Adding coordinate transformations to plot3d

[sagetrac-olazo]

While developing a command called transform_plot3d, that generalized ploting in diferent coordinate systems, Jason Grout suggested to me that such a command would be better implemented within plot3d.

I agreed to that, so I propose an adition to plot3d's syntax: "plot3d(function,var1range,var2range,transformation=None,**kwds)" where transformation is a 4-tuple containing 3 functions of arity 3, and a variable which is to be interpreted as the function to be ploted. Like this (rcos(fi),rsin(fi),z,r), so the function will be ploted as r.

Examples can be found in http://www.sagenb.org/home/pub/1328/.

I've just added a patch.

CC: @sagetrac-wcauchois @jasongrout @sagetrac-mhampton @sagetrac-olazo @kcrisman

Component: graphics

Author: Bill Cauchois, Oscar Gerardo Lazo Arjona, Jason Grout

Reviewer: Karl-Dieter Crisman, Jason Grout

Merged: sage-4.3.4.alpha0

Issue created by migration from https://trac.sagemath.org/ticket/7872

[sagetrac-olazo]

Description changed:

--- 
+++ 
@@ -37,3 +37,5 @@
 Examples can be found in [http://www.sagenb.org/home/omologos/9/](http://www.sagenb.org/home/omologos/9/).
 
 Spherical and cylindrical plots are now meant to be purely derived from plot3d. So tickets [https://github.com/sagemath/sage/issues/7850](https://github.com/sagemath/sage/issues/7850) and [https://github.com/sagemath/sage/issues/7869](https://github.com/sagemath/sage/issues/7869) should be updated
+
+For the sake of consistency, it would also be good if a similar option was added to plot: plot(f,xrange,transform=None), in order to support polar_plot from plot

[sagetrac-olazo]

Description changed:

--- 
+++ 
@@ -36,6 +36,6 @@
 
 Examples can be found in [http://www.sagenb.org/home/omologos/9/](http://www.sagenb.org/home/omologos/9/).
 
-Spherical and cylindrical plots are now meant to be purely derived from plot3d. So tickets [https://github.com/sagemath/sage/issues/7850](https://github.com/sagemath/sage/issues/7850) and [https://github.com/sagemath/sage/issues/7869](https://github.com/sagemath/sage/issues/7869) should be updated
+Spherical and cylindrical plots are now meant to be purely derived from plot3d. So tickets #7850 and #7869 should be updated.
 
 For the sake of consistency, it would also be good if a similar option was added to plot: plot(f,xrange,transform=None), in order to support polar_plot from plot

[sagetrac-olazo]

Description changed:

--- 
+++ 
@@ -34,7 +34,7 @@
         return parametric_plot(R,v1ran,v2ran,**kwds)
 ```
 
-Examples can be found in [http://www.sagenb.org/home/omologos/9/](http://www.sagenb.org/home/omologos/9/).
+Examples can be found in [http://www.sagenb.org/home/pub/1328/](http://www.sagenb.org/home/pub/1328/).
 
 Spherical and cylindrical plots are now meant to be purely derived from plot3d. So tickets #7850 and #7869 should be updated.
 

[sagetrac-wcauchois]

comment:4

Hi! William directed me to your thread on sage-devel. Since I have experience working on 3D plotting, I think I could help integrate this code into Sage.

[sagetrac-wcauchois]

based on sage 4.3.1.alpha1

[sagetrac-wcauchois]

comment:5

Attachment: trac_7872.patch.gz

The patch I just attached represents my initial work on this issue. I added Oscar's code to plot3d() to implement the transformation keyword parameter, and I added the two new plotting functions spherical_plot3d and cylindrical_plot3d.

I made some minor changes to the original code. I moved the formulae for the transformations for spherical and cylindrical coordinates out of the body of plot3d, and into the bodies of spherical_plot3d and cylindrical_plot3d, since I thought that was a better place for them. I also added some error handling; the urange and vrange given to plot3d may be 2-tuples, in which case the variables are implicit -- but we expect urange[0] and vrange[0] to be the plot variables.

We need to add some documentation for the new features. I think I can draw upon the examples Oscar provided in his published worksheets to create doctests for the new functions. Oscar, could you help me come up with descriptions of cylindrical_plot3d and spherical_plot3d for use in their docstrings? And more examples are always helpful.

[sagetrac-olazo]

comment:6

More examples now available at the bottom of: http://sagenb.org/home/pub/1328/. I'll do the descriptions later.

[sagetrac-olazo]

comment:7

I have attatced a proposal for a docstring in spherical_plot #7850 . Also, I checked your code. Do you think it is best to use "spherical_plot3d" instead of "spherical_plot"? I find the 3d redundant, and I like to type less. Also, I noticed that your implementation will not allow adaptative refinement to be used together with "transformation". I have never used that option and I don't know whether it is important. When my plots are not sufficiently rounded I use plot_points, and that usually does the trick.

[sagetrac-olazo]

Description changed:

--- 
+++ 
@@ -2,40 +2,6 @@
 
 I agreed to that, so I propose an adition to plot3d's syntax: "plot3d(function,var1range,var2range,transformation=None,**kwds)" where transformation is a 4-tuple containing 3 functions of arity 3, and a variable which is to be interpreted as the function to be ploted. Like this (r*cos(fi),r*sin(fi),z,r), so the function will be ploted as r.
 
-It's inclution within plot3d would be something on the likes of
-
-```
-def plot3d_new(f,v1ran,v2ran,transformation=None,**kwds):
-    if transformation==None:
-        return plot3d(f,v1ran,v2ran,**kwds)
-    else:
-        v1=v1ran[0]
-        v2=v2ran[0]
-
-        if transformation=='spherical':
-            r=var('r')
-            transformation=(r*cos(v1)*sin(v2),r*sin(v1)*sin(v2),r*cos(v2),r)
-        elif transformation=='cylindrical':
-            r=var('r')
-            transformation=(r*cos(v1),r*sin(v1),v2,r)
-        elif str(type(transformation))=="<type 'str'>":
-            print 'Warning: the transformation given is not amongst the options, it will be ignored'
-            return plot3d(f,v1ran,v2ran,**kwds)
-
-        fvar=transformation[3]
-        transformation=(transformation[0],transformation[1],transformation[2])
-
-        try:
-            R=[t.subs({fvar:f}) for t in transformation]
-        except:
-            def subs_func(t):
-                return lambda x,y: t.subs({fvar:f(x,y), v1:x, v2:y})
-            R=map(subs_func,transformation)
-        return parametric_plot(R,v1ran,v2ran,**kwds)
-```
-
 Examples can be found in [http://www.sagenb.org/home/pub/1328/](http://www.sagenb.org/home/pub/1328/).
 
-Spherical and cylindrical plots are now meant to be purely derived from plot3d. So tickets #7850 and #7869 should be updated.
-
-For the sake of consistency, it would also be good if a similar option was added to plot: plot(f,xrange,transform=None), in order to support polar_plot from plot
+I've just added a patch.

[sagetrac-olazo]

Attachment: 13535.patch.gz