Three Quadratic Functions¶

MIT License

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import numpy as np

import matplotlib.pyplot as pt

Consider the three equations:

$$y=x^2+\delta$$$$z=x^2-\delta$$$$y=z^2+\delta$$

delta = 0.5

from mpl_toolkits.mplot3d import Axes3D

fig = pt.figure()

ax = fig.add_subplot(111, projection='3d')



res = 10



x, z = np.mgrid[-3:3:res*1j,-3:3:res*1j]

y = x**2 + delta



ax.plot_surface(x, y, z, color="red", cstride=1, rstride=1)



if 1:

    y, x = np.mgrid[-3:3:res*1j,-3:3:res*1j]

    z = x**2 - delta

    

    ax.plot_surface(x, y, z, color="green", cstride=1, rstride=1)



if 0:

    x, z = np.mgrid[-3:3:res*1j,-3:3:res*1j]

    y = z**2 + delta

    

    ax.plot_surface(x, y, z, color="blue", cstride=1, rstride=1)

Plotly¶

Try another plotting tool. Needs


pip install plotly

jupyter labextension install jupyterlab-plotly

import plotly.graph_objects as go

from plotly.subplots import make_subplots

res = 10

delta = 0.5

x, z = np.mgrid[-3:3:res*1j,-3:3:res*1j]

y = x**2 + delta





fig= go.Figure()

#ax.plot_surface(x, y, z, color="red", cstride=1, rstride=1)

fig.add_trace(go.Surface(x=x, y=y, z=z, opacity=0.75, showscale=False, surfacecolor=np.ones_like(z),colorscale='reds',showlegend=True))



if 1:

    y, x = np.mgrid[-3:3:res*1j,-3:3:res*1j]

    z = x**2 - delta

    

    #ax.plot_surface(x, y, z, color="green", cstride=1, rstride=1)

    fig.add_trace(go.Surface(x=x, y=y, z=z, opacity=0.75, showscale=False, surfacecolor=np.ones_like(z),colorscale='greens',showlegend=True))



if 1:

    x, z = np.mgrid[-3:3:res*1j,-3:3:res*1j]

    y = z**2 + delta

    

    #ax.plot_surface(x, y, z, color="blue", cstride=1, rstride=1)

    fig.add_trace(go.Surface(x=x, y=y, z=z, opacity=0.75, showscale=False, surfacecolor=np.ones_like(z),colorscale='blues', showlegend=True))

fig.show()

Paraview/Vtk¶

Still can't see intersections very well. Need yet another plotting tool. :)

!rm -f 1.vts 2.vts 3.vts

from pyvisfile.vtk import write_structured_grid



res = 50



x, z = np.mgrid[-3:3:res*1j,-3:3:res*1j]

y = x**2 + delta

mesh = np.array([x, y, z])



write_structured_grid("1.vts", mesh.reshape(3, res, 1, res))



# ----------------------------------



y, x = np.mgrid[-3:3:res*1j,-3:3:res*1j]

z = x**2 - delta

mesh = np.array([x, y, z])



write_structured_grid("2.vts", mesh.reshape(3, res, res, 1))



# ----------------------------------



x, z = np.mgrid[-3:3:res*1j,-3:3:res*1j]

y = z**2 + delta

mesh = np.array([x, y, z])



write_structured_grid("3.vts", mesh.reshape(3, res, 1, res))