path: root/src/libslic3r/SLA/SupportTreeBuildsteps.cpp

#include <libslic3r/SLA/SupportTreeBuildsteps.hpp>

#include <libslic3r/SLA/SpatIndex.hpp>
#include <libnest2d/optimizers/nlopt/genetic.hpp>
#include <libnest2d/optimizers/nlopt/subplex.hpp>
#include <boost/log/trivial.hpp>

namespace Slic3r {
namespace sla {

using libnest2d::opt::initvals;
using libnest2d::opt::bound;
using libnest2d::opt::StopCriteria;
using libnest2d::opt::GeneticOptimizer;
using libnest2d::opt::SubplexOptimizer;

template<class C, class Hit = IndexedMesh::hit_result>
static Hit min_hit(const C &hits)
{
    auto mit = std::min_element(hits.begin(), hits.end(),
                                [](const Hit &h1, const Hit &h2) {
                                    return h1.distance() < h2.distance();
                                });

    return *mit;
}

//IndexedMesh::hit_result query_hit(const SupportableMesh &msh, const Head &h)
//{
//    static const size_t SAMPLES = 8;

//    // Move away slightly from the touching point to avoid raycasting on the
//    // inner surface of the mesh.

//    const double& sd = msh.cfg.safety_distance_mm;

//    auto& m = msh.emesh;
//    using HitResult = IndexedMesh::hit_result;

//    // Hit results
//    std::array<HitResult, SAMPLES> hits;

//    Vec3d s1 = h.pos, s2 = h.junction_point();

//    struct Rings {
//        double rpin;
//        double rback;
//        Vec3d  spin;
//        Vec3d  sback;
//        PointRing<SAMPLES> ring;

//        Vec3d backring(size_t idx) { return ring.get(idx, sback, rback); }
//        Vec3d pinring(size_t idx) { return ring.get(idx, spin, rpin); }
//    } rings {h.r_pin_mm + sd, h.r_back_mm + sd, s1, s2, h.dir};

//    // We will shoot multiple rays from the head pinpoint in the direction
//    // of the pinhead robe (side) surface. The result will be the smallest
//    // hit distance.

//    auto hitfn = [&m, &rings, sd](HitResult &hit, size_t i) {
//        // Point on the circle on the pin sphere
//        Vec3d ps = rings.pinring(i);
//        // This is the point on the circle on the back sphere
//        Vec3d p = rings.backring(i);

//        // Point ps is not on mesh but can be inside or
//        // outside as well. This would cause many problems
//        // with ray-casting. To detect the position we will
//        // use the ray-casting result (which has an is_inside
//        // predicate).

//        Vec3d n = (p - ps).normalized();
//        auto  q = m.query_ray_hit(ps + sd * n, n);

//        if (q.is_inside()) { // the hit is inside the model
//            if (q.distance() > rings.rpin) {
//                // If we are inside the model and the hit
//                // distance is bigger than our pin circle
//                // diameter, it probably indicates that the
//                // support point was already inside the
//                // model, or there is really no space
//                // around the point. We will assign a zero
//                // hit distance to these cases which will
//                // enforce the function return value to be
//                // an invalid ray with zero hit distance.
//                // (see min_element at the end)
//                hit = HitResult(0.0);
//            } else {
//                // re-cast the ray from the outside of the
//                // object. The starting point has an offset
//                // of 2*safety_distance because the
//                // original ray has also had an offset
//                auto q2 = m.query_ray_hit(ps + (q.distance() + 2 * sd) * n, n);
//                hit     = q2;
//            }
//        } else
//            hit = q;
//    };

//    ccr::enumerate(hits.begin(), hits.end(), hitfn);

//    return min_hit(hits);
//}

//IndexedMesh::hit_result query_hit(const SupportableMesh &msh, const Bridge &br, double safety_d)
//{

//    static const size_t SAMPLES = 8;

//    Vec3d dir = (br.endp - br.startp).normalized();
//    PointRing<SAMPLES> ring{dir};

//    using Hit = IndexedMesh::hit_result;

//    // Hit results
//    std::array<Hit, SAMPLES> hits;

//    double sd = std::isnan(safety_d) ? msh.cfg.safety_distance_mm : safety_d;

//    auto hitfn = [&msh, &br, &ring, dir, sd] (Hit &hit, size_t i) {

//        // Point on the circle on the pin sphere
//        Vec3d p = ring.get(i, br.startp, br.r + sd);

//        auto hr = msh.emesh.query_ray_hit(p + br.r * dir, dir);

//        if(hr.is_inside()) {
//            if(hr.distance() > 2 * br.r + sd) hit = Hit(0.0);
//            else {
//                // re-cast the ray from the outside of the object
//                hit = msh.emesh.query_ray_hit(p + (hr.distance() + 2 * sd) * dir, dir);
//            }
//        } else hit = hr;
//    };

//    ccr::enumerate(hits.begin(), hits.end(), hitfn);

//    return min_hit(hits);
//}

SupportTreeBuildsteps::SupportTreeBuildsteps(SupportTreeBuilder &   builder,
                                             const SupportableMesh &sm)
    : m_cfg(sm.cfg)
    , m_mesh(sm.emesh)
    , m_support_pts(sm.pts)
    , m_support_nmls(sm.pts.size(), 3)
    , m_builder(builder)
    , m_points(sm.pts.size(), 3)
    , m_thr(builder.ctl().cancelfn)
{
    // Prepare the support points in Eigen/IGL format as well, we will use
    // it mostly in this form.
    
    long i = 0;
    for (const SupportPoint &sp : m_support_pts) {
        m_points.row(i)(X) = double(sp.pos(X));
        m_points.row(i)(Y) = double(sp.pos(Y));
        m_points.row(i)(Z) = double(sp.pos(Z));
        ++i;
    }
}

bool SupportTreeBuildsteps::execute(SupportTreeBuilder &   builder,
                                    const SupportableMesh &sm)
{
    if(sm.pts.empty()) return false;
    
    builder.ground_level = sm.emesh.ground_level() - sm.cfg.object_elevation_mm;

    SupportTreeBuildsteps alg(builder, sm);

