feat(phase3d+3e): port EuclideanCyclicFunctional + add SphericalFunctional gauge-fix
Phase 3d — EuclideanCyclicFunctional:
• euclidean_geometry.hpp: t-value / atan2 corner-angle formula with
centering trick (μ = (Λ̃₁₂+Λ̃₂₃+Λ̃₃₁)/6) for numerical stability
• euclidean_functional.hpp: EuclideanMaps bundle, gradient (G_v = Θ_v − Σα_v,
G_e = α_opp⁺ + α_opp⁻ − φ_e), 10-point GL path-integral energy,
gradient_check_euclidean — identical halfedge convention to SphericalFunctional
• test_euclidean_functional.cpp: 11 tests (1 skip) covering angle formula,
right-isosceles triangle, angle sum = π, degenerate detection, gradient
checks on triangle/quad-strip/tetrahedron/fan-5/mixed-pinned, NaN check
Phase 3e — Spherical gauge-fix:
• spherical_gauge_shift(): Newton + backtracking line search to find t*
where ΣG_v(x + t·1) = 0 (maximises E along the global scale direction);
bisection used when sign change is detectable, Newton+backtrack otherwise
• apply_spherical_gauge(): in-place wrapper
• 3 new tests: GaugeFix_SpherTetVertexZerosSumGv, GaugeFix_ApplyInPlace,
GaugeFix_AlreadyAtGaugeReturnsTNearZero
Total: 45 cgal tests pass, 3 skipped (@Ignore Hessian stubs, one per functional)
Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
This commit is contained in:
Tarik Moussa
325
code/include/euclidean_functional.hpp
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325
code/include/euclidean_functional.hpp
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#pragma once
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// euclidean_functional.hpp
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//
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// Energy and gradient of the Euclidean discrete conformal functional
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// (EuclideanCyclicFunctional) evaluated on a ConformalMesh.
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//
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// Ported from de.varylab.discreteconformal.functional.EuclideanCyclicFunctional.
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//
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// ┌──────────────────────────────────────────────────────────────────────────┐
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// │ DOFs │
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// │ x[v_idx[v]] = u_v – conformal factor at vertex v │
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// │ x[e_idx[e]] = λ_e – edge log-length variable (optional) │
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// │ -1 means "pinned" (u_v = 0 / λ_e = 0, only λ° contributes) │
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// │ │
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// │ Effective log-length (always additive, unlike SphericalFunctional): │
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// │ Λ̃_ij = λ°_ij + u_i + u_j + (x[e_idx[e]] if variable, else 0) │
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// │ │
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// │ Side length: l_ij = exp(Λ̃_ij / 2) │
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// │ │
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// │ Gradient: │
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// │ ∂E/∂u_v = Θ_v − Σ_{faces adj. v} α_v(face) │
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// │ ∂E/∂λ_e = α_opp(face⁺) + α_opp(face⁻) − φ_e │
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// │ │
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// │ Energy: │
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// │ Computed as the path integral E(x) = ∫₀¹ ⟨G(tx), x⟩ dt │
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// │ using 10-point Gauss-Legendre quadrature (same as SphericalFunctional)│
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// │ This is E(0)=0 by construction and exact for conservative G. │
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// └──────────────────────────────────────────────────────────────────────────┘
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//
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// Halfedge convention (identical to SphericalFunctional):
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// h0 = mesh.halfedge(f), h1 = next(h0), h2 = next(h1)
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// v1 = source(h0), v2 = source(h1), v3 = source(h2)
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// h_alpha[h0] = α3 (angle at v3, opposite edge h0 = v1v2)
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// h_alpha[h1] = α1 (angle at v1, opposite edge h1 = v2v3)
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// h_alpha[h2] = α2 (angle at v2, opposite edge h2 = v3v1)
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//
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// Property-map name prefix: "ev:" (vertex) and "ee:" (edge).
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#include "conformal_mesh.hpp"
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#include "euclidean_geometry.hpp"
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#include <CGAL/boost/graph/iterator.h>
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#include <vector>
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#include <cmath>
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#include <cstdint>
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namespace conformallab {
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// ── Property-map type aliases ─────────────────────────────────────────────────
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using EuclVMapD = ConformalMesh::Property_map<Vertex_index, double>;
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using EuclVMapI = ConformalMesh::Property_map<Vertex_index, int>;
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using EuclEMapD = ConformalMesh::Property_map<Edge_index, double>;
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using EuclEMapI = ConformalMesh::Property_map<Edge_index, int>;
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// ── Persistent map bundle ─────────────────────────────────────────────────────
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struct EuclideanMaps {
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EuclVMapI v_idx; ///< DOF index per vertex (-1 = pinned / u_v = 0)
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EuclEMapI e_idx; ///< DOF index per edge (-1 = no edge DOF)
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EuclVMapD theta_v; ///< target cone angle Θ_v (default 2π)
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EuclEMapD phi_e; ///< target edge turn angle φ_e (default π)
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EuclEMapD lambda0; ///< base log-length λ°_e (default 0.0)
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};
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// Create and attach property maps with sensible defaults.
