///|/ Copyright (c) Prusa Research 2019 - 2023 Enrico Turri @enricoturri1966, Oleksandra Iushchenko @YuSanka, Vojtěch Bubník @bubnikv, Tomáš Mészáros @tamasmeszaros, Lukáš Matěna @lukasmatena, Filip Sykala @Jony01
///|/
///|/ PrusaSlicer is released under the terms of the AGPLv3 or higher
///|/
#include "libslic3r/libslic3r.h"
#include "Selection.hpp"

#include "3DScene.hpp"
#include "GLCanvas3D.hpp"
#include "GUI_App.hpp"
#include "GUI.hpp"
#include "GUI_ObjectManipulation.hpp"
#include "GUI_ObjectList.hpp"
#include "Camera.hpp"
#include "Plater.hpp"
#include "MsgDialog.hpp"

#include "Gizmos/GLGizmoBase.hpp"

#include "slic3r/Utils/UndoRedo.hpp"

#include <LocalesUtils.hpp>
#include "libslic3r/Model.hpp"
#include "libslic3r/PresetBundle.hpp"
#include "libslic3r/BuildVolume.hpp"

#include <GL/glew.h>

#include <boost/algorithm/string/predicate.hpp>
#include <boost/log/trivial.hpp>

#include <CGAL/Simple_cartesian.h>
#include <CGAL/Min_sphere_of_spheres_d.h>
#include <CGAL/Min_sphere_of_points_d_traits_3.h>

static const Slic3r::ColorRGBA UNIFORM_SCALE_COLOR     = Slic3r::ColorRGBA::ORANGE();
static const Slic3r::ColorRGBA SOLID_PLANE_COLOR       = Slic3r::ColorRGBA::ORANGE();
static const Slic3r::ColorRGBA TRANSPARENT_PLANE_COLOR = { 0.8f, 0.8f, 0.8f, 0.5f };

namespace Slic3r {
namespace GUI {

Selection::VolumeCache::VolumeCache(const Geometry::Transformation& volume_transform, const Geometry::Transformation& instance_transform)
    : m_volume(volume_transform)
    , m_instance(instance_transform)
{
}

bool Selection::Clipboard::is_sla_compliant() const
{
//    if (m_mode == Selection::Volume)
//        return false;

//    for (const ModelObject* o : m_model->objects) {
//        if (o->is_multiparts())
//            return false;

//        for (const ModelVolume* v : o->volumes) {
//            if (v->is_modifier())
//                return false;
//        }
//    }

    return true;
}

Selection::Clipboard::Clipboard()
{
    m_model.reset(new Model);
}

void Selection::Clipboard::reset()
{
    m_model->clear_objects();
}

bool Selection::Clipboard::is_empty() const
{
    return m_model->objects.empty();
}

ModelObject* Selection::Clipboard::add_object()
{
    return m_model->add_object();
}

ModelObject* Selection::Clipboard::get_object(unsigned int id)
{
    return (id < (unsigned int)m_model->objects.size()) ? m_model->objects[id] : nullptr;
}

const ModelObjectPtrs& Selection::Clipboard::get_objects() const
{
    return m_model->objects;
}

Selection::Selection()
    : m_volumes(nullptr)
    , m_model(nullptr)
    , m_enabled(false)
    , m_mode(Instance)
    , m_type(Empty)
    , m_valid(false)
    , m_scale_factor(1.0f)
{
    this->set_bounding_boxes_dirty();
    m_axes.set_stem_radius(0.5f);
    m_axes.set_stem_length(20.0f);
    m_axes.set_tip_radius(1.5f);
    m_axes.set_tip_length(5.0f);
}


void Selection::set_volumes(GLVolumePtrs* volumes)
{
    m_volumes = volumes;
    update_valid();
}

// Init shall be called from the OpenGL render function, so that the OpenGL context is initialized!
bool Selection::init()
{
    m_arrow.init_from(straight_arrow(10.0f, 5.0f, 5.0f, 10.0f, 1.0f));
    m_curved_arrow.init_from(circular_arrow(16, 10.0f, 5.0f, 10.0f, 5.0f, 1.0f));
#if ENABLE_RENDER_SELECTION_CENTER
    m_vbo_sphere.init_from(its_make_sphere(0.75, PI / 12.0));
#endif // ENABLE_RENDER_SELECTION_CENTER

    return true;
}

void Selection::set_model(Model* model)
{
    m_model = model;
    update_valid();
}

void Selection::add(unsigned int volume_idx, bool as_single_selection, bool check_for_already_contained)
{
    if (!m_valid || (unsigned int)m_volumes->size() <= volume_idx)
        return;

    const GLVolume* volume = (*m_volumes)[volume_idx];

    if (wxGetApp().plater()->printer_technology() == ptSLA && volume->is_modifier &&
        m_model->objects[volume->object_idx()]->volumes[volume->volume_idx()]->is_modifier())
        return;

    // wipe tower is already selected
    if (is_wipe_tower() && volume->is_wipe_tower)
        return;

    bool keep_instance_mode = (m_mode == Instance) && !as_single_selection;
    bool already_contained = check_for_already_contained && contains_volume(volume_idx);

    // resets the current list if needed
    bool needs_reset = as_single_selection && !already_contained;
    needs_reset |= volume->is_wipe_tower;
    needs_reset |= is_wipe_tower() && !volume->is_wipe_tower;
    needs_reset |= as_single_selection && !is_any_modifier() && volume->is_modifier;
    needs_reset |= is_any_modifier() && !volume->is_modifier;

    if (!already_contained || needs_reset) {
        wxGetApp().plater()->take_snapshot(_L("Selection-Add"), UndoRedo::SnapshotType::Selection);

        if (needs_reset)
            clear();

        if (!keep_instance_mode)
            m_mode = volume->is_modifier ? Volume : Instance;
    }
    else
      // keep current mode
      return;

    switch (m_mode)
    {
    case Volume:
    {
        if (volume->volume_idx() >= 0 && (is_empty() || volume->instance_idx() == get_instance_idx()))
            do_add_volume(volume_idx);

        break;
    }
    case Instance:
    {
        Plater::SuppressSnapshots suppress(wxGetApp().plater());
        add_instance(volume->object_idx(), volume->instance_idx(), as_single_selection);
        break;
    }
    }

    update_type();
    this->set_bounding_boxes_dirty();
}

void Selection::remove(unsigned int volume_idx)
{
    if (!m_valid || (unsigned int)m_volumes->size() <= volume_idx)
        return;

    if (!contains_volume(volume_idx))
        return;

    wxGetApp().plater()->take_snapshot(_L("Selection-Remove"), UndoRedo::SnapshotType::Selection);

