1342.sagews

As a continuation of the recent cloning of ploting methods found in mathematica. I've started a clone of RevolutionPlot3D.
http://reference.wolfram.com/mathematica/ref/RevolutionPlot3D.html

My version, however, can specify the axis of rotation of the curve, given as a line paralel to the z axis, located in the point of coordinates $(x,y)$. And also, the posibility to display the revolved curve.

The corresponding ticket is http://trac.sagemath.org/sage_trac/ticket/7889

def revolution_plot(cur,trange,phirange=None,axis=(0,0),showcurve=False,**kwds):
    def findvar(expr):
        try:
            vart=cur.args()[0]
        except:
            vart=var('t')
        return vart

    if phirange==None:#this if-else provides a phirange
        phi=var('phi')
        phirange=(phi,0,2*pi)
    else:
        phi=phirange[0]
        phirange=(phi,phirange[1],phirange[2])

    if str(type(cur)) == "<type 'tuple'>":#this if-else provides a vector v to be ploted
        vart=findvar(cur[0])        
        R=sqrt((cur[0]-axis[0])^2+axis[1]^2)
        v=(R*cos(phi)+axis[0],R*sin(phi)+axis[1],cur[1])
        curveplot=parametric_plot3d((cur[0],0,cur[1]),trange,thickness=2,rgbcolor=(1,0,0))
    elif str(type(cur))== "<type 'list'>":
        vart=findvar(cur[0])        
        R=sqrt((cur[0]-axis[0])^2+axis[1]^2)
        v=(R*cos(phi)+axis[0],R*sin(phi)+axis[1],cur[1])
        curveplot=parametric_plot3d((cur[0],0,cur[1]),trange,thickness=2,rgbcolor=(1,0,0))
    else:
        vart=findvar(cur)
        R=sqrt((vart-axis[0])^2+(axis[1])^2)
        v=(R*cos(phi)+axis[0],R*sin(phi)+axis[1],cur)
        curveplot=parametric_plot3d((vart,0,cur),trange,thickness=2,rgbcolor=(1,0,0))
        
    if showcurve:
        return parametric_plot3d(v,trange,phirange,**kwds)+curveplot
    return parametric_plot3d(v,trange,phirange,**kwds)

Let's clone the examples in the link above

var('t,fi')
torus=(2+cos(2*pi*t),sin(2*pi*t))
pot=t^4-t^2
k=2

def g(t):
    if t>0.5:
        return t
    else:
        return t^2

plot=revolution_plot(pot,(t,0,1),showcurve=True,opacity=0.5).show(aspect_ratio=(1,1,3))

revolution_plot(torus,(t,0,1),showcurve=True,opacity=0.5).show(aspect_ratio=(1,1,1))

Now let's revolve those curves around different axes and see what happens.

plot=revolution_plot(pot,(t,0,1),axis=(1,0),showcurve=True,opacity=0.5).show(aspect_ratio=(1,1,3))

plot=revolution_plot(pot,(t,0,1),axis=(0.5,0.5),showcurve=True,opacity=0.5).show(aspect_ratio=(1,1,3))

revolution_plot(torus,(t,0,1),axis=(1.5,1),showcurve=True,opacity=0.5).show(aspect_ratio=(1,1,1))

revolution_plot(torus,(t,0,1),axis=(2,1),showcurve=True,opacity=0.5).show(aspect_ratio=(1,1,1))

Non-symbolical functions have been troublesome. I would appreciate help to support themwhich I can't explain...
Mathematica also supports revolutions of 3d curves, that will require further thinking.

Now another example shamelessly stolen from Mathematica:

revolution_plot((sin(t)+sin(9*t)/5,cos(t)+cos(9*t)/5),(t,0,pi),(fi,0,pi),plotpoints=[150,150]).show(aspect_ratio=(1,1,1),frame=False)