    // Let's define the individual steps of the processing. We can experiment
    // later with the ordering and the dependencies between them.
    enum Steps {
        BEGIN,
        FILTER,
        PINHEADS,
        CLASSIFY,
        ROUTING_GROUND,
        ROUTING_NONGROUND,
        CASCADE_PILLARS,
        MERGE_RESULT,
        DONE,
        ABORT,
        NUM_STEPS
        //...
    };
    
    // Collect the algorithm steps into a nice sequence
    std::array<std::function<void()>, NUM_STEPS> program = {
        [] () {
            // Begin...
            // Potentially clear up the shared data (not needed for now)
        },
        
        std::bind(&SupportTreeBuildsteps::filter, &alg),
        
        std::bind(&SupportTreeBuildsteps::add_pinheads, &alg),
        
        std::bind(&SupportTreeBuildsteps::classify, &alg),
        
        std::bind(&SupportTreeBuildsteps::routing_to_ground, &alg),
        
        std::bind(&SupportTreeBuildsteps::routing_to_model, &alg),
        
        std::bind(&SupportTreeBuildsteps::interconnect_pillars, &alg),
        
        std::bind(&SupportTreeBuildsteps::merge_result, &alg),
        
        [] () {
            // Done
        },
        
        [] () {
            // Abort
        }
    };
    
    Steps pc = BEGIN;
    
    if(sm.cfg.ground_facing_only) {
        program[ROUTING_NONGROUND] = []() {
            BOOST_LOG_TRIVIAL(info)
                << "Skipping model-facing supports as requested.";
        };
    }
    
    // Let's define a simple automaton that will run our program.
    auto progress = [&builder, &pc] () {
        static const std::array<std::string, NUM_STEPS> stepstr {
            "Starting",
            "Filtering",
            "Generate pinheads",
            "Classification",
            "Routing to ground",
            "Routing supports to model surface",
            "Interconnecting pillars",
            "Merging support mesh",
            "Done",
            "Abort"
        };
        
        static const std::array<unsigned, NUM_STEPS> stepstate {
            0,
            10,
            30,
            50,
            60,
            70,
            80,
            99,
            100,
            0
        };
        
        if(builder.ctl().stopcondition()) pc = ABORT;
        
        switch(pc) {
        case BEGIN: pc = FILTER; break;
        case FILTER: pc = PINHEADS; break;
        case PINHEADS: pc = CLASSIFY; break;
        case CLASSIFY: pc = ROUTING_GROUND; break;
        case ROUTING_GROUND: pc = ROUTING_NONGROUND; break;
        case ROUTING_NONGROUND: pc = CASCADE_PILLARS; break;
        case CASCADE_PILLARS: pc = MERGE_RESULT; break;
        case MERGE_RESULT: pc = DONE; break;
        case DONE:
        case ABORT: break;
        default: ;
        }
        
        builder.ctl().statuscb(stepstate[pc], stepstr[pc]);
    };
    
    // Just here we run the computation...
    while(pc < DONE) {
        progress();
        program[pc]();
    }
    
    return pc == ABORT;
}

IndexedMesh::hit_result SupportTreeBuildsteps::pinhead_mesh_intersect(
    const Vec3d &s, const Vec3d &dir, double r_pin, double r_back, double width)
{
    static const size_t SAMPLES = 8;
    
    // Move away slightly from the touching point to avoid raycasting on the
    // inner surface of the mesh.
    
    const double& sd = m_cfg.safety_distance_mm;
    
    auto& m = m_mesh;
    using HitResult = IndexedMesh::hit_result;
    
    // Hit results
    std::array<HitResult, SAMPLES> hits;
    
    struct Rings {
        double rpin;
        double rback;
        Vec3d  spin;
        Vec3d  sback;
        PointRing<SAMPLES> ring;
        
        Vec3d backring(size_t idx) { return ring.get(idx, sback, rback); }
        Vec3d pinring(size_t idx) { return ring.get(idx, spin, rpin); }
    } rings {r_pin + sd, r_back + sd, s, s + width * dir, dir};
    
    // We will shoot multiple rays from the head pinpoint in the direction
    // of the pinhead robe (side) surface. The result will be the smallest
    // hit distance.
    
    ccr::enumerate(hits.begin(), hits.end(), 
                   [&m, &rings, sd](HitResult &hit, size_t i) {
    
       // Point on the circle on the pin sphere
       Vec3d ps = rings.pinring(i);
       // This is the point on the circle on the back sphere
       Vec3d p = rings.backring(i);
       
       // Point ps is not on mesh but can be inside or
       // outside as well. This would cause many problems
       // with ray-casting. To detect the position we will
       // use the ray-casting result (which has an is_inside
       // predicate).       
    
       Vec3d n = (p - ps).normalized();
       auto  q = m.query_ray_hit(ps + sd * n, n);
    
       if (q.is_inside()) { // the hit is inside the model
           if (q.distance() > rings.rpin) {
               // If we are inside the model and the hit
               // distance is bigger than our pin circle
               // diameter, it probably indicates that the
               // support point was already inside the
               // model, or there is really no space
               // around the point. We will assign a zero
               // hit distance to these cases which will
               // enforce the function return value to be
               // an invalid ray with zero hit distance.
               // (see min_element at the end)
               hit = HitResult(0.0);
           } else {
               // re-cast the ray from the outside of the
               // object. The starting point has an offset
               // of 2*safety_distance because the
               // original ray has also had an offset
               auto q2 = m.query_ray_hit(ps + (q.distance() + 2 * sd) * n, n);
               hit = q2;
           }
       } else
           hit = q;
    });
    
    return min_hit(hits);
}

IndexedMesh::hit_result SupportTreeBuildsteps::bridge_mesh_intersect(
    const Vec3d &src, const Vec3d &dir, double r, double sd)
{
    static const size_t SAMPLES = 8;
    PointRing<SAMPLES> ring{dir};
    
    using Hit = IndexedMesh::hit_result;
    
    // Hit results
    std::array<Hit, SAMPLES> hits;
    
    ccr::enumerate(hits.begin(), hits.end(), 
                [this, r, src, /*ins_check,*/ &ring, dir, sd] (Hit &hit, size_t i) {

