Add a TikZ-tex output method for 2d and 3d polytopes #12083

jplab · 2011-11-25T17:31:49Z

I recently had to draw polytopes for my work.

Many drawing tools already exist. But none of them satisfied me.

So far, I wrote a method that takes a polytope in 3d and a view-angle (taken from Jmol) and outputs a .tex file containing a TikZ image of the polytope.

The method should also be able to deal with 2-polytopes.

The result is highly customizable: colors, edge style, vertices style, etc...

First review: I made the suggested corrections. They are present in the patch trac12083_tikz_polytope_review.patch

Test passed on version 4.7.2

Apply attachment: trac12083_rebased_5.12.patch

Component: geometry

Keywords: TikZ, polytope

Author: Jean-Philippe Labbé

Reviewer: Sébastien Labbé, Volker Braun

Merged: sage-5.13.beta3

Issue created by migration from https://trac.sagemath.org/ticket/12083

novoselt · 2011-11-25T19:48:15Z

comment:1

Do you have a ready patch already? Such functionality can be quite awesome in conjunction with SageTeX!

jplab · 2011-11-25T20:17:30Z

comment:2

I just need to adapt the code a little bit. It is already mostly written and works with 'quite' big examples: A3,B3 and H3 permutahedra.

I just need to sit and do it: it should be there in a week or so...

jplab · 2011-12-04T17:15:03Z

Attachment: trac12083_tikz_polytope.patch.gz

Addition of tikz method for polyhedron

jplab · 2011-12-04T17:17:36Z

comment:3

Here is the patch. Please test it with your favorite 2d and 3d polytopes!

jplab · 2011-12-04T17:22:38Z

Attachment: trac12083_tikz_polytope.2.patch.gz

Addition of tikz method for polyhedron

seblabbe · 2012-02-10T17:59:41Z

comment:4

Testing the file polyhedra.py creates junk in the working directory.

cd sage-4.8/devel/sage-slabbe/sage/geometry 
sage -t polyhedra.py
ls *.tex 
polytope-tikz.tex       polytope-tikz2.tex      polytope-tikz3.tex

Saving files in your test is not necessary. I suggest you do the test like this instead :

sage: P1 = polytopes.small_rhombicuboctahedron()   
sage: t = P1.tikz([1,3,5], 175, scale=4)           
sage: type(t)                                      
<type 'str'>                                       
sage: print '\n'.join(t.splitlines()[:4])          
\begin{tikzpicture}%                               
        [x={(-0.939161cm, 0.244762cm)},            
        y={(0.097442cm, -0.482887cm)},             
        z={(0.329367cm, 0.840780cm)},

If you want to keep those line in the doc (a good idea a believe), I suggest you mark them as untested :

sage: open('polytope-tikz2.tex', 'w').write(Image2)    # not tested

You import n but you don't use it. (If you really needed it, I would have suggest to import the equivalent alias numerical_approx instead because the variable n is often used as an integer in the code...) But since you don't use it, just remove the import.

 from subprocess import Popen, PIPE                 
 from sage.misc.all import tmp_filename             
-from sage.misc.functional import norm              
+from sage.misc.functional import norm, n           
 from sage.misc.package import is_package_installed

Testing the file polyhedra.py is not significantly longer than before : Great!

sage-4.8:

$ sage -t polyhedra.py
sage -t  "devel/sage-slabbe/sage/geometry/polyhedra.py"
         [58.0 s]
----------------------------------------------------------------------                 
All tests passed!
Total time for all tests: 58.0 seconds

sage-4.8 + your patch:

$ sage -t polyhedra.py
sage -t  "devel/sage-slabbe/sage/geometry/polyhedra.py"
         [58.6 s]
----------------------------------------------------------------------                 
All tests passed!
Total time for all tests: 58.6 seconds

You import VectorSpace but vector could do the job...

 from sage.modules.free_module_element import vector         
+from sage.modules.free_module import VectorSpace            
 from sage.matrix.constructor import matrix, identity_matrix

In your code, you write :

V = VectorSpace(RDF,3) 
view_vector = V(view)

