TopoOffsetTriMesh.h

#pragma once
#include <wmtk/TriMesh.h>
#include <wmtk/TriOptimizerMesh.h>
#include <algorithm>
#include <array>
#include <atomic>
#include <cstdint>
#include <functional>
#include <map>
#include <mutex>
#include <set>
#include <wmtk/optimization/EnergySum.hpp>
#include <wmtk/optimization/solver.hpp>
#include <wmtk/threading/enumerable_thread_specific.hpp>
#include "OffsetPotential.hpp"
#include "Parameters.h"
#include "SimplicialComplexBVH.hpp"
#include "TagEnvelopes.hpp"
 
using CellTag = std::set<int64_t>;
 
namespace wmtk::components::topological_offset {
 
 
const int64_t TEMP_OFFSET_TRI_TAG = -1;
const CellTag TEMP_OFFSET_TRI_TAG_SET{TEMP_OFFSET_TRI_TAG};
 
class VertexExtra2d
{
public:
    int label = 0;
    bool m_is_on_input = false; // on the input complex
    bool m_is_on_offset = false; // on the offset boundary itself
    bool m_is_on_region = false; // on some OTHER tag region's boundary
    Vector2d m_turn_start = Vector2d::Zero();
    bool m_turn_start_valid = false;
 
    uint64_t m_boundary_mask = 0;
 
    uint32_t m_born_epoch = 0;
};
 
 
class EdgeExtra2d
{
public:
    int label = 0;
    bool on_curve = false;
};
 
 
class FaceExtra2d
{
public:
    int label = 0;
    bool rest_valid = false;
    std::array<Eigen::Vector2d, 3> rest_pos;
};
 
 
class TopoOffsetTriMesh : public wmtk::TriOptimizerMesh
{
public: // mode for splitting in marching tets
    enum class EdgeSplitMode {
        Midpoint = 0, // construction: simplicial embedding AND marching_tris
        Optimization = 2 // the optimization phase; the shared engine places the vertex
    };
 
public:
    int m_vtu_counter = 0;
    std::array<size_t, 3> m_init_counts = {{0, 0, 0}};
    size_t m_tags_count;
    int64_t m_curve_tag = -1;
    MatrixXd m_curve_V;
    MatrixXi m_curve_E;
    void classify_curve_edges();
    std::shared_ptr<SimplicialComplexBVH> m_input_complex_bvh;
 
    std::shared_ptr<OffsetPotential2D> m_offset_potential;
 
    int m_n_regions = 0; 
    std::vector<std::shared_ptr<OffsetPotential2D>> m_region_potentials; 
    std::vector<int64_t> m_phi_vert_region; 
    std::vector<int64_t> m_phi_seg_region; 
    std::vector<int64_t> m_phi_face_region; 
    std::vector<int64_t> m_phi_point_region; 
    std::vector<int> m_face_region; 
    std::vector<int> m_vertex_region; 
    void init_region_potentials(double delta, double effective_factor);
    void assign_band_regions();
    void log_front_profile(size_t vid);
    int vertex_region(const size_t vid) const
    {
        return vid < m_vertex_region.size() ? m_vertex_region[vid] : -1;
    }
    int edge_region(const size_t va, const size_t vb) const
    {
        const int a = vertex_region(va), b = vertex_region(vb);
        return (a >= 0 && a == b) ? a : -1;
    }
    const OffsetPotential2D& potential_for_region(const int region) const
    {
        return (region >= 0 && size_t(region) < m_region_potentials.size())
                   ? *m_region_potentials[size_t(region)]
                   : *m_offset_potential;
    }
    const OffsetPotential2D& potential_for(const size_t vid) const
    {
        return potential_for_region(vertex_region(vid));
    }
    std::shared_ptr<const OffsetPotential2D> potential_ptr_for(const size_t vid) const
    {
        const int r = vertex_region(vid);
        return (r >= 0 && size_t(r) < m_region_potentials.size()) ? m_region_potentials[size_t(r)]
                                                                  : m_offset_potential;
    }
    const OffsetPotential2D& potential_for_edge(const size_t va, const size_t vb) const
    {
        return potential_for_region(edge_region(va, vb));
    }
    const OffsetPotential2D& potential_for_face(const size_t fid) const
    {
        return potential_for_region(fid < m_face_region.size() ? m_face_region[fid] : -1);
    }
 
    std::map<int64_t, std::shared_ptr<SampleEnvelope>> m_tag_envelopes;
 
    struct TagPolyline2d
    {
        std::vector<Eigen::Vector2i> E; 
        std::vector<std::vector<int>> at_vertex; 
    };
    std::vector<Eigen::Vector2d> m_env_polyline_V;
    std::map<int64_t, TagPolyline2d> m_tag_polyline;
 
    std::map<int64_t, int> m_tag_bit;
 
    mutable std::map<uint64_t, std::shared_ptr<SampleEnvelope>> m_isect_cache;
    mutable std::mutex m_isect_mutex;
 
    mutable std::map<uint64_t, std::shared_ptr<SampleEnvelope>> m_offset_isect_cache;
 
    std::shared_ptr<SampleEnvelope> containment_for(uint64_t region_mask, bool on_offset) const;
 
    bool project_into_containment(size_t vid, Vector2d& x) const;
 
    int64_t tangent_curve_tag(size_t vid, const Vector2d& x) const;
 
    bool walk_along_curve(int64_t tag, const Vector2d& x, double s, Vector2d& out) const;
 
    bool curve_tangent(int64_t tag, const Vector2d& x, const Vector2d& prefer, Vector2d& tau) const;
 
    enum class OptPhase { A, B, Single };
 
    bool phase_places_front() const { return m_phase != OptPhase::A; }
 
    OptPhase m_phase = OptPhase::A;
 