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// theta_v = 2π (flat vertex), phi_e = π (interior edge, flat surface).
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inline EuclideanMaps setup_euclidean_maps(ConformalMesh& mesh)
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{
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constexpr double TWO_PI = 2.0 * 3.14159265358979323846;
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constexpr double PI = 3.14159265358979323846;
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EuclideanMaps m;
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m.v_idx = mesh.add_property_map<Vertex_index, int> ("ev:idx", -1 ).first;
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m.e_idx = mesh.add_property_map<Edge_index, int> ("ee:idx", -1 ).first;
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m.theta_v= mesh.add_property_map<Vertex_index, double>("ev:theta", TWO_PI ).first;
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m.phi_e = mesh.add_property_map<Edge_index, double>("ee:phi", PI ).first;
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m.lambda0= mesh.add_property_map<Edge_index, double>("ee:lam0", 0.0 ).first;
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return m;
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}
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// Assign DOF indices 0..n-1 for all vertices only (no edge DOFs).
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inline int assign_euclidean_vertex_dof_indices(ConformalMesh& mesh, EuclideanMaps& m)
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{
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int idx = 0;
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for (auto v : mesh.vertices()) m.v_idx[v] = idx++;
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return idx;
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}
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// Assign DOF indices for all vertices AND all edges.
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inline int assign_euclidean_all_dof_indices(ConformalMesh& mesh, EuclideanMaps& m)
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{
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int idx = 0;
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for (auto v : mesh.vertices()) m.v_idx[v] = idx++;
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for (auto e : mesh.edges()) m.e_idx[e] = idx++;
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return idx;
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}
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// Count variable DOFs (vertices + edges).
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inline int euclidean_dimension(const ConformalMesh& mesh, const EuclideanMaps& m)
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{
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int dim = 0;
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for (auto v : mesh.vertices()) if (m.v_idx[v] >= 0) ++dim;
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for (auto e : mesh.edges()) if (m.e_idx[e] >= 0) ++dim;
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return dim;
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}
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// Set lambda0 from mesh vertex positions (Euclidean):
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// λ°_e = 2·log(|p_i − p_j|) (natural log of Euclidean edge length squared)
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//
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// This gives exp(Λ̃_ij / 2) = l_ij at x=0.
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inline void compute_euclidean_lambda0_from_mesh(ConformalMesh& mesh, EuclideanMaps& m)
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{
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for (auto e : mesh.edges()) {
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auto h = mesh.halfedge(e);
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auto p1 = mesh.point(mesh.source(h));
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auto p2 = mesh.point(mesh.target(h));
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double dx = p1.x() - p2.x();
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double dy = p1.y() - p2.y();
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double dz = p1.z() - p2.z();
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double len = std::sqrt(dx*dx + dy*dy + dz*dz);
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if (len > 1e-15)
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m.lambda0[e] = 2.0 * std::log(len);
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else
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m.lambda0[e] = -30.0; // degenerate edge
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}
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}
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// ── Internal helpers ──────────────────────────────────────────────────────────
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static inline double eucl_dof_val(int idx, const std::vector<double>& x)
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{
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return idx >= 0 ? x[static_cast<std::size_t>(idx)] : 0.0;
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}
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static inline std::size_t eucl_hidx(Halfedge_index h)
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{
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return static_cast<std::size_t>(static_cast<std::uint32_t>(h));
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}
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// ── Gradient ──────────────────────────────────────────────────────────────────
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//
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// G_v = Θ_v − Σ_{faces adj. v} α_v(face)
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// G_e = α_opp(face⁺) + α_opp(face⁻) − φ_e
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//
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// Corner-angle storage (h_alpha):
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// h_alpha[h] = corner angle OPPOSITE to the edge of halfedge h in its face.
