#8169: include TOPCOM
----------------------------+-----------------------------------------------
Reporter: vbraun | Owner: AlexGhitza
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-feature
Component: geometry | Keywords:
Author: Volker Braun | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
----------------------------+-----------------------------------------------
Changes (by vbraun):
* status: needs_info => needs_work
Old description:
> TOPCOM is a C++ program for triangulating polyhedra. More generally, it
> can find a single triangulation as well as enumerate all triangulations
> of a "point configuration", that is, the convex hull of points in
> euclidean space such that all vertices of simplices of the triangulation
> are in the given (finite) list of points.
>
> One problem with the upstream distribution is that it statically links
> many helper programs, yielding almost 200mb of binaries. Therefore, I
> suggest the following:
>
> - dynamically link TOPCOM via libtools to reduce size
> - Write a sage<->TOPCOM interface at sage.geometry.triangulation.py
>
> As an initial submission, my libtoolized TOPCOM spkg is here:
>
> http://www.stp.dias.ie/~vbraun/TOPCOM-0.16.2.spkg
>
> and a first draft of triangulation.py is attached. The basic usage is
>
> {{{
> sage: points = PointConfiguration([[0,0],[0,1],[1,0],[1,1],[-1,-1]]);
> sage: points
> A point configuration in QQ^2 consisting of 5 points.
> sage: triang = points.triangulate() # find one triangulation
> sage: triang
> A triangulation in QQ^2 consisting of 4 simplices.
> sage: triang.plot(axes=False)
> }}}
>
> After we confirm that the libtoolized TOPCOM builds on all sage
> platforms, I'll contact upstream for eventual inclusion of the autotools
> sources.
>
> Note: see #8115 for a modified cddlib (required by TOPCOM) that provides
> a non-static cddlib library.
New description:
TOPCOM is a C++ program for triangulating polyhedra. More generally, it
can find a single triangulation as well as enumerate all triangulations of
a "point configuration", that is, the convex hull of points in euclidean
space such that all vertices of simplices of the triangulation are in the
given (finite) list of points.
One problem with the upstream distribution is that it statically links
many helper programs, yielding almost 200mb of binaries. Therefore, I
suggest the following:
- dynamically link TOPCOM via libtools to reduce size
- Write a sage<->TOPCOM interface at sage.geometry.triangulation.py
As an initial submission, my libtoolized TOPCOM spkg is here:
http://www.stp.dias.ie/~vbraun/TOPCOM-0.16.2.p2.spkg
and a first draft of triangulation.py is attached. The basic usage is
{{{
sage: points = PointConfiguration([[0,0],[0,1],[1,0],[1,1],[-1,-1]]);
sage: points
A point configuration in QQ^2 consisting of 5 points. The
triangulations of this point configuration are assumed to
be connected, not necessarily fine, not necessarily regular.
sage: triang = points.triangulate() # find one triangulation
sage: triang
(<0,1,2>, <0,1,4>, <0,2,4>, <1,2,3>)
sage: triang[0]
(0, 1, 2)
sage: list( points.triangulations() )
[(<0,1,2>, <0,1,4>, <0,2,4>, <1,2,3>),
(<0,1,3>, <0,1,4>, <0,2,3>, <0,2,4>),
(<1,2,3>, <1,2,4>),
(<1,3,4>, <2,3,4>)]
sage: triang.plot(axes=False)
}}}
After we confirm that the libtoolized TOPCOM builds on all sage platforms,
I'll contact upstream for eventual inclusion of the autotools sources.
Note: see #8115 for a modified cddlib (required by TOPCOM) that provides a
non-static cddlib library.
--
Comment:
I've dealt with 3. and 4. in comment 15, and 6. in comment 16. Now
generally tuples instead of lists are returned, and a new `class Point` is
added which has methods for affine, projective, or reduced (with
linearities removed) coordinates. This should also fix Marshall's
problems.
Now `PointConfiguration`/`Triangulation` have a Parent/Element
relationship. In particular, the `PointConfiguration` is unique and
immutable. The `restrict_to_...` interface for restricting the admissible
triangulations has been slightly changed, and now returns a '''new'''
`PointConfiguration`. I think that also fits better with the general Sage
philosophy.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8169#comment:26>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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