    // Phase B is one sweep over every vertex per pass: a front vertex is placed by
    // smooth_offset_vertex_backtracking(), an interior one relaxed by the shared smoother, in
    // mesh order -- see smooth_before().
 
    bool m_freeze_front = false;
 
    enum class EnvelopeSetup { PerTag, WallComplex };
    EnvelopeSetup envelope_setup() const
    {
        return m_offset_params.deform_others ? EnvelopeSetup::WallComplex : EnvelopeSetup::PerTag;
    }
    static constexpr int64_t m_wall_tag = -2; 
    static constexpr int64_t m_complex_tag = -3; 
    std::string envelope_key_name(int64_t tag) const;
    bool edge_is_complex_boundary(const Tuple& e) const;
    void build_boundary_envelopes(const char* when, EnvelopeSetup setup);
 
    // No Phi test gates collapse and swap: the envelope is the constraint, and the offset
    // criterion belongs to Phase B's own placement. The coarsening bar is applied where 3D
    // applies it -- absolute, and only in m_coarsen_mode.
 
    std::shared_ptr<SampleEnvelope> m_offset_envelope;
 
    void rebuild_offset_envelope();
 
    void check_no_vertex_on_both_surfaces(const char* when) const;
 
    void optimize_offset_single_phase();
 
    double phase_b_front_gradient_linf();
    double m_front_gradient_reference = 0.;
 
    EdgeSplitMode m_edge_split_mode = EdgeSplitMode::Midpoint;
 
    // tag name maps
    std::map<std::string, int64_t> m_tag_name_to_id;
    std::map<int64_t, std::string> m_tag_id_to_name;
    CellTag m_offset_output_tag_ids;
 
    // if in 'singlebody' mode
    bool m_singlebody = false;
    int64_t m_single_tag;
 
    // just for retaining in output. dont actually use
    bool m_has_envelope = false;
    MatrixXd m_V_envelope;
    MatrixXi m_F_envelope;
 
    static constexpr int INPUT_SURFACE_CLASS = 0;
    static constexpr int OFFSET_SURFACE_CLASS = 1;
 
    Parameters& m_offset_params;
 
    using VertexExtraCol = wmtk::AttributeCollection<VertexExtra2d>;
    using EdgeExtraCol = wmtk::AttributeCollection<EdgeExtra2d>;
    using FaceExtraCol = wmtk::AttributeCollection<FaceExtra2d>;
    // m_vertex_attribute, m_edge_attribute and m_face_attribute are the base's; these three
    // are registered alongside them in its attribute groups.
    VertexExtraCol m_vertex_extra;
    EdgeExtraCol m_edge_extra;
    FaceExtraCol m_face_extra;
 
    TopoOffsetTriMesh(Parameters& _m_offset_params, int _num_threads = 0)
        : wmtk::TriOptimizerMesh(_m_offset_params)
        , m_offset_params(_m_offset_params)
    {
        NUM_THREADS = _num_threads;
        m_vertex_attr_group.add(&m_vertex_extra);
        m_edge_attr_group.add(&m_edge_extra);
        m_face_attr_group.add(&m_face_extra);
 
        // As in 3D. The per-vertex Newton solver logs a line per smoothing attempt at info level,
        // which is one line per vertex per pass and buries the run's own output.
        optimization::deactivate_opt_logger();
    }
 
    ~TopoOffsetTriMesh() override = default;
 
    void set_vertex_position(const size_t vid, const Vector2d& p)
    {
        m_vertex_attribute[vid].m_posf = p;
        m_vertex_attribute[vid].m_pos = to_rational(p);
        m_vertex_attribute[vid].m_is_rounded = true;
    }
 
    bool edge_is_offset(const size_t eid) const
    {
        return m_edge_attribute[eid].m_is_surface_fs &&
               m_edge_attribute[eid].m_surface_class == OFFSET_SURFACE_CLASS;
    }
    bool edge_is_region(const size_t eid) const
    {
        return m_edge_attribute[eid].m_is_surface_fs &&
               m_edge_attribute[eid].m_surface_class != OFFSET_SURFACE_CLASS;
    }
    struct EdgeSnapshot2d
    {
        EdgeAttributes tags;
        EdgeExtra2d extra;
    };
    struct FaceSnapshot2d
    {
        FaceAttributes attrs;
        FaceExtra2d extra;
    };
    EdgeSnapshot2d edge_snapshot(const size_t eid) const
    {
        return EdgeSnapshot2d{m_edge_attribute[eid], m_edge_extra[eid]};
    }
    void restore_edge(const size_t eid, const EdgeSnapshot2d& s)
    {
        m_edge_attribute[eid] = s.tags;
        m_edge_extra[eid] = s.extra;
    }
    FaceSnapshot2d face_snapshot(const size_t fid) const
    {
        return FaceSnapshot2d{m_face_attribute[fid], m_face_extra[fid]};
    }
    void restore_face(const size_t fid, const FaceSnapshot2d& s)
    {
        m_face_attribute[fid] = s.attrs;
        m_face_extra[fid] = s.extra;
    }
 
