matplotlib **凹**非网格数据的轮廓/轮廓 [英] matplotlib contour/contourf of **concave** non-gridded data

问题描述

我想对未栅格化的3D数据(x，y，z)进行matplotlib contour或contourf绘图，该数据在某种程度上在x和y中呈C形(请参见草图)-因此，数据周围的外壳在x和y中是凹形的.

I'd like to do a matplotlib contour or contourf plot of non-gridded 3D data (x, y, z) which is somehow C-shaped in x and y (see sketch) -- therefore part of the enclosing hull around the data is concave in x and y.

通常，我首先通过对非网格3D数据进行插值来进行绘制

Usually I do plots of non-gridded 3D data by first interpolating it with

from matplotlib.mlab import griddata
griddata...

但是这会在数据的凹入部分中产生伪像，从而通过插值填充凹入部分.

but this generates artifacts in the concave part of the data such that the concave part is filled by the interpolation.

是否可以进行插值或等高线f/等高线图 数据的凹部受到尊重吗?

Is it possible to do the interpolating or contourf/contour plots such that the concave part of the data is respected?

推荐答案

根据条件进行屏蔽

下面是一个示例，该示例说明了如何使用tricontourf进行遮罩以获取凹形，而无需在数据外部插入部分.它依赖于根据条件屏蔽数据的能力.

Masking by condition

Below is an example on how to use tricontourf with masking to obtain a concave shape without interpolated portions outside the data. It relies on the ability to mask the data depending on a condition.

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

# create some data
rawx = np.random.rand(500)
rawy = np.random.rand(len(rawx))
cond01 = (rawx-1)**2 + rawy**2 <=1
cond02 = (rawx-0.7)**2 + rawy**2 >0.3
x = rawx[cond01 & cond02]
y = rawy[cond01 & cond02]
f = lambda x,y: np.sin(x*4)+np.cos(y)
z = f(x,y)
# now, x,y are points within a partially concave shape

triang0 = tri.Triangulation(x, y)
triang = tri.Triangulation(x, y)
x2 = x[triang.triangles].mean(axis=1) 
y2 = y[triang.triangles].mean(axis=1)
#note the very obscure mean command, which, if not present causes an error.
#now we need some masking condition.
# this is easy in this case where we generated the data according to the same condition
cond1 = (x2-1)**2 + y2**2 <=1
cond2 = (x2-0.7)**2 + (y2)**2 >0.3
mask = np.where(cond1 & cond2,0,1)
# apply masking
triang.set_mask(mask)


fig, (ax, ax2) = plt.subplots(ncols=2, figsize=(6,3))
ax.set_aspect("equal")
ax2.set_aspect("equal")

ax.tricontourf(triang0, z,  cmap="Oranges")
ax.scatter(x,y, s=3, color="k")

ax2.tricontourf(triang, z,  cmap="Oranges")
ax2.scatter(x,y, s=3, color="k")

ax.set_title("tricontourf without mask")
ax2.set_title("tricontourf with mask")
ax.set_xlim(0,1)
ax.set_ylim(0,1)
ax2.set_xlim(0,1)
ax2.set_ylim(0,1)

plt.show()

如果您无法获得确切的条件，但是在点之间具有最大的边长(距离)，则可以采用以下解决方案.它将遮盖所有至少有一个边大于某个最大距离的三角形.如果点密度很高，则可以很好地应用.

If you do not have access to the exact condition, but have a maximum side-length (distance) between points, the following would be a solution. It would mask out all triangles for which at least one side is longer than some maximum distance. This can be well applied if the point density is rather high.

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

# create some data
rawx = np.random.rand(500)
rawy = np.random.rand(len(rawx))
cond01 = (rawx-1)**2 + rawy**2 <=1
cond02 = (rawx-0.7)**2 + rawy**2 >0.3
x = rawx[cond01 & cond02]
y = rawy[cond01 & cond02]
f = lambda x,y: np.sin(x*4)+np.cos(y)
z = f(x,y)
# now, x,y are points within a partially concave shape

triang1 = tri.Triangulation(x, y)
triang2 = tri.Triangulation(x, y)
triang3 = tri.Triangulation(x, y)

def apply_mask(triang, alpha=0.4):
    # Mask triangles with sidelength bigger some alpha
    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)
    # apply masking
    triang.set_mask(maxi > alpha)

apply_mask(triang2, alpha=0.1)
apply_mask(triang3, alpha=0.3)

fig, (ax1, ax2, ax3) = plt.subplots(ncols=3, figsize=(9,3))

ax1.tricontourf(triang1, z,  cmap="Oranges")
ax1.scatter(x,y, s=3, color="k")

ax2.tricontourf(triang2, z,  cmap="Oranges")
ax2.scatter(x,y, s=3, color="k")

ax3.tricontourf(triang3, z,  cmap="Oranges")
ax3.scatter(x,y, s=3, color="k")

ax1.set_title("tricontourf without mask")
ax2.set_title("with mask (alpha=0.1)")
ax3.set_title("with mask (alpha=0.3)")

for ax in (ax1, ax2, ax3):
    ax.set(xlim=(0,1), ylim=(0,1), aspect="equal")

plt.show()

可以看出，在此处找到正确的参数(alpha)可能需要一些调整.

As can be seen, finding the correct parameter (alpha) here is may need some tweaking.

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