Superquad with gui exampleΒΆ

This example uses MayaVi to show the evolution of a superquadric (, which are ellipsoidal surfaces parametrised by two parameters,lpha and eta. The equations that are used to determine the superquadric are (in spherical-polar coordinates):

(x = A(sin^{lpha}(phi)*cos^{eta}( heta))) (y = B(sin^{lpha}(phi)*sin^{eta}( heta))) (z = C(cos^{lpha}(phi)))

Note that when we set A=B=C=r, and lpha = eta = 1, we get the equation for a sphere in spherical polar coordinate.

Use the controls at the bottom of the plot to adjust lpha and eta, and watch as the figure transforms accordingly!

Python source code:

# Author: Pratik Mallya <>
# Copyright (c) 2008-2020, Enthought, Inc.
# License: BSD Style.

import numpy as np
from enthought.traits.api import HasTraits, Range, Instance, \
from enthought.traits.ui.api import View, Item, HGroup
from enthought.tvtk.pyface.scene_editor import SceneEditor
from import \
from enthought.mayavi.core.ui.mayavi_scene import MayaviScene

def fexp(x,p):
    """a different kind of exponentiation"""
    return (np.sign(x) * (np.abs(x)**p))

def tens_fld(A,B,C,P,Q):
    """this module plots superquadratic surfaces with the given parameters"""
    phi, theta = np.mgrid[0:np.pi:80j, 0:2*np.pi:80j]
    x = A * (fexp(np.sin(phi),P)) * (fexp(np.cos(theta),Q))
    y = B * (fexp(np.sin(phi),P)) * (fexp(np.sin(theta),Q))
    z = C * (fexp(np.cos(phi),P))
    return x , y , z 

class Visualization(HasTraits):
    alpha = Range(0.0, 4.0, 1.0/4)
    beta  = Range(0.0, 4.0, 1.0/4)
    scene = Instance(MlabSceneModel, ())

    def __init__(self):
        # Do not forget to call the parent's __init__
        x, y, z, = tens_fld(1, 1, 1, self.beta, self.alpha)
        self.plot = self.scene.mlab.mesh(x, y, z, colormap='copper', representation='surface')

    def update_plot(self):
        x, y, z, = tens_fld(1, 1, 1, self.beta, self.alpha)
        self.plot.mlab_source.set(x = x, y = y, z = z)

    # the layout of the dialog created
    view = View(Item('scene', editor = SceneEditor(scene_class=MayaviScene),
                    height = 750, width=750, show_label=False),
                        '_', 'beta', 'alpha',

visualization = Visualization()