This example uses MayaVi to show the evolution of a superquadric (http://en.wikipedia.org/wiki/Superquadrics), 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: `superquad_with_gui.py`

```
# Author: Pratik Mallya <pmallya@enthought.com>
# Copyright (c) 2008-2020, Enthought, Inc.

import numpy as np
from enthought.traits.api import HasTraits, Range, Instance, \
on_trait_change
from enthought.traits.ui.api import View, Item, HGroup
from enthought.tvtk.pyface.scene_editor import SceneEditor
from enthought.mayavi.tools.mlab_scene_model import \
MlabSceneModel
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__
HasTraits.__init__(self)
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')

@on_trait_change('beta,alpha')
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),
HGroup(
'_', 'beta', 'alpha',
),
)

visualization = Visualization()
visualization.configure_traits()

```