void test_linear_ring()
{
trace.beginBlock("linear ring");
const Domain domain(Point(-5,-5), Point(5,5));
typedef DiscreteExteriorCalculus<1, 2, EigenLinearAlgebraBackend> Calculus;
Calculus calculus;
calculus.initKSpace<Domain>(domain);
for (int kk=-8; kk<10; kk++) calculus.insertSCell( calculus.myKSpace.sCell(Point(-8,kk), kk%2 == 0 ? Calculus::KSpace::POS : Calculus::KSpace::NEG) );
for (int kk=-8; kk<10; kk++) calculus.insertSCell( calculus.myKSpace.sCell(Point(kk,10), kk%2 == 0 ? Calculus::KSpace::POS : Calculus::KSpace::NEG) );
for (int kk=10; kk>-8; kk--) calculus.insertSCell( calculus.myKSpace.sCell(Point(10,kk)) );
for (int kk=10; kk>-8; kk--) calculus.insertSCell( calculus.myKSpace.sCell(Point(kk,-8)) );
calculus.updateIndexes();
{
trace.info() << calculus << endl;
Board2D board;
board << domain;
board << calculus;
board.saveSVG("ring_structure.svg");
}
const Calculus::PrimalDerivative0 d0 = calculus.derivative<0, PRIMAL>();
display_operator_info("d0", d0);
const Calculus::PrimalHodge0 h0 = calculus.hodge<0, PRIMAL>();
display_operator_info("h0", h0);
const Calculus::DualDerivative0 d0p = calculus.derivative<0, DUAL>();
display_operator_info("d0p", d0p);
const Calculus::PrimalHodge1 h1 = calculus.hodge<1, PRIMAL>();
display_operator_info("h1", h1);
const Calculus::PrimalIdentity0 laplace = calculus.laplace<PRIMAL>();
display_operator_info("laplace", laplace);
const int laplace_size = calculus.kFormLength(0, PRIMAL);
const Eigen::MatrixXd laplace_dense(laplace.myContainer);
for (int ii=0; ii<laplace_size; ii++)
FATAL_ERROR( laplace_dense(ii,ii) == 2 );
FATAL_ERROR( laplace_dense.array().rowwise().sum().abs().sum() == 0 );
FATAL_ERROR( laplace_dense.transpose() == laplace_dense );
trace.endBlock();
}
void propa_2d()
{
trace.beginBlock("2d propagation");
typedef DiscreteExteriorCalculus<2, 2, EigenLinearAlgebraBackend> Calculus;
typedef DiscreteExteriorCalculusFactory<EigenLinearAlgebraBackend> CalculusFactory;
{
trace.beginBlock("solving time dependent equation");
const Calculus::Scalar cc = 8; // px/s
trace.info() << "cc = " << cc << endl;
const Z2i::Domain domain(Z2i::Point(0,0), Z2i::Point(29,29));
const Calculus calculus = CalculusFactory::createFromDigitalSet(generateDiskSet(domain), false);
//! [time_laplace]
const Calculus::DualIdentity0 laplace = calculus.laplace<DUAL>() + 1e-8 * calculus.identity<0, DUAL>();
//! [time_laplace]
trace.info() << "laplace = " << laplace << endl;
trace.beginBlock("finding eigen pairs");
//! [time_eigen]
typedef Eigen::SelfAdjointEigenSolver<Eigen::MatrixXd> EigenSolverMatrix;
const EigenSolverMatrix eigen_solver(laplace.myContainer);
const Eigen::VectorXd eigen_values = eigen_solver.eigenvalues();
const Eigen::MatrixXd eigen_vectors = eigen_solver.eigenvectors();
//! [time_eigen]
trace.info() << "eigen_values_range = " << eigen_values.minCoeff() << "/" << eigen_values.maxCoeff() << endl;
trace.endBlock();
//! [time_omega]
const Eigen::VectorXd angular_frequencies = cc * eigen_values.array().sqrt();
//! [time_omega]
Eigen::VectorXcd initial_wave = Eigen::VectorXcd::Zero(calculus.kFormLength(0, DUAL));
//set_initial_phase_null(calculus, initial_wave);
set_initial_phase_dir_yy(calculus, initial_wave);
{
Board2D board;
board << domain;
board << CustomStyle("KForm", new KFormStyle2D(-1, 1));
board << Calculus::DualForm0(calculus, initial_wave.real());
board.saveSVG("propagation_time_wave_initial_coarse.svg");
}
//! [time_init_proj]
Eigen::VectorXcd initial_projections = eigen_vectors.transpose() * initial_wave;
//! [time_init_proj]
// low pass
//! [time_low_pass]
const Calculus::Scalar lambda_cutoff = 4.5;
const Calculus::Scalar angular_frequency_cutoff = 2*M_PI * cc / lambda_cutoff;
int cutted = 0;
for (int kk=0; kk<initial_projections.rows(); kk++)
{
const Calculus::Scalar angular_frequency = angular_frequencies(kk);
if (angular_frequency < angular_frequency_cutoff) continue;
initial_projections(kk) = 0;
cutted ++;
}
//! [time_low_pass]
trace.info() << "cutted = " << cutted << "/" << initial_projections.rows() << endl;
