Databases
StackOverflow2013
Postsdbo
PO
 

Note that there are some explanatory texts on larger screens.

plurals
  1. PO
    primarykey
    data
    text
    <p>You can trick matplotlib into plotting implicit equations in 3D. Just make a one-level contour plot of the equation for each z value within the desired limits. You can repeat the process along the y and z axes as well for a more solid-looking shape.</p> <pre><code>from mpl_toolkits.mplot3d import axes3d import matplotlib.pyplot as plt import numpy as np def plot_implicit(fn, bbox=(-2.5,2.5)): ''' create a plot of an implicit function fn ...implicit function (plot where fn==0) bbox ..the x,y,and z limits of plotted interval''' xmin, xmax, ymin, ymax, zmin, zmax = bbox*3 fig = plt.figure() ax = fig.add_subplot(111, projection='3d') A = np.linspace(xmin, xmax, 100) # resolution of the contour B = np.linspace(xmin, xmax, 15) # number of slices A1,A2 = np.meshgrid(A,A) # grid on which the contour is plotted for z in B: # plot contours in the XY plane X,Y = A1,A2 Z = fn(X,Y,z) cset = ax.contour(X, Y, Z+z, [z], zdir='z') # [z] defines the only level to plot for this contour for this value of z for y in B: # plot contours in the XZ plane X,Z = A1,A2 Y = fn(X,y,Z) cset = ax.contour(X, Y+y, Z, [y], zdir='y') for x in B: # plot contours in the YZ plane Y,Z = A1,A2 X = fn(x,Y,Z) cset = ax.contour(X+x, Y, Z, [x], zdir='x') # must set plot limits because the contour will likely extend # way beyond the displayed level. Otherwise matplotlib extends the plot limits # to encompass all values in the contour. ax.set_zlim3d(zmin,zmax) ax.set_xlim3d(xmin,xmax) ax.set_ylim3d(ymin,ymax) plt.show() </code></pre> <p>Here's the plot of the Goursat Tangle:</p> <pre><code>def goursat_tangle(x,y,z): a,b,c = 0.0,-5.0,11.8 return x**4+y**4+z**4+a*(x**2+y**2+z**2)**2+b*(x**2+y**2+z**2)+c plot_implicit(goursat_tangle) </code></pre> <p><img src="https://i.stack.imgur.com/7s2yC.png" alt="alt text"></p> <p>You can make it easier to visualize by adding depth cues with creative colormapping:</p> <p><img src="https://i.stack.imgur.com/93caD.png" alt="alt text"></p> <p>Here's how the OP's plot looks:</p> <pre><code>def hyp_part1(x,y,z): return -(x**2) - (y**2) + (z**2) - 1 plot_implicit(hyp_part1, bbox=(-100.,100.)) </code></pre> <p><img src="https://i.stack.imgur.com/mcreb.png" alt="alt text"></p> <p>Bonus: You can use python to functionally combine these implicit functions:</p> <pre><code>def sphere(x,y,z): return x**2 + y**2 + z**2 - 2.0**2 def translate(fn,x,y,z): return lambda a,b,c: fn(x-a,y-b,z-c) def union(*fns): return lambda x,y,z: np.min( [fn(x,y,z) for fn in fns], 0) def intersect(*fns): return lambda x,y,z: np.max( [fn(x,y,z) for fn in fns], 0) def subtract(fn1, fn2): return intersect(fn1, lambda *args:-fn2(*args)) plot_implicit(union(sphere,translate(sphere, 1.,1.,1.)), (-2.,3.)) </code></pre> <p><img src="https://i.stack.imgur.com/mk6d3.png" alt="alt text"></p>
    singulars
    1. This table or related slice is empty.
    1. POPlotting implicit equations in 3d
      singulars
      1. PTQuestion
    1. PTAnswer
    1. USPaul
    1. USPaul
    plurals
    1. This table or related slice is empty.
    1. This table or related slice is empty.
    1. POPlotting implicit equations in 3d
      singulars
      1. PTQuestion
    1. This table or related slice is empty.
    1. VO
      singulars
      1. PO
      1. This table or related slice is empty.
      1. VTUpMod
    2. VO
      singulars
      1. PO
      1. This table or related slice is empty.
      1. VTUpMod
    3. VO
      singulars
      1. PO
      1. This table or related slice is empty.
      1. VTUpMod
    1. CO@bpowah: According to matplotlib reference projection = '3d' is invalid. Perhaps projection = 'rectilinear'?
      singulars
      1. PO
      1. USqutron
    2. COI remember getting that error before upgrading to matplotlib 1.0.1. I forget how to get around it for previous versions.
      singulars
      1. PO
      1. USPaul
    3. CO@bpowah: Oh, you're using newer matplotlib version. Anyway I'll try to figure this out. Thanks))
      singulars
      1. PO
      1. USqutron
 

Querying!

 
Guidance
A row detail

Detail views are divided into sections. All the information in the data section comes from columns in the selected row. The other sections display data from other, related rows.

Related data can be related in a to-one or a to-many fashion. Captions of data related in a to-many fashion link to a list view showing a filtered view of the table.

Try moving around until you find a non-empty to-many entry and click on the label to get to one. You can move back to the root by clicking on the database name in the header.

SQuiL has stopped working due to an internal error.

If you are curious you may find further information in the browser console, which is accessible through the devtools (F12).

Reload