        // Point on the circle on the pin sphere
        Vec3d p = ring.get(i, src, r + sd);
        
        auto hr = m_mesh.query_ray_hit(p + r * dir, dir);
        
        if(/*ins_check && */hr.is_inside()) {
            if(hr.distance() > 2 * r + sd) hit = Hit(0.0);
            else {
                // re-cast the ray from the outside of the object
                hit = m_mesh.query_ray_hit(p + (hr.distance() + EPSILON) * dir, dir);
            }
        } else hit = hr;
    });
    
    return min_hit(hits);
}

bool SupportTreeBuildsteps::interconnect(const Pillar &pillar,
                                         const Pillar &nextpillar)
{
    // We need to get the starting point of the zig-zag pattern. We have to
    // be aware that the two head junctions are at different heights. We
    // may start from the lowest junction and call it a day but this
    // strategy would leave unconnected a lot of pillar duos where the
    // shorter pillar is too short to start a new bridge but the taller
    // pillar could still be bridged with the shorter one.
    bool was_connected = false;
    
    Vec3d supper = pillar.startpoint();
    Vec3d slower = nextpillar.startpoint();
    Vec3d eupper = pillar.endpoint();
    Vec3d elower = nextpillar.endpoint();
    
    double zmin = m_builder.ground_level + m_cfg.base_height_mm;
    eupper(Z) = std::max(eupper(Z), zmin);
    elower(Z) = std::max(elower(Z), zmin);
    
    // The usable length of both pillars should be positive
    if(slower(Z) - elower(Z) < 0) return false;
    if(supper(Z) - eupper(Z) < 0) return false;
    
    double pillar_dist = distance(Vec2d{slower(X), slower(Y)},
                                  Vec2d{supper(X), supper(Y)});
    double bridge_distance = pillar_dist / std::cos(-m_cfg.bridge_slope);
    double zstep = pillar_dist * std::tan(-m_cfg.bridge_slope);
    
    if(pillar_dist < 2 * m_cfg.head_back_radius_mm ||
        pillar_dist > m_cfg.max_pillar_link_distance_mm) return false;
    
    if(supper(Z) < slower(Z)) supper.swap(slower);
    if(eupper(Z) < elower(Z)) eupper.swap(elower);
    
    double startz = 0, endz = 0;
    
    startz = slower(Z) - zstep < supper(Z) ? slower(Z) - zstep : slower(Z);
    endz = eupper(Z) + zstep > elower(Z) ? eupper(Z) + zstep : eupper(Z);
    
    if(slower(Z) - eupper(Z) < std::abs(zstep)) {
        // no space for even one cross
        
        // Get max available space
        startz = std::min(supper(Z), slower(Z) - zstep);
        endz = std::max(eupper(Z) + zstep, elower(Z));
        
        // Align to center
        double available_dist = (startz - endz);
        double rounds = std::floor(available_dist / std::abs(zstep));
        startz -= 0.5 * (available_dist - rounds * std::abs(zstep));
    }
    
    auto pcm = m_cfg.pillar_connection_mode;
    bool docrosses =
        pcm == PillarConnectionMode::cross ||
        (pcm == PillarConnectionMode::dynamic &&
         pillar_dist > 2*m_cfg.base_radius_mm);
    
    // 'sj' means starting junction, 'ej' is the end junction of a bridge.
    // They will be swapped in every iteration thus the zig-zag pattern.
    // According to a config parameter, a second bridge may be added which
    // results in a cross connection between the pillars.
    Vec3d sj = supper, ej = slower; sj(Z) = startz; ej(Z) = sj(Z) + zstep;
    
    // TODO: This is a workaround to not have a faulty last bridge
    while(ej(Z) >= eupper(Z) /*endz*/) {
        if(bridge_mesh_distance(sj, dirv(sj, ej), pillar.r) >= bridge_distance)
        {
            m_builder.add_crossbridge(sj, ej, pillar.r);
            was_connected = true;
        }
        
        // double bridging: (crosses)
        if(docrosses) {
            Vec3d sjback(ej(X), ej(Y), sj(Z));
            Vec3d ejback(sj(X), sj(Y), ej(Z));
            if (sjback(Z) <= slower(Z) && ejback(Z) >= eupper(Z) &&
                bridge_mesh_distance(sjback, dirv(sjback, ejback),
                                      pillar.r) >= bridge_distance) {
                // need to check collision for the cross stick
                m_builder.add_crossbridge(sjback, ejback, pillar.r);
                was_connected = true;
            }
        }
        
        sj.swap(ej);
        ej(Z) = sj(Z) + zstep;
    }
    
    return was_connected;
}

bool SupportTreeBuildsteps::connect_to_nearpillar(const Head &head,
                                                  long        nearpillar_id)
{
    auto nearpillar = [this, nearpillar_id]() -> const Pillar& {
        return m_builder.pillar(nearpillar_id);
    };
    
    if (m_builder.bridgecount(nearpillar()) > m_cfg.max_bridges_on_pillar) 
        return false;
    
    Vec3d headjp = head.junction_point();
    Vec3d nearjp_u = nearpillar().startpoint();
    Vec3d nearjp_l = nearpillar().endpoint();
    
    double r = head.r_back_mm;
    double d2d = distance(to_2d(headjp), to_2d(nearjp_u));
    double d3d = distance(headjp, nearjp_u);
    
    double hdiff = nearjp_u(Z) - headjp(Z);
    double slope = std::atan2(hdiff, d2d);
    
    Vec3d bridgestart = headjp;
    Vec3d bridgeend = nearjp_u;
    double max_len = r * m_cfg.max_bridge_length_mm / m_cfg.head_back_radius_mm;
    double max_slope = m_cfg.bridge_slope;
    double zdiff = 0.0;
    
    // check the default situation if feasible for a bridge
    if(d3d > max_len || slope > -max_slope) {
        // not feasible to connect the two head junctions. We have to search
        // for a suitable touch point.
        
