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plot surface plus vector field

asked 2015-03-06 15:45:30 -0500

c_williams gravatar image

updated 2015-03-06 18:14:29 -0500

tmonteil gravatar image

My apologies for posting a (hopefully) simple question. I want to plot a surface with the gradient field in the plane underneath. I can create the surface and vector field separately, but I get an error when I try to show them on the same axes. It seems that the vector field is a different type. Does anyone know how to induce the vector field so it can be plotted as part of a 3d plot?

I'd like to do something like this:

f(x,y)=y/(1-x+y)
P=plot3d(f(x,y),(x,0,1),(y,0,1))
gradf=vector([y/(x-y-1)^2,(1-x)/(x-y-1)^2])
VF=plot_vector_field(gradf,(x,0,1),(y,0,1))
show(P+VF)

Everything but that last step works great, and then I get an error message:

NotImplementedError: 3D plotting not implemented for PlotField defined by a 20 x 20 vector grid

Can anyone suggest a workaround? Thanks for your help!

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answered 2015-03-06 18:13:26 -0500

tmonteil gravatar image

updated 2015-03-06 18:31:12 -0500

When you sum a 2d plot with a 3d plot, Sage tries to embed the 2d plot in the 3d space, with the plot3d method. Unfortunately, this is not implemented for plot defined by vector fields (yet):

sage: VF.plot3d()
NotImplementedError: 3D plotting not implemented for PlotField defined by a 20 x 20 vector grid

A workaround is to define your vector field in 3d and plot it near the plane $z=0$:

sage: gradf = vector([y/(x-y-1)^2, (1-x)/(x-y-1)^2, 0])
sage: z = SR.symbol('z')
sage: VF = plot_vector_field3d(gradf, (x,0,1), (y,0,1), (z,0,0.0001), plot_points=10)
sage: show(P+VF)
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Asked: 2015-03-06 15:45:30 -0500

Seen: 152 times

Last updated: Mar 06 '15