The simplest way to build a three-dimensional surface of given three-dimensional points

Question

I have many (289) three-dimensional points with xyz coordinates that look like this:

When building a three-dimensional space with points in order, but I have problems with the surface There are several points:

for i in range(30): output.write(str(X[i])+' '+str(Y[i])+' '+str(Z[i])+'\n') -0.807237702464 0.904373229492 111.428744443 -0.802470821517 0.832159465335 98.572957317 -0.801052795982 0.744231916692 86.485869328 -0.802505546206 0.642324228721 75.279804677 -0.804158144115 0.52882485495 65.112895758 -0.806418040943 0.405733109371 56.1627277595 -0.808515314192 0.275100227689 48.508994388 -0.809879521648 0.139140394575 42.1027499025 -0.810645106092 -7.48279012695e-06 36.8668106345 -0.810676720161 -0.139773175337 32.714580273 -0.811308686707 -0.277276065449 29.5977405865 -0.812331692291 -0.40975978382 27.6210856615 -0.816075037319 -0.535615685086 27.2420699235 -0.823691366944 -0.654350489595 29.1823292975 -0.836688691603 -0.765630198427 34.2275056775 -0.854984518665 -0.86845932028 43.029581434 -0.879261949054 -0.961799684483 55.9594146815 -0.740499820944 0.901631050387 97.0261463995 -0.735011699497 0.82881933383 84.971061395 -0.733021568161 0.740454485354 73.733621269 -0.732821755233 0.638770044767 63.3815970475 -0.733876941678 0.525818698874 54.0655910105 -0.735055978521 0.403303715698 45.90859502 -0.736448900325 0.273425879041 38.935709456 -0.737556181137 0.13826504904 33.096106049 -0.738278724065 -9.73058423274e-06 28.359664343 -0.738507612286 -0.138781586244 24.627237837 -0.738539663773 -0.275090412979 21.857410904 -0.739099040189 -0.406068448513 20.1110519655 -0.741152200369 -0.529726022182 19.7019157715 

There are no equal values ​​of X and Y. X is from -0.8 to 0.8, Y is from -0.9 to 0.9, and z is from 0 to 111.

If possible, how to make a three-dimensional surface using these points?

Answer 1

Please look at Axes3D.plot_surface or other Axes3D methods. Here you can find examples and inspiration, here or here .

Edit:

Z-data that is not on a regular XY grid (equal distances between grid points in one dimension) is not trivial to construct as a triangulated surface. For a given set of irregular (X, Y) coordinates, there are several possible triangulations. One triangulation can be calculated using the Delaunay "nearest neighbor" algorithm. This can be done in matplotlib. However, this is still a bit tedious:

http://matplotlib.1069221.n5.nabble.com/Plotting-3D-Irregularly-Triangulated-Surfaces-An-Example-td9652.html

It looks like support will be improved:

http://matplotlib.org/examples/pylab_examples/tripcolor_demo.html http://matplotlib.1069221.n5.nabble.com/Custom-plot-trisurf-triangulations-tt39003.html

Using http://docs.enthought.com/mayavi/mayavi/auto/example_surface_from_irregular_data.html I was able to find a very simple Mayavi based solution:

 import numpy as np from mayavi import mlab X = np.array([0, 1, 0, 1, 0.75]) Y = np.array([0, 0, 1, 1, 0.75]) Z = np.array([1, 1, 1, 1, 2]) # Define the points in 3D space # including color code based on Z coordinate. pts = mlab.points3d(X, Y, Z, Z) # Triangulate based on X, Y with Delaunay 2D algorithm. # Save resulting triangulation. mesh = mlab.pipeline.delaunay2d(pts) # Remove the point representation from the plot pts.remove() # Draw a surface based on the triangulation surf = mlab.pipeline.surface(mesh) # Simple plot. mlab.xlabel("x") mlab.ylabel("y") mlab.zlabel("z") mlab.show() 

This is a very simple example based on 5 points. 4 of them are at level z 1:

