Multiple 3D plots in one panel -> graphics_array and 3D?

edit

Okay, just to illustrate the non-Jmol approach I had in mind:

# matplotlib-based version
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import axes3d
import numpy as np
var("x y alpha")

Fp1_11 = 5*x+3*y
Fp1_12 = (2*(x+y)^(1/3)*cos(alpha)+(1+alpha/10)^((y)))*20
Fp1_21 = sin(x*y+alpha)
Fp1_22 = alpha*((x^2+y^2))^(1/2)
fns = [Fp1_11, Fp1_12, Fp1_21, Fp1_22]

@interact
def fplot(alpha=(1.0,5)):
    fig = plt.figure()
    fig.subplots_adjust(wspace=0.05, hspace=0.05,left=0.05, right=0.95)
    for i, fn in enumerate(fns, 1):
        ax = fig.add_subplot(2,2,i,projection='3d')
        xx = np.linspace(-10, 10, 50)
        yy = xx
        X, Y = np.meshgrid(xx, yy)
        # the next line is ugly, but it works
        Z = np.array(list(np.float(fn.subs(x=x_,y=y_,alpha=alpha)) for x_, y_ in zip(X.flatten(), Y.flatten())))
        Z = Z.reshape(X.shape)
        ax.plot_surface(X, Y, Z, rstride=8, cstride=8, alpha=0.3)
        cset = ax.contour(X, Y, Z, zdir='z', offset=-100)
        #cset = ax.contour(X, Y, Z, zdir='x', offset=-10)
        #cset = ax.contour(X, Y, Z, zdir='y', offset=10)
        ax.set_xlabel('X')
        ax.set_xlim3d(-10, 10)
        ax.set_ylabel('Y')
        ax.set_ylim3d(-10, 10)
        ax.set_zlabel('Z')
        ax.set_zlim3d(-100, 100)
    plt.savefig("fplot.png")

gives something like

where if you adjust alpha the plots change. No rotation, and it's not that speedy, but it's functional. Also note that I didn't bother checking that my limits were sensible, or give enough space to the ticks, etc. [Update: looks like I forgot an import. Also some minor edits for aesthetic reasons.]

I looked around too, and I couldn't see a way to convert a 3D graphics object to a plain graphics object. I did, however, notice the translate function, which could provide a workaround: you could translate your objects by different amounts so that .show() results in something like a graphics array. This is even better, in some ways, because it remains a 3D object, which you can render in various different ways. Here's an example:

sage: graphiclist = [dodecahedron(),sphere(color='red'),sphere(color='yellow')]
sage: h = sum(graphiclist[i].translate((2*i,0,0)) for i in range(len(graphiclist)))
sage: h.show()

And the result is:

Of course translating by multiples of (2,0,0) worked out because each of the 3D graphics I started with was in the cube [-1,1]^3, but you could write a function to determine the bounding boxes of your objects and translate them by the maximum box-width.

I have the same problem, but I have found a trivial workaround that works in 6.4.1. I generate two 3D plots and I want to be able to manipulate them interactively, side by side. However, as you experienced, I saw only the second plot. My workaround still doesn't let you have the plots side by side horizontally, but they are side by side vertically. In my notebook worksheet I generate both 3D graphics objects in cell_1, but then, I apply show() on one of them in cell_2 and the other one in cell_3. I have then two interactive Jmol 3D plots right on top of each other and I can interactively manipulate them separately.

Of course, I can also export the plots as Jmol scripts (using the right-click Jmol menu) and then use the standalone Jmol program to show them side by side in two different Jmol windows.

Hope this helps,

Istvan