    void label_offset_boundary();
 
    bool face_in_region(const size_t fid) const;
 
    bool face_is_input_complex(const size_t fid) const;
 
    bool vertex_is_on_surface(const size_t vid) const override;
    bool edge_is_on_surface(const std::array<size_t, 2>& vids) const override;
 
    void optimize_offset(const std::filesystem::path& output_file);
 
    bool face_is_offset_band(const size_t fid) const;
 
 
    std::pair<double, double> compute_distance_deviation() const;
 
    mutable size_t m_worst_dist_vid = static_cast<size_t>(-1);
    void log_worst_dist_vertex() const;
 
    bool edge_is_offset_surface_live(const Tuple& e) const;
 
    void init_offset_sizing_field();
 
    std::vector<std::array<double, 8>> optimization_metrics;
    std::vector<std::array<int, 3>> churn_counts;
    std::vector<std::array<int, 3>> op_counts;
    int m_ab_round = 0;
    mutable size_t m_debug_seq = 0;
    mutable int m_debug_pass = 0;
    mutable int m_debug_last_round = -1;
    mutable char m_debug_last_phase = '?';
    double m_gradient_reference = 0.;
    bool m_converged = false;
    bool m_quality_converged = true;
    double m_quality_max_amips = 0.;
 
    std::atomic<int> iter_cnt_split_born{0};
    std::atomic<int> iter_cnt_recollapsed{0};
    std::atomic<int> iter_cnt_recollapsed_same_pass{0};
    std::atomic<int> iter_cnt_split = 0, iter_cnt_collapse = 0, iter_cnt_swap = 0;
    std::atomic<int> iter_cnt_collapse_offset_removed{0};
    std::atomic<int> iter_cnt_collapse_offset_reject{0};
    std::atomic<int> iter_cnt_swap_offset_reject{0};
    std::atomic<int> iter_cnt_split_offset_before{0};
    std::atomic<int> iter_cnt_split_offset{0};
    struct OptSplitCache2d
    {
        std::map<size_t, int> face_label;
        size_t v1_id = 0;
        size_t v2_id = 0;
        uint64_t edge_bits = 0;
        double parent_q_max = -1.;
        double parent_flatness = 1.;
    };
    wmtk::threading::enumerable_thread_specific<OptSplitCache2d> m_opt_split_cache;
 
    bool marching_split_edge_before(const Tuple& t);
    bool marching_split_edge_after(const Tuple& t);
 
    bool collapse_edge_before(const Tuple& t) override;
 
    bool swap_edge_before(const Tuple& t) override;
 
    bool swap_edge_after(const Tuple& t) override;
    bool collapse_before_vertex(size_t v1, size_t v2) override;
    void collapse_after_vertex(size_t v1, size_t v2) override;
    void split_after_vertex(size_t v_new) override;
 
    bool split_adjust_position(size_t v_new, const std::vector<Tuple>& children) override;
 
    bool smooth_before(const Tuple& t) override;
    bool smooth_after(const Tuple& t) override;
 
    bool vertex_is_on_domain_boundary(const size_t vid) const
    {
        return !m_vertex_attribute[vid].on_bbox_faces.empty();
    }
    bool edge_is_on_domain_boundary(const size_t eid) const
    {
        return m_edge_attribute[eid].m_is_bbox_fs >= 0;
    }
 
    void init_surfaces_and_boundaries();
 
    void mark_input_complex_vertices();
 
    void warn_if_offset_reaches_domain_boundary() const;
 
    struct SmoothTrace
    {
        std::atomic<int> attempted{0}; 
        std::atomic<int> before_bbox{0}; 
        std::atomic<int> before_unrounded{0}; 
        std::atomic<int> before_phase_b_not_offset{
            0}; 
        std::atomic<int> before_phase_b_enveloped_background{0}; 
        std::atomic<int> before_phase_b_enveloped_offset{0}; 
        std::atomic<int> offset_attempted{0}; 
        std::atomic<int> offset_accepted{0}; 
        std::atomic<int> interior_attempted{0}; 
        std::atomic<int> region_attempted{0}; 
        std::atomic<long long> res_before_nano{0};
        std::atomic<long long> res_after_nano{0};
        std::atomic<long long> res_max_before_nano{0};
        std::atomic<long long> res_max_after_nano{0};
 
        void reset()
        {
            for (std::atomic<int>* c :
                 {&attempted,
                  &before_bbox,
                  &before_unrounded,
                  &before_phase_b_not_offset,
                  &before_phase_b_enveloped_background,
                  &before_phase_b_enveloped_offset,
                  &offset_attempted,
                  &offset_accepted,
                  &interior_attempted,
                  &region_attempted}) {
                c->store(0);
            }
            for (std::atomic<long long>* c :
                 {&res_before_nano, &res_after_nano, &res_max_before_nano, &res_max_after_nano}) {
                c->store(0);
            }
        }
    };
    SmoothTrace m_smooth_trace;
 