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// h_alpha[h0] = α3, h_alpha[h1] = α1, h_alpha[h2] = α2
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// (same convention as SphericalFunctional)
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inline std::vector<double> euclidean_gradient(
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ConformalMesh& mesh,
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const std::vector<double>& x,
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const EuclideanMaps& m)
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{
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const int n = euclidean_dimension(mesh, m);
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std::vector<double> G(static_cast<std::size_t>(n), 0.0);
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// Per-halfedge corner-angle storage.
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const std::size_t nh = mesh.number_of_halfedges();
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std::vector<double> h_alpha(nh, 0.0);
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// ── Pass 1: compute corner angles per face ────────────────────────────────
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for (auto f : mesh.faces()) {
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Halfedge_index h0 = mesh.halfedge(f);
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Halfedge_index h1 = mesh.next(h0);
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Halfedge_index h2 = mesh.next(h1);
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Vertex_index v1 = mesh.source(h0);
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Vertex_index v2 = mesh.source(h1);
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Vertex_index v3 = mesh.source(h2);
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Edge_index e12 = mesh.edge(h0);
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Edge_index e23 = mesh.edge(h1);
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Edge_index e31 = mesh.edge(h2);
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// Effective log-lengths (always additive: u_i + u_j regardless of DOF status)
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double u1 = eucl_dof_val(m.v_idx[v1], x);
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double u2 = eucl_dof_val(m.v_idx[v2], x);
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double u3 = eucl_dof_val(m.v_idx[v3], x);
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double lam12 = m.lambda0[e12] + u1 + u2 + eucl_dof_val(m.e_idx[e12], x);
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double lam23 = m.lambda0[e23] + u2 + u3 + eucl_dof_val(m.e_idx[e23], x);
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double lam31 = m.lambda0[e31] + u3 + u1 + eucl_dof_val(m.e_idx[e31], x);
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auto fa = euclidean_angles(lam12, lam23, lam31);
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if (!fa.valid) continue; // degenerate triangle: contributes 0
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// h_alpha[h] = corner angle OPPOSITE to h's edge:
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// h0 (edge v1v2) → opposite corner at v3 → α3
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// h1 (edge v2v3) → opposite corner at v1 → α1
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// h2 (edge v3v1) → opposite corner at v2 → α2
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h_alpha[eucl_hidx(h0)] = fa.alpha3;
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h_alpha[eucl_hidx(h1)] = fa.alpha1;
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h_alpha[eucl_hidx(h2)] = fa.alpha2;
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}
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// ── Pass 2: accumulate vertex gradient ───────────────────────────────────
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// G_v = Θ_v − Σ h_alpha[prev(h)] for each incoming non-border h to v.
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for (auto v : mesh.vertices()) {
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int iv = m.v_idx[v];
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if (iv < 0) continue;
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double sum_alpha = 0.0;
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for (auto h : CGAL::halfedges_around_target(v, mesh)) {
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if (mesh.is_border(h)) continue;
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sum_alpha += h_alpha[eucl_hidx(mesh.prev(h))];
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}
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G[static_cast<std::size_t>(iv)] = m.theta_v[v] - sum_alpha;
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}
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// ── Pass 3: accumulate edge gradient ─────────────────────────────────────
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// G_e = α_opp(f⁺) + α_opp(f⁻) − φ_e
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// α_opp of edge e in face f = h_alpha[halfedge h of e pointing INTO f].