        double Zdown = headjp(Z) + d2d * std::tan(-max_slope);
        Vec3d touchjp = bridgeend; touchjp(Z) = Zdown;
        double D = distance(headjp, touchjp);
        zdiff = Zdown - nearjp_u(Z);
        
        if(zdiff > 0) {
            Zdown -= zdiff;
            bridgestart(Z) -= zdiff;
            touchjp(Z) = Zdown;
            
            double t = bridge_mesh_distance(headjp, DOWN, r);
            
            // We can't insert a pillar under the source head to connect
            // with the nearby pillar's starting junction
            if(t < zdiff) return false;
        }
        
        if(Zdown <= nearjp_u(Z) && Zdown >= nearjp_l(Z) && D < max_len)
            bridgeend(Z) = Zdown;
        else
            return false;
    }
    
    // There will be a minimum distance from the ground where the
    // bridge is allowed to connect. This is an empiric value.
    double minz = m_builder.ground_level + 4 * head.r_back_mm;
    if(bridgeend(Z) < minz) return false;
    
    double t = bridge_mesh_distance(bridgestart, dirv(bridgestart, bridgeend), r);
    
    // Cannot insert the bridge. (further search might not worth the hassle)
    if(t < distance(bridgestart, bridgeend)) return false;
    
    std::lock_guard<ccr::BlockingMutex> lk(m_bridge_mutex);
    
    if (m_builder.bridgecount(nearpillar()) < m_cfg.max_bridges_on_pillar) {
        // A partial pillar is needed under the starting head.
        if(zdiff > 0) {
            m_builder.add_pillar(head.id, headjp.z() - bridgestart.z());
            m_builder.add_junction(bridgestart, r);
            m_builder.add_bridge(bridgestart, bridgeend, r);
        } else {
            m_builder.add_bridge(head.id, bridgeend);
        }
        
        m_builder.increment_bridges(nearpillar());
    } else return false;
    
    return true;
}

bool SupportTreeBuildsteps::create_ground_pillar(const Vec3d &jp,
                                                 const Vec3d &sourcedir,
                                                 double       radius,
                                                 long         head_id)
{
    double sd           = m_cfg.pillar_base_safety_distance_mm;
    long   pillar_id    = SupportTreeNode::ID_UNSET;
    bool   can_add_base = radius >= m_cfg.head_back_radius_mm;
    double base_r       = can_add_base ? m_cfg.base_radius_mm : 0.;
    double gndlvl       = m_builder.ground_level;
    if (!can_add_base) gndlvl -= m_mesh.ground_level_offset();
    Vec3d  endp         = {jp(X), jp(Y), gndlvl};
    double min_dist     = sd + base_r + EPSILON;
    bool   normal_mode  = true;
    Vec3d  dir          = sourcedir;

    auto to_floor = [&gndlvl](const Vec3d &p) { return Vec3d{p.x(), p.y(), gndlvl}; };

    if (m_cfg.object_elevation_mm < EPSILON)
    {
        // get a suitable direction for the corrector bridge. It is the
        // original sourcedir's azimuth but the polar angle is saturated to the
        // configured bridge slope.
        auto [polar, azimuth] = dir_to_spheric(dir);
        polar = PI - m_cfg.bridge_slope;
        Vec3d dir = spheric_to_dir(polar, azimuth).normalized();

        // Check the distance of the endpoint and the closest point on model
        // body. It should be greater than the min_dist which is
        // the safety distance from the model. It includes the pad gap if in
        // zero elevation mode.
        //
        // Try to move along the established bridge direction to dodge the
        // forbidden region for the endpoint.
        double t = -radius;
        bool succ = true;
        while (std::sqrt(m_mesh.squared_distance(to_floor(endp))) < min_dist ||
               !std::isinf(bridge_mesh_distance(endp, DOWN, radius))) {
            t += radius;
            endp = jp + t * dir;
            normal_mode = false;

            if (t > m_cfg.max_bridge_length_mm || endp(Z) < gndlvl) {
                if (head_id >= 0) m_builder.add_pillar(head_id, 0.);
                succ = false;
                break;
            }
        }

        if (!succ) {
            if (can_add_base) {
                can_add_base = false;
                base_r       = 0.;
                gndlvl -= m_mesh.ground_level_offset();
                min_dist     = sd + base_r + EPSILON;
                endp         = {jp(X), jp(Y), gndlvl + radius};

                t = -radius;
                while (std::sqrt(m_mesh.squared_distance(to_floor(endp))) < min_dist ||
                       !std::isinf(bridge_mesh_distance(endp, DOWN, radius))) {
                    t += radius;
                    endp = jp + t * dir;
                    normal_mode = false;

                    if (t > m_cfg.max_bridge_length_mm || endp(Z) < (gndlvl + radius)) {
                        if (head_id >= 0) m_builder.add_pillar(head_id, 0.);
                        return false;
                    }
                }
            } else return false;
        }
    }

    double h = (jp - endp).norm();

    // Check if the deduced route is sane and exit with error if not.
    if (bridge_mesh_distance(jp, dir, radius) < h) {
        if (head_id >= 0) m_builder.add_pillar(head_id, 0.);
        return false;
    }

    // Straigh path down, no area to dodge
    if (normal_mode) {
        pillar_id = head_id >= 0 ? m_builder.add_pillar(head_id, h) :
                                   m_builder.add_pillar(endp, h, radius);

        if (can_add_base)
            add_pillar_base(pillar_id);
    } else {

        // Insert the bridge to get around the forbidden area
        Vec3d pgnd{endp.x(), endp.y(), gndlvl};
        pillar_id = m_builder.add_pillar(pgnd, endp.z() - gndlvl, radius);

        if (can_add_base)
            add_pillar_base(pillar_id);

        m_builder.add_bridge(jp, endp, radius);
        m_builder.add_junction(endp, radius);

        // Add a degenerated pillar and the bridge.
        // The degenerate pillar will have zero length and it will
        // prevent from queries of head_pillar() to have non-existing
        // pillar when the head should have one.
        if (head_id >= 0)
            m_builder.add_pillar(head_id, 0.);
    }

    if(pillar_id >= 0) // Save the pillar endpoint in the spatial index
        m_pillar_index.guarded_insert(endp, unsigned(pillar_id));

    return true;
}

void SupportTreeBuildsteps::filter()
{
    // Get the points that are too close to each other and keep only the
    // first one
    auto aliases = cluster(m_points, D_SP, 2);
    