    GLVolume* volume = (*m_volumes)[volume_idx];

    switch (m_mode)
    {
    case Volume:
    {
        do_remove_volume(volume_idx);
        break;
    }
    case Instance:
    {
        do_remove_instance(volume->object_idx(), volume->instance_idx());
        break;
    }
    }

    update_type();
    this->set_bounding_boxes_dirty();
}

void Selection::add_object(unsigned int object_idx, bool as_single_selection)
{
    if (!m_valid)
        return;

    std::vector<unsigned int> volume_idxs = get_volume_idxs_from_object(object_idx);
    if ((!as_single_selection && contains_all_volumes(volume_idxs)) ||
        (as_single_selection && matches(volume_idxs)))
        return;

    wxGetApp().plater()->take_snapshot(_L("Selection-Add Object"), UndoRedo::SnapshotType::Selection);

    // resets the current list if needed
    if (as_single_selection)
        clear();

    m_mode = Instance;

    do_add_volumes(volume_idxs);

    update_type();
    this->set_bounding_boxes_dirty();
}

void Selection::remove_object(unsigned int object_idx)
{
    if (!m_valid)
        return;

    wxGetApp().plater()->take_snapshot(_L("Selection-Remove Object"), UndoRedo::SnapshotType::Selection);

    do_remove_object(object_idx);

    update_type();
    this->set_bounding_boxes_dirty();
}

void Selection::add_instance(unsigned int object_idx, unsigned int instance_idx, bool as_single_selection)
{
    if (!m_valid)
        return;

    const std::vector<unsigned int> volume_idxs = get_volume_idxs_from_instance(object_idx, instance_idx);
    if ((!as_single_selection && contains_all_volumes(volume_idxs)) ||
        (as_single_selection && matches(volume_idxs)))
        return;

    wxGetApp().plater()->take_snapshot(_L("Selection-Add Instance"), UndoRedo::SnapshotType::Selection);

    // resets the current list if needed
    if (as_single_selection)
        clear();

    m_mode = Instance;

    do_add_volumes(volume_idxs);

    update_type();
    this->set_bounding_boxes_dirty();
}

void Selection::remove_instance(unsigned int object_idx, unsigned int instance_idx)
{
    if (!m_valid)
        return;

    wxGetApp().plater()->take_snapshot(_L("Selection-Remove Instance"), UndoRedo::SnapshotType::Selection);

    do_remove_instance(object_idx, instance_idx);

    update_type();
    this->set_bounding_boxes_dirty();
}

void Selection::add_volume(unsigned int object_idx, unsigned int volume_idx, int instance_idx, bool as_single_selection)
{
    if (!m_valid)
        return;

    std::vector<unsigned int> volume_idxs = get_volume_idxs_from_volume(object_idx, instance_idx, volume_idx);
    if ((!as_single_selection && contains_all_volumes(volume_idxs)) ||
        (as_single_selection && matches(volume_idxs)))
        return;

    // resets the current list if needed
    if (as_single_selection)
        clear();

    m_mode = Volume;

    do_add_volumes(volume_idxs);

    update_type();
    this->set_bounding_boxes_dirty();
}

void Selection::remove_volume(unsigned int object_idx, unsigned int volume_idx)
{
    if (!m_valid)
        return;

    for (unsigned int i = 0; i < (unsigned int)m_volumes->size(); ++i) {
        GLVolume* v = (*m_volumes)[i];
        if (v->object_idx() == (int)object_idx && v->volume_idx() == (int)volume_idx)
            do_remove_volume(i);
    }

    update_type();
    this->set_bounding_boxes_dirty();
}

void Selection::add_volumes(EMode mode, const std::vector<unsigned int>& volume_idxs, bool as_single_selection)
{
    if (!m_valid)
        return;

    if ((!as_single_selection && contains_all_volumes(volume_idxs)) ||
        (as_single_selection && matches(volume_idxs)))
        return;

    // resets the current list if needed
    if (as_single_selection)
        clear();

    m_mode = mode;
    for (unsigned int i : volume_idxs) {
        if (i < (unsigned int)m_volumes->size())
            do_add_volume(i);
    }

    update_type();
    this->set_bounding_boxes_dirty();
}

void Selection::remove_volumes(EMode mode, const std::vector<unsigned int>& volume_idxs)
{
    if (!m_valid)
        return;

    m_mode = mode;
    for (unsigned int i : volume_idxs) {
        if (i < (unsigned int)m_volumes->size())
            do_remove_volume(i);
    }

    update_type();
    this->set_bounding_boxes_dirty();
}

void Selection::add_all()
{
    if (!m_valid)
        return;

    unsigned int count = 0;
    for (unsigned int i = 0; i < (unsigned int)m_volumes->size(); ++i) {
        if (!(*m_volumes)[i]->is_wipe_tower)
            ++count;
    }

    if ((unsigned int)m_list.size() == count)
        return;
    
    wxGetApp().plater()->take_snapshot(_(L("Selection-Add All")), UndoRedo::SnapshotType::Selection);

    m_mode = Instance;
    clear();

    for (unsigned int i = 0; i < (unsigned int)m_volumes->size(); ++i) {
        if (!(*m_volumes)[i]->is_wipe_tower)
            do_add_volume(i);
    }

    update_type();
    this->set_bounding_boxes_dirty();
}

void Selection::remove_all()
{
    if (!m_valid)
        return;

    if (is_empty())
        return;
  
