I still can't get this code to work.
In lieu of any external solutions, I've tried to hack something
together in sage itself, using the standard 3d functionality.
Basically it involves drawing a series of implicit plot 3d countours,
then cutting into them with a small plane and drawing a 2d countour
based on that plane. I also found it useful to make the plotting
interactive. It's better than nothing I suppose. Here is some example
code
var('x y z u v')
f=lambda x,y,z: (y-x^2)+sin(z)
F=lambda X: f(X[0,0],X[1,0],X[2,0])
#3D level countours of function
p_slices=sum([ implicit_plot3d(f(x,y,z)==w, (x, -3, 3), (y, -3,3), (z,
-3,3),opacity=0.1,color="green") for w in [-1,-0.5,..,1] ])
@interact
def _(phi = slider(-pi/2,pi/2,pi/20,default=pi/2),theta = slider(-
pi,pi,pi/20,default=0),\
x0=slider(-1,1,0.1,default=0),y0=slider(-1,1,0.1,default=0),z0=slider(-1,1,0.1,default=0),
\
R=slider(0.1,10,0.1,default=1)):
p=matrix([x0,y0,z0]).transpose()
#center of 2D plot
e1=matrix([cos(theta)*sin(phi), sin(theta)*sin(phi), -
cos(phi)]).transpose() #u axis of 2D plot
e2=matrix([-sin(theta), cos(theta),
0]).transpose() #v axis of 2D plot
V=lambda u,v: p
+u*e1+v*e2 #map
u,v to x,y,z
#pcon=density_plot(F(V(u,v)),(u,-R,R),(v,-R,R),cmap="gray")
pcon=contour_plot(F(V(u,v)),(u,-R,R),(v,-
R,R),cmap="gray",fill=false)
pcon.set_aspect_ratio(1)
pplane=parametric_plot3d( [V(u,v)[0,0],V(u,v)[1,0],V(u,v)[2,0]],
(u,-R,R),(v,-R,R),opacity=0.6,color="red") #location of plane in 3D
(pplane+p_slices).show(aspect_ratio=[1,1,1])
show(pcon)
However, once again I find myself frustrated by plot3ds refusal to
allow itself to be position beside other plots. Consequently, the
plots will not all fit in one screen for me.