    PtIndices filtered_indices;
    filtered_indices.reserve(aliases.size());
    m_iheads.reserve(aliases.size());
    m_iheadless.reserve(aliases.size());
    for(auto& a : aliases) {
        // Here we keep only the front point of the cluster.
        filtered_indices.emplace_back(a.front());
    }
    
    // calculate the normals to the triangles for filtered points
    auto nmls = sla::normals(m_points, m_mesh, m_cfg.head_front_radius_mm,
                             m_thr, filtered_indices);
    
    // Not all of the support points have to be a valid position for
    // support creation. The angle may be inappropriate or there may
    // not be enough space for the pinhead. Filtering is applied for
    // these reasons.
    
    ccr::SpinningMutex mutex;
    auto addfn = [&mutex](PtIndices &container, unsigned val) {
        std::lock_guard<ccr::SpinningMutex> lk(mutex);
        container.emplace_back(val);
    };
    
    auto filterfn = [this, &nmls, addfn](unsigned fidx, size_t i) {
        m_thr();
        
        auto n = nmls.row(Eigen::Index(i));
        
        // for all normals we generate the spherical coordinates and
        // saturate the polar angle to 45 degrees from the bottom then
        // convert back to standard coordinates to get the new normal.
        // Then we just create a quaternion from the two normals
        // (Quaternion::FromTwoVectors) and apply the rotation to the
        // arrow head.
        
        auto [polar, azimuth] = dir_to_spheric(n);
        
        // skip if the tilt is not sane
        if(polar < PI - m_cfg.normal_cutoff_angle) return;
            
        // We saturate the polar angle to 3pi/4
        polar = std::max(polar, 3*PI / 4);

        // save the head (pinpoint) position
        Vec3d hp = m_points.row(fidx);

        // The distance needed for a pinhead to not collide with model.
        double w = m_cfg.head_width_mm +
                   m_cfg.head_back_radius_mm +
                   2*m_cfg.head_front_radius_mm;

        double pin_r = double(m_support_pts[fidx].head_front_radius);

        // Reassemble the now corrected normal
        auto nn = spheric_to_dir(polar, azimuth).normalized();

        // check available distance
        IndexedMesh::hit_result t
            = pinhead_mesh_intersect(hp, // touching point
                                     nn, // normal
                                     pin_r,
                                     m_cfg.head_back_radius_mm,
                                     w);

        if(t.distance() <= w) {

            // Let's try to optimize this angle, there might be a
            // viable normal that doesn't collide with the model
            // geometry and its very close to the default.

            StopCriteria stc;
            stc.max_iterations = m_cfg.optimizer_max_iterations;
            stc.relative_score_difference = m_cfg.optimizer_rel_score_diff;
            stc.stop_score = w; // space greater than w is enough
            GeneticOptimizer solver(stc);
            solver.seed(0); // we want deterministic behavior

            auto oresult = solver.optimize_max(
                [this, pin_r, w, hp](double plr, double azm)
                {
                    auto dir = spheric_to_dir(plr, azm).normalized();

                    double score = pinhead_mesh_intersect(
                        hp, dir, pin_r, m_cfg.head_back_radius_mm, w).distance();

                    return score;
                },
                initvals(polar, azimuth), // start with what we have
                bound(3 * PI / 4, PI),    // Must not exceed the tilt limit
                bound(-PI, PI) // azimuth can be a full search
                );

            if(oresult.score > w) {
                polar = std::get<0>(oresult.optimum);
                azimuth = std::get<1>(oresult.optimum);
                nn = spheric_to_dir(polar, azimuth).normalized();
                t = IndexedMesh::hit_result(oresult.score);
            }
        }

        // save the verified and corrected normal
        m_support_nmls.row(fidx) = nn;

        if (t.distance() > w) {
            // Check distance from ground, we might have zero elevation.
            if (hp(Z) + w * nn(Z) < m_builder.ground_level) {
                addfn(m_iheadless, fidx);
            } else {
                // mark the point for needing a head.
                addfn(m_iheads, fidx);
            }
        } else if (polar >= 3 * PI / 4) {
            // Headless supports do not tilt like the headed ones
            // so the normal should point almost to the ground.
            addfn(m_iheadless, fidx);
        }

    };
    
    ccr::enumerate(filtered_indices.begin(), filtered_indices.end(), filterfn);
    
    m_thr();
}

void SupportTreeBuildsteps::add_pinheads()
{
    for (unsigned i : m_iheads) {
        m_thr();
        m_builder.add_head(
            i,
            m_cfg.head_back_radius_mm,
            m_support_pts[i].head_front_radius,
            m_cfg.head_width_mm,
            m_cfg.head_penetration_mm,
            m_support_nmls.row(i),         // dir
            m_support_pts[i].pos.cast<double>() // displacement
            );
    }

    for (unsigned i : m_iheadless) {
        const auto R = double(m_support_pts[i].head_front_radius);

        // The support point position on the mesh
        Vec3d sph = m_support_pts[i].pos.cast<double>();

        // Get an initial normal from the filtering step
        Vec3d n = m_support_nmls.row(i);

        // First we need to determine the available space for a mini pinhead.
        // The goal is the move away from the model a little bit to make the
        // contact point small as possible and avoid pearcing the model body.
        double pin_space = std::min(2 * R, bridge_mesh_distance(sph, n, R, 0.));

        if (pin_space <= 0) continue;

        m_iheads.emplace_back(i);
        m_builder.add_head(i, R, R, pin_space,
                           m_cfg.head_penetration_mm, n, sph);
    }
}

void SupportTreeBuildsteps::classify()
{
    // We should first get the heads that reach the ground directly
    PtIndices ground_head_indices;
    ground_head_indices.reserve(m_iheads.size());
    m_iheads_onmodel.reserve(m_iheads.size());
    
