File size: 2,649 Bytes
5b89cb9 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 | #include <test_common.h>
#include <igl/cat.h>
#include <igl/triangle/scaf.h>
#include <igl/slice.h>
#include <igl/harmonic.h>
#include <igl/boundary_loop.h>
#include <igl/map_vertices_to_circle.h>
#include <igl/flip_avoiding_line_search.h>
// Assert that building the SCAF equation system via scaf_system() and
// solving it manually yields the same result as calling scaf_solve() directly.
TEST_CASE("scaf_system: Test scaf_system() vs scaf_solve()", "[igl]")
{
// Read cube mesh
Eigen::MatrixXd V;
Eigen::MatrixXi F;
igl::read_triangle_mesh(test_common::data_path("cube.obj"), V, F);
// Cut to disk
F = F.topRows(F.rows() - 1).eval();
// Compute Tutte's embedding
Eigen::MatrixXd uv_init;
{
Eigen::MatrixXd bnd_uv;
std::vector<int> boundary;
igl::boundary_loop(F, boundary);
Eigen::VectorXi bnd = Eigen::Map<Eigen::VectorXi>(boundary.data(), boundary.size());
igl::map_vertices_to_circle(V, bnd, bnd_uv);
igl::harmonic(F, bnd, bnd_uv ,1, uv_init);
uv_init.conservativeResize(V.rows(), 2);
}
// Init empty constraint vectors
Eigen::VectorXi b;
Eigen::MatrixXd bc;
// Run one scaf iteration as reference
igl::triangle::SCAFData s_ref;
{
igl::triangle::scaf_precompute(V, F, uv_init, s_ref, igl::MappingEnergyType::SYMMETRIC_DIRICHLET, b, bc, 0);
igl::triangle::scaf_solve(s_ref, 1);
}
// Obtain SCAF linear system perform iteration manually
igl::triangle::SCAFData s_test;
{
// Set up system
igl::triangle::scaf_precompute(V, F, uv_init, s_test, igl::MappingEnergyType::SYMMETRIC_DIRICHLET, b, bc, 0);
Eigen::SparseMatrix<double> L;
Eigen::VectorXd rhs;
igl::triangle::scaf_system(s_test, L, rhs);
// Solve
Eigen::SimplicialLDLT<Eigen::SparseMatrix<double>> solver;
auto x = solver.compute(L).solve(rhs);
// Write result to uv_target
Eigen::MatrixXd uv_target = s_test.w_uv;
const int n_v_var = s_test.w_uv.rows() - s_test.frame_ids.size();
for (int i = 0; i < n_v_var; ++i)
{
int row = i;
if (i >= s_test.v_num)
row += s_test.frame_ids.size();
uv_target(row, 0) = x[i];
uv_target(row, 1) = x[i + n_v_var];
}
// Line search
std::function<double(Eigen::MatrixXd&)> E =
[&s_test](Eigen::MatrixXd &uv) { return igl::triangle::scaf::compute_energy(s_test, uv, true); };
Eigen::MatrixXi w_T;
igl::cat(1, s_test.m_T, s_test.s_T, w_T);
igl::flip_avoiding_line_search(w_T, s_test.w_uv, uv_target, E, -1);
}
// Compare both results
REQUIRE(s_test.w_uv == s_ref.w_uv);
}
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