dec/exampleDiscreteExteriorCalculusUsage.cpp

Example of vector field manipulation using Discrete Exterior Calculus.

See also

Introduction

Flat sharped primal gradient vector field.

 
 
#include <string>
 
#include "DECExamplesCommon.h"
 
// always include EigenSupport.h before any other Eigen headers
#include "DGtal/math/linalg/EigenSupport.h"
#include "DGtal/dec/DiscreteExteriorCalculus.h"
#include "DGtal/dec/DiscreteExteriorCalculusSolver.h"
#include "DGtal/dec/DiscreteExteriorCalculusFactory.h"
 
#include "DGtal/io/boards/Board2D.h"
#include "DGtal/io/readers/GenericReader.h"
 
using namespace std;
using namespace DGtal;
 
void usage2d()
{
    trace.beginBlock("2d discrete exterior calculus usage");
 
    const Z2i::Domain domain(Z2i::Point(0,0), Z2i::Point(9,9));
 
    typedef DiscreteExteriorCalculus<2, 2, EigenLinearAlgebraBackend> Calculus;
    typedef DiscreteExteriorCalculusFactory<EigenLinearAlgebraBackend> CalculusFactory;
 
    // create discrete exterior calculus from set without border
    {
    Calculus calculus = CalculusFactory::createFromDigitalSet(generateRingSet(domain), false);
 
    calculus.eraseCell(calculus.myKSpace.uSpel(Z2i::Point(8, 5)));
 
    calculus.updateIndexes();
 
        trace.info() << calculus << endl;
 
        Board2D board;
        board << domain;
        board << calculus;
        board.saveSVG("usage_calculus_without_border.svg");
    }
 
    // create discrete exterior calculus from set with border
    Calculus calculus = CalculusFactory::createFromDigitalSet(generateRingSet(domain), true);
 
    calculus.eraseCell(calculus.myKSpace.uSpel(Z2i::Point(8, 5)));
    calculus.eraseCell(calculus.myKSpace.uCell(Z2i::Point(18, 11)));
 
    calculus.updateIndexes();
 
    trace.info() << calculus << endl;
 
    {
        Board2D board;
        board << domain;
        board << calculus;
        board.saveSVG("usage_calculus_with_border.svg");
    }
 
    const Z2i::Point center(13,7);
 
    // primal path
    {
        trace.info() << "primal path" << endl;
 
        // create primal 0-form and fill it with euclidian metric
        Calculus::PrimalForm0 primal_zero_form(calculus);
        for (Calculus::Index index=0; index<primal_zero_form.length(); index++)
        {
            const Calculus::SCell& cell = primal_zero_form.getSCell(index);
            const Calculus::Scalar& value = Z2i::l2Metric(calculus.myKSpace.sKCoords(cell), center)/2;
            primal_zero_form.myContainer(index) = value;
        }
        // one can do linear algebra operation between equaly typed kforms
        const Calculus::PrimalForm0 foo = 2 * primal_zero_form + primal_zero_form;
 
        {
            Board2D board;
            board << domain;
            board << calculus;
            board << primal_zero_form;
            board.saveSVG("usage_primal_zero_form.svg");
        }
 
        // create primal gradient vector field and primal derivative one form
        const Calculus::PrimalDerivative0 primal_zero_derivative = calculus.derivative<0, PRIMAL>();
        const Calculus::PrimalForm1 primal_one_form = primal_zero_derivative * primal_zero_form;
        const Calculus::PrimalVectorField primal_vector_field = calculus.sharp(primal_one_form);
 
        {
            Board2D board;
            board << domain;
            board << calculus;
            board << primal_one_form;
            board << primal_vector_field;
            board.saveSVG("usage_primal_one_form.svg");
        }
 
        // test primal flat and sharp
        const Calculus::PrimalForm1 flat_sharp_primal_one_form = calculus.flat(primal_vector_field);
        const Calculus::PrimalVectorField sharp_flat_primal_vector_field = calculus.sharp(flat_sharp_primal_one_form);
 
        {
            Board2D board;
            board << domain;
            board << calculus;
            board << flat_sharp_primal_one_form;
            board << sharp_flat_primal_vector_field;
            board.saveSVG("usage_primal_one_form_sharp_flat.svg");
        }
 
        // create dual gradient vector field and hodge*d dual one form
        const Calculus::PrimalHodge1 primal_one_hodge = calculus.hodge<1, PRIMAL>();
        const Calculus::DualForm1 dual_one_form = primal_one_hodge * primal_zero_derivative * primal_zero_form;
        const Calculus::DualVectorField dual_vector_field = calculus.sharp(dual_one_form);
 
        {
            Board2D board;
            board << domain;
            board << calculus;
            board << dual_one_form;
            board << dual_vector_field;
            board << primal_vector_field;
            board.saveSVG("usage_primal_one_form_hodge.svg");
        }
    }
 
    // dual path
    {
        trace.info() << "dual path" << endl;
 
        // create dual 0-form and fill it with euclidian metric
        Calculus::DualForm0 dual_zero_form(calculus);
        for (Calculus::Index index=0; index<dual_zero_form.length(); index++)
        {
            const Calculus::SCell& cell = dual_zero_form.getSCell(index);
            const Calculus::Scalar& value = Z2i::l2Metric(calculus.myKSpace.sKCoords(cell), center)/2;
            dual_zero_form.myContainer(index) = value;
        }
 
        {
            Board2D board;
            board << domain;
            board << calculus;
            board << dual_zero_form;
            board.saveSVG("usage_dual_zero_form.svg");
        }
 
        // create dual gradient vector field and dual derivative one form
        const Calculus::DualDerivative0 dual_zero_derivative = calculus.derivative<0, DUAL>();
        const Calculus::DualForm1 dual_one_form = dual_zero_derivative * dual_zero_form;
        const Calculus::DualVectorField dual_vector_field = calculus.sharp(dual_one_form);
 
        {
            Board2D board;
            board << domain;
            board << calculus;
            board << dual_one_form;
            board << dual_vector_field;
            board.saveSVG("usage_dual_one_form.svg");
        }
 
        // test primal flat and sharp
        const Calculus::DualForm1 flat_sharp_dual_one_form = calculus.flat(dual_vector_field);
        const Calculus::DualVectorField sharp_flat_dual_vector_field = -calculus.sharp(flat_sharp_dual_one_form);
 
        {
            Board2D board;
            board << domain;
            board << calculus;
            board << flat_sharp_dual_one_form;
            board << -sharp_flat_dual_vector_field;
            board.saveSVG("usage_dual_one_form_sharp_flat.svg");
        }
 
        // create primal gradient vector field and hodge*d primal one form
        const Calculus::DualHodge1 dual_one_hodge = calculus.hodge<1, DUAL>();
        const Calculus::PrimalForm1 primal_one_form = dual_one_hodge * dual_zero_derivative * dual_zero_form;
        const Calculus::PrimalVectorField primal_vector_field = calculus.sharp(primal_one_form);
 
        {
            Board2D board;
            board << domain;
            board << calculus;
            board << primal_one_form;
            board << primal_vector_field;
            board << dual_vector_field;
            board.saveSVG("usage_dual_one_form_hodge.svg");
        }
    }
 
    trace.endBlock();
}
 
int main()
{
    usage2d();
 
    return 0;
}