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for (auto e : mesh.edges()) {
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int ie = m.e_idx[e];
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if (ie < 0) continue;
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auto h = mesh.halfedge(e);
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auto ho = mesh.opposite(h);
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double sum = -m.phi_e[e];
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if (!mesh.is_border(h)) sum += h_alpha[eucl_hidx(h)];
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if (!mesh.is_border(ho)) sum += h_alpha[eucl_hidx(ho)];
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G[static_cast<std::size_t>(ie)] = sum;
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}
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return G;
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}
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// ── Energy via Gauss-Legendre path integral ───────────────────────────────────
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//
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// E(x) = ∫₀¹ ⟨G(tx), x⟩ dt (10-point GL quadrature, same as SphericalFunctional)
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inline double euclidean_energy(
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ConformalMesh& mesh,
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const std::vector<double>& x,
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const EuclideanMaps& m)
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{
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static const double gl_s[10] = {
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-0.9739065285171717, -0.8650633666889845,
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-0.6794095682990244, -0.4333953941292472,
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-0.1488743389816312, 0.1488743389816312,
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0.4333953941292472, 0.6794095682990244,
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0.8650633666889845, 0.9739065285171717
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};
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static const double gl_w[10] = {
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0.0666713443086881, 0.1494513491505806,
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0.2190863625159820, 0.2692667193099963,
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0.2955242247147529, 0.2955242247147529,
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0.2692667193099963, 0.2190863625159820,
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0.1494513491505806, 0.0666713443086881
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};
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const std::size_t n = x.size();
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double E = 0.0;
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for (int k = 0; k < 10; ++k) {
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double t = (1.0 + gl_s[k]) * 0.5;
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double wt = gl_w[k] * 0.5;
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std::vector<double> tx(n);
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for (std::size_t i = 0; i < n; ++i) tx[i] = t * x[i];
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auto G = euclidean_gradient(mesh, tx, m);
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double dot = 0.0;
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for (std::size_t i = 0; i < n; ++i) dot += G[i] * x[i];
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E += wt * dot;
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}
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return E;
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}
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// ── Full evaluation (energy + gradient) ──────────────────────────────────────
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struct EuclideanResult {
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double energy = 0.0;
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std::vector<double> gradient;
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};
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inline EuclideanResult evaluate_euclidean(
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ConformalMesh& mesh,
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const std::vector<double>& x,
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const EuclideanMaps& m,
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bool need_energy = true,
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bool need_gradient = true)
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{
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EuclideanResult res;
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if (need_gradient)
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res.gradient = euclidean_gradient(mesh, x, m);
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if (need_energy)
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res.energy = euclidean_energy(mesh, x, m);
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return res;
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}
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// ── Finite-difference gradient check ─────────────────────────────────────────
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//
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// Tests |G[i] − (E(x+εeᵢ) − E(x−εeᵢ))/(2ε)| / max(1,|G[i]|) < tol
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// for all variable DOFs.
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inline bool gradient_check_euclidean(
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ConformalMesh& mesh,
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const std::vector<double>& x0,
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const EuclideanMaps& m,
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double eps = 1e-5,
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double tol = 1e-4)
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{
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auto G = euclidean_gradient(mesh, x0, m);
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const int n = static_cast<int>(G.size());
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std::vector<double> xp = x0, xm = x0;
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bool ok = true;
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for (int i = 0; i < n; ++i) {
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std::size_t si = static_cast<std::size_t>(i);
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xp[si] = x0[si] + eps;
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xm[si] = x0[si] - eps;
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double Ep = euclidean_energy(mesh, xp, m);
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double Em = euclidean_energy(mesh, xm, m);
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xp[si] = xm[si] = x0[si]; // restore
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double fd = (Ep - Em) / (2.0 * eps);
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double err = std::abs(G[si] - fd);
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double scale = std::max(1.0, std::abs(G[si]));
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if (err / scale > tol) ok = false;
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}
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return ok;
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}
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} // namespace conformallab
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91
code/include/euclidean_geometry.hpp
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91
code/include/euclidean_geometry.hpp
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@@ -0,0 +1,91 @@
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#pragma once
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// euclidean_geometry.hpp
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//
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// Corner-angle formula for Euclidean triangles in the discrete conformal
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// (log-length) parametrisation.
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//
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// Ported from de.varylab.discreteconformal.functional.EuclideanCyclicFunctional.
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//
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// In the discrete conformal parametrisation a Euclidean triangle is described by
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// its three effective log-lengths Λ̃_ij = λ°_ij + u_i + u_j (+ edge DOF).
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// The corresponding side lengths are l_ij = exp(Λ̃_ij / 2).
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//
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// Vertex ordering convention (matches EuclideanCyclicFunctional.java):
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// v1 is opposite edge l23, v2 is opposite l31, v3 is opposite l12.
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//
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// t-value trick (Springborn 2008 §3):
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// t12 = −l12 + l23 + l31 = 2(s − l12)
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// t23 = +l12 − l23 + l31 = 2(s − l23)
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// t31 = +l12 + l23 − l31 = 2(s − l31)
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// denom = sqrt(t12 · t23 · t31 · l123) = 4 · Area
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//
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// α_v = 2 · atan2( product of t-values adjacent to v, denom )
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//
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// The centering trick (l_ij ← exp((Λ̃_ij − 2·μ)/2), μ = (Λ̃12+Λ̃23+Λ̃31)/6)
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// rescales all three sides by the same factor, leaving angles unchanged but
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// keeping the arguments of exp in a safe numerical range.
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#include <cmath>
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namespace conformallab {
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struct EuclideanFaceAngles {
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double alpha1; ///< corner angle at v1 (opposite l23)
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double alpha2; ///< corner angle at v2 (opposite l31)
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double alpha3; ///< corner angle at v3 (opposite l12)
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bool valid;
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};
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// ── From side lengths ─────────────────────────────────────────────────────────
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//
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// Given three Euclidean side lengths l12, l23, l31 > 0 satisfying the triangle
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// inequality, compute the corner angles.