 (0, 0) (0, 1) (1, 0) (1, 1) 

One of them is at z-level 2:

 (0.75, 0.75) 

The Delaunay algorithm gets the correct triangulation, and the surface is drawn as expected:

I ran the above code on Windows after installing Python (x, y) using the command

 ipython -wthread script.py 

Answer 2

Solution with matplotlib:

 #!/usr/bin/python3 import sys import matplotlib import matplotlib.pyplot as plt from matplotlib.ticker import MaxNLocator from matplotlib import cm from mpl_toolkits.mplot3d import Axes3D import numpy from numpy.random import randn from scipy import array, newaxis # ====== ## data: DATA = array([ [-0.807237702464, 0.904373229492, 111.428744443], [-0.802470821517, 0.832159465335, 98.572957317], [-0.801052795982, 0.744231916692, 86.485869328], [-0.802505546206, 0.642324228721, 75.279804677], [-0.804158144115, 0.52882485495, 65.112895758], [-0.806418040943, 0.405733109371, 56.1627277595], [-0.808515314192, 0.275100227689, 48.508994388], [-0.809879521648, 0.139140394575, 42.1027499025], [-0.810645106092, -7.48279012695e-06, 36.8668106345], [-0.810676720161, -0.139773175337, 32.714580273], [-0.811308686707, -0.277276065449, 29.5977405865], [-0.812331692291, -0.40975978382, 27.6210856615], [-0.816075037319, -0.535615685086, 27.2420699235], [-0.823691366944, -0.654350489595, 29.1823292975], [-0.836688691603, -0.765630198427, 34.2275056775], [-0.854984518665, -0.86845932028, 43.029581434], [-0.879261949054, -0.961799684483, 55.9594146815], [-0.740499820944, 0.901631050387, 97.0261463995], [-0.735011699497, 0.82881933383, 84.971061395], [-0.733021568161, 0.740454485354, 73.733621269], [-0.732821755233, 0.638770044767, 63.3815970475], [-0.733876941678, 0.525818698874, 54.0655910105], [-0.735055978521, 0.403303715698, 45.90859502], [-0.736448900325, 0.273425879041, 38.935709456], [-0.737556181137, 0.13826504904, 33.096106049], [-0.738278724065, -9.73058423274e-06, 28.359664343], [-0.738507612286, -0.138781586244, 24.627237837], [-0.738539663773, -0.275090412979, 21.857410904], [-0.739099040189, -0.406068448513, 20.1110519655], [-0.741152200369, -0.529726022182, 19.7019157715], ]) Xs = DATA[:,0] Ys = DATA[:,1] Zs = DATA[:,2] # ====== ## plot: fig = plt.figure() ax = fig.add_subplot(111, projection='3d') surf = ax.plot_trisurf(Xs, Ys, Zs, cmap=cm.jet, linewidth=0) fig.colorbar(surf) ax.xaxis.set_major_locator(MaxNLocator(5)) ax.yaxis.set_major_locator(MaxNLocator(6)) ax.zaxis.set_major_locator(MaxNLocator(5)) fig.tight_layout() plt.show() # or: # fig.savefig('3D.png') 

Result:

Probably not very pretty. But it will be if you provide more points.

Answer 3

I am doing this with some lines in python using PANDAS, the plot is beautiful!

 from mpl_toolkits.mplot3d import Axes3D import matplotlib.pyplot as plt from matplotlib import cm import numpy as np import pandas as pd from sys import argv file = argv[1] x,y,z = np.loadtxt(file, unpack=True) df = pd.DataFrame({'x': x, 'y': y, 'z': z}) fig = plt.figure() ax = Axes3D(fig) surf = ax.plot_trisurf(df.x, df.y, df.z, cmap=cm.jet, linewidth=0.1) fig.colorbar(surf, shrink=0.5, aspect=5) plt.savefig('teste.pdf') plt.show() 

Collapsing Wave Equations

A little prettier! In my case, I use colormap JET Colormaps Matplotlib , but there are other types of color and quality maps. Take a look at the link earlier.