    // First we decide which heads reach the ground and can be full
    // pillars and which shall be connected to the model surface (or
    // search a suitable path around the surface that leads to the
    // ground -- TODO)
    for(unsigned i : m_iheads) {
        m_thr();
        
        auto& head = m_builder.head(i);
        double r = head.r_back_mm;
        Vec3d headjp = head.junction_point();
        
        // collision check
        auto hit = bridge_mesh_intersect(headjp, DOWN, r);
        
        if(std::isinf(hit.distance())) ground_head_indices.emplace_back(i);
        else if(m_cfg.ground_facing_only)  head.invalidate();
        else m_iheads_onmodel.emplace_back(i);
        
        m_head_to_ground_scans[i] = hit;
    }
    
    // We want to search for clusters of points that are far enough
    // from each other in the XY plane to not cross their pillar bases
    // These clusters of support points will join in one pillar,
    // possibly in their centroid support point.
    
    auto pointfn = [this](unsigned i) {
        return m_builder.head(i).junction_point();
    };
    
    auto predicate = [this](const PointIndexEl &e1,
                            const PointIndexEl &e2) {
        double d2d = distance(to_2d(e1.first), to_2d(e2.first));
        double d3d = distance(e1.first, e2.first);
        return d2d < 2 * m_cfg.base_radius_mm
               && d3d < m_cfg.max_bridge_length_mm;
    };

    m_pillar_clusters = cluster(ground_head_indices, pointfn, predicate,
                                m_cfg.max_bridges_on_pillar);
}

void SupportTreeBuildsteps::routing_to_ground()
{
    ClusterEl cl_centroids;
    cl_centroids.reserve(m_pillar_clusters.size());
    
    for (auto &cl : m_pillar_clusters) {
        m_thr();
        
        // place all the centroid head positions into the index. We
        // will query for alternative pillar positions. If a sidehead
        // cannot connect to the cluster centroid, we have to search
        // for another head with a full pillar. Also when there are two
        // elements in the cluster, the centroid is arbitrary and the
        // sidehead is allowed to connect to a nearby pillar to
        // increase structural stability.
        
        if (cl.empty()) continue;
        
        // get the current cluster centroid
        auto &      thr    = m_thr;
        const auto &points = m_points;

        long lcid = cluster_centroid(
            cl, [&points](size_t idx) { return points.row(long(idx)); },
            [thr](const Vec3d &p1, const Vec3d &p2) {
                thr();
                return distance(Vec2d(p1(X), p1(Y)), Vec2d(p2(X), p2(Y)));
            });

        assert(lcid >= 0);
        unsigned hid = cl[size_t(lcid)]; // Head ID
        
        cl_centroids.emplace_back(hid);
        
        Head &h = m_builder.head(hid);
        
        if (!create_ground_pillar(h.junction_point(), h.dir, h.r_back_mm, h.id)) {
            BOOST_LOG_TRIVIAL(warning)
                << "Pillar cannot be created for support point id: " << hid;
            m_iheads_onmodel.emplace_back(h.id);
            continue;
        }
    }
    
    // now we will go through the clusters ones again and connect the
    // sidepoints with the cluster centroid (which is a ground pillar)
    // or a nearby pillar if the centroid is unreachable.
    size_t ci = 0;
    for (auto cl : m_pillar_clusters) {
        m_thr();
        
        auto cidx = cl_centroids[ci++];
        
        // TODO: don't consider the cluster centroid but calculate a
        // central position where the pillar can be placed. this way
        // the weight is distributed more effectively on the pillar.
        
        auto centerpillarID = m_builder.head_pillar(cidx).id;
        
        for (auto c : cl) {
            m_thr();
            if (c == cidx) continue;
            
            auto &sidehead = m_builder.head(c);
            
            if (!connect_to_nearpillar(sidehead, centerpillarID) &&
                !search_pillar_and_connect(sidehead)) {
                Vec3d pstart = sidehead.junction_point();
                // Vec3d pend = Vec3d{pstart(X), pstart(Y), gndlvl};
                // Could not find a pillar, create one
                create_ground_pillar(pstart, sidehead.dir, sidehead.r_back_mm, sidehead.id);
            }
        }
    }
}

bool SupportTreeBuildsteps::connect_to_ground(Head &head, const Vec3d &dir)
{
    auto hjp = head.junction_point();
    double r = head.r_back_mm;
    double t = bridge_mesh_distance(hjp, dir, head.r_back_mm);
    double d = 0, tdown = 0;
    t = std::min(t, m_cfg.max_bridge_length_mm * r / m_cfg.head_back_radius_mm);

    while (d < t && !std::isinf(tdown = bridge_mesh_distance(hjp + d * dir, DOWN, r)))
        d += r;
    
    if(!std::isinf(tdown)) return false;
    
    Vec3d endp = hjp + d * dir;
    bool ret = false;

    if ((ret = create_ground_pillar(endp, dir, head.r_back_mm))) {
        m_builder.add_bridge(head.id, endp);
        m_builder.add_junction(endp, head.r_back_mm);
    }
    
    return ret;
}

bool SupportTreeBuildsteps::connect_to_ground(Head &head)
{
    if (connect_to_ground(head, head.dir)) return true;
    
    // Optimize bridge direction:
    // Straight path failed so we will try to search for a suitable
    // direction out of the cavity.
    auto [polar, azimuth] = dir_to_spheric(head.dir);
    
    StopCriteria stc;
    stc.max_iterations = m_cfg.optimizer_max_iterations;
    stc.relative_score_difference = m_cfg.optimizer_rel_score_diff;
    stc.stop_score = 1e6;
    GeneticOptimizer solver(stc);
    solver.seed(0); // we want deterministic behavior
    
    double r_back = head.r_back_mm;
    Vec3d hjp = head.junction_point();    
    auto oresult = solver.optimize_max(
        [this, hjp, r_back](double plr, double azm) {
            Vec3d n = spheric_to_dir(plr, azm).normalized();
            return bridge_mesh_distance(hjp, n, r_back);
        },
        initvals(polar, azimuth),  // let's start with what we have
        bound(3*PI/4, PI),  // Must not exceed the slope limit
        bound(-PI, PI)      // azimuth can be a full range search
        );
    