// Not taking the snapshot with non-empty Redo stack will likely be more confusing than losing the Redo stack.
// Let's wait for user feedback.
//    if (!wxGetApp().plater()->can_redo())
        wxGetApp().plater()->take_snapshot(_L("Selection-Remove All"), UndoRedo::SnapshotType::Selection);

    m_mode = Instance;
    clear();
}

void Selection::set_deserialized(EMode mode, const std::vector<std::pair<size_t, size_t>> &volumes_and_instances)
{
    if (! m_valid)
        return;

    m_mode = mode;
    for (unsigned int i : m_list)
        (*m_volumes)[i]->selected = false;
    m_list.clear();
    for (unsigned int i = 0; i < (unsigned int)m_volumes->size(); ++ i)
		if (std::binary_search(volumes_and_instances.begin(), volumes_and_instances.end(), (*m_volumes)[i]->geometry_id))
			do_add_volume(i);
    update_type();
    set_bounding_boxes_dirty();
}

void Selection::clear()
{
    if (!m_valid)
        return;

    if (m_list.empty())
        return;

    // ensure that the volumes get the proper color before next call to render (expecially needed for transparent volumes)
    for (unsigned int i : m_list) {
        GLVolume& volume = *(*m_volumes)[i];
        volume.selected = false;
        volume.set_render_color(volume.color.is_transparent());
    }

    m_list.clear();

    update_type();
    set_bounding_boxes_dirty();

    // this happens while the application is closing
    if (wxGetApp().obj_manipul() == nullptr)
        return;

    // resets the cache in the sidebar
    wxGetApp().obj_manipul()->reset_cache();

    // #et_FIXME fake KillFocus from sidebar
    wxGetApp().plater()->canvas3D()->handle_sidebar_focus_event("", false);
}

// Update the selection based on the new instance IDs.
void Selection::instances_changed(const std::vector<size_t> &instance_ids_selected)
{
    assert(m_valid);
    assert(m_mode == Instance);
    m_list.clear();

    const PrinterTechnology pt = wxGetApp().plater()->printer_technology();

    for (unsigned int volume_idx = 0; volume_idx < (unsigned int)m_volumes->size(); ++ volume_idx) {
        const GLVolume *volume = (*m_volumes)[volume_idx];
        if (pt == ptSLA && volume->is_modifier &&
            m_model->objects[volume->object_idx()]->volumes[volume->volume_idx()]->is_modifier())
            continue;
        auto it = std::lower_bound(instance_ids_selected.begin(), instance_ids_selected.end(), volume->geometry_id.second);
		if (it != instance_ids_selected.end() && *it == volume->geometry_id.second)
            this->do_add_volume(volume_idx);
    }
    update_type();
    this->set_bounding_boxes_dirty();
}

// Update the selection based on the map from old indices to new indices after m_volumes changed.
// If the current selection is by instance, this call may select newly added volumes, if they belong to already selected instances.
void Selection::volumes_changed(const std::vector<size_t> &map_volume_old_to_new)
{
    assert(m_valid);
    assert(m_mode == Volume);
    IndicesList list_new;
    for (unsigned int idx : m_list)
        if (map_volume_old_to_new[idx] != size_t(-1)) {
            unsigned int new_idx = (unsigned int)map_volume_old_to_new[idx];
            (*m_volumes)[new_idx]->selected = true;
            list_new.insert(new_idx);
        }
    m_list = std::move(list_new);
    update_type();
    this->set_bounding_boxes_dirty();
}

bool Selection::is_any_connector() const
{
    const int obj_idx = get_object_idx();

    if ((is_any_volume() || is_any_modifier() || is_mixed()) && // some solid_part AND/OR modifier is selected 
        obj_idx >= 0 && m_model->objects[obj_idx]->is_cut()) {
        const ModelVolumePtrs& obj_volumes = m_model->objects[obj_idx]->volumes;
        for (size_t vol_idx = 0; vol_idx < obj_volumes.size(); vol_idx++)
            if (obj_volumes[vol_idx]->is_cut_connector())
                for (const GLVolume* v  : *m_volumes)
                    if (v->object_idx() == obj_idx && v->volume_idx() == (int)vol_idx && v->selected)
                        return true;
    }
    return false;
}

bool Selection::is_any_cut_volume() const
{
    const int obj_idx = get_object_idx();
    return is_any_volume() && obj_idx >= 0 && m_model->objects[obj_idx]->is_cut();
}

bool Selection::is_single_full_instance() const
{
    if (m_type == SingleFullInstance)
        return true;

    if (m_type == SingleFullObject)
        return get_instance_idx() != -1;

    if (m_list.empty() || m_volumes->empty())
        return false;

    int object_idx = m_valid ? get_object_idx() : -1;
    if (object_idx < 0 || (int)m_model->objects.size() <= object_idx)
        return false;

    int instance_idx = (*m_volumes)[*m_list.begin()]->instance_idx();

    std::set<int> volumes_idxs;
    for (unsigned int i : m_list) {
        const GLVolume* v = (*m_volumes)[i];
        if (object_idx != v->object_idx() || instance_idx != v->instance_idx())
            return false;

        int volume_idx = v->volume_idx();
        if (volume_idx >= 0)
            volumes_idxs.insert(volume_idx);
    }

    return m_model->objects[object_idx]->volumes.size() == volumes_idxs.size();
}

bool Selection::is_from_single_object() const
{
    const int idx = get_object_idx();
    return 0 <= idx && idx < int(m_model->objects.size());
}

bool Selection::is_sla_compliant() const
{
//    if (m_mode == Volume)
//        return false;

