#4875: Polyhedron.show(fill=True) fails
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Reporter: abergeron | Owner: was
Type: defect | Status: new
Priority: major | Milestone: sage-3.4.1
Component: graphics | Keywords:
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Changes (by wcauchois):
* cc: wcauchois (added)
Comment:
This bug was hard to track down! But I believe the root cause is in
Polyhedron.render_solid(), when the method gives invalid faces to
IndexFaceSet. This causes issues later on, inside IndexFaceSet, when
certain CPython methods with little to no error checking index into those
faces.
These faces are incorrect because
Polyhedron.triangulated_facial_incidences() does not properly triangulate
the facial incidences. Look at this:
{{{
sage: Polyhedron(vertices = [[1, 2, 3], [0,1,0],
[1,1,1]]).triangulated_facial_incidences()
[[0, [0, 2]], [1, [0, 1]], [2, [1, 2]]]
}}}
Triangles in 3-space should consist of 3 vertices, not 2!
triangulated_facial_incidences() naively handles the case where
`vert_number != self.dim()` (see polyhedra.py:678) by simply appending the
original facial incidence.
The output from facial_incidences() looks like this:
{{{
sage: Polyhedron(vertices = [[1, 2, 3], [0,1,0],
[1,1,1]]).facial_incidences()
[[0, [0, 2]], [1, [0, 1]], [2, [1, 2]]]
}}}
Just FYI, the facial incidences are computed using cddlib. Here's a log of
Sage's interaction with cddlib:
{{{
sage: P = Polyhedron(vertices = [[1, 2, 3], [0,1,0], [1,1,1]])
sage: vert_to_ieq(P._vertices, rays=P._rays, cdd_type=P._cdd_type,
verbose=True)
V-representation
begin
3 4 rational
1 1 2 3
1 0 1 0
1 1 1 1
end
Input is a V-representation
H-representation
linearity 1 4
begin
4 4 rational
1 -1 0 0
1 1 -1 0
-1 0 1 0
2 -1 -2 1
end
V-representation
begin
3 4 rational
1 1 2 3
1 0 1 0
1 1 1 1
end
Here is the incidence list:
begin
4 3
1 2 : 1 3
2 2 : 1 2
3 2 : 2 3
4 3 : 1 2 3
end
Here is the adjacency list:
begin
4 4
1 2 : 2 3
2 2 : 1 3
3 2 : 1 2
4 0 :
end
A Polyhedron with 3 vertices.
}}}
I would love to fix this bug, but unfortunately I don't have the
mathematical knowledge to improve triangulated_facial_incidences().
Hopefully now that the source of the bug is clear, someone with more
intimate knowledge of polyhedra can fix it!
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4875#comment:2>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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