    mutable wmtk::threading::enumerable_thread_specific<std::pair<double, Vector2d>> m_needle_pre;
    mutable std::atomic<size_t> m_needle_smooth_offered{0};
    mutable std::atomic<size_t> m_needle_smooth_reached{0};
    mutable std::atomic<size_t> m_needle_smooth_fixed{0};
    mutable std::atomic<size_t> m_needle_smooth_stationary{0};
    mutable std::atomic<size_t> m_needle_smooth_reports{0};
 
    double ring_max_quality(size_t vid) const;
 
    double face_flatness(size_t fid) const;
 
    void needle_forensics() const;
 
    void record_flatness(const char* op, double parent_flat, size_t child_fid) const;
    mutable std::atomic<size_t> m_flat_created_split{0};
    mutable std::atomic<size_t> m_flat_created_collapse{0};
    mutable std::atomic<size_t> m_flat_worsened_split{0};
    mutable std::atomic<size_t> m_flat_genesis_reports{0};
    static constexpr double kFlatThreshold = 1e-3;
    mutable wmtk::threading::enumerable_thread_specific<double> m_collapse_parent_flatness;
    mutable wmtk::threading::enumerable_thread_specific<double> m_collapse_survivor_sizing;
    void log_smooth_trace() const;
 
 
    void log_region_edge_mask_health(const std::string& when) const;
 
    void audit_surface_containment(const std::string& when) const;
 
    mutable std::atomic<int> m_placement_env_entry_outside{0};
 
    mutable std::atomic<int> m_placement_projected{0};
 
    mutable std::atomic<int> m_placement_tangential{0};
 
 
    bool vertex_is_on_region(const size_t vid) const
    {
        return m_vertex_extra[vid].m_is_on_region || !m_vertex_attribute[vid].on_bbox_faces.empty();
    }
 
    uint64_t tag_bits(const CellTag& tags) const
    {
        uint64_t bits = 0;
        for (const int64_t t : tags) {
            const auto it = m_tag_bit.find(t);
            if (it != m_tag_bit.end()) bits |= (uint64_t(1) << it->second);
        }
        return bits;
    }
 
    uint64_t vertex_boundary_mask(const size_t vid) const
    {
        return vertex_is_on_region(vid) ? m_vertex_extra[vid].m_boundary_mask : uint64_t(0);
    }
 
    uint64_t edge_mask(const std::array<size_t, 2>& vids) const
    {
        return vertex_boundary_mask(vids[0]) & vertex_boundary_mask(vids[1]);
    }
 
    uint64_t edge_boundary_bits(const Tuple& e) const
    {
        const std::optional<Tuple> opp = e.switch_face(*this);
        if (!opp) {
            return tag_bits(m_face_attribute[e.fid(*this)].tags); // domain wall
        }
        const auto& t0 = m_face_attribute[e.fid(*this)].tags;
        const auto& t1 = m_face_attribute[opp->fid(*this)].tags;
        CellTag diff;
        std::set_symmetric_difference(
            t0.begin(),
            t0.end(),
            t1.begin(),
            t1.end(),
            std::inserter(diff, diff.begin()));
        return tag_bits(diff);
    }
 
    std::shared_ptr<SampleEnvelope> envelope_for_mask(uint64_t mask) const;
 
    std::shared_ptr<SampleEnvelope> surface_envelope_for_edge(
        const std::array<size_t, 2>& vids) const override
    {
        // Boundary geometry first, in both phases: a segment on any tag-region boundary may not
        // drift out of that boundary's tube, and one on several boundaries -- a junction -- is
        // held in their intersection. The mask carries the input complex too, since every complex
        // simplex lies on tag boundaries, and E_t is built from the input mesh before construction
        // touches it, so the per-tag tubes hold the as-loaded geometry.
        //
        // Keyed on the vertices, not the edge: every caller is an operation asking about a segment
        // it is about to create or has just created, whose own edge attributes are not written
        // yet. The endpoints' masks are, maintained by the operations themselves (AND at a split,
        // OR at a collapse).
        uint64_t mask = edge_mask(vids);
        bool all_offset = true;
        for (const size_t v : vids) {
            all_offset = all_offset && m_vertex_extra[v].m_is_on_offset;
        }
 