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//
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// Returns valid=false if the triangle inequality is violated (any t-value ≤ 0).
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inline EuclideanFaceAngles euclidean_angles_from_lengths(
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double l12, double l23, double l31)
|
||||
{
|
||||
const double t12 = -l12 + l23 + l31; // 2*(s − l12)
|
||||
const double t23 = +l12 - l23 + l31; // 2*(s − l23)
|
||||
const double t31 = +l12 + l23 - l31; // 2*(s − l31)
|
||||
|
||||
if (t12 <= 0.0 || t23 <= 0.0 || t31 <= 0.0)
|
||||
return {0.0, 0.0, 0.0, false};
|
||||
|
||||
const double l123 = l12 + l23 + l31;
|
||||
const double denom2 = t12 * t23 * t31 * l123; // = (4·Area)²
|
||||
if (denom2 <= 0.0)
|
||||
return {0.0, 0.0, 0.0, false};
|
||||
|
||||
const double denom = std::sqrt(denom2);
|
||||
|
||||
// α at v1 (opposite l23): adjacent t-values are t12 and t31
|
||||
// α at v2 (opposite l31): adjacent t-values are t12 and t23
|
||||
// α at v3 (opposite l12): adjacent t-values are t23 and t31
|
||||
return {
|
||||
2.0 * std::atan2(t12 * t31, denom),
|
||||
2.0 * std::atan2(t12 * t23, denom),
|
||||
2.0 * std::atan2(t23 * t31, denom),
|
||||
true
|
||||
};
|
||||
}
|
||||
|
||||
// ── From effective log-lengths Λ̃ ─────────────────────────────────────────────
|
||||
//
|
||||
// Converts to side lengths l_ij = exp(Λ̃_ij / 2), applying the centering
|
||||
// trick for numerical safety, then delegates to euclidean_angles_from_lengths.
|
||||
//
|
||||
// The centering constant μ = (Λ̃12 + Λ̃23 + Λ̃31) / 6 ensures
|
||||
// l12 · l23 · l31 = 1 (geometric mean = 1)
|
||||
// which keeps all l values near 1 and prevents float overflow for large |Λ̃|.
|
||||
inline EuclideanFaceAngles euclidean_angles(
|
||||
double lam12, double lam23, double lam31)
|
||||
{
|
||||
const double mu = (lam12 + lam23 + lam31) / 6.0;
|
||||
const double l12 = std::exp((lam12 - 2.0 * mu) * 0.5);
|
||||
const double l23 = std::exp((lam23 - 2.0 * mu) * 0.5);
|
||||
const double l31 = std::exp((lam31 - 2.0 * mu) * 0.5);
|
||||
return euclidean_angles_from_lengths(l12, l23, l31);
|
||||
}
|
||||
|
||||
} // namespace conformallab
|
||||
@@ -354,4 +354,122 @@ inline bool gradient_check_spherical(
|
||||
return ok;
|
||||
}
|
||||
|
||||
// ── Gauge-fix for closed spherical surfaces ───────────────────────────────────
|
||||
//
|
||||
// On a closed (boundaryless) spherical surface the energy E(u + t·1) has a
|
||||
// unique maximum w.r.t. t ∈ ℝ (the "global scale" gauge mode). Without
|
||||
// fixing this gauge the functional is unbounded below and no solver converges.
|
||||
//
|
||||
// This function returns the scalar shift t* such that
|
||||
// Σ_v G_v(x + t*·1_v) = 0
|
||||
// i.e., the derivative of E(u+t·1) w.r.t. t is zero at t = t*.
|
||||
//
|
||||
// Apply the shift by adding t* to every vertex DOF in x.
|
||||
//
|
||||
// Implementation: bisection on f(t) = Σ_v G_v(x + t·1_v).
|
||||
// f is strictly monotone decreasing (second derivative < 0) for a convex
|
||||
// functional, so bisection converges in O(log₂(2·bracket/tol)) iterations.
|
||||
//
|
||||
// Parameters:
|
||||
// bracket – initial search interval [−bracket, +bracket] (default 50)
|
||||
// tol – absolute tolerance on t* (default 1e-8)
|
||||
//
|
||||
// Returns 0.0 if the zero cannot be bracketed (already at gauge maximum,
|
||||
// or open surface — no shift needed).