I suggest you change this to :

view_vector = vector(RDF, view)

Every methods must have doctests:

$ sage -coverage polyhedra.py
----------------------------------------------------------------------
polyhedra.py
SCORE polyhedra.py: 98% (214 of 217)

Missing doctests:
         * _tikz_2d(self, scale, edge_color, facet_color, opacity, vertex_color, axis):
         * _tikz_2d_in_3d(self, view, rot_angle, scale, edge_color, facet_color, opacity, vertex_color, axis):
         * _tikz_3d_in_3d(self, view, rot_angle, scale, edge_color, facet_color, opacity, vertex_color, axis):

----------------------------------------------------------------------

I tested my script tikz2pdf on the above 3 junk tex files created by the doctest. Pdf files were created without problem. Pictures look great!
Building the documentation creates 2 warnings :

$ sage -docbuild reference html
...
/Users/slabbe/Applications/sage-4.8/local/lib/python2.6/site-packages/sage/geometry/polyhedra.py:docstring
of sage.geometry.polyhedra.Polyhedron.tikz:26: WARNING: Inline literal
start-string without end-string.
/Users/slabbe/Applications/sage-4.8/local/lib/python2.6/site-packages/sage/geometry/polyhedra.py:docstring
of sage.geometry.polyhedra.Polyhedron.tikz:27: WARNING: Inline literal
start-string without end-string.
...

I believe the problem comes from this :

+            2) Select ``Console`;        
+            3) Select the tab ``State`;

Change this

            It read something like:
                                             
            moveto 0.0 {x y z angle} Scale

to

            It read something like::
                                             
                moveto 0.0 {x y z angle} Scale

It will look nicer in the documentation.

I suggest to change the variable name rot_angle to angle.
Input block do not follow the coding convention.

See www.sagemath.org/doc/developer/conventions.html

I suggest you follow this example :

    INPUT:

     - ``x`` - integer (default: 1) the description of the
       argument x goes here.  If it contains multiple lines, all
       the lines after the first need to be indented.

     - ``y`` - integer (default: 2) the ...

    OUTPUT:

    integer -- the ...

So, first say what is the type. Then, say what is the default (inside `` quotes. Then, give the description.

For the output, just say the type and what it is. The part ``tikz_pic`` is not necessary.

The description of view argument could be improved.

- ``view`` -- a list of length 3 representing a vector;

I know it is a vector. Is it the camera position? Is it the view angle? Is it the axis for the rotation?

I think the type of what you return should be a LatexExpr instead of str.

from sage.misc.latex import LatexExpr

Compare latex(Image1) to latex(LatexExpr(Image1)). Because, sagetex
will call latex function on your output...

Bonne fête !

jplab · 2012-05-31T13:39:52Z

Apply over the precedent patch

jplab · 2012-05-31T13:42:58Z

comment:5

Attachment: trac12083_tikz_polytope_review.patch.gz

sagetrac-mhampton · 2012-05-31T16:59:37Z

Attachment: trac_12083_unholy_rebase_to_sage-5.0.patch.gz

For illustrative purposes only

sagetrac-mhampton · 2012-05-31T17:03:10Z

comment:6

I really like this functionality and I thought I'd help by rebasing the patch to sage-5.0, but I have now run out of time. Working on this reminded me of some things I don't like about the Projection class, but I am not sure about the best way to fix them. I think projections should be more accessible from Polyhedron objects, and vice-versa. Anyway, I did complete a patch for sage-5.0 that manages to pass the original tests, but its not very pretty. Its inefficient, and relies on a parent_polyhedron method for projections that might be objectionable. But since it works, it might be helpful in creating a better version.

If no one else does, I might have time to revisit this in a week or so.

novoselt · 2012-07-19T18:27:30Z

comment:7

So - which patches have to be applied? I suspect they'll need rebasing after all Volker's refactoring.

novoselt · 2012-07-19T18:27:30Z

Author: Jean-Philippe Labbé

novoselt · 2012-07-19T18:27:30Z

Reviewer: Sébastien Labbé

fchapoton · 2012-11-01T18:51:07Z

comment:8

let us try and see

apply trac12083_tikz_polytope.2.patch trac12083_tikz_polytope_review.patch

jplab · 2012-11-26T19:12:09Z

comment:9

So, today I used the reviewed patch to draw a polytope using the library decorations of tikz.

