surface plots in matplotlib

Question

I have a list of 3-tuples representing a set of points in 3D space  I want to plot a surface that covers all these points   The plot surface function in the mplot3d package requires as arguments X Y and Z to be 2d arrays  Is plot surface the right function to plot surface and how do I transform my data into the required format   data     x1 y1 z1   x2 y2 z2         xn yn zn

User · Answer

In Matlab I did something similar using the delaunay function on the x, y coords only (not the z), then plotting with trimesh or trisurf, using z as the height.

SciPy has the Delaunay class, which is based on the same underlying QHull library that the Matlab's delaunay function is, so you should get identical results.

From there, it should be a few lines of code to convert this Plotting 3D Polygons in python-matplotlib example into what you wish to achieve, as Delaunay gives you the specification of each triangular polygon.

User · Answer

For surfaces it s a bit different than a list of 3-tuples  you should pass in a grid for the domain in 2d arrays    If all you have is a list of 3d points  rather than some function f x  y  - gt  z  then you will have a problem because there are multiple ways to triangulate that 3d point cloud into a surface     Here s a smooth surface example   import numpy as np from mpl toolkits mplot3d import Axes3D     Axes3D import has side effects  it enables using projection  3d  in add subplot import matplotlib pyplot as plt import random  def fun x  y       return x  2   y  fig   plt figure   ax   fig add subplot 111  projection  3d   x   y   np arange -3 0  3 0  0 05  X  Y   np meshgrid x  y  zs   np array fun np ravel X   np ravel Y    Z   zs reshape X shape   ax plot surface X  Y  Z   ax set xlabel  X Label   ax set ylabel  Y Label   ax set zlabel  Z Label    plt show

User · Answer

This is not a general solution but might help many of those who just typed   quot matplotlib surface plot quot  in Google and landed here  Suppose you have data     x1 y1 z1   x2 y2 z2         xn yn zn    then you can get three 1-d lists using x  y  z   zip  data   Now you can of course create 3d scatterplot using three 1-d lists  But  why can t in general this data be used to create surface plot  To understand that  consider an empty 3-d plot    Now  suppose for each possible value of  x  y  on a  quot discrete quot  regular grid  you have a z value  then there s no issue  amp  you can in fact get a surface plot  import numpy as np from matplotlib import pyplot as plt from mpl toolkits mplot3d import Axes3D from matplotlib import cm  x   np linspace 0  10  6      0  2    10    6 distinct values y   np linspace 0  20  5      0  5    20    5 distinct values z   np linspace 0  100  30     6   5   30 values  1 for each possible combination of  x y   X  Y   np meshgrid x  y  Z   np reshape z  X shape     Z shape must be equal to X shape   Y shape  fig   plt figure   ax   fig add subplot 111  projection  3d    ax plot surface X  Y  Z   ax set xlabel  X Label   ax set ylabel  Y Label   ax set zlabel  Z Label   plt show     What s happens when you haven t got z for all possible combinations of  x  y   Then at the point  at intersection of two black lines on x-y plane on blank plot above   we don t know what is the value of z  It could be anything  we don t know how  high  or  low  our surface should be at that point  although it can be approximated using other functions  surface plot requires that you supply it arguments where X shape   Y shape   Z shape

User · Answer

Just to chime in  Emanuel had the answer that I  and probably many others  are looking for  If you have 3d scattered data in 3 separate arrays  pandas is an incredible help and works much better than the other options  To elaborate  suppose your x y z are some arbitrary variables  In my case these were c gamma  and errors because I was testing a support vector machine  There are many potential choices to plot the data    scatter3D cParams  gammas  avg errors array  - this works but is overly simplistic plot wireframe cParams  gammas  avg errors array  - this works  but will look ugly if your data isn t sorted nicely  as is potentially the case with massive chunks of real scientific data ax plot3D cParams  gammas  avg errors array  - similar to wireframe   Wireframe plot of the data    3d scatter of the data    The code looks like this        fig   plt figure       ax   fig gca projection  3d       ax set xlabel  c parameter       ax set ylabel  gamma parameter       ax set zlabel  Error rate        ax plot wireframe cParams  gammas  avg errors array       ax plot3D cParams  gammas  avg errors array       ax scatter3D cParams  gammas  avg errors array  zdir  z  cmap  viridis        df   pd DataFrame   x   cParams   y   gammas   z   avg errors array       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    plots avgErrs vs C andgamma type  s png   k       plt show     Here is the final output