//    for (unsigned int i : m_list) {
//        if ((*m_volumes)[i]->is_modifier)
//            return false;
//    }

    return true;
}

bool Selection::is_single_text() const
{
    if (!is_single_volume_or_modifier())
      return false;

    const GLVolume* gl_volume = (*m_volumes)[*m_list.begin()];
    const ModelVolume* model_volume = m_model->objects[gl_volume->object_idx()]->volumes[gl_volume->volume_idx()];
    
    return model_volume && model_volume->text_configuration.has_value();
}

bool Selection::contains_all_volumes(const std::vector<unsigned int>& volume_idxs) const
{
    for (unsigned int i : volume_idxs) {
        if (m_list.find(i) == m_list.end())
            return false;
    }

    return true;
}

bool Selection::contains_any_volume(const std::vector<unsigned int>& volume_idxs) const
{
    for (unsigned int i : volume_idxs) {
        if (m_list.find(i) != m_list.end())
            return true;
    }

    return false;
}

bool Selection::contains_sinking_volumes(bool ignore_modifiers) const
{
    for (const GLVolume* v : *m_volumes) {
        if (!ignore_modifiers || !v->is_modifier) {
            if (v->is_sinking())
                return true;
        }
    }
    return false;
}

bool Selection::matches(const std::vector<unsigned int>& volume_idxs) const
{
    unsigned int count = 0;

    for (unsigned int i : volume_idxs) {
        if (m_list.find(i) != m_list.end())
            ++count;
        else
            return false;
    }

    return count == (unsigned int)m_list.size();
}

int Selection::get_object_idx() const
{
    return (m_cache.content.size() == 1) ? m_cache.content.begin()->first : -1;
}

int Selection::get_instance_idx() const
{
    if (m_cache.content.size() == 1) {
        const InstanceIdxsList& idxs = m_cache.content.begin()->second;
        if (idxs.size() == 1)
            return *idxs.begin();
    }

    return -1;
}

const Selection::InstanceIdxsList& Selection::get_instance_idxs() const
{
    assert(m_cache.content.size() == 1);
    return m_cache.content.begin()->second;
}

const GLVolume* Selection::get_volume(unsigned int volume_idx) const
{
    return (m_valid && (volume_idx < (unsigned int)m_volumes->size())) ? (*m_volumes)[volume_idx] : nullptr;
}

GLVolume* Selection::get_volume(unsigned int volume_idx)
{
    return (m_valid && (volume_idx < (unsigned int)m_volumes->size())) ? (*m_volumes)[volume_idx] : nullptr;
}

const BoundingBoxf3& Selection::get_bounding_box() const
{
    if (!m_bounding_box.has_value()) {
        std::optional<BoundingBoxf3>* bbox = const_cast<std::optional<BoundingBoxf3>*>(&m_bounding_box);
        *bbox = BoundingBoxf3();
        if (m_valid) {
            for (unsigned int i : m_list) {
                (*bbox)->merge((*m_volumes)[i]->transformed_convex_hull_bounding_box());
            }
        }
    }
    return *m_bounding_box;
}

const BoundingBoxf3& Selection::get_unscaled_instance_bounding_box() const
{
    assert(is_single_full_instance());

    if (!m_unscaled_instance_bounding_box.has_value()) {
        std::optional<BoundingBoxf3>* bbox = const_cast<std::optional<BoundingBoxf3>*>(&m_unscaled_instance_bounding_box);
        *bbox = BoundingBoxf3();
        if (m_valid) {
            for (unsigned int i : m_list) {
                const GLVolume& volume = *(*m_volumes)[i];
                if (volume.is_modifier)
                    continue;
                Transform3d trafo = volume.get_instance_transformation().get_matrix_no_scaling_factor() * volume.get_volume_transformation().get_matrix();
                trafo.translation().z() += volume.get_sla_shift_z();
                (*bbox)->merge(volume.transformed_convex_hull_bounding_box(trafo));
            }
        }
    }
    return *m_unscaled_instance_bounding_box;
}

const BoundingBoxf3& Selection::get_scaled_instance_bounding_box() const
{
    assert(is_single_full_instance());

    if (!m_scaled_instance_bounding_box.has_value()) {
        std::optional<BoundingBoxf3>* bbox = const_cast<std::optional<BoundingBoxf3>*>(&m_scaled_instance_bounding_box);
        *bbox = BoundingBoxf3();
        if (m_valid) {
            for (unsigned int i : m_list) {
                const GLVolume& volume = *(*m_volumes)[i];
                if (volume.is_modifier)
                    continue;
                Transform3d trafo = volume.get_instance_transformation().get_matrix() * volume.get_volume_transformation().get_matrix();
                trafo.translation().z() += volume.get_sla_shift_z();
                (*bbox)->merge(volume.transformed_convex_hull_bounding_box(trafo));
            }
        }
    }
    return *m_scaled_instance_bounding_box;
}

const BoundingBoxf3& Selection::get_full_unscaled_instance_bounding_box() const
{
    assert(is_single_full_instance());

    if (!m_full_unscaled_instance_bounding_box.has_value()) {
        std::optional<BoundingBoxf3>* bbox = const_cast<std::optional<BoundingBoxf3>*>(&m_full_unscaled_instance_bounding_box);
        *bbox = BoundingBoxf3();
        if (m_valid) {
            for (unsigned int i : m_list) {
                const GLVolume& volume = *(*m_volumes)[i];
                Transform3d trafo = volume.get_instance_transformation().get_matrix_no_scaling_factor() * volume.get_volume_transformation().get_matrix();
                trafo.translation().z() += volume.get_sla_shift_z();
                (*bbox)->merge(volume.transformed_convex_hull_bounding_box(trafo));
            }
        }
    }
    return *m_full_unscaled_instance_bounding_box;
}

const BoundingBoxf3& Selection::get_full_scaled_instance_bounding_box() const
{
    assert(is_single_full_instance());

    if (!m_full_scaled_instance_bounding_box.has_value()) {
        std::optional<BoundingBoxf3>* bbox = const_cast<std::optional<BoundingBoxf3>*>(&m_full_scaled_instance_bounding_box);
        *bbox = BoundingBoxf3();
        if (m_valid) {
            for (unsigned int i : m_list) {
                const GLVolume& volume = *(*m_volumes)[i];
                Transform3d trafo = volume.get_instance_transformation().get_matrix() * volume.get_volume_transformation().get_matrix();
                trafo.translation().z() += volume.get_sla_shift_z();
                (*bbox)->merge(volume.transformed_convex_hull_bounding_box(trafo));
            }
        }
    }
    return *m_full_scaled_instance_bounding_box;
}

const BoundingBoxf3& Selection::get_full_unscaled_instance_local_bounding_box() const
{
    assert(is_single_full_instance());

    if (!m_full_unscaled_instance_local_bounding_box.has_value()) {
        std::optional<BoundingBoxf3>* bbox = const_cast<std::optional<BoundingBoxf3>*>(&m_full_unscaled_instance_local_bounding_box);
        *bbox = BoundingBoxf3();
        if (m_valid) {
            for (unsigned int i : m_list) {
                const GLVolume& volume = *(*m_volumes)[i];
                Transform3d trafo = volume.get_volume_transformation().get_matrix();
                trafo.translation().z() += volume.get_sla_shift_z();
                (*bbox)->merge(volume.transformed_convex_hull_bounding_box(trafo));
            }
        }
    }
    return *m_full_unscaled_instance_local_bounding_box;
}

const std::pair<BoundingBoxf3, Transform3d>& Selection::get_bounding_box_in_current_reference_system() const
{
    static int last_coordinates_type = -1;

    assert(!is_empty());