|
||||
inline double spherical_gauge_shift(
|
||||
ConformalMesh& mesh,
|
||||
const std::vector<double>& x,
|
||||
const SphericalMaps& m,
|
||||
double bracket = 50.0,
|
||||
double tol = 1e-8)
|
||||
{
|
||||
// Helper: sum of all vertex gradient components at x + t·1_v.
|
||||
auto sum_Gv = [&](double t) -> double {
|
||||
// Build a shifted copy of x (only vertex DOFs shifted).
|
||||
std::vector<double> xt = x;
|
||||
for (auto v : mesh.vertices()) {
|
||||
int iv = m.v_idx[v];
|
||||
if (iv >= 0)
|
||||
xt[static_cast<std::size_t>(iv)] += t;
|
||||
}
|
||||
auto G = spherical_gradient(mesh, xt, m);
|
||||
double sum = 0.0;
|
||||
for (auto v : mesh.vertices()) {
|
||||
int iv = m.v_idx[v];
|
||||
if (iv >= 0)
|
||||
sum += G[static_cast<std::size_t>(iv)];
|
||||
}
|
||||
return sum;
|
||||
};
|
||||
|
||||
// ── Try bisection first (works when there is a sign change in [−bracket, +bracket]) ──
|
||||
double a = -bracket, b = bracket;
|
||||
double fa = sum_Gv(a), fb = sum_Gv(b);
|
||||
|
||||
if (fa * fb <= 0.0) {
|
||||
for (int iter = 0; iter < 120; ++iter) {
|
||||
double c = 0.5 * (a + b);
|
||||
double fc = sum_Gv(c);
|
||||
if (std::abs(fc) < tol || (b - a) < tol) return c;
|
||||
if (fa * fc < 0.0) { b = c; fb = fc; }
|
||||
else { a = c; fa = fc; }
|
||||
}
|
||||
return 0.5 * (a + b);
|
||||
}
|
||||
|
||||
// ── No sign change (zero may lie at a domain boundary). ───────────────────
|
||||
// Use damped Newton's method with backtracking line search.
|
||||
// f'(t) estimated by forward finite difference.
|
||||
// When the Newton step overshoots the valid domain (ΣG_v jumps back up
|
||||
// because faces become degenerate), backtracking halves the step until
|
||||
// |f| strictly decreases.
|
||||
const double fd_eps = 1e-5;
|
||||
double t = 0.0;
|
||||
double ft = sum_Gv(t);
|
||||
|
||||
for (int iter = 0; iter < 120; ++iter) {
|
||||
if (std::abs(ft) < tol) return t;
|
||||
|
||||
double ftp = sum_Gv(t + fd_eps);
|
||||
double dft = (ftp - ft) / fd_eps;
|
||||
if (std::abs(dft) < 1e-14) return t; // gradient flat — give up
|
||||
|
||||
double dt_raw = -ft / dft;
|
||||
|
||||
// Backtracking line search: halve dt until |f| decreases.
|
||||
double alpha = 1.0;
|
||||
bool improved = false;
|
||||
for (int back = 0; back < 40; ++back) {
|
||||
double t_try = t + alpha * dt_raw;
|
||||
t_try = std::max(-bracket, std::min(bracket, t_try));
|
||||
double ft_try = sum_Gv(t_try);
|
||||
if (std::abs(ft_try) < std::abs(ft)) {
|
||||
t = t_try;
|
||||
ft = ft_try;
|
||||
improved = true;
|
||||
break;
|
||||
}
|
||||
alpha *= 0.5;
|
||||
}
|
||||
if (!improved) return t; // cannot reduce further
|
||||
}
|
||||
return t;
|
||||
}
|
||||
|
||||
// Apply the gauge shift in-place: x_v ← x_v + t* for all variable vertices.
|
||||
inline void apply_spherical_gauge(
|
||||
ConformalMesh& mesh,
|
||||
std::vector<double>& x,
|
||||
const SphericalMaps& m,
|
||||
double bracket = 50.0,
|
||||
double tol = 1e-8)
|
||||
{
|
||||
double t = spherical_gauge_shift(mesh, x, m, bracket, tol);
|
||||
for (auto v : mesh.vertices()) {
|
||||
int iv = m.v_idx[v];
|
||||
if (iv >= 0)
|
||||
x[static_cast<std::size_t>(iv)] += t;
|
||||
}
|
||||
}
|
||||
|
||||
} // namespace conformallab
|
||||
|
||||
Reference in New Issue
Block a user