Polygon

ls_blue = LinearRing( [ [25.16,-88.42], [26.24,-87.34], [26.0,-88.42] ] )
ls_red  = LinearRing( [ [24.04, -89.54], [27.32, -86.26], [26.0, -89] ] )
inter = ls_blue.intersection(ls_red) 

-inter 显示感兴趣的段上没有线相交(下图中看到的几乎重叠的段，[25.16，-88.42]，[26.24，-87.34])和所有预期结果

p_blue = Polygon( [ [25.16,-88.42], [26.24,-87.34], [26.0,-88.42] ] )
p_red  = Polygon( [ [ [24.04, -89.54], [27.32, -86.26], [26.0, -89] ] ] )
p_xor = p_blue.symmetric_difference(p_red) 

-感兴趣的段(下图中看到的几乎重叠的段，[25.16，-88.42]，[26.24，-87.34])包含在 p_xor 多边形之一中，并且所有结果都是预期的

请注意，LinearRing 仅是多边形的边界。

示例 LinearRings/Polygons 的图表:/image/jcnFa.jpg

在这种情况下，对称差异多边形和交点将按预期计算。

但是，这个示例实际上是一些较大点系列的子集。在这些较大的点系列中，异或多边形和线的交点不会按预期计算。

两点系列如下:

c_upper = Polygon([[ -38.68 ,  -116.82 ], [ -37.6 ,  -116.79 ], [ 45.72 ,  -116.79 ], [ 45.96 ,  -116.59 ], [ 46.26 ,  -115.51 ], [ 46.26 ,  -74.39 ], [ 45.75 ,  -73.31 ], [ 45.72 ,  -73.27 ], [ 44.53 ,  -74.39 ], [ 43.55 ,  -75.26 ], [ 42.47 ,  -76.14 ], [ 41.39 ,  -76.59 ], [ 40.27 ,  -77.64 ], [ 39.22 ,  -78.51 ], [ 37.06 ,  -79.77 ], [ 35.98 ,  -80.67 ], [ 33.81 ,  -81.93 ], [ 32.73 ,  -82.79 ], [ 31.65 ,  -83.2 ], [ 29.49 ,  -85.0 ], [ 28.4 ,  -85.62 ], [ 27.32 ,  -86.26 ], [ 24.04 ,  -89.54 ], [ 23.03 ,  -90.62 ], [ 22.6 ,  -91.7 ], [ 21.76 ,  -92.78 ], [ 20.86 ,  -93.87 ], [ 20.67 ,  -94.95 ], [ 19.71 ,  -96.03 ], [ 19.52 ,  -97.11 ], [ 18.67 ,  -98.16 ], [ 18.63 ,  -98.19 ], [ 18.32 ,  -99.28 ], [ 17.49 ,  -100.36 ], [ 17.01 ,  -101.44 ], [ 16.5 ,  -102.28 ], [ 16.34 ,  -102.52 ], [ 15.51 ,  -103.6 ], [ 15.16 ,  -104.69 ], [ 14.34 ,  -105.67 ], [ 14.24 ,  -105.77 ], [ 13.97 ,  -106.85 ], [ 13.25 ,  -107.72 ], [ 13.1 ,  -107.93 ], [ 12.14 ,  -109.01 ], [ 11.5 ,  -110.1 ], [ 11.09 ,  -110.57 ], [ 10.43 ,  -111.18 ], [ 8.93 ,  -112.29 ], [ 7.84 ,  -112.86 ], [ 6.82 ,  -113.34 ], [ 6.76 ,  -113.38 ], [ 5.68 ,  -113.58 ], [ 4.6 ,  -113.67 ], [ 3.52 ,  -113.38 ], [ 2.43 ,  -112.97 ], [ 1.35 ,  -112.36 ], [ 1.24 ,  -112.26 ], [ 0.27 ,  -111.55 ], [ -0.32 ,  -111.18 ], [ -0.81 ,  -110.81 ], [ -1.89 ,  -109.66 ], [ -2.43 ,  -109.01 ], [ -3.01 ,  -107.93 ], [ -4.92 ,  -105.77 ], [ -5.74 ,  -104.69 ], [ -6.19 ,  -103.6 ], [ -7.09 ,  -102.52 ], [ -7.91 ,  -101.44 ], [ -8.35 ,  -100.36 ], [ -9.26 ,  -99.28 ], [ -9.92 ,  -98.19 ], [ -10.52 ,  -97.11 ], [ -11.54 ,  -96.03 ], [ -12.44 ,  -94.95 ], [ -13.22 ,  -93.87 ], [ -13.83 ,  -92.78 ], [ -14.88 ,  -91.74 ], [ -15.96 ,  -91.03 ], [ -17.04 ,  -90.29 ], [ -17.94 ,  -89.54 ], [ -19.21 ,  -88.42 ], [ -20.99 ,  -87.37 ], [ -21.37 ,  -87.16 ], [ -22.45 ,  -86.26 ], [ -23.53 ,  -85.81 ], [ -24.62 ,  -85.06 ], [ -25.7 ,  -84.1 ], [ -26.78 ,  -83.78 ], [ -27.74 ,  -83.05 ], [ -28.94 ,  -82.0 ], [ -30.03 ,  -81.69 ], [ -31.11 ,  -80.79 ], [ -32.19 ,  -79.83 ], [ -33.27 ,  -79.64 ], [ -34.35 ,  -78.68 ], [ -35.44 ,  -77.79 ], [ -36.52 ,  -77.37 ], [ -37.6 ,  -76.46 ], [ -38.68 ,  -75.51 ], [ -39.76 ,  -75.06 ], [ -40.08 ,  -75.47 ], [ -40.31 ,  -76.55 ], [ -40.31 ,  -77.64 ], [ -40.29 ,  -78.72 ], [ -40.29 ,  -114.42 ], [ -40.31 ,  -115.51 ], [ -39.76 ,  -116.56 ], [ -39.72 ,  -116.59 ]])

c_lower = Polygon([[ -38.68 ,  -116.82 ], [ -37.6 ,  -116.79 ], [ 45.72 ,  -116.79 ], [ 45.96 ,  -116.59 ], [ 46.26 ,  -115.51 ], [ 46.26 ,  -73.31 ], [ 45.72 ,  -72.26 ], [ 44.63 ,  -73.27 ], [ 43.52 ,  -74.39 ], [ 42.47 ,  -75.38 ], [ 41.39 ,  -76.34 ], [ 40.31 ,  -77.22 ], [ 39.22 ,  -77.67 ], [ 38.11 ,  -78.72 ], [ 37.06 ,  -79.59 ], [ 36.68 ,  -79.8 ], [ 34.9 ,  -80.85 ], [ 33.81 ,  -81.81 ], [ 32.73 ,  -82.63 ], [ 31.65 ,  -83.08 ], [ 30.46 ,  -84.13 ], [ 29.49 ,  -84.94 ], [ 29.04 ,  -85.21 ], [ 27.32 ,  -86.33 ], [ 26.24 ,  -87.34 ], [ 25.16 ,  -88.42 ], [ 24.11 ,  -89.54 ], [ 23.66 ,  -90.62 ], [ 22.9 ,  -91.7 ], [ 21.95 ,  -92.78 ], [ 21.75 ,  -93.87 ], [ 20.8 ,  -94.95 ], [ 20.61 ,  -96.03 ], [ 19.71 ,  -97.11 ], [ 19.42 ,  -98.19 ], [ 18.57 ,  -99.28 ], [ 18.15 ,  -100.36 ], [ 17.49 ,  -101.44 ], [ 16.66 ,  -102.52 ], [ 16.29 ,  -103.6 ], [ 15.39 ,  -104.69 ], [ 15.13 ,  -105.77 ], [ 14.24 ,  -106.85 ], [ 13.29 ,  -107.93 ], [ 12.86 ,  -109.01 ], [ 11.95 ,  -110.1 ], [ 11.09 ,  -111.01 ], [ 10.01 ,  -111.97 ], [ 8.93 ,  -112.55 ], [ 7.84 ,  -113.17 ], [ 6.76 ,  -113.31 ], [ 5.68 ,  -113.57 ], [ 4.6 ,  -113.57 ], [ 3.52 ,  -113.25 ], [ 2.43 ,  -112.9 ], [ 0.27 ,  -111.93 ], [ -0.63 ,  -111.18 ], [ -0.81 ,  -111.01 ], [ -2.81 ,  -109.01 ], [ -2.98 ,  -108.83 ], [ -3.73 ,  -107.93 ], [ -4.47 ,  -106.85 ], [ -5.14 ,  -105.73 ], [ -6.06 ,  -104.69 ], [ -6.95 ,  -103.6 ], [ -7.27 ,  -102.52 ], [ -8.29 ,  -101.44 ], [ -9.12 ,  -100.36 ], [ -9.44 ,  -99.28 ], [ -10.4 ,  -98.19 ], [ -11.22 ,  -97.11 ], [ -11.6 ,  -96.03 ], [ -12.62 ,  -94.95 ], [ -13.8 ,  -93.6 ], [ -14.39 ,  -92.78 ], [ -14.88 ,  -92.17 ], [ -15.32 ,  -91.7 ], [ -15.96 ,  -91.1 ], [ -16.54 ,  -90.62 ], [ -18.12 ,  -89.38 ], [ -19.17 ,  -88.46 ], [ -20.29 ,  -87.41 ], [ -21.37 ,  -87.1 ], [ -22.45 ,  -86.2 ], [ -23.53 ,  -85.24 ], [ -24.62 ,  -84.94 ], [ -25.59 ,  -84.13 ], [ -26.78 ,  -83.08 ], [ -27.86 ,  -82.82 ], [ -30.03 ,  -80.92 ], [ -30.13 ,  -80.88 ], [ -31.11 ,  -80.61 ], [ -32.08 ,  -79.8 ], [ -33.27 ,  -78.69 ], [ -34.35 ,  -78.3 ], [ -35.44 ,  -77.48 ], [ -36.52 ,  -76.52 ], [ -37.6 ,  -75.51 ], [ -38.68 ,  -74.96 ], [ -39.39 ,  -74.39 ], [ -39.76 ,  -74.12 ], [ -40.01 ,  -74.39 ], [ -40.31 ,  -75.47 ], [ -40.29 ,  -77.64 ], [ -40.29 ,  -114.42 ], [ -40.31 ,  -115.51 ], [ -39.76 ,  -116.56 ], [ -39.72 ,  -116.59 ]])

当按照与之前相同的方式进行计算时，感兴趣的线段 ([25.16,-88.42], [26.24,-87.34]) 不包含在 XOR 多边形中或作为线交点，尽管其两个端点是作为点的交集的一部分。

我的算法依赖于这样的想法:不相交的线段将成为 symmetry_difference 函数生成的多边形的一部分，因此显然上述情况会产生不良结果，我发现这相当令人不安。

我的问题是:是什么导致了案例之间的交集和对称差分运算之间的差异？

PS:如果出于可视化目的需要更多图像，请告诉我，我将创建它们。

Answer 1

这是一个精度问题，因为红色节点不是蓝色节点的一部分。对一条线上的点进行插值在计算上并不精确。您可以通过将一个几何图形捕捉到另一个几何图形来解决此问题，但要在精度误差范围内。请参阅shapely's snap function来做到这一点。

from shapely.ops import snap

print(ls_blue.intersection(snap(ls_red, ls_blue, 1e-8)))
# LINESTRING (25.16 -88.42, 26.24 -87.34)

# or try
p_blue.symmetric_difference(snap(p_red, p_blue, 1e-8))