    ECoordinatesType coordinates_type = wxGetApp().obj_manipul()->get_coordinates_type();
    if (m_mode == Instance && coordinates_type == ECoordinatesType::Local)
        coordinates_type = ECoordinatesType::World;

    if (last_coordinates_type != int(coordinates_type))
        const_cast<std::optional<std::pair<BoundingBoxf3, Transform3d>>*>(&m_bounding_box_in_current_reference_system)->reset();

    if (!m_bounding_box_in_current_reference_system.has_value()) {
        last_coordinates_type = int(coordinates_type);
        *const_cast<std::optional<std::pair<BoundingBoxf3, Transform3d>>*>(&m_bounding_box_in_current_reference_system) = get_bounding_box_in_reference_system(coordinates_type);
    }

    return *m_bounding_box_in_current_reference_system;
}

std::pair<BoundingBoxf3, Transform3d> Selection::get_bounding_box_in_reference_system(ECoordinatesType type) const
{
    //
    // trafo to current reference system
    //
    Transform3d trafo;
    switch (type)
    {
    case ECoordinatesType::World:    { trafo = Transform3d::Identity(); break; }
    case ECoordinatesType::Instance: { trafo = get_first_volume()->get_instance_transformation().get_matrix(); break; }
    case ECoordinatesType::Local:    { trafo = get_first_volume()->world_matrix(); break; }
    }

    //
    // trafo basis in world coordinates
    //
    Geometry::Transformation t(trafo);
    t.reset_scaling_factor();
    const Transform3d basis_trafo = t.get_matrix_no_offset();
    std::vector<Vec3d> axes = { Vec3d::UnitX(), Vec3d::UnitY(), Vec3d::UnitZ() };
    for (size_t i = 0; i < axes.size(); ++i) {
        axes[i] = basis_trafo * axes[i];
    }

    //
    // calculate bounding box aligned to trafo basis
    //
    Vec3d min = { DBL_MAX, DBL_MAX, DBL_MAX };
    Vec3d max = { -DBL_MAX, -DBL_MAX, -DBL_MAX };
    for (unsigned int id : m_list) {
        const GLVolume& vol = *get_volume(id);
        const Transform3d vol_world_rafo = vol.world_matrix();
        const TriangleMesh* mesh = vol.convex_hull();
        if (mesh == nullptr) {
            // workaround to avoid a crash, see spe-2295 -> Crash when re-cutting with dowel connectors
            const int obj_id = vol.object_idx();
            const int vol_id = vol.volume_idx();
            if (int(m_model->objects[obj_id]->volumes.size()) <= vol_id)
                continue;
            mesh = &m_model->objects[vol.object_idx()]->volumes[vol.volume_idx()]->mesh();
        }
        assert(mesh != nullptr);
        for (const stl_vertex& v : mesh->its.vertices) {
            const Vec3d world_v = vol_world_rafo * v.cast<double>();
            for (int i = 0; i < 3; ++i) {
                const double i_comp = world_v.dot(axes[i]);
                min(i) = std::min(min(i), i_comp);
                max(i) = std::max(max(i), i_comp);
            }
        }
    }

    const Vec3d box_size = max - min;
    Vec3d half_box_size = 0.5 * box_size;
    Geometry::Transformation out_trafo(trafo);
    Vec3d center = 0.5 * (min + max);

    // Fix for non centered volume 
    // by move with calculated center(to volume center) and extend half box size
    // e.g. for right aligned embossed text
    if (m_list.size() == 1 &&
        type == ECoordinatesType::Local) {
        const GLVolume& vol = *get_volume(*m_list.begin());
        const Transform3d vol_world_trafo = vol.world_matrix();
        Vec3d world_zero = vol_world_trafo * Vec3d::Zero();
        for (size_t i = 0; i < 3; i++){
            // move center to local volume zero
            center[i] = world_zero.dot(axes[i]);
            // extend half size to bigger distance from center
            half_box_size[i] = std::max(
                abs(center[i] - min[i]),
                abs(center[i] - max[i]));
        }
    }
    
    const BoundingBoxf3 out_box(-half_box_size, half_box_size);
    out_trafo.set_offset(basis_trafo * center);
    return { out_box, out_trafo.get_matrix_no_scaling_factor() };
}

BoundingBoxf Selection::get_screen_space_bounding_box()
{
    BoundingBoxf ss_box;
    if (!is_empty()) {
        const auto& [box, box_trafo] = get_bounding_box_in_current_reference_system();

        // vertices
        std::vector<Vec3d> vertices = {
            { box.min.x(), box.min.y(), box.min.z() },
            { box.max.x(), box.min.y(), box.min.z() },
            { box.max.x(), box.max.y(), box.min.z() },
            { box.min.x(), box.max.y(), box.min.z() },
            { box.min.x(), box.min.y(), box.max.z() },
            { box.max.x(), box.min.y(), box.max.z() },
            { box.max.x(), box.max.y(), box.max.z() },
            { box.min.x(), box.max.y(), box.max.z() }
        };

        const Camera& camera = wxGetApp().plater()->get_camera();
        const Matrix4d projection_view_matrix = camera.get_projection_matrix().matrix() * camera.get_view_matrix().matrix();
        const std::array<int, 4>& viewport = camera.get_viewport();