        // The ambiguous case: both endpoints can be on region boundaries and on the offset front
        // at once -- a real state, and the point of tracking the two families separately. The
        // endpoint-mask AND is then necessary but not sufficient for the segment lying on a shared
        // boundary: two vertices on different junctions can share a tag bit by coincidence and be
        // joined by an offset chord nowhere near that tag's curve, which a container it was never
        // meant to satisfy then refuses to refine. Ask the edge's own class, the only record that
        // distinguishes a chord from a boundary.
        //
        // Reading the slot is safe here and would not be unconditionally: the base checks a
        // split's two child segments before writing their attributes, so their slots still hold a
        // recycled edge's class. A split child never reaches this branch -- its mask and its
        // offset flag are mutually exclusive by construction, so one of `mask` and `all_offset` is
        // always empty -- and the m_is_surface_fs guard leaves both constraints standing rather
        // than dropping one when a slot is illegible.
        if (mask != 0 && all_offset) {
            if (const auto found = try_tuple_from_edge(vids)) {
                const size_t eid = std::get<1>(*found);
                if (m_edge_attribute[eid].m_is_surface_fs) {
                    if (edge_is_offset(eid)) {
                        mask = 0; // an offset edge lies on no region boundary
                    } else {
                        all_offset = false; // a region edge is not the offset front
                    }
                }
            }
        }
        // Both families compose: whatever holds this segment holds it at once. Phase A holds the
        // offset where Phase B left it; Phase B is what moves it, so it contributes nothing there
        // -- and null before the offset exists at all, which is the pre-pass.
        const std::shared_ptr<SampleEnvelope> base = containment_for(mask, all_offset);
        if (base || m_deform_tags.empty()) return base;
        // deform_others' ops-only tube: a released boundary is held by no mask -- its vertices
        // were freed so smoothing can carry the object -- which would leave the operations free
        // to decimate and reposition it. A segment the masks and the offset class do not claim,
        // but which lies on a released boundary by its incident faces' current tags, is held to
        // the tube around the boundary's current shape. A fresh split child can misread its
        // recycled face slots for this one check, and is at worst skipped or over-held once.
        if (const auto found = try_tuple_from_edge(vids)) {
            if (edge_borders_released_boundary(std::get<0>(*found))) return released_envelope();
        }
        return nullptr;
    }
 
    bool smoothing_position_is_allowed(const size_t, const Vector2d&) const override
    {
        return true;
    }
 
    std::shared_ptr<SampleEnvelope> smoothing_energy_envelope(const size_t vid) const override
    {
        if (m_vertex_extra[vid].m_is_on_offset && !vertex_is_on_region(vid)) {
            return nullptr;
        }
        const uint64_t mask = vertex_boundary_mask(vid);
        if (mask == 0) {
            // Reachable only for a construction artefact (a wall-chord midpoint flagged
            // on-surface with disjoint endpoint masks); its containment is vacuous too, so no
            // pull is behavior-neutral. Not an error.
            return nullptr;
        }
        std::shared_ptr<SampleEnvelope> best;
        double worst_d2 = -1.;
        for (const auto& [tag, env] : m_tag_envelopes) {
            const auto it = m_tag_bit.find(tag);
            if (it == m_tag_bit.end() || !(mask & (uint64_t(1) << it->second))) continue;
            if (!best) {
                best = env;
                if ((mask & (mask - 1)) == 0) break; // single bit: no violation contest to run
                worst_d2 = env->squared_distance(m_vertex_attribute[vid].m_posf);
                continue;
            }
            const double d2 = env->squared_distance(m_vertex_attribute[vid].m_posf);
            if (d2 > worst_d2) {
                worst_d2 = d2;
                best = env;
            }
        }
        return best;
    }
 
    std::shared_ptr<SampleEnvelope> smoothing_containment_envelope(const size_t vid) const override
    {
        // Both families, composed -- not a choice between them. A vertex where the offset front
        // meets one or more region boundaries is on all of them at once, and the three cases fall
        // out of one expression: pure-offset (mask 0) gives the offset tube in Phase A and null in
        // Phase B, pure-region gives its tubes' intersection in both, and a junction of the two
        // gives the intersection of everything.
        return containment_for(vertex_boundary_mask(vid), m_vertex_extra[vid].m_is_on_offset);
    }
 
    bool smooth_front_vertex_phase_b(const Tuple& t);
    double front_vertex_normal_gradient(size_t vid) const;
    Vector2d front_vertex_move_direction(size_t vid) const;
    bool front_vertex_alignment_traps_1d_solve(size_t vid) const;
    double front_vertex_conv_ratio(size_t vid) const;
    double edge_conv_ratio(const Tuple& e) const;
    mutable size_t m_front_gradient_worst_vid =
        static_cast<size_t>(-1); 
    Vector2d front_vertex_normal(size_t vid) const;
    std::shared_ptr<polysolve::nonlinear::Problem> phase_b_front_objective(
        size_t vid,
        const Vector2d& x) const;
    std::shared_ptr<polysolve::nonlinear::Problem> smoothing_extra_energy(
        const size_t vid) const override
    {
        std::shared_ptr<polysolve::nonlinear::Problem> front;
        if (phase_places_front() && m_offset_potential && m_vertex_extra[vid].m_is_on_offset &&
            vertex_boundary_mask(vid) == 0) {
            front = phase_b_front_energy(vid, potential_ptr_for(vid));
        }
        const std::shared_ptr<polysolve::nonlinear::Problem> rest = rest_energy_for_vertex(vid);
        if (!front) return rest;
        if (!rest) return front;
        auto sum = std::make_shared<optimization::EnergySum>();
        sum->add_energy(front);
        sum->add_energy(rest);
        return sum;
    }
 