User · Answer

I just came across this same problem   I have evenly spaced data that is in 3 1-D arrays instead of the 2-D arrays that matplotlib s plot surface wants   My data happened to be in a pandas DataFrame so here is the matplotlib plot surface example with the modifications to plot 3 1-D arrays     from mpl toolkits mplot3d import Axes3D from matplotlib import cm from matplotlib ticker import LinearLocator  FormatStrFormatter import matplotlib pyplot as plt import numpy as np  X   np arange -5  5  0 25  Y   np arange -5  5  0 25  X  Y   np meshgrid X  Y  R   np sqrt X  2   Y  2  Z   np sin R   fig   plt figure   ax   fig gca projection  3d   surf   ax plot surface X  Y  Z  rstride 1  cstride 1  cmap cm coolwarm      linewidth 0  antialiased False  ax set zlim -1 01  1 01   ax zaxis set major locator LinearLocator 10   ax zaxis set major formatter FormatStrFormatter    02f     fig colorbar surf  shrink 0 5  aspect 5  plt title  Original Code     That is the original example   Adding this next bit on creates the same plot from 3 1-D arrays          MODIFICATION TO EXAMPLE BEGINS HERE        import pandas as pd from scipy interpolate import griddata   create 1D-arrays from the 2D-arrays x   X reshape 1600  y   Y reshape 1600  z   Z reshape 1600  xyz     x   x   y   y   z   z     put the data into a pandas DataFrame  this is what my data looks like  df   pd DataFrame xyz  index range len xyz  x          re-create the 2D-arrays x1   np linspace df  x   min    df  x   max    len df  x   unique     y1   np linspace df  y   min    df  y   max    len df  y   unique     x2  y2   np meshgrid x1  y1  z2   griddata  df  x    df  y     df  z     x2  y2   method  cubic    fig   plt figure   ax   fig gca projection  3d   surf   ax plot surface x2  y2  z2  rstride 1  cstride 1  cmap cm coolwarm      linewidth 0  antialiased False  ax set zlim -1 01  1 01   ax zaxis set major locator LinearLocator 10   ax zaxis set major formatter FormatStrFormatter    02f     fig colorbar surf  shrink 0 5  aspect 5  plt title  Meshgrid Created from 3 1D Arrays          MODIFICATION TO EXAMPLE ENDS HERE         plt show     Here are the resulting figures

User · Answer

Just to add some further thoughts which may help others with irregular domain type problems  For a situation where the user has three vectors lists  x y z representing a 2D solution where z is to be plotted on a rectangular grid as a surface  the  plot trisurf    comments by ArtifixR are applicable  A similar example but with non rectangular domain is   import matplotlib pyplot as plt from matplotlib import cm from mpl toolkits mplot3d import Axes3D     problem parameters nu   50  nv   50 u   np linspace 0  2 np pi  nu    v   np linspace 0  np pi  nv    xx   np zeros  nu nv  dtype  d   yy   np zeros  nu nv  dtype  d   zz   np zeros  nu nv  dtype  d      populate x y z arrays for i in range nu     for j in range nv       xx i j    np sin v j   np cos u i       yy i j    np sin v j   np sin u i       zz i j    np exp -4  xx i j   2   yy i j   2     bell curve    convert arrays to vectors x   xx flatten   y   yy flatten   z   zz flatten      Plot solution surface fig   plt figure figsize  6 6   ax   Axes3D fig  ax plot trisurf x  y  z  cmap cm jet  linewidth 0                  antialiased False  ax set title r trisurf example  fontsize 16  color  k   ax view init 60  35  fig tight layout   plt show     The above code produces     However  this may not solve all problems  particular where the problem is defined on an irregular domain  Also  in the case where the domain has one or more concave areas  the delaunay triangulation may result in generating spurious triangles exterior to the domain  In such cases  these rogue triangles have to be removed from the triangulation in order to achieve the correct surface representation  For these situations  the user may have to explicitly include the delaunay triangulation calculation so that these triangles can be removed programmatically  Under these circumstances  the following code could replace the previous plot code    import matplotlib tri as mtri  import scipy spatial   plot final solution pts   np vstack  x  y   T tess   scipy spatial Delaunay pts    tessilation    Create the matplotlib Triangulation object xx   tess points    0  yy   tess points    1  tri   tess vertices   or tess simplices depending on scipy version                                                                  NOTE  If 2D domain has concave properties one has to         remove delaunay triangles that are exterior to the domain          This operation is problem specific          For simple situations create a polygon of the         domain from boundary nodes and identify triangles         in  tri  outside the polygon  Then delete them from          tri            lt ADD THE CODE HERE gt                                                                 triDat   mtri Triangulation x pts    0   y pts    1   triangles tri     Plot solution surface fig   plt figure figsize  6 6   ax   fig gca projection  3d   ax plot trisurf triDat  z  linewidth 0  edgecolor  none                   antialiased False  cmap cm jet  ax set title r trisurf with delaunay triangulation              fontsize 16  color  k   plt show     Example plots are given below illustrating solution 1  with spurious triangles  and 2  where they have been removed       I hope the above may be of help to people with concavity situations in the solution data