        const double half_w = 0.5 * double(viewport[2]);
        const double h = double(viewport[3]);
        const double half_h = 0.5 * h;
        for (const Vec3d& v : vertices) {
            const Vec3d world = box_trafo * v;
            const Vec4d clip = projection_view_matrix * Vec4d(world.x(), world.y(), world.z(), 1.0);
            const Vec3d ndc = Vec3d(clip.x(), clip.y(), clip.z()) / clip.w();
            const Vec2d ss = Vec2d(half_w * ndc.x() + double(viewport[0]) + half_w, h - (half_h * ndc.y() + double(viewport[1]) + half_h));
            ss_box.merge(ss);
        }
    }

    return ss_box;
}

const std::pair<Vec3d, double> Selection::get_bounding_sphere() const
{
    if (!m_bounding_sphere.has_value()) {
        std::optional<std::pair<Vec3d, double>>* sphere = const_cast<std::optional<std::pair<Vec3d, double>>*>(&m_bounding_sphere);
        *sphere = { Vec3d::Zero(), 0.0 };

        using K = CGAL::Simple_cartesian<float>;
        using Traits = CGAL::Min_sphere_of_points_d_traits_3<K, float>;
        using Min_sphere = CGAL::Min_sphere_of_spheres_d<Traits>;
        using Point = K::Point_3;

        std::vector<Point> points;
        if (m_valid) {
            for (unsigned int i : m_list) {
                const GLVolume& volume = *(*m_volumes)[i];
                const TriangleMesh* hull = volume.convex_hull();
                const indexed_triangle_set& its = (hull != nullptr) ?
                    hull->its : m_model->objects[volume.object_idx()]->volumes[volume.volume_idx()]->mesh().its;
                const Transform3f matrix = volume.world_matrix().cast<float>();
                for (const Vec3f& v : its.vertices) {
                    const Vec3f vv = matrix * v;
                    points.push_back(Point(vv.x(), vv.y(), vv.z()));
                }
            }

            Min_sphere ms(points.begin(), points.end());
            const float* center_x = ms.center_cartesian_begin();
            (*sphere)->first = { *center_x, *(center_x + 1), *(center_x + 2) };
            (*sphere)->second = ms.radius();
        }
    }

    return *m_bounding_sphere;
}

void Selection::setup_cache()
{
    if (!m_valid)
        return;

    set_caches();
}

void Selection::translate(const Vec3d& displacement, TransformationType transformation_type)
{
    if (!m_valid)
        return;

    // Emboss use translate in local coordinate
    assert(transformation_type.relative() || 
           transformation_type.local());

    for (unsigned int i : m_list) {
        GLVolume& v = *(*m_volumes)[i];
        const VolumeCache& volume_data = m_cache.volumes_data[i];
        if (m_mode == Instance && !is_wipe_tower()) {
            assert(is_from_fully_selected_instance(i));
            if (transformation_type.instance()) {
                const Geometry::Transformation& inst_trafo = volume_data.get_instance_transform();
                v.set_instance_offset(inst_trafo.get_offset() + inst_trafo.get_rotation_matrix() * displacement);
            }
            else
                transform_instance_relative(v, volume_data, transformation_type, Geometry::translation_transform(displacement), m_cache.dragging_center);
        }
        else {
            if (transformation_type.local() && transformation_type.absolute()) {
                const Geometry::Transformation& vol_trafo = volume_data.get_volume_transform();
                const Geometry::Transformation& inst_trafo = volume_data.get_instance_transform();
                v.set_volume_offset(vol_trafo.get_offset() + inst_trafo.get_scaling_factor_matrix().inverse() * vol_trafo.get_rotation_matrix() * displacement);
            }
            else {
                Vec3d relative_disp = displacement;
                if (transformation_type.world() && transformation_type.instance())
                    relative_disp = volume_data.get_instance_transform().get_scaling_factor_matrix().inverse() * relative_disp;

                transform_volume_relative(v, volume_data, transformation_type, Geometry::translation_transform(relative_disp), m_cache.dragging_center);
            }
        }
    }

#if !DISABLE_INSTANCES_SYNCH
    if (m_mode == Instance)
        synchronize_unselected_instances(SyncRotationType::NONE);
    else if (m_mode == Volume)
        synchronize_unselected_volumes();
#endif // !DISABLE_INSTANCES_SYNCH

    ensure_not_below_bed();
    set_bounding_boxes_dirty();
    wxGetApp().plater()->canvas3D()->requires_check_outside_state();
}

// Rotate an object around one of the axes. Only one rotation component is expected to be changing.
void Selection::rotate(const Vec3d& rotation, TransformationType transformation_type)
{
    if (!m_valid)
        return;

    assert(transformation_type.relative() || (transformation_type.absolute() && transformation_type.local()));

    bool requires_general_synchronization = false;

    for (unsigned int i : m_list) {
        Transform3d rotation_matrix = Geometry::rotation_transform(rotation);
        GLVolume& v = *(*m_volumes)[i];
        const VolumeCache& volume_data = m_cache.volumes_data[i];
        const Geometry::Transformation& inst_trafo = volume_data.get_instance_transform();
        if (m_mode == Instance && !is_wipe_tower()) {
            assert(is_from_fully_selected_instance(i));
            if (transformation_type.instance()) {
                // ensure that the instance rotates as a rigid body
                Transform3d inst_rotation_matrix = inst_trafo.get_rotation_matrix();
                if (inst_trafo.is_left_handed()) {
                    Geometry::TransformationSVD inst_svd(inst_trafo);
                    inst_rotation_matrix = inst_svd.u * inst_svd.v.transpose();
                    // ensure the rotation has the proper direction
                    if (!rotation.normalized().cwiseAbs().isApprox(Vec3d::UnitX()))
                        rotation_matrix = rotation_matrix.inverse();
                }

                const Transform3d inst_matrix_no_offset = inst_trafo.get_matrix_no_offset();
                rotation_matrix = inst_matrix_no_offset.inverse() * inst_rotation_matrix * rotation_matrix * inst_rotation_matrix.inverse() * inst_matrix_no_offset;

                // rotate around selection center
                const Vec3d inst_pivot = inst_trafo.get_matrix_no_offset().inverse() * (m_cache.rotation_pivot - inst_trafo.get_offset());
                rotation_matrix = Geometry::translation_transform(inst_pivot) * rotation_matrix * Geometry::translation_transform(-inst_pivot);

