DEC: Discrete Exterior Calculus

This new package adds discrete exterior calculus features to DGtal. It contains:
 
   - new `dec` packages (dec operators, test files, examples, documentation)
   - new `linalg` with linear algebra concepts and backends (Eigen at this point) 

As you would see, this PR, mostly managed by @elcerdo,  is quite huge and some documentation pages are still "work-in-progress". I send a PR just to start including this great package into DGtal and to clean things up thanks to your comments.
Le 10/07/2014 13:45, Pierre Gueth a écrit :
> In src/DGtal/dec/DiscreteExteriorCalculus.h:
> 
>> +    typedef typename LinearAlgebraBackend::SparseMatrix SparseMatrix;
>> +
>> +    BOOST_CONCEPT_ASSERT(( concepts::CDynamicVector<DenseVector> ));
>> +    BOOST_CONCEPT_ASSERT(( concepts::CDynamicMatrix<DenseMatrix> ));
>> +    BOOST_CONCEPT_ASSERT(( concepts::CDynamicMatrix<SparseMatrix> ));
>> +    BOOST_CONCEPT_ASSERT(( concepts::CLinearAlgebra<DenseVector, SparseMatrix> ));
>> +    BOOST_CONCEPT_ASSERT(( concepts::CLinearAlgebra<DenseVector, DenseMatrix> ));
>> +
>> +    BOOST_STATIC_ASSERT(( boost::is_same<Dimension, Order>::value ));
>> +
>> +    /**
>> +     * Static dimension.
>> +     */
>> +    BOOST_STATIC_CONSTANT( Dimension, dimension = dim );
>> +
>> +    typedef DGtal::KhalimskySpaceND<dim, TInteger> KSpace;
> 
> I don't think this will works for any cellular complex.
> There should at least be a one to one correspondance between primal and
> dual cells...
> 
> Is there another model of CCellularGridSpaceND besides KhalimskySpaceND?

I have written another model CodedKhalimskySpaceND in my branch
FastKSpace. For now, it is a backport from an old work of mine that is
still experimental. It seems to work fine, it is a bit faster than
KhalimskySpaceND but would be more interesting if I couple it with a new
model of CDigitalSet (a characteristic set with a vector of bits as
container).
The thing is that the whole module IO is not fully satisfying the
concept CCellularGridSpaceND and used some functions specific to
KhalimskySpaceND.
Jaco

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