Function map_boundary_to_sphere

scripts/map_to_sphere.py:35–66

(mesh, basename)

    return mesh;

def map_boundary_to_sphere(mesh, basename):
    bd_mesh = pymesh.form_mesh(mesh.vertices, mesh.faces);
    bd_mesh, info = pymesh.remove_isolated_vertices(bd_mesh);
    bd_vertices = np.copy(bd_mesh.vertices);

    assembler = pymesh.Assembler(bd_mesh);
    L = assembler.assemble("graph_laplacian");

    # First, Laplacian smoothing to improve triangle quality.
    for i in range(100):
        c = np.mean(bd_vertices, axis=0);
        bd_vertices = bd_vertices - c;
        r = np.amax(norm(bd_vertices, axis=1));
        bd_vertices /= r;

        bd_vertices += L * bd_vertices;

        if i%10 == 0:
            sphere_mesh = pymesh.form_mesh(bd_vertices, bd_mesh.faces);
            pymesh.save_mesh("{}_flow_{:03}.msh".format(basename, i), sphere_mesh);

    # Then, run mean curvature flow.
    sphere_mesh = pymesh.form_mesh(bd_vertices, bd_mesh.faces);
    sphere_mesh = mean_curvature_flow(sphere_mesh, 100, use_graph_laplacian=True);
    pymesh.save_mesh("{}_flow_final.msh".format(basename), sphere_mesh);
    bd_vertices = sphere_mesh.vertices;

    # Lastly, project vertices onto unit sphere.
    bd_vertex_indices = info["ori_vertex_index"];
    bd_vertex_positions = np.divide(bd_vertices, norm(bd_vertices,
        axis=1).reshape((-1,1)));
    return bd_vertex_indices, bd_vertex_positions;

def init_harmonic_system(L, bd_indices, constraints, is_variable):
    rhs = -L[:,bd_indices].dot(constraints);