1322.sagews

# 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')

(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_spherical_plot3d(2,(t,0,pi/4),(p,0,pi))

oscar_spherical_plot3d=make_coordinate_plot3d([r*cos(p)*sin(t), r*sin(p)*sin(t), r*cos(t)], function_variable=r, parameter_variables=[t,p])

var('x,y')

(x, y)

oscar_spherical_plot3d(2,(x,0,pi/4),(y,0,pi))

var('x,y,z,t')

(x, y, z, t)

cylindrical_plot3d=make_coordinate_plot3d([r*cos(t)*z, r*sin(t)*z, z], function_variable=z, parameter_variables=[r,t])

cylindrical_plot3d(t,(r,0,3),(t,0,3*pi))