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Diffstat (limited to 'src/Coxeter_triangulation/example/manifold_tracing_custom_function.cpp')
-rw-r--r-- | src/Coxeter_triangulation/example/manifold_tracing_custom_function.cpp | 87 |
1 files changed, 87 insertions, 0 deletions
diff --git a/src/Coxeter_triangulation/example/manifold_tracing_custom_function.cpp b/src/Coxeter_triangulation/example/manifold_tracing_custom_function.cpp new file mode 100644 index 00000000..fe2051bb --- /dev/null +++ b/src/Coxeter_triangulation/example/manifold_tracing_custom_function.cpp @@ -0,0 +1,87 @@ +#include <iostream> + +#include <gudhi/Coxeter_triangulation.h> +#include <gudhi/Functions/Function_Sm_in_Rd.h> +#include <gudhi/Implicit_manifold_intersection_oracle.h> +#include <gudhi/Manifold_tracing.h> +#include <gudhi/Coxeter_triangulation/Cell_complex/Cell_complex.h> +#include <gudhi/Functions/Linear_transformation.h> + +#include <gudhi/IO/build_mesh_from_cell_complex.h> +#include <gudhi/IO/output_meshes_to_medit.h> + +using namespace Gudhi::coxeter_triangulation; + +/* A definition of a function that defines a 2d surface embedded in R^4, but that normally + * lives on a complex projective plane. + * In terms of harmonic coordinates [x:y:z] of points on the complex projective plane, + * the equation of the manifold is x^3*y + y^3*z + z^3*x = 0. + * The embedding consists of restricting the manifold to the affine subspace z = 1. + */ +struct Function_surface_on_CP2_in_R4 { + Eigen::VectorXd operator()(const Eigen::VectorXd& p) const { + // The real and imaginary parts of the variables x and y + double xr = p(0), xi = p(1), yr = p(2), yi = p(3); + Eigen::VectorXd result(cod_d()); + + // Squares and cubes of real and imaginary parts used in the computations + double xr2 = xr * xr, xi2 = xi * xi, yr2 = yr * yr, yi2 = yi * yi, xr3 = xr2 * xr, xi3 = xi2 * xi, yr3 = yr2 * yr, + yi3 = yi2 * yi; + + // The first coordinate of the output is Re(x^3*y + y^3 + x) + result(0) = xr3 * yr - 3 * xr * xi2 * yr - 3 * xr2 * xi * yi + xi3 * yi + yr3 - 3 * yr * yi2 + xr; + // The second coordinate of the output is Im(x^3*y + y^3 + x) + result(1) = 3 * xr2 * xi * yr + xr3 * yi - 3 * xr * xi2 * yi - xi3 * yr + 3 * yr2 * yi - yi3 + xi; + return result; + } + + std::size_t amb_d() const { return 4; }; + std::size_t cod_d() const { return 2; }; + + Eigen::VectorXd seed() const { + Eigen::VectorXd result = Eigen::VectorXd::Zero(4); + return result; + } + + Function_surface_on_CP2_in_R4() {} +}; + +int main(int argc, char** argv) { + // The function for the (non-compact) manifold + Function_surface_on_CP2_in_R4 fun; + + // Seed of the function + Eigen::VectorXd seed = fun.seed(); + + // Creating the function that defines the boundary of a compact region on the manifold + double radius = 3.0; + Function_Sm_in_Rd fun_sph(radius, 3, seed); + + // Defining the intersection oracle + auto oracle = make_oracle(fun, fun_sph); + + // Define a Coxeter triangulation scaled by a factor lambda. + // The triangulation is translated by a random vector to avoid violating the genericity hypothesis. + double lambda = 0.2; + Coxeter_triangulation<> cox_tr(oracle.amb_d()); + cox_tr.change_offset(Eigen::VectorXd::Random(oracle.amb_d())); + cox_tr.change_matrix(lambda * cox_tr.matrix()); + + // Manifold tracing algorithm + using MT = Manifold_tracing<Coxeter_triangulation<> >; + using Out_simplex_map = typename MT::Out_simplex_map; + std::vector<Eigen::VectorXd> seed_points(1, seed); + Out_simplex_map interior_simplex_map, boundary_simplex_map; + manifold_tracing_algorithm(seed_points, cox_tr, oracle, interior_simplex_map, boundary_simplex_map); + + // Constructing the cell complex + std::size_t intr_d = oracle.amb_d() - oracle.cod_d(); + Cell_complex<Out_simplex_map> cell_complex(intr_d); + cell_complex.construct_complex(interior_simplex_map, boundary_simplex_map); + + // Output the cell complex to a file readable by medit + output_meshes_to_medit(3, "manifold_on_CP2_with_boundary", + build_mesh_from_cell_complex(cell_complex, Configuration(true, true, true, 1, 5, 3), + Configuration(true, true, true, 2, 13, 14))); + return 0; +} |