                // Detects if the rotation is equivalent to a world rotation around the Z axis
                // If not, force for a full synchronization of unselected instances
                if (!requires_general_synchronization) {
                    const Geometry::Transformation& vol_trafo = volume_data.get_volume_transform();
                    const Transform3d old_world_rotation_matrix = (inst_trafo * vol_trafo).get_rotation_matrix();
                    const Transform3d new_world_rotation_matrix = (inst_trafo * Geometry::Transformation(rotation_matrix) * vol_trafo).get_rotation_matrix();
                    if (std::abs((old_world_rotation_matrix * Vec3d::UnitX()).z() - (new_world_rotation_matrix * Vec3d::UnitX()).z()) > EPSILON)
                        requires_general_synchronization = true;
                    else if (std::abs((old_world_rotation_matrix * Vec3d::UnitY()).z() - (new_world_rotation_matrix * Vec3d::UnitY()).z()) > EPSILON)
                        requires_general_synchronization = true;
                    else if (std::abs((old_world_rotation_matrix * Vec3d::UnitZ()).z() - (new_world_rotation_matrix * Vec3d::UnitZ()).z()) > EPSILON)
                        requires_general_synchronization = true;
                }
            }
            transform_instance_relative(v, volume_data, transformation_type, rotation_matrix, m_cache.rotation_pivot);
        }
        else {
            if (!is_single_volume_or_modifier()) {
                assert(transformation_type.world());
                transform_volume_relative(v, volume_data, transformation_type, rotation_matrix, m_cache.rotation_pivot);
            }
            else {
                if (transformation_type.instance()) {
                    // ensure that the volume rotates as a rigid body
                    const Transform3d inst_scale_matrix = inst_trafo.get_scaling_factor_matrix();
                    rotation_matrix = inst_scale_matrix.inverse() * rotation_matrix * inst_scale_matrix;
                }
                else {
                    if (transformation_type.local()) {
                        // ensure that the volume rotates as a rigid body
                        const Geometry::Transformation& vol_trafo = volume_data.get_volume_transform();
                        const Transform3d vol_matrix_no_offset = vol_trafo.get_matrix_no_offset();
                        const Transform3d inst_scale_matrix = inst_trafo.get_scaling_factor_matrix();
                        Transform3d vol_rotation_matrix = vol_trafo.get_rotation_matrix();
                        if (vol_trafo.is_left_handed()) {
                            Geometry::TransformationSVD vol_svd(vol_trafo);
                            vol_rotation_matrix = vol_svd.u * vol_svd.v.transpose();
                            // ensure the rotation has the proper direction
                            if (!rotation.normalized().cwiseAbs().isApprox(Vec3d::UnitX()))
                                rotation_matrix = rotation_matrix.inverse();
                        }
                        rotation_matrix = vol_matrix_no_offset.inverse() * inst_scale_matrix.inverse() * vol_rotation_matrix * rotation_matrix *
                            vol_rotation_matrix.inverse() * inst_scale_matrix * vol_matrix_no_offset;
                    }
                }
                transform_volume_relative(v, volume_data, transformation_type, rotation_matrix, m_cache.rotation_pivot);
            }
        }
    }

#if !DISABLE_INSTANCES_SYNCH
    if (m_mode == Instance) {
        int rot_axis_max = 0;
        rotation.cwiseAbs().maxCoeff(&rot_axis_max);
        const SyncRotationType type = (transformation_type.instance() && requires_general_synchronization) ||
                                      (!transformation_type.instance() && rot_axis_max != 2) ||
                                      rotation.isApprox(Vec3d::Zero()) ?
            SyncRotationType::GENERAL : SyncRotationType::NONE;
        synchronize_unselected_instances(type);
    }
    else if (m_mode == Volume)
        synchronize_unselected_volumes();
#endif // !DISABLE_INSTANCES_SYNCH

    set_bounding_boxes_dirty();
    wxGetApp().plater()->canvas3D()->requires_check_outside_state();
}

void Selection::flattening_rotate(const Vec3d& normal)
{
    // We get the normal in untransformed coordinates. We must transform it using the instance matrix, find out
    // how to rotate the instance so it faces downwards and do the rotation. All that for all selected instances.
    // The function assumes that is_from_single_object() holds.
    assert(Slic3r::is_approx(normal.norm(), 1.));

    if (!m_valid)
        return;

    for (unsigned int i : m_list) {
        GLVolume& v = *(*m_volumes)[i];
        // Normal transformed from the object coordinate space to the world coordinate space.
        const Geometry::Transformation& old_inst_trafo = v.get_instance_transformation();
        const Vec3d tnormal = old_inst_trafo.get_matrix().matrix().block(0, 0, 3, 3).inverse().transpose() * normal;
        // Additional rotation to align tnormal with the down vector in the world coordinate space.
        const Transform3d rotation_matrix = Transform3d(Eigen::Quaterniond().setFromTwoVectors(tnormal, -Vec3d::UnitZ()));
        v.set_instance_transformation(old_inst_trafo.get_offset_matrix() * rotation_matrix * old_inst_trafo.get_matrix_no_offset());
    }

#if !DISABLE_INSTANCES_SYNCH
    // Apply the same transformation also to other instances,
    // but respect their possibly diffrent z-rotation.
    if (m_mode == Instance)
        synchronize_unselected_instances(SyncRotationType::GENERAL);
#endif // !DISABLE_INSTANCES_SYNCH

    this->set_bounding_boxes_dirty();
}

void Selection::scale(const Vec3d& scale, TransformationType transformation_type)
{
    scale_and_translate(scale, Vec3d::Zero(), transformation_type);
}

void Selection::scale_to_fit_print_volume(const BuildVolume& volume)
{
    auto fit = [this](double s, Vec3d offset, bool undoredo_snapshot) {
        if (s <= 0.0 || s == 1.0)
            return false;

        if (undoredo_snapshot)
            wxGetApp().plater()->take_snapshot(_L("Scale To Fit"));

        TransformationType type;
        type.set_world();
        type.set_relative();
        type.set_joint();

        // apply scale
        setup_cache();
        scale(s * Vec3d::Ones(), type);
        wxGetApp().plater()->canvas3D()->do_scale(""); // avoid storing another snapshot