    // ------- deform_others: other input regions deform instead of being envelope-held -------
 
    std::set<int64_t> m_deform_tags;
    std::set<int64_t> m_source_tags;
    mutable std::shared_ptr<SampleEnvelope> m_released_envelope;
    mutable std::atomic<bool> m_released_tube_dirty{false};
    mutable std::mutex m_released_mutex;
    std::shared_ptr<SampleEnvelope> released_envelope() const;
    bool edge_borders_released_boundary(const Tuple& e) const;
    bool face_is_deformable(size_t fid) const;
    bool m_plastic_active = false; 
    bool face_is_plastic(size_t fid) const
    {
        // Everything outside the band: ambient, the other objects and the input complex's
        // interior alike -- one material. The complex's boundary is what its tube holds.
        return m_plastic_active && m_face_extra[fid].label != 2;
    }
    void stamp_plastic_rests();
    bool smooth_plastic_vertex(const Tuple& t);
    bool face_is_released_band(size_t fid) const;
    void stamp_rest_face(size_t fid);
    void release_deformable_regions();
    std::shared_ptr<polysolve::nonlinear::Problem> rest_energy_for_vertex(size_t vid) const;
    std::shared_ptr<polysolve::nonlinear::Problem> phase_b_front_energy(
        size_t vid,
        const std::shared_ptr<const OffsetPotential2D>& pot) const;
 
    std::tuple<double, double> optimization_quality_stats() override;
 
    double optimization_stop_metric() const override
    {
        // Single is TriWild's loop, so its stop metric is TriWild's.
        return m_phase != OptPhase::B ? wmtk::TriOptimizerMesh::optimization_stop_metric() : 1.;
    }
 
    int offset_residual_samples() const { return m_offset_params.offset_residual_samples; }
 
    double offset_residual_tolerance() const
    {
        // Derived from the tolerance, not from the knob. grad E . n = 2 (Phi - c) (grad Phi . n),
        // so with |grad Phi| = s at the level set a bound g on the normal gradient is the length
        // bound |Phi - c| <= g / (2 s^2). The tolerance is rel x a measured maximum, so this must
        // follow it rather than reading the knob.
        const double s = m_offset_potential ? m_offset_potential->level_set_slope() : 1.;
        return std::max(0.5 * offset_gradient_tolerance() / (s * s), 1e-16);
    }
 
    double offset_gradient_tolerance() const
    {
        // A fraction of a measured maximum, not of an analytic estimate. m_gradient_reference is
        // max |2 (Phi - c) grad Phi . n| over the offset-surface vertices as constructed, taken
        // once before the A/B loop starts; everything this bar serves -- the convergence criterion
        // and every Phase B local stop -- compares the full gradient norm at those same vertices
        // against it, so both sides come from one measurement pass and no per-field calibration.
        //
        // Never measured on the single-phase path, so this sits at the 1e-16 floor there; the
        // single-phase convergence bar uses m_front_gradient_reference instead.
        return std::max(m_offset_params.front_conv_rel * m_gradient_reference, 1e-16);
    }
 
    double gradient_reference() const { return m_gradient_reference; }
 
    void check_offset_within_support(const char* when) const;
 
    struct DistanceSplit
    {
        double max_reachable = 0., avg_reachable = 0.;
        double max_pinned = 0.;
        size_t n_reachable = 0, n_pinned = 0;
        double max_at_vertex = 0., max_in_edge = 0.;
        size_t n_outside_support = 0;
        size_t worst_outside_vid = static_cast<size_t>(-1);
        double worst_outside_dist = 0.;
    };
    DistanceSplit distance_deviation_split() const;
 
    DistanceSplit residual_split() const;
    std::vector<bool> band_vertex_mask() const;
 
    double max_band_vertex_distance() const;
    double band_vertex_distance_error(const size_t vid) const;
 
    double band_vertex_residual(const size_t vid) const;
 
    struct EdgeSamples
    {
        double max = 0.;
        double sum = 0.;
        size_t n = 0;
    };
 
    EdgeSamples offset_edge_samples(const Tuple& e) const;
 
    template <typename Visit>
    void for_each_offset_edge_sample(const Tuple& e, Visit&& visit) const
    {
        const int k = m_offset_params.offset_residual_samples;
        if (k <= 0) return;
        const Vector2d p0 = m_vertex_attribute[e.vid(*this)].m_posf;
        const Vector2d p1 = m_vertex_attribute[e.switch_vertex(*this).vid(*this)].m_posf;
        for (int i = 1; i <= k; ++i) {
            const double t = double(i) / double(k + 1);
            visit(Vector2d((1. - t) * p0 + t * p1));
        }
    }
 
    struct GradientSplit
    {
        double max_reachable = 0., avg_reachable = 0.;
        double max_pinned = 0.;
        size_t n_reachable = 0, n_pinned = 0;
        double max_at_vertex = 0., max_in_edge = 0.;
        double max_in_edge_pinned = 0.;
        double max_normal_aligned = 0.;
        size_t n_edge_samples = 0;
        size_t n_skipped_inverted = 0, n_skipped_unrounded = 0;
        size_t worst_vid = static_cast<size_t>(-1);
    };
    GradientSplit gradient_split(bool include_edge_samples = true) const;
 