    Vec3d bridgedir = spheric_to_dir(oresult.optimum).normalized();
    return connect_to_ground(head, bridgedir);
}

bool SupportTreeBuildsteps::connect_to_model_body(Head &head)
{
    if (head.id <= SupportTreeNode::ID_UNSET) return false;
    
    auto it = m_head_to_ground_scans.find(unsigned(head.id));
    if (it == m_head_to_ground_scans.end()) return false;
    
    auto &hit = it->second;

    if (!hit.is_hit()) {
        // TODO scan for potential anchor points on model surface
        return false;
    }

    Vec3d hjp = head.junction_point();
    double zangle = std::asin(hit.direction()(Z));
    zangle = std::max(zangle, PI/4);
    double h = std::sin(zangle) * head.fullwidth();

    // The width of the tail head that we would like to have...
    h = std::min(hit.distance() - head.r_back_mm, h);
    
    if(h <= 0.) return false;
    
    Vec3d endp{hjp(X), hjp(Y), hjp(Z) - hit.distance() + h};
    auto center_hit = m_mesh.query_ray_hit(hjp, DOWN);

    double hitdiff = center_hit.distance() - hit.distance();
    Vec3d hitp = std::abs(hitdiff) < 2*head.r_back_mm?
                     center_hit.position() : hit.position();

    long pillar_id = m_builder.add_pillar(head.id, hjp.z() - endp.z());
    Pillar &pill = m_builder.pillar(pillar_id);

    Vec3d taildir = endp - hitp;
    double dist = (hitp - endp).norm() + m_cfg.head_penetration_mm;
    double w = dist - 2 * head.r_pin_mm - head.r_back_mm;

    if (w < 0.) {
        BOOST_LOG_TRIVIAL(error) << "Pinhead width is negative!";
        w = 0.;
    }

    m_builder.add_anchor(head.r_back_mm, head.r_pin_mm, w,
                         m_cfg.head_penetration_mm, taildir, hitp);

    m_pillar_index.guarded_insert(pill.endpoint(), pill.id);
    
    return true;
}

bool SupportTreeBuildsteps::search_pillar_and_connect(const Head &source)
{
    // Hope that a local copy takes less time than the whole search loop.
    // We also need to remove elements progressively from the copied index.
    PointIndex spindex = m_pillar_index.guarded_clone();

    long nearest_id = SupportTreeNode::ID_UNSET;

    Vec3d querypt = source.junction_point();

    while(nearest_id < 0 && !spindex.empty()) { m_thr();
        // loop until a suitable head is not found
        // if there is a pillar closer than the cluster center
        // (this may happen as the clustering is not perfect)
        // than we will bridge to this closer pillar

        Vec3d qp(querypt(X), querypt(Y), m_builder.ground_level);
        auto qres = spindex.nearest(qp, 1);
        if(qres.empty()) break;

        auto ne = qres.front();
        nearest_id = ne.second;

        if(nearest_id >= 0) {
            if (size_t(nearest_id) < m_builder.pillarcount()) {
                if(!connect_to_nearpillar(source, nearest_id) ||
                    m_builder.pillar(nearest_id).r < source.r_back_mm) {
                    nearest_id = SupportTreeNode::ID_UNSET;    // continue searching
                    spindex.remove(ne);       // without the current pillar
                }
            }
        }
    }

    return nearest_id >= 0;
}

void SupportTreeBuildsteps::routing_to_model()
{   
    // We need to check if there is an easy way out to the bed surface.
    // If it can be routed there with a bridge shorter than
    // min_bridge_distance.

    ccr::enumerate(m_iheads_onmodel.begin(), m_iheads_onmodel.end(),
                   [this] (const unsigned idx, size_t) {
        m_thr();
        
        auto& head = m_builder.head(idx);
        
        // Search nearby pillar
        if (search_pillar_and_connect(head)) { return; }
        
        // Cannot connect to nearby pillar. We will try to search for
        // a route to the ground.
        if (connect_to_ground(head)) { return; }
        
        // No route to the ground, so connect to the model body as a last resort
        if (connect_to_model_body(head)) { return; }
        
        // We have failed to route this head.
        BOOST_LOG_TRIVIAL(warning)
                << "Failed to route model facing support point. ID: " << idx;
        
        head.invalidate();
    });
}

void SupportTreeBuildsteps::interconnect_pillars()
{
    // Now comes the algorithm that connects pillars with each other.
    // Ideally every pillar should be connected with at least one of its
    // neighbors if that neighbor is within max_pillar_link_distance
    
    // Pillars with height exceeding H1 will require at least one neighbor
    // to connect with. Height exceeding H2 require two neighbors.
    double H1 = m_cfg.max_solo_pillar_height_mm;
    double H2 = m_cfg.max_dual_pillar_height_mm;
    double d = m_cfg.max_pillar_link_distance_mm;
    
    //A connection between two pillars only counts if the height ratio is
    // bigger than 50%
    double min_height_ratio = 0.5;
    
    std::set<unsigned long> pairs;
    
    // A function to connect one pillar with its neighbors. THe number of
    // neighbors is given in the configuration. This function if called
    // for every pillar in the pillar index. A pair of pillar will not
    // be connected multiple times this is ensured by the 'pairs' set which
    // remembers the processed pillar pairs
    auto cascadefn =
        [this, d, &pairs, min_height_ratio, H1] (const PointIndexEl& el)
    {
        Vec3d qp = el.first;    // endpoint of the pillar
        
        const Pillar& pillar = m_builder.pillar(el.second); // actual pillar
        
        // Get the max number of neighbors a pillar should connect to
        unsigned neighbors = m_cfg.pillar_cascade_neighbors;
        
        // connections are already enough for the pillar
        if(pillar.links >= neighbors) return;
        
        double max_d = d * pillar.r / m_cfg.head_back_radius_mm;
        // Query all remaining points within reach
        auto qres = m_pillar_index.query([qp, max_d](const PointIndexEl& e){
            return distance(e.first, qp) < max_d;
        });
        
