#4164: [with patch, needs work] Make triangulated_facial_incidences() work in
all
cases (and decomment render_solid())
----------------------+-----------------------------------------------------
Reporter: anakha | Owner: anakha
Type: defect | Status: assigned
Priority: major | Milestone: sage-3.1.3
Component: graphics | Resolution:
Keywords: |
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Changes (by mhampton):
* summary: [with patch, needs review] Make
triangulated_facial_incidences() work in all
cases (and decomment render_solid()) => [with
patch, needs work] Make
triangulated_facial_incidences() work in all
cases (and decomment render_solid())
Comment:
First of all let me say thanks for working on this. There are some
problems with these patches though:
1) They don't pass doctesting on my machine. This is because of some
output order differences. Did you test the final combination of all three
patches? Otherwise it might be architecture-specific but looking at your
code that seems unlikely.
2) In higher dimensions, "triangulation" usually means a decomposition
into simplices - so in four dimensions the elements of a triangulation of
a face should be tetrahedra. It occurs to me that it would perhaps be
best to write a function in the Polyhedra class that triangulates (in this
sense) the polyhedra itself, and then for
.triangulated_facial_incideneces() call this function on the polyhedrons
generated by each face.
3) Things seem to break for bigger examples. For instance, an octohedron:
{{{
sage: p_oct = Polyhedron(vertices =
[[0,1],[0,2],[1,0],[2,0],[3,1],[3,2],[1,3],[2,3]])
sage: p_oct.triangulated_facial_incidences()
[[0, [3, 4, 3]],
[1, [2, 3, 2]],
[2, [0, 2, 0]],
[3, [0, 1, 0]],
[4, [1, 6, 1]],
[5, [6, 7, 6]],
[6, [5, 7, 5]],
[7, [4, 5, 4]]]
}}}
Notice that the triangulation consists of the edges.
Do you have a reference for the algorithm you are using, or are you coming
up with one yourself?
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4164#comment:4>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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