将散点图转换为轮廓图，每个点都变成高地 [英] Convert Scatter to Contour, every dot turns into a highland

问题描述

如何基于散点图构建等高线图(特别是地形图)，以便将每个散点转换为给定半径内最高的圆形区域，即相邻区域是否低于原始点的区域?

How to build a Contour plot (specifically, topographic map) based on a Scatter plot, so that every scatter dot is converted into a circular area being the highest one in a given radius, i.e., any adjoining area is lower than the original dot’s area?

在示例性图像上，黄色邻接区域低于高地#6.请注意，我不是要建立数据密度图.

On the exemplary image, the yellow adjoining area is lower than the highland #6. Note, I am not trying to build a data density plot.

所有输入的散点都高于绿草水平.

All input scatter dots are higher than the green grass level.

我试图按照问题制作轮廓，使用matplotlib的griddata插值x，y和z坐标的散布. 在第二张图上，您可以看到插值后生成的原始叠加散点图和轮廓图.但是，点#6并非像第一幅图像那样最高，并且雪山从原始的白色点#1移开了.

I tried to interpolate the x, y, and z coordinates using matplotlib’s griddata as proposed in question Make contour of scatter. On the second figure you see the original superimposed scatter plot and contour plot generated after interpolation. However, the dot #6 is not the highest one like it is on the first image, and the snow-capped mountain is shifted from the original white dot #1.

这是我的坐标:

x = [34, 74, 34, 70, 4, 42, 10, 56, 50, 0, 15, 104, 53, 27]
y = [44, 52, 21, 25, 34, 54, 70, 77, 0, 50, 5, 53, 18, 86]
z = [0.9, 0.8, 0.8, 0.8, 0.7, 0.7, 0.7, 0.7, 0.7, 0.6, 0.6, 0.6, 0.6, 0.6]

任何想法都受到高度赞赏.

Any ideas are highly appreciated.

推荐答案

我使用bivariate_normal函数获取每个点的高程.这是可以尝试的工作代码:

I use bivariate_normal function to get elevation for each point. Here is the working code to try:

import numpy as np
import matplotlib.cm as cm
import matplotlib.pyplot as plt
import matplotlib.mlab as mlab

# data
x = np.array([34, 74, 34, 70, 4, 42, 10, 56, 50, 0, 15, 104, 53, 27])
y = np.array([44, 52, 21, 25, 34, 54, 70, 77, 0, 50, 5, 53, 18, 86])
z = np.array([0.9, 0.8, 0.8, 0.9, 0.7, 0.7, 0.7, 0.7, 0.7, 0.6, 0.6, 0.6, 0.6, 0.6])

# the radius that needs to specified for each point
# radius = sigmax=sigmay for bivariate_normal
#rad = [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]  # OK
rad = [4, 6, 7, 3, 5, 5, 7, 6, 6, 7, 6, 7, 6, 7]   # better

# get limits of plot
xmin, xmax = x.min(), x.max()
ymin, ymax = y.min(), y.max()

# some settings
delta = 0.5

# create mesh grid for plotting area
xs = np.arange(xmin-delta, xmax+delta*2, delta)
ys = np.arange(ymin-delta, ymax+delta*2, delta)
XX, YY = np.meshgrid(xs, ys)

# compute elevation Z for each point in the grid mesh
ZZ=0
for mx, my, mz, mr in zip(x, y, z, rad):
    sigmax = mr
    sigmay = mr
    vm = mlab.bivariate_normal(0, 0, sigmax, sigmay, 0, 0)  # max value

    # mz and vm are used to correct the elevation obtained from bivar-normal
    ZZ += mlab.bivariate_normal(XX, YY, sigmax, sigmay, mx, my) * mz / vm

# prep fig, ax
fig = plt.figure(figsize=(9, 9))
ax = fig.add_subplot(111)

# choose cmap as you need
ctf=plt.contourf(XX, YY, ZZ, linewidth=1, cmap=cm.gist_earth_r)
plt.scatter(x, y, s=rad, color='r', zorder=10)

plt.xlim(xmin-delta, xmax+delta)
plt.ylim(ymin-delta, ymax+delta)

plt.colorbar(ctf)
plt.show()

结果图:

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