        // sort the result by distance (have to check if this is needed)
        std::sort(qres.begin(), qres.end(),
                  [qp](const PointIndexEl& e1, const PointIndexEl& e2){
                      return distance(e1.first, qp) < distance(e2.first, qp);
                  });
        
        for(auto& re : qres) { // process the queried neighbors
            
            if(re.second == el.second) continue; // Skip self
            
            auto a = el.second, b = re.second;
            
            // Get unique hash for the given pair (order doesn't matter)
            auto hashval = pairhash(a, b);
            
            // Search for the pair amongst the remembered pairs
            if(pairs.find(hashval) != pairs.end()) continue;
            
            const Pillar& neighborpillar = m_builder.pillar(re.second);
            
            // this neighbor is occupied, skip
            if (neighborpillar.links >= neighbors) continue;
            if (neighborpillar.r < pillar.r) continue;
            
            if(interconnect(pillar, neighborpillar)) {
                pairs.insert(hashval);
                
                // If the interconnection length between the two pillars is
                // less than 50% of the longer pillar's height, don't count
                if(pillar.height < H1 ||
                    neighborpillar.height / pillar.height > min_height_ratio)
                    m_builder.increment_links(pillar);
                
                if(neighborpillar.height < H1 ||
                    pillar.height / neighborpillar.height > min_height_ratio)
                    m_builder.increment_links(neighborpillar);
                
            }
            
            // connections are enough for one pillar
            if(pillar.links >= neighbors) break;
        }
    };
    
    // Run the cascade for the pillars in the index
    m_pillar_index.foreach(cascadefn);
    
    // We would be done here if we could allow some pillars to not be
    // connected with any neighbors. But this might leave the support tree
    // unprintable.
    //
    // The current solution is to insert additional pillars next to these
    // lonely pillars. One or even two additional pillar might get inserted
    // depending on the length of the lonely pillar.
    
    size_t pillarcount = m_builder.pillarcount();
    
    // Again, go through all pillars, this time in the whole support tree
    // not just the index.
    for(size_t pid = 0; pid < pillarcount; pid++) {
        auto pillar = [this, pid]() { return m_builder.pillar(pid); };
        
        // Decide how many additional pillars will be needed:
        
        unsigned needpillars = 0;
        if (pillar().bridges > m_cfg.max_bridges_on_pillar)
            needpillars = 3;
        else if (pillar().links < 2 && pillar().height > H2) {
            // Not enough neighbors to support this pillar
            needpillars = 2;
        } else if (pillar().links < 1 && pillar().height > H1) {
            // No neighbors could be found and the pillar is too long.
            needpillars = 1;
        }
        
        needpillars = std::max(pillar().links, needpillars) - pillar().links;
        if (needpillars == 0) continue;
        
        // Search for new pillar locations:
        
        bool   found    = false;
        double alpha    = 0; // goes to 2Pi
        double r        = 2 * m_cfg.base_radius_mm;
        Vec3d  pillarsp = pillar().startpoint();
        
        // temp value for starting point detection
        Vec3d sp(pillarsp(X), pillarsp(Y), pillarsp(Z) - r);
        
        // A vector of bool for placement feasbility
        std::vector<bool>  canplace(needpillars, false);
        std::vector<Vec3d> spts(needpillars); // vector of starting points
        
        double gnd      = m_builder.ground_level;
        double min_dist = m_cfg.pillar_base_safety_distance_mm +
                          m_cfg.base_radius_mm + EPSILON;
        
        while(!found && alpha < 2*PI) {
            for (unsigned n = 0;
                 n < needpillars && (!n || canplace[n - 1]);
                 n++)
            {
                double a = alpha + n * PI / 3;
                Vec3d  s = sp;
                s(X) += std::cos(a) * r;
                s(Y) += std::sin(a) * r;
                spts[n] = s;
                
                // Check the path vertically down
                Vec3d check_from = s + Vec3d{0., 0., pillar().r};
                auto hr = bridge_mesh_intersect(check_from, DOWN, pillar().r);
                Vec3d gndsp{s(X), s(Y), gnd};
                
                // If the path is clear, check for pillar base collisions
                canplace[n] = std::isinf(hr.distance()) &&
                              std::sqrt(m_mesh.squared_distance(gndsp)) >
                                  min_dist;
            }
            
            found = std::all_of(canplace.begin(), canplace.end(),
                                [](bool v) { return v; });
            
            // 20 angles will be tried...
            alpha += 0.1 * PI;
        }
        
        std::vector<long> newpills;
        newpills.reserve(needpillars);

        if (found)
            for (unsigned n = 0; n < needpillars; n++) {
                Vec3d s = spts[n];
                Pillar p(Vec3d{s.x(), s.y(), gnd}, s.z() - gnd, pillar().r);

                if (interconnect(pillar(), p)) {
                    Pillar &pp = m_builder.pillar(m_builder.add_pillar(p));

                    add_pillar_base(pp.id);

                    m_pillar_index.insert(pp.endpoint(), unsigned(pp.id));

                    m_builder.add_junction(s, pillar().r);
                    double t = bridge_mesh_distance(pillarsp, dirv(pillarsp, s),
                                                    pillar().r);
                    if (distance(pillarsp, s) < t)
                        m_builder.add_bridge(pillarsp, s, pillar().r);

                    if (pillar().endpoint()(Z) > m_builder.ground_level)
                        m_builder.add_junction(pillar().endpoint(),
                                               pillar().r);

                    newpills.emplace_back(pp.id);
                    m_builder.increment_links(pillar());
                    m_builder.increment_links(pp);
                }
            }

        if(!newpills.empty()) {
            for(auto it = newpills.begin(), nx = std::next(it);
                 nx != newpills.end(); ++it, ++nx) {
                const Pillar& itpll = m_builder.pillar(*it);
                const Pillar& nxpll = m_builder.pillar(*nx);
                if(interconnect(itpll, nxpll)) {
                    m_builder.increment_links(itpll);
                    m_builder.increment_links(nxpll);
                }
            }
            
            m_pillar_index.foreach(cascadefn);
        }
    }
}

}} // namespace Slic3r::sla