Is there a way to graph level curves of a function $f(x,y)$ in 3D at their respective heights? (Much like contourplot3d in Maple.) Thanks.
To make things clearer: what I'd like to see is a 3D plot with level curves (not surfaces). We start with a function of 2 variables (not three) and I'd like to see the 'exploded' contour plot so that the level curves are graphed at their respective z-altitudes. Makes sense?
Below is a bit of a hack, but I think it does what you want.
var('x,y,z')
f(x,y)=x^2+3*y^2
levels=[1,2,3,4]
epsilon=0.1
p=plot3d(f(x,y),(x,-2,2),(y,-2,2),color='khaki',opacity=0.7)
for h in levels:
p+=implicit_plot3d(f(x,y)==h,(x,-2,2),(y,-2,2),(z,h,h+epsilon))
show(p)
Thanks for the solution, though, like you said, it's a little bit of a hack.
You can use contour_plot and can specify the heights you want as follows.
var('x,y')
contour_plot(x^3+x*y,(x,-4,4),(y,-4,4),contours=[0,1,2,3])
For a 3D version, see 3D contours.
Indeed, what I'd like to see is a 3D plot with level curves (**not surfaces**). We start with a function of 2 variables (**not three**) and I'd like to see the 'exploded' contour plot so that the level curves are graphed at their respective $z$-altitudes. Makes sense?
One can use gnuplot (in Sage)
sage: gnuplot_console()
#and then
set contour surface
set cntrparam levels incremental -10,2,10
unset surface
set isosamples 100,100
splot [-4:4] [-4:4] [-11:11] x**2-y**2
Thanks, that looks interesting but I would rather avoid having to use gnuplot.
Asked: 2012-08-01 19:52:54 +0100
Seen: 3,139 times
Last updated: Aug 02 '12
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