#4164: [with patch, needs work] Make triangulated_facial_incidences() work in
all
cases (and decomment render_solid())
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Reporter: anakha | Owner: anakha
Type: defect | Status: assigned
Priority: major | Milestone: sage-3.1.3
Component: graphics | Resolution:
Keywords: |
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Comment (by anakha):
Replying to [comment:4 mhampton]:
> 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.
I think I should never post patches past midnight, because this is when I
always forget something like this.
> 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.
I can't think right now of an algorithm that will triangulate according to
your description in an arbitrary dimension. I will think about it for a
while though.
> 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.
This is what I expected. Since the polyhedron itself is in 2D the edges
are in 1D so they correspond to the edges. I asked you this question
before with a square and you told me it was normal.
If it is not supposed to do that, then facial_incidences() is broken.
Take a look at it.
> Do you have a reference for the algorithm you are using, or are you
coming up with one yourself?
I am more or less coming up with it myself. The actual triangulation of
2D surfaces is pretty standard in computer graphics (walk the points of
the polygon building a triangle strip) but it obviously does not cover the
cases where surfaces are in 4D. That's where I innovate (or just do
something random it seems).
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4164#comment:5>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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