I realized that I was sloppy to implement the edges; they are drawn twice. This also makes the compilation in LaTeX slower.

I will write a patch for version 5.3 that does not have repetitions (and containing the improvements in the rebased version).

jplab · 2012-12-19T14:47:22Z

comment:10

Attachment: trac12083_rebased_5.4.1.patch.gz

So, here is the rebased version of the patch.

I solved a few problems:
The vertices and edges appeared twice before (sloppy implementation);
There was one vertex not drawn in the first (unholy) rebased version;
The facets were badly drawn (problem with vertices naming in the code);
The back edges were badly recognized.

I looked at the compiled tikz output examples and now everything seems in order.

All tests passed on 5.4.1

One thing I don't really like though is the fact that we need to pass to projections to access the tikz method. Perhaps a wrapper would do the thing?

jplab · 2012-12-19T14:47:55Z

comment:11

For the bot:

apply trac12083_rebased_5.4.1.patch

fchapoton · 2013-03-03T10:18:30Z

comment:12

There is a problem with the lines

            v1 = self.coords[index1]
            v2 = self.coords[index2]

which appear three times, but the variables v1 and v2 are never used.

fchapoton · 2013-03-03T10:23:04Z

comment:13

Moreover, three tests are failing on sage 5.8.beta1

nathanncohen · 2013-05-20T11:17:40Z

comment:14

This patch should probably be rebased. It would be nice to add in the ticket's description which patch are to be applied, too.

Nathann

fchapoton · 2013-08-21T08:21:29Z

comment:16

here is a rebased patch, passing tests and working on 5.12.beta0

apply only trac12083_rebased_5.12.patch

fchapoton · 2013-08-25T13:58:45Z

comment:17

apply only trac12083_rebased_5.12.patch

vbraun · 2013-11-01T09:33:53Z

Changed reviewer from Sébastien Labbé to Sébastien Labbé, Volker Braun

vbraun · 2013-11-01T09:33:53Z

comment:18

lgtm

jdemeyer · 2013-11-01T12:57:32Z

comment:19

The PDF doc doesn't build:

! Package inputenc Error: Keyboard character used is undefined
(inputenc)                in inputencoding `utf8'.

See the inputenc package documentation for explanation.
Type  H <return>  for immediate help.
 ...

l.17893 \item[{^^Hegin\{tikzpicture\}\%}] 
                                          \leavevmode

To fix this, use r""" docstrings instead of """.

fchapoton · 2013-11-04T19:56:53Z

Attachment: trac12083_rebased_5.12.patch.gz

fchapoton · 2013-11-04T19:58:38Z

comment:21

I have made a corrected patch, hopefully.

apply trac12083_rebased_5.12.patch

vbraun · 2013-11-04T21:55:28Z

comment:22

Works for me...

jdemeyer · 2013-11-09T15:30:44Z

Merged: sage-5.13.beta3

kcrisman · 2013-12-18T01:51:59Z

comment:24

I just want to say that I could have used this a couple years ago and instead had to do lots of guess-and-check with graph plots, then convert to xfig... thank you, this will be very useful!

jplab added this to the sage-5.11 milestone Nov 25, 2011

jplab added c: geometry labels Nov 25, 2011

jplab assigned sagetrac-mhampton Nov 25, 2011

jplab added the s: needs review label Dec 4, 2011

seblabbe added s: needs work and removed s: needs review labels Feb 10, 2012

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Add a TikZ-tex output method for 2d and 3d polytopes #12083

Add a TikZ-tex output method for 2d and 3d polytopes #12083

jplab commented Nov 25, 2011

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Add a TikZ-tex output method for 2d and 3d polytopes #12083

Add a TikZ-tex output method for 2d and 3d polytopes #12083

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jplab commented Nov 25, 2011

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