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2019-11-18 19:57:01 -0600 received badge  Popular Question (source)
2012-03-01 04:48:47 -0600 commented answer using @interact

You are awesome

2012-03-01 04:48:32 -0600 marked best answer using @interact

You just need to use the show command to force Sage to show the plot. The code below works for me.

@interact 
def _(center =6 -x^2, spin = x): 
    var('u') 
    var('t') 
    r(x) = abs(spin(x) - center(x)) 
    p=parametric_plot3d((t, r(t)*sin(u)+center(t), r(t)*cos(u)), (u, 0, 2*pi), (t, 0, 2), mesh=True)
    show(p)
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2012-02-29 08:55:20 -0600 asked a question using @interact

I have this code which works just fine and produces an image:

var('u') 
center(x) =sqrt(x) 
spin(x) = 2- 1/4 * x^2 
r(x) = abs(spin(x) - center(x)) 
parametric_plot3d((x, r(x)*sin(u)+center(x), r(x)*cos(u)), (u, 0, 2*pi), (x, 0, 2), mesh=True)

However, I would like to use a @interact to be able to change the functions named center and spin. I tried this (and a few variations)

@interact
def _(center =6 -x^2, spin = x):
  var('u')
  var('t')  
  r(x) = abs(spin(x) - center(x))
  parametric_plot3d((t, r(t)*sin(u)+center(x=t), r(t)*cos(u)), (u, 0, 2*pi), (t, 0, 2), mesh=True)

and while I don't get an error, I also don't get a picture for some reason. Any suggestions?