User · Answer

You can read data direct from some file and plot  from mpl toolkits mplot3d import Axes3D import matplotlib pyplot as plt from matplotlib import cm import numpy as np from sys import argv  x y z   np loadtxt  your file   unpack True   fig   plt figure   ax   Axes3D fig  surf   ax plot trisurf x  y  z  cmap cm jet  linewidth 0 1  fig colorbar surf  shrink 0 5  aspect 5  plt savefig  teste pdf   plt show     If necessary you can pass vmin and vmax to define the colorbar range  e g   surf   ax plot trisurf x  y  z  cmap cm jet  linewidth 0 1  vmin 0  vmax 2000      Bonus Section  I was wondering how to do some interactive plots  in this case with artificial data  from   future   import print function from ipywidgets import interact  interactive  fixed  interact manual import ipywidgets as widgets from IPython display import Image  from mpl toolkits mplot3d import Axes3D import matplotlib pyplot as plt import numpy as np from mpl toolkits import mplot3d  def f x  y       return np sin np sqrt x    2   y    2    def plot i        fig   plt figure       ax   plt axes projection  3d        theta   2   np pi   np random random 1000      r   i   np random random 1000      x   np ravel r   np sin theta       y   np ravel r   np cos theta       z   f x  y       ax plot trisurf x  y  z  cmap  viridis   edgecolor  none       fig tight layout    interactive plot   interactive plot  i  2  10   interactive plot

User · Answer

It is not possible to directly make a 3d surface using your data  I would recommend you to build an interpolation model using some tools like pykridge  The process will include three steps    Train an interpolation model using pykridge Build a grid from X and Y using meshgrid Interpolate values for Z    Having created your grid and the corresponding Z values  now you re ready to go with plot surface  Note that depending on the size of your data  the meshgrid function can run for a while  The workaround is to create evenly spaced samples using np linspace for X and Y axes  then apply interpolation to infer the necessary Z values  If so  the interpolated values might different from the original Z because X and Y have changed

User · Answer

check the official example  X Y and Z are indeed 2d arrays  numpy meshgrid   is a simple way to get 2d x y mesh out of 1d x and y values   http   matplotlib sourceforge net mpl examples mplot3d surface3d demo py  here s pythonic way to convert your 3-tuples to 3 1d arrays   data     1 2 3    10 20 30    11  22  33    110  220  330   X Y Z   zip  data  In  7   X Out 7    1  10  11  110  In  8   Y Out 8    2  20  22  220  In  9   Z Out 9    3  30  33  330    Here s mtaplotlib delaunay triangulation  interpolation   it converts 1d x y z into something compliant       http   matplotlib sourceforge net api mlab api html matplotlib mlab griddata

[python] surface plots in matplotlib

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