{
const Eigen::VectorXcd wave = eigen_vectors * initial_projections;
Board2D board;
board << domain;
board << CustomStyle("KForm", new KFormStyle2D(-1, 1));
board << Calculus::DualForm0(calculus, wave.real());
board.saveSVG("propagation_time_wave_initial_smoothed.svg");
}
const int kk_max = 60;
trace.progressBar(0,kk_max);
for (int kk=0; kk<kk_max; kk++)
{
//! [time_solve_time]
const Calculus::Scalar time = kk/20.;
const Eigen::VectorXcd current_projections = (angular_frequencies * std::complex<double>(0,time)).array().exp() * initial_projections.array();
const Eigen::VectorXcd current_wave = eigen_vectors * current_projections;
//! [time_solve_time]
std::stringstream ss;
ss << "propagation_time_wave_solution_" << std::setfill('0') << std::setw(3) << kk << ".svg";
Board2D board;
board << domain;
board << CustomStyle("KForm", new KFormStyle2D(-1, 1));
board << Calculus::DualForm0(calculus, current_wave.real());
board.saveSVG(ss.str().c_str());
trace.progressBar(kk+1,kk_max);
}
trace.info() << endl;
trace.endBlock();
}
{
trace.beginBlock("forced oscillations");
const Z2i::Domain domain(Z2i::Point(0,0), Z2i::Point(50,50));
const Calculus calculus = CalculusFactory::createFromDigitalSet(generateDiskSet(domain), false);
const Calculus::DualIdentity0 laplace = calculus.laplace<DUAL>();
trace.info() << "laplace = " << laplace << endl;
trace.beginBlock("finding eigen pairs");
typedef Eigen::SelfAdjointEigenSolver<Eigen::MatrixXd> EigenSolverMatrix;
const EigenSolverMatrix eigen_solver(laplace.myContainer);
const Eigen::VectorXd laplace_eigen_values = eigen_solver.eigenvalues();
const Eigen::MatrixXd laplace_eigen_vectors = eigen_solver.eigenvectors();
trace.info() << "eigen_values_range = " << laplace_eigen_values.minCoeff() << "/" << laplace_eigen_values.maxCoeff() << endl;
trace.endBlock();
Calculus::DualForm0 concentration(calculus);
{
const Z2i::Point point(25,25);
const Calculus::Cell cell = calculus.myKSpace.uSpel(point);
const Calculus::Index index = calculus.getCellIndex(cell);
concentration.myContainer(index) = 1;
}
{
Board2D board;
board << domain;
board << concentration;
board.saveSVG("propagation_forced_concentration.svg");
}
for (int ll=0; ll<6; ll++)
{
//! [forced_lambda]
const Calculus::Scalar lambda = 4*20.75/(1+2*ll);
//! [forced_lambda]
trace.info() << "lambda = " << lambda << endl;
//! [forced_dalembert_eigen]
const Eigen::VectorXd dalembert_eigen_values = (laplace_eigen_values.array() - (2*M_PI/lambda)*(2*M_PI/lambda)).array().inverse();
const Eigen::MatrixXd concentration_to_wave = laplace_eigen_vectors * dalembert_eigen_values.asDiagonal() * laplace_eigen_vectors.transpose();
//! [forced_dalembert_eigen]
//! [forced_wave]
Calculus::DualForm0 wave(calculus, concentration_to_wave * concentration.myContainer);
//! [forced_wave]
wave.myContainer /= wave.myContainer(calculus.getCellIndex(calculus.myKSpace.uSpel(Z2i::Point(25,25))));
{
trace.info() << "saving samples" << endl;
const Calculus::Properties properties = calculus.getProperties();
{
std::stringstream ss;
ss << "propagation_forced_samples_hv_" << ll << ".dat";
std::ofstream handle(ss.str().c_str());
for (int kk=0; kk<=50; kk++)
{
const Z2i::Point point_horizontal(kk,25);
const Z2i::Point point_vertical(25,kk);
const Calculus::Scalar xx = 2 * (kk/50. - .5);
handle << xx << " ";
handle << sample_dual_0_form<Calculus>(properties, wave, point_horizontal) << " ";
handle << sample_dual_0_form<Calculus>(properties, wave, point_vertical) << endl;
}
}
{
std::stringstream ss;
ss << "propagation_forced_samples_diag_" << ll << ".dat";
std::ofstream handle(ss.str().c_str());
for (int kk=0; kk<=50; kk++)
{
const Z2i::Point point_diag_pos(kk,kk);
const Z2i::Point point_diag_neg(kk,50-kk);
const Calculus::Scalar xx = 2 * sqrt(2) * (kk/50. - .5);
handle << xx << " ";
handle << sample_dual_0_form<Calculus>(properties, wave, point_diag_pos) << " ";
handle << sample_dual_0_form<Calculus>(properties, wave, point_diag_neg) << endl;
}
}
}
{
std::stringstream ss;