        // center selection on print bed
        setup_cache();
        offset.z() = -get_bounding_box().min.z();
        TransformationType trafo_type;
        trafo_type.set_relative();
        translate(offset, trafo_type);
        wxGetApp().plater()->canvas3D()->do_move(""); // avoid storing another snapshot

        wxGetApp().obj_manipul()->set_dirty();
        return undoredo_snapshot;
    };

    auto fit_rectangle = [this, fit](const BuildVolume& volume, bool undoredo_snapshot, double* max_height = nullptr) {
        const BoundingBoxf3 print_volume = volume.bounding_volume();
        Vec3d print_volume_size = print_volume.size();
        print_volume_size.z() = (max_height != nullptr) ? *max_height : volume.max_print_height();

        // adds 1/100th of a mm on both xy sides to avoid false out of print volume detections due to floating-point roundings
        Vec3d box_size = get_bounding_box().size();
        box_size.x() += 0.02;
        box_size.y() += 0.02;

        const double sx = print_volume_size.x() / box_size.x();
        const double sy = print_volume_size.y() / box_size.y();
        const double sz = print_volume_size.z() / box_size.z();

        return fit(std::min(sx, std::min(sy, sz)), print_volume.center() - get_bounding_box().center(), undoredo_snapshot);
    };

    auto fit_circle = [this, fit](const BuildVolume& volume, bool undoredo_snapshot, double* max_height = nullptr) {
        const Geometry::Circled& print_circle = volume.circle();
        double print_circle_radius = unscale<double>(print_circle.radius);

        if (print_circle_radius == 0.0)
            return false;

        Points points;
        double max_z = 0.0;
        for (unsigned int i : m_list) {
            const GLVolume& v = *(*m_volumes)[i];
            if (v.convex_hull() == nullptr) {
                // E.g. negative meshes do not have a convex hull... (hotfix for SPE-2361)
                continue;
            }
            TriangleMesh hull_3d = *v.convex_hull();
            hull_3d.transform(v.world_matrix());
            max_z = std::max(max_z, hull_3d.bounding_box().size().z());
            const Polygon hull_2d = hull_3d.convex_hull();
            points.insert(points.end(), hull_2d.begin(), hull_2d.end());
        }

        if (points.empty())
            return false;

        const Geometry::Circled circle = Geometry::smallest_enclosing_circle_welzl(points);
        // adds 1/100th of a mm on all sides to avoid false out of print volume detections due to floating-point roundings
        const double circle_radius = unscale<double>(circle.radius) + 0.01;

        if (circle_radius == 0.0 || max_z == 0.0)
            return false;

        const double print_volume_max_z = (max_height != nullptr) ? *max_height : volume.max_print_height();
        const double s = std::min(print_circle_radius / circle_radius, print_volume_max_z / max_z);
        const Vec3d sel_center = get_bounding_box().center();
        const Vec3d offset = s * (Vec3d(unscale<double>(circle.center.x()), unscale<double>(circle.center.y()), 0.5 * max_z) - sel_center);
        const Vec3d print_center = { unscale<double>(print_circle.center.x()), unscale<double>(print_circle.center.y()), 0.5 * volume.max_print_height() };
        return fit(s, print_center - (sel_center + offset), undoredo_snapshot);
    };

    if (is_empty() || m_mode == Volume)
        return;

    assert(is_single_full_instance());

    // used to keep track whether the undo/redo snapshot has already been taken 
    bool undoredo_snapshot = false;

    if (wxGetApp().plater()->printer_technology() == ptSLA) {
        // remove SLA auxiliary volumes from the selection to ensure that the proper bounding box is calculated
        std::vector<unsigned int> to_remove;
        for (unsigned int i : m_list) {
            if ((*m_volumes)[i]->volume_idx() < 0)
                to_remove.push_back(i);
        }

        if (!to_remove.empty())
            remove_volumes(m_mode, to_remove);
    }

    // FIXME: It should really only account for the model parts when scaling to fit. Not for modifiers,
    // support enforcers / blockers and negative meshes.


    switch (volume.type())
    {
    case BuildVolume::Type::Rectangle: { undoredo_snapshot = fit_rectangle(volume, !undoredo_snapshot); break; }
    case BuildVolume::Type::Circle:    { undoredo_snapshot = fit_circle(volume, !undoredo_snapshot); break; }
    default: { break; }
    }

    if (wxGetApp().plater()->printer_technology() == ptFFF) {
        // check whether the top layer exceeds the maximum height of the print volume
        // and, in case, reduce the scale accordingly
        const auto [slicing_parameters, profile] = wxGetApp().plater()->canvas3D()->get_layers_height_data(get_object_idx());
        auto layers = generate_object_layers(slicing_parameters, profile);
        auto layers_it = layers.rbegin();
        while (layers_it != layers.rend() && *layers_it > volume.bounding_volume().max.z()) {
            ++layers_it;
        }
        if (layers_it != layers.rbegin() && layers_it != layers.rend()) {
            switch (volume.type())
            {
            case BuildVolume::Type::Rectangle: { fit_rectangle(volume, !undoredo_snapshot, &(*layers_it)); break; }
            case BuildVolume::Type::Circle:    { fit_circle(volume, !undoredo_snapshot, &(*layers_it)); break; }
            default: { break; }
            }
        }
    }
}

void Selection::mirror(Axis axis, TransformationType transformation_type)
{
    const Vec3d mirror((axis == X) ? -1.0 : 1.0, (axis == Y) ? -1.0 : 1.0, (axis == Z) ? -1.0 : 1.0);
    scale_and_translate(mirror, Vec3d::Zero(), transformation_type);
}

void Selection::scale_and_translate(const Vec3d& scale, const Vec3d& world_translation, TransformationType transformation_type)
{
    if (!m_valid)
      return;

    Vec3d relative_scale = scale;
    if (transformation_type.absolute()) {
        // converts to relative scale
        if (m_mode == Instance) {
            if (is_single_full_instance()) {
                BoundingBoxf3 current_box = get_bounding_box_in_current_reference_system().first;
                BoundingBoxf3 original_box;
                if (transformation_type.world())
                    original_box = get_full_unscaled_instance_bounding_box();
                