    struct EnergyCriterion
    {
        double
            max_vertex = 0.,
            max_edge =
                0.; 
        double bar = 1.; 
        size_t n_vertices = 0, n_edges = 0, n_unmeasurable = 0;
        size_t n_pressed = 0, n_edges_pressed = 0; 
        size_t worst_vid = static_cast<size_t>(-1);
        Vector2d worst_edge_mid = Vector2d::Zero();
        double worst_edge_len = 0.;
        size_t n_edges_over = 0, n_edges_over_on_level = 0;
        double max_edge_on_level = 0.;
        Vector2d worst_on_level_mid = Vector2d::Zero();
        double tube = 0.;
        size_t n_placed = 0, n_travelling = 0, n_pressed_on = 0, n_stuck = 0;
        size_t n_pressed_touching = 0; 
        size_t n_at_floor = 0; 
        size_t worst_stuck_vid = static_cast<size_t>(-1);
        double worst_stuck_rho = 0.;
        struct Refinable
        {
            size_t a, b;
            double sag, len;
        };
        std::vector<Refinable> refinable;
        bool vertices_ok() const { return max_vertex <= bar; }
        bool edges_ok() const { return max_edge <= bar; }
        bool converged() const { return vertices_ok() && n_unmeasurable == 0; }
        bool converged_single() const { return converged() && refinable.empty(); }
        double ratio() const { return bar > 0. ? std::max(max_vertex, max_edge) / bar : 0.; }
    };
    EnergyCriterion energy_criterion();
    bool front_vertex_touches_other(size_t vid) const;
    double front_chord_target(size_t va, size_t vb, double len, double sag, double tube) const;
 
    size_t refine_front_from_sag(const std::vector<EnergyCriterion::Refinable>& edges);
    std::optional<EnergyCriterion> m_energy_verdict;
    double edge_interpolation_residual(const Tuple& e) const;
 
    Vector2d offset_vertex_normal(const size_t vid) const;
 
 
    void report_outside_support(const char* when, const DistanceSplit& s) const;
    bool band_vertex_is_reachable(const size_t vid) const
    {
        // An envelope-held offset vertex is pinned: it must stay within envelope_size of the input
        // region boundary AND sit on Phi = c, target_distance away. Those are not simultaneously
        // satisfiable, so its residual gradient is a statement about the constraint rather than
        // about the offset's quality, and leaving it in max_reachable makes convergence impossible
        // by construction. Structural, not left to whether the tolerance happens to hide it.
        //
        // Still reported, never silent: the pinned half of every band measure is logged beside the
        // reachable half, the same contract vertex_is_on_domain_boundary() gets below. This is a
        // retreat, to be reverted the moment a placement that works exists.
        if (m_vertex_extra[vid].m_is_on_offset && vertex_boundary_mask(vid) != 0) return false;
 
        return !vertex_is_on_domain_boundary(vid);
    }
 
    std::vector<char> m_placement_pressed;
 
    size_t refine_sizing_around_worst(double max_metric) override;
 
    void log_stuck_refine_census(double max_metric, double filter_energy);
 
    void log_refine_block_census(const std::string& when, double filter_energy) const;
 
    bool collapse_quality_allowed(size_t v1, size_t v2, double q, double ring_max) const override;
 
    mutable std::atomic<size_t> m_deg_split_created{0};
    mutable std::atomic<size_t> m_deg_collapse_offered{0};
    mutable std::atomic<size_t> m_deg_collapse_allowed{0};
    mutable std::atomic<size_t> m_deg_collapse_by_ringmax{0};
    mutable std::atomic<size_t> m_deg_collapse_by_stop{0};
    mutable std::atomic<size_t> m_deg_collapse_by_unrounded{0};
    std::array<size_t, 6> m_deg_prev_counts{{0, 0, 0, 0, 0, 0}};
 
    void report_needle(const char* op, size_t fid, double parent_q) const;
    static constexpr size_t kNeedleReports = 12;
    static constexpr double kNeedleQuality = 1e6;
    mutable std::atomic<size_t> m_needle_reports{0};
 
    void needle_scan(const char* when) const;
    void collapse_pass_begin() override;
 
    std::set<std::pair<long, long>> m_stuck_prev_cells;
    size_t m_stuck_calls = 0;
 
    bool optimization_bare_coarsen_passes() const override { return false; }
 
    bool collapse_edge_after(const Tuple& t) override;
    double face_criterion_rel(const size_t fid) const;
    void write_smoothing_debug_output(const std::string& path) const override
    {
        const char ph = (m_phase == OptPhase::A) ? 'A' : (m_phase == OptPhase::B ? 'B' : 'S');
        if (m_ab_round != m_debug_last_round || ph != m_debug_last_phase) {
            m_debug_last_round = m_ab_round;
            m_debug_last_phase = ph;
            m_debug_pass = 0;
        }
        // What this frame is, as a compact token: round, phase, pass within the phase, and the
        // operation it follows (from m_debug_pass_name -- the shared driver writes several frames
        // per operation group). Phase B and the single phase write one per sweep.
        std::string label = path;
        if (path.rfind("debug_", 0) == 0) {
            label = fmt::format(
                "r{}{}{}{}",
                m_ab_round,
                ph,
                ++m_debug_pass,
                m_debug_pass_name.empty() ? std::string() : "_" + m_debug_pass_name);
        } else if (path.rfind("phase_", 0) == 0) {
            label = fmt::format("r{}{}_end", m_ab_round, ph);
        }
        // The file name is the sequence number and nothing else, so ParaView groups the frames into
        // one time series: it needs the digits last, right before the extension, and every frame
        // of a series to share its prefix. The label goes to <output>_frames.txt, one
        // "NNNNN<tab>label" line per frame, which is what the polyscope viewer reads for its
        // slider.
        const size_t idx = m_debug_seq++;
        append_frame_label(idx, label);
        const_cast<TopoOffsetTriMesh*>(this)->write_vtu(
            m_offset_params.output_path + fmt::format("_{:05d}", idx));
    }
 
    void append_frame_label(size_t idx, const std::string& label) const;
 
    void init_from_image(
        const MatrixXd& V,
        const MatrixXi& F,
        const MatrixSi& F_tags,
        const MatrixXd& V_env,
        const MatrixXi& F_env,
        const std::vector<std::string>& tag_names,
        const std::string& curve_name = "");
 
    bool ambient_assert();
 
    void label_input_complex();
 
    bool empty_input_complex();
 
    void init_input_complex_bvh();
 
    void init_offset_potential();
 