ss << "propagation_forced_wave_" << ll << ".svg";
Board2D board;
board << domain;
board << CustomStyle("KForm", new KFormStyle2D(-.5, 1));
board << wave;
board.saveSVG(ss.str().c_str());
}
}
trace.endBlock();
}
trace.endBlock();
}
int main(int argc, char* argv[])
{
using DGtal::trace;
using std::endl;
using DGtal::PRIMAL;
using DGtal::DUAL;
const Options options = parse_options(argc, argv);
const KSpace kspace;
const Calculus calculus;
const FlatVector original_face_normals;
if (!ends_with(options.image_filename, ".csv"))
{
ASSERT( !options.image_filename.empty() );
typedef DGtal::Z3i::Domain Domain;
typedef DGtal::ImageSelector<Domain, unsigned char>::Type ImageUChar;
trace.info() << "image_filename=" << options.image_filename << endl;
ImageUChar image_uchar = DGtal::GenericReader<ImageUChar>::import(options.image_filename);
const Domain domain = image_uchar.domain();
trace.info() << "domain=" << domain << endl;
const Point center = (domain.upperBound()+domain.lowerBound())/2;
trace.info() << "center=" << center << endl;
const ImageShape<ImageUChar> shape(&image_uchar, center);
const_cast<KSpace&>(kspace).init(domain.lowerBound()-center-Point::diagonal(1), domain.upperBound()-center+Point::diagonal(1), true);
std::tie(const_cast<Calculus&>(calculus), const_cast<FlatVector&>(original_face_normals)) =
initCalculusAndNormalsWithNoise(kspace, shape, options.normal_radius, options.noise_level);
}
if (ends_with(options.image_filename, ".csv"))
{
ASSERT( !options.image_filename.empty() );
trace.info() << "csv_filename=" << options.image_filename << endl;
std::tie(const_cast<Calculus&>(calculus), const_cast<FlatVector&>(original_face_normals)) =
initCalculusAndNormalsFromSurfelNormalsCSV(options.image_filename);
}
const FlatVector original_vertex_normals = vertexNormals(calculus, original_face_normals);
const FlatVector original_positions;
const FlatVector regularized_positions;
const FlatVector original_centers;
const FlatVector regularized_centers;
std::tie(const_cast<FlatVector&>(original_positions),
const_cast<FlatVector&>(regularized_positions),
const_cast<FlatVector&>(original_centers),
const_cast<FlatVector&>(regularized_centers)) =
approximateSurface(calculus, original_face_normals,
ApproxParams({options.regularization_position, options.regularization_center, options.align, options.fairness, options.barycenter}));
ASSERT( original_positions.size() == 3*calculus.kFormLength(0, PRIMAL) );
ASSERT( regularized_positions.size() == 3*calculus.kFormLength(0, PRIMAL) );
ASSERT( original_centers.size() == 3*calculus.kFormLength(2, PRIMAL) );
ASSERT( regularized_centers.size() == 3*calculus.kFormLength(2, PRIMAL) );
{
trace.beginBlock( "computing energies" );
{
double position_energy = 0;
double align_energy = 0;
std::tie( position_energy, align_energy ) = approximateSurfaceEnergies(
calculus, original_face_normals, original_positions );
align_energy *= options.align;
position_energy *= options.regularization_position;
trace.info() << "original_energies=" << position_energy << " "
<< align_energy << " " << position_energy + align_energy
<< endl;
}
{
double position_energy = 0;
double align_energy = 0;
std::tie(position_energy, align_energy) = approximateSurfaceEnergies(calculus, original_face_normals, regularized_positions);
align_energy *= options.align;
position_energy *= options.regularization_position;
trace.info() << "regularized_energies=" << position_energy << " " << align_energy << " " << position_energy+align_energy << endl;
}
trace.endBlock();
}
{
ASSERT( !options.regularized_obj_filename.empty() );
trace.info() << "regularized_obj_filename=" << options.regularized_obj_filename << endl;
exportOBJ(calculus, regularized_positions, options.regularized_obj_filename);
}
if (!options.cubical_obj_filename.empty())
{
ASSERT( !options.cubical_obj_filename.empty() );
trace.info() << "cubical_obj_filename=" << options.cubical_obj_filename << endl;
exportOBJ(calculus, original_positions, options.cubical_obj_filename);
}
return 0;
}