OKlibrary  0.2.1.6
OrthogonalTriples.hpp File Reference

Plans regarding the elementary algorithms for handling orthogonal triples in 3-dimensional Euclidean space. More...

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## Detailed Description

Plans regarding the elementary algorithms for handling orthogonal triples in 3-dimensional Euclidean space.

Todo:
The following todo's are about the reusable components in QuantumPhysics/OrthogonalTriples.cpp, which should be moved to appropriate library files (where they are tested).
Todo:
Output CNFs SAT_translation should use the components in InputOutput.
Todo:
Input and output of graphs
• With output_graph and read in Hypergraphs/Colourings/GreedyColouring.cpp we have a simple text format.
• There is also a simple format used in yEd?
• Perhaps this is better; we should have the possibilities for comments, and perhaps for vertex and edge properties.
• This all shold go into a dedicated graph-module.
Todo:
Input and Output Use Messages and ProgramOptions.
Todo:
Linear algebra Move the components
• vector_product (not in Boost::Ublas ?)
• orthogonal (checking needs to be improved) to appropriate modules, and test them.
Todo:
Hypergraphs In output_remaining_edges, output_hypergraph and extract_triangles a certain interface for hypergraphs is used --- compare this with the concepts for hypergraphs (see Hypergraphs/concepts/plans/general.hpp).
Todo:
Orthogonality relation The function orthogonality_relation should be generalised, so that an arbitrary binrary predicate can be used.
Todo:
Extract triangles The function extract_triangles should go into the general graph/hypergraph module. Are there better algorithms?
Todo:
Copying graphs Why does
```#include <boost/graph/copy.hpp>
UndirectedGraphM g_m(num_vertices(g));
boost::copy_graph(g, g_m);
```

not work??? Perhaps the problem is, that boost::copy_graph also wants to set the property in g_m ???

Todo:
We need a new function "completion", which, given a point configuration, adds the unique orthogonal direction to every pair which is not contained in a triple. For the Peres 33-point configuration one then needs to check, whether the 24 pairs yield 24 new points (likely not). The completion happens via the vector product, and another function checks whether two directions given by two vectors are equal or not.

Definition in file OrthogonalTriples.hpp.