3D surface and line plots

I recently included S3Dlib as a third-party package to Matplotlib. From my biased perspective :grin:, numerous examples in the documentation qualify to be in the showcase. The following is one of the simplest surface plots with the functional description given in Wikipedia.

klein_bottle

import numpy as np
from matplotlib import pyplot as plt
import s3dlib.surface as s3d

# 1. Define function to examine ....................................
def klein_bottle(rtp) :
    r,v,u = rtp
    cU, sU = np.cos(u), np.sin(u)
    cV, sV = np.cos(v), np.sin(v)
    x = -(2/15)*cU* \
        (  ( 3 )*cV + \
           ( -30 + 90*np.power(cU,4) - 60*np.power(cU,6) + 5*cU*cV )*sU )
    y = -(1/15)*sU* \
        (  ( 3 - 3*np.power(cU,2) -48*np.power(cU,4) +48*np.power(cU,6) )*cV + \
           (-60 + ( 5*cU - 5*np.power(cU,3) - 80*np.power(cU,5) + 80*np.power(cU,7) )*cV  )*sU )
    z = (2/15)*( 3 + 5*cU*sU )*sV
    return x,y,z

# 2. Setup and map surface .........................................
rez=6
surface = s3d.SphericalSurface(rez)
surface.map_geom_from_op( klein_bottle, returnxyz=True )
surface.set_surface_alpha(.5)
surface.transform(s3d.eulerRot(20,-80),translate=[0,0,2])

# 3. Construct figure, add surface, show ...........................
fig = plt.figure(figsize=plt.figaspect(1))
ax = plt.axes(projection='3d')
minmax = (-1.5,1.5)
ax.set(xlim=minmax, ylim=minmax, zlim=minmax)
ax.set_axis_off()
ax.view_init(elev=20, azim=-125)
ax.set_title(surface.name)

d = [0,-1,0.5]
surface.shade(ax=ax,direction=d).hilite(ax=ax,direction=d)
ax.add_collection3d( surface )

fig.tight_layout()
plt.show()

The ability to construct contours directly from surfaces is shown below, along with using images to define geometry and color.

earthContours

from matplotlib import pyplot as plt
import s3dlib.surface as s3d

# 2. Setup and map surfaces .........................................
rez = 6
earth = s3d.SphericalSurface(rez,name='Elevation Contours')
earth.map_color_from_image('data/earth.png')
earth.map_geom_from_image('data/elevation.png',0.05)

elev = earth.contourLineSet(8,coor='s')
elev.set_linewidth(0.5)

# 3. Construct figure, add surface, show ............................
fig = plt.figure(figsize=plt.figaspect(1), facecolor='k' )
ax = plt.axes(projection='3d', facecolor='k')
ax.set_title(earth.name,color='w')
minmax = (-0.8,0.8)
ax.set(xlim=minmax, ylim=minmax, zlim=minmax)
ax.set_axis_off()
ax.view_init(25,-150)

ax.add_collection3d(elev.fade(ax=ax))

fig.tight_layout(pad=0)
plt.show()

The images referenced in the above script are available in the documentation. Both image sources are from the NASA visible earth catalog.

The following is a collection of several figures which were constructed ‘just of fun’. All code for these is available in the documentation examples.

five_figures

The above Mandelbrot surface S3Dlib construction used the code ‘directly’ from the Matplotlib showcase example for the functional definition.

Since S3Dlib is used to construct objects for Matplotlib rendering, animations are relatively straight forward using the matplotlib.animation module. Numerous animation examples, with code, are shown in the documentation animations examples.

I’m curious to see anyone’s ‘just for fun’ figures or ‘real-world’ application surfaces.

2 Likes

Very cool stuff, Dr.Z!

I see that in the tutorial you can import .obj file to s3d surface object, lets say I have some vertices and faces (all in numpy arrays), can I use them to generate a s3d surface easily? If that’s case, I can use it to plot many of my FEM results.

If you are plotting surfaces, probably no problem. Use the surface base class Surface3DCollection which takes the first two arguments as vertex coordinates and face indices… Both can be numpy arrays.

Several examples in the documentation use this base class to construct surfaces, e.g.

https://s3dlib.org/examples/functional/cube.html
https://s3dlib.org/examples/functional/arch_solid.html
https://s3dlib.org/examples/functional/hypercube.html

Note: faces may be triangular or quadrilateral. However, if a single surface has both types using lists, the execution time will be considerably slower for large models. Also, quadrilateral faces will be bisected into two triangles when the object is constructed.