    MatrixXd m_phi_V;
    MatrixXi m_phi_E;
    MatrixXi m_phi_F; 
    std::vector<int> m_phi_P;
 
    bool split_edge_before(const Tuple& t) override;
    bool split_edge_after(const Tuple& t) override;
    bool split_face_before(const Tuple& t) override;
    bool split_face_after(const Tuple& t) override;
    bool invariants(const std::vector<Tuple>& tris) override;
 
    void pre_optimize_input_mesh();
 
    void execute_offset(const std::filesystem::path& output_file);
 
    void marching_tris();
 
 
 
    bool is_simplicially_embedded() const;
 
    bool tri_is_simp_emb(const Tuple& t) const;
 
    void simplicial_embedding();
 
    void set_offset_tri_tags();
 
    bool offset_is_manifold();
 
 
    void write_phi_grid(const std::string& path, int n) const;
 
    void write_input_complex(const std::string& path);
    void write_vtu(const std::string& path);
    // void write_msh(const std::string& file);
    void write_msh_groups(const std::string& file);
 
private:
    struct EdgeSplitCache
    {
        size_t v1_id;
        size_t v2_id;
        Vector2d new_v_pos;
        VertexExtra2d new_v_extra;
 
        // cache edge attributes
        EdgeSnapshot2d split_eattr;
        std::map<simplex::Edge, EdgeSnapshot2d> existing_eattr;
 
        // cache face attributes
        std::map<size_t, FaceSnapshot2d> opp_v_fattr;
    };
    wmtk::threading::enumerable_thread_specific<EdgeSplitCache> edge_split_cache;
 
    struct FaceSplitCache
    {
        size_t v1_id;
        size_t v2_id;
        size_t v3_id;
        Vector2d new_v_pos;
        VertexExtra2d new_v_extra;
 
        std::map<simplex::Edge, EdgeSnapshot2d> existing_eattr; // 3 orig edges
        FaceSnapshot2d split_fattr; // split face attributes
    };
    wmtk::threading::enumerable_thread_specific<FaceSplitCache> face_split_cache;
 
private: // helpers
    bool any_tag_present(const CellTag& tag1, const CellTag& tag2) const
    {
        for (const int64_t& i : tag1) {
            if (tag2.find(i) != tag2.end()) {
                return true;
            }
        }
        return false;
    }
 
    void sort_edges_by_length(std::vector<simplex::Edge>& edges)
    {
        std::sort(
            edges.begin(),
            edges.end(),
            [this](const simplex::Edge& e1, const simplex::Edge& e2) {
                double len1 = (m_vertex_attribute[e1.vertices()[0]].m_posf -
                               m_vertex_attribute[e1.vertices()[1]].m_posf)
                                  .squaredNorm();
                double len2 = (m_vertex_attribute[e2.vertices()[0]].m_posf -
                               m_vertex_attribute[e2.vertices()[1]].m_posf)
                                  .squaredNorm();
                return len1 > len2;
            });
    }
 
public: // helpers
    size_t edge_id_from_simplex(const simplex::Edge& e) const
    {
        const auto& verts = e.vertices();
        const auto incident = simplex_incident_triangles(e);
        const auto& faces = incident.faces();
 
        assert(!faces.empty()); // throw error here otherwise
 
        const size_t f_id = tuple_from_simplex(faces.front()).fid(*this);
        const Tuple t_edge = tuple_from_edge(verts[0], verts[1], f_id);
        return t_edge.eid(*this);
    }
 
    Tuple get_tuple_from_edge(const simplex::Edge& e) const
    {
        const auto& v = e.vertices();
        const auto faces = simplex_incident_triangles(e).faces();
        assert(!faces.empty());
        const size_t fid = tuple_from_simplex(faces.front()).fid(*this);
        return tuple_from_edge(v[0], v[1], fid);
    }
 
    std::vector<Tuple> get_edge_adjacent_faces(const Tuple& f) const
    {
        std::vector<Tuple> adj_tris;
        auto tri_1 = f.switch_face(*this);
        if (tri_1) {
            adj_tris.push_back(tri_1.value());
        }
        auto tri_2 = f.switch_edge(*this).switch_face(*this);
        if (tri_2) {
            adj_tris.push_back(tri_2.value());
        }
        auto tri_3 = f.switch_vertex(*this).switch_edge(*this).switch_face(*this);
        if (tri_3) {
            adj_tris.push_back(tri_3.value());
        }
        return adj_tris;
    }
};
 
 
} // namespace wmtk::components::topological_offset