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.
The other major problem is the complete and total lack of colour
coding of plots. Does anyone know of a way to control the colour
output of 2D countour plots or density plots, so as to make the colour
scheme consisten across both the 2D and 3D plots (or at least to stop
the colour scheme rescaling every time the 2D square plane segment is
moved.
On May 7, 4:56 pm, Jorge E. ´Sanchez Sanchez <hnr...@hotmail.com>
wrote:
> I'm so sorry to hear that, it's really a pity, perhaps the problem is that
> you are not quite familiar to mayavi,
> I'm sending a code I modify to plot an interpolation of Mexico's City (data
> points file included) , and some nice pictures I got with mayavi.
>
> Regards,
> Jorge
>
>
>
>
>
>
>
> > Date: Fri, 6 May 2011 17:24:42 -0700
> > Subject: [sage-support] Re: Plotting Functions of 3 variables
> > From: obsessivemathsfr...@gmail.com
> > To: sage-support@googlegroups.com
>
> > Actually, never mind all that. Mayavi simply rufuses to work properly
> > on my system and the documentation on sage integration is just too
> > scant.
>
> > I will just have to make do with implicit_plot3d and the like. I was
> > wondering if there is any way of integrating an implicit_plot3d plot
> > and a "slice" image plot of the function together as in this Mayavi
> > example
>
> >http://code.enthought.com/projects/mayavi/docs/development/html/mayav...
>
> > On May 7, 12:28 am, ObsessiveMathsFreak
> > <obsessivemathsfr...@gmail.com> wrote:
> > > Well, I finally managed to install these packages, but mayavi seem
> > > very flakey. Some example taken from the mayavi site work, others do
> > > not.
>
> > > Is there a list of updated sage examples for mayavi somehwhere? In
> > > particular, are there any examples of plotting 3D data sets?
>
> > > On May 6, 2:16 am, Jorge E. ´Sanchez Sanchez <hnr...@hotmail.com>
> > > wrote:
>
> > > > I have made a few months ago the upgrade of mayavi experimental spkg to
> > > > version 3.5,
> > > > I forgot the ticket info now (you can search it by the name
> > > > ets-3.5.0-20101024.p0.spkg), to install it you have to
> > > > follow the guidelines in Jaap's
> > > > page:http://sage.math.washington.edu/home/jsp/SPKGS/ETS, just instead of
> > > > the ets-3.2, I suggest you to use the one I mentioned before, besides
> > > > mayavi it also includes also the Graph Canvas,
> > > > Scimath, SetupDocs and Traits Enthought Python parafernalia, I have
> > > > been since then working with it inside sage,
> > > > without any problem.
>
> > > > Regards
> > > > Jorge
>
> > > > > Date: Thu, 5 May 2011 12:40:55 -0700
> > > > > Subject: [sage-support] Re: Plotting Functions of 3 variables
> > > > > From: obsessivemathsfr...@gmail.com
> > > > > To: sage-support@googlegroups.com
>
> > > > > _None_ of those experimental packages work on my system. The first
> > > > > dependancy, wxPython-2.8.7.1.spkg give the following error (after
> > > > > taking ages compiling)
>
> > > > > In file included from ../src/gtk/gsockgtk.cpp:21:
> > > > > ../include/wx/gsocket.h:40: error: using typedef-name ‘GSocket’ after
> > > > > ‘class’
> > > > > /usr/include/glib-2.0/gio/giotypes.h:132: error: ‘GSocket’ has a
> > > > > previous declaration here
> > > > > In file included from ../include/wx/gsocket.h:179,
> > > > > from ../src/gtk/gsockgtk.cpp:21:
> > > > > ../include/wx/unix/gsockunx.h:40: error: using typedef-name ‘GSocket’
> > > > > after ‘class’
> > > > > /usr/include/glib-2.0/gio/giotypes.h:132: error: ‘GSocket’ has a
> > > > > previous declaration here
> > > > > ../src/gtk/gsockgtk.cpp: In function ‘void _GSocket_GDK_Input(void*,
> > > > > gint, GdkInputCondition)’:
> > > > > ../src/gtk/gsockgtk.cpp:34: error: ‘struct _GSocket’ has no member
> > > > > named ‘Detected_Read’
> > > > > ../src/gtk/gsockgtk.cpp:36: error: ‘struct _GSocket’ has no member
> > > > > named ‘Detected_Write’
> > > > > ../src/gtk/gsockgtk.cpp: In member function ‘virtual bool
> > > > > GSocketGUIFunctionsTableConcrete::Init_Socket(GSocket*)’:
> > > > > ../src/gtk/gsockgtk.cpp:56: error: ‘struct _GSocket’ has no member
> > > > > named ‘m_gui_dependent’
> > > > > ../src/gtk/gsockgtk.cpp:57: error: ‘struct _GSocket’ has no member
> > > > > named ‘m_gui_dependent’
> > > > > ../src/gtk/gsockgtk.cpp: In member function ‘virtual void
> > > > > GSocketGUIFunctionsTableConcrete::Destroy_Socket(GSocket*)’:
> > > > > ../src/gtk/gsockgtk.cpp:67: error: ‘struct _GSocket’ has no member
> > > > > named ‘m_gui_dependent’
> > > > > ../src/gtk/gsockgtk.cpp: In member function ‘virtual void
> > > > > GSocketGUIFunctionsTableConcrete::Install_Callback(GSocket*,
> > > > > GSocketEvent)’:
> > > > > ../src/gtk/gsockgtk.cpp:72: error: ‘struct _GSocket’ has no member
> > > > > named ‘m_gui_dependent’
> > > > > ../src/gtk/gsockgtk.cpp:75: error: ‘struct _GSocket’ has no member
> > > > > named ‘m_fd’
> > > > > ../src/gtk/gsockgtk.cpp:83: error: ‘struct _GSocket’ has no member
> > > > > named ‘m_server’
> > > > > ../src/gtk/gsockgtk.cpp:90: error: ‘struct _GSocket’ has no member
> > > > > named ‘m_fd’
> > > > > ../src/gtk/gsockgtk.cpp: In member function ‘virtual void
> > > > > GSocketGUIFunctionsTableConcrete::Uninstall_Callback(GSocket*,
> > > > > GSocketEvent)’:
> > > > > ../src/gtk/gsockgtk.cpp:98: error: ‘struct _GSocket’ has no member
> > > > > named ‘m_gui_dependent’
> > > > > ../src/gtk/gsockgtk.cpp:108: error: ‘struct _GSocket’ has no member
> > > > > named ‘m_server’
> > > > > make: *** [monodll_gsockgtk.o] Error 1
> > > > > Error building wx widgets.
>
> > > > > real 1m54.899s
> > > > > user 1m22.910s
> > > > > sys 0m12.030s
> > > > > sage: An error occurred while installing wxPython-2.8.7.1
>
> > > > > The others give various different errors. For instance, I'm
> > > > > encountering the "allow-hosts" error seen in this thread
>
> > > > >http://groups.google.com/group/sage-support/browse_thread/thread/b634...
>
> > > > > But I don't even know if it was resolved in that thread or not.
>
> > > > > IS there a way of getting any of these packages installed? Should I
> > > > > update my sage installation to a newer version(currently 4.6.2)?
>
> > > > > On May 5, 8:24 pm, kcrisman <kcris...@gmail.com> wrote:
> > > > > > On May 5, 1:43 pm, ObsessiveMathsFreak
> > > > > > <obsessivemathsfr...@gmail.com>
> > > > > > wrote:
>
> > > > > > > Thanks but, these methods are not wholly adequate for my purposes.
>
> > > > > > > I have been investigating the mayavi python package and the
> > > > > > > examples
> > > > > > > given
> > > > > > > herehttp://code.enthought.com/projects/mayavi/docs/development/html/mayav...
>
> > > > > > > Apparently sagemath has support for mayavi, but when I follow the
> > > > > > > instructions
> > > > > > > herehttp://www.sagemath.org/doc/numerical_sage/installation_osx.html
>
> > > > > > > I get an error
>
> > > > > > > sage: install_package("python-2.5.1-framework")
> > > > > > > ValueError: There is no package name starting with 'python-2.5.1-
> > > > > > > framework'.
>
> > > > > > Looking at
>
> > > > > > ./sage -optional
>
> > > > > > I don't get these. I think they are all experimental.
>
> > > > > > > And so on for the other commands in the page.
>
> > > > > > > I'm wondering if mayavi has been removed from sage, or whether its
> > > > > > > functionality is now part of the core packages?
>
> > > > > > No, it's there, and not in Sage -
> > > > > > seehttp://www.sagemath.org/packages/experimental/
> > > > > > But probably the steps to use it need updating. You may also want
> > > > > > to
> > > > > > search the lists - there are a fair number of threads about it.
>
> > > > > > I can't find the python framework one - can someone else help with
> > > > > > the
> > > > > > status of that?
>
> > > > > > - kcrisman
>
> > > > > --
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>
> > --
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>
>
> mayavixmpls.tar.gz
> 1032KViewDownload
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