python - 在 matplotlib 中使用三角剖分时如何处理在我的几何边缘之间形成的(不需要的)三角形

Question

我有一个用空间中的 (x,y) 点列表定义的几何体。我想用这些数据创建一个三角形网格，所以我尝试了 Triangulation function in matplotlib以此目的。但是，由于我的几何体有一些曲线，算法在我的零件的边缘之间生成不需要的三角形:

红色曲线是几何图形的边缘。

有什么办法可以解决这个问题吗？也许三角测量功能不是我需要的，在这种情况下，您有什么建议可以使用吗？

以下代码来自this example .在示例中，他们通过显式命名三个点来定义三角形，而不是我想通过调用函数使用的 Delaunay 三角剖分:triang = tri.Triangulation(x, y)，这将给我与我的原始图片相同的行为。

import matplotlib.pyplot as plt
import matplotlib.tri as tri
import numpy as np

xy = np.asarray([
    [-0.101, 0.872], [-0.080, 0.883], [-0.069, 0.888], [-0.054, 0.890],
    [-0.045, 0.897], [-0.057, 0.895], [-0.073, 0.900], [-0.087, 0.898],
    [-0.090, 0.904], [-0.069, 0.907], [-0.069, 0.921], [-0.080, 0.919],
    [-0.073, 0.928], [-0.052, 0.930], [-0.048, 0.942], [-0.062, 0.949],
    [-0.054, 0.958], [-0.069, 0.954], [-0.087, 0.952], [-0.087, 0.959],
    [-0.080, 0.966], [-0.085, 0.973], [-0.087, 0.965], [-0.097, 0.965],
    [-0.097, 0.975], [-0.092, 0.984], [-0.101, 0.980], [-0.108, 0.980],
    [-0.104, 0.987], [-0.102, 0.993], [-0.115, 1.001], [-0.099, 0.996],
    [-0.101, 1.007], [-0.090, 1.010], [-0.087, 1.021], [-0.069, 1.021],
    [-0.052, 1.022], [-0.052, 1.017], [-0.069, 1.010], [-0.064, 1.005],
    [-0.048, 1.005], [-0.031, 1.005], [-0.031, 0.996], [-0.040, 0.987],
    [-0.045, 0.980], [-0.052, 0.975], [-0.040, 0.973], [-0.026, 0.968],
    [-0.020, 0.954], [-0.006, 0.947], [ 0.003, 0.935], [ 0.006, 0.926],
    [ 0.005, 0.921], [ 0.022, 0.923], [ 0.033, 0.912], [ 0.029, 0.905],
    [ 0.017, 0.900], [ 0.012, 0.895], [ 0.027, 0.893], [ 0.019, 0.886],
    [ 0.001, 0.883], [-0.012, 0.884], [-0.029, 0.883], [-0.038, 0.879],
    [-0.057, 0.881], [-0.062, 0.876], [-0.078, 0.876], [-0.087, 0.872],
    [-0.030, 0.907], [-0.007, 0.905], [-0.057, 0.916], [-0.025, 0.933],
    [-0.077, 0.990], [-0.059, 0.993]])
x = np.degrees(xy[:, 0])
y = np.degrees(xy[:, 1])

triang = tri.Triangulation(x, y)
fig1, ax1 = plt.subplots()
ax1.set_aspect('equal')
ax1.triplot(triang, 'bo-', lw=1)

Answer 1

如果您有内部形状的轮廓来绘制三角剖分，您可以应用@ThomasKühn 的答案。

否则，点与点之间可能有一个最大距离，超过该距离的三角形不应被考虑在内。在这种情况下，您可以将这些三角形屏蔽掉。

import matplotlib.pyplot as plt
import matplotlib.tri as tri
import numpy as np

xy = np.asarray([
    [-0.101, 0.872], [-0.080, 0.883], [-0.069, 0.888], [-0.054, 0.890],
    [-0.045, 0.897], [-0.057, 0.895], [-0.073, 0.900], [-0.087, 0.898],
    [-0.090, 0.904], [-0.069, 0.907], [-0.069, 0.921], [-0.080, 0.919],
    [-0.073, 0.928], [-0.052, 0.930], [-0.048, 0.942], [-0.062, 0.949],
    [-0.054, 0.958], [-0.069, 0.954], [-0.087, 0.952], [-0.087, 0.959],
    [-0.080, 0.966], [-0.085, 0.973], [-0.087, 0.965], [-0.097, 0.965],
    [-0.097, 0.975], [-0.092, 0.984], [-0.101, 0.980], [-0.108, 0.980],
    [-0.104, 0.987], [-0.102, 0.993], [-0.115, 1.001], [-0.099, 0.996],
    [-0.101, 1.007], [-0.090, 1.010], [-0.087, 1.021], [-0.069, 1.021],
    [-0.052, 1.022], [-0.052, 1.017], [-0.069, 1.010], [-0.064, 1.005],
    [-0.048, 1.005], [-0.031, 1.005], [-0.031, 0.996], [-0.040, 0.987],
    [-0.045, 0.980], [-0.052, 0.975], [-0.040, 0.973], [-0.026, 0.968],
    [-0.020, 0.954], [-0.006, 0.947], [ 0.003, 0.935], [ 0.006, 0.926],
    [ 0.005, 0.921], [ 0.022, 0.923], [ 0.033, 0.912], [ 0.029, 0.905],
    [ 0.017, 0.900], [ 0.012, 0.895], [ 0.027, 0.893], [ 0.019, 0.886],
    [ 0.001, 0.883], [-0.012, 0.884], [-0.029, 0.883], [-0.038, 0.879],
    [-0.057, 0.881], [-0.062, 0.876], [-0.078, 0.876], [-0.087, 0.872],
    [-0.030, 0.907], [-0.007, 0.905], [-0.057, 0.916], [-0.025, 0.933],
    [-0.077, 0.990], [-0.059, 0.993]])
x = np.degrees(xy[:, 0])
y = np.degrees(xy[:, 1])

triang = tri.Triangulation(x, y)

fig1, ax1 = plt.subplots()
ax1.set_aspect('equal')

# plot all triangles
ax1.triplot(triang, 'bo-', lw=0.2)

# plot only triangles with sidelength smaller some max_radius
max_radius = 2
triangles = triang.triangles

# Mask off unwanted triangles.
xtri = x[triangles] - np.roll(x[triangles], 1, axis=1)
ytri = y[triangles] - np.roll(y[triangles], 1, axis=1)
maxi = np.max(np.sqrt(xtri**2 + ytri**2), axis=1)
triang.set_mask(maxi > max_radius)

ax1.triplot(triang, color="indigo", lw=2.6)


plt.show()

细线显示所有三角形(点的凸包)，粗线仅显示边长不大于某些最大值的三角形(在本例中选择为 2).

此线程可能同样相关:matplotlib contour/contourf of **concave** non-gridded data