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TODO.txt
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TODO.txt
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******************************** PILE ********************************
Change the code of the mesh constructor so there is no need to rearrange the order after for building the graph (yuck)
Rewrite triangulater with flips?
construct mesh and graphes in thread?
Edit doc.
Investigate this:
Ok so wait
can you look at the function
DiscreteFlowFactory<Point, Map>::run()
maybe you wrote an extra "updateSupError" in there?
do you remember?
it feels like the second one maybe shouldn't be there
wait... maybe that's why it drops to zero
wait no sorry I think I spoke too fast
no it looks fine
because when it breaks, it updates once more, and this time it is comparing the new values to the new values, so thinks there is zero error
******************************** IMPROVE CODE ********************************
assert vs throw
track down code duplication
move semantics http://stackoverflow.com/questions/3106110/what-are-move-semantics
hunt memory leaks, test with valgrind
use auto
use C++ arrays instead of vectors in some places? Eg: std::vector< std::vector<Point> > getTrianglesUp() : could this be a std::vector<Point[3]> or something?
******************************** BUGS: ********************************
Program should handle when a nonconvex fundamental domain is given, at the moment it will just crash (or not) when constructing the mesh.
(still happening?)
More generally, get the exception handling ready to work (catch errors in MainApplication)
************************* FUTURE PLANS ***************************
0. Meet at least N days per year, where N>>1
1. Think about discretization of Energy. In particular:
- should we take into account energy accumulated at vertices (/edges)?
- what are better weights for the energy?
- etc
2. Think about equivariance: Explain the picture of the (almost) harmonic map from a rho to its Dehn twist.
3. Improve choice of steiner points and cuts
4. Improve choice of fundamental domain (try dirichlet?)
6. H3 and SL(2,C)-character variety
7. Paths in the character variety...
8. Hopf differential? Energy?
9. Do youtube video!
10. Improve triangulations by adding points to the cuts?
11. Attempt optimalStep with *different* steps at different mesh points.
12. Optimization using Newton's method to minimize Energy.
13. See section PAPER.
14. Implementation with flat structures in the domain (making triangulation easier)
15. Implementation with SL(3,R) coordinates in target and Goldman coordinates
16. Implementation with SO(2,2) -> ADS(3)
************************* APPLICATIONS ***************************
Other people:
- Daniele Alessandrini's idea to test Goldman conjecture (about affine sphere or something) (the other surface is koszul winberg)
- Show a path of harmonic maps when moving between components of the SL2R character variety.
- Jean-Marc's question about convexity (and the Weil-Petersson metric)
- Asymptotic behavior
- Mike Wolf shit
Us:
- Investigating Hitchin metric
- minimal surfaces parametrization, (globally minimizing energy) -- "evidence for Labourie's conjecture"
************************* OPTIMIZATION ***************************
Optimization of heat flow:
- use profiler
- try acceleration à la circle packings (see tests.cpp)
- recursive depth
- Newton method
**************************** PAPER ********************************
5. Applications (see APPLICATIONS)