spherical plot

[olazo]

This command is now supposed to be derived from the code in this ticket #7872

[jason]

Here is a rough cut of a generic function:  http://sagenb.org/home/pub/1322/

# TODO: figure out a way to determine if f is an expression or callable symbolic function for the if statement.

def make_coordinate_plot3d(transformation, function_variable,parameter_variables):
   def new_plot(f, var1_range, var2_range,**kwds):
       f_is_expression=True
       
       if f_is_expression:
           # if f is an expression, then we can use .subs.  This is faster, because parametric_plot3d
           # can then use fast_float
           if len(var1_range)==3:
               vars=[var1_range[0], var2_range[0]]
           else:
               vars=sage.symbolic.ring.var('v1,v2')
           plot_func=[t.subs({function_variable:f, parameter_variables[0]:vars[0], parameter_variables[1]:vars[1]})
                       for t in transformation]
       else:
           # if f is not a symbolic expression or function, use the following
           # We could make this faster by using fast_float on the components of transformation
           # We need to do the function and map instead of just a list comprehension because
           # of python scoping; see http://lackingrhoticity.blogspot.com/2009/04/python-variable-binding-semantics-part.html
           def subs_func(t):
               return lambda x,y: t.subs({function_variable:f(x,y), parameter_variables[0]:x, parameter_variables[1]:y})
           plot_func=map(subs_func,transformation)

       return parametric_plot3d(plot_func, var1_range, var2_range,**kwds)
   return new_plot 

 	
var('r,t,p') 
jason_spherical_plot3d=make_coordinate_plot3d([r*cos(t)*sin(p), r*sin(t)*sin(p), r*cos(p)], function_variable=r, parameter_variables=[t,p]) 

[jason]

Here's the relevant sage-devel thread:  http://groups.google.com/group/sage-devel/browse_thread/thread/8e38cdd8048eb39c

Thanks again for working on this!

Here are some comments about the implementation up at  http://www.sagenb.org/home/pub/1323/, just based on reading the code.

1. To be consistent with the plotting functions, it would also need to support something like:

spherical_plot3d(lambda x,y: x+y, (0,2*pi), (0,pi))

That's the purpose behind the convoluted second half of the make_coordinate_plot3d function (because symbolic functions can't be multiplied by lambda functions).

2. It's better to use "zran is None" rather than "zran==None". It's a much faster test.

3. There is still some dependence on variable names if the variable name is not specified. This should give an error, or at least a deprecation warning, as it is no longer a supported syntax for plotting:

spherical_plot3d(phi*theta, (0,2*pi),(0,pi))

(note that the expression has two variables, but I haven't said which variable corresponds to which range. This is particularly confusing with spherical plots, since there are two opposite conventions.

4. except statements should catch specific exceptions (e.g., "except ValueError?"), instead of just triggering on any error.

5. I'm not sure there's any difference between the transform_plot3d and just plainly calling parametric_plot3d. transform_plot3d seems to just basically be a rename of parametric_plot3d.

[jason]

See also #7850 for a cylindrical plotting function

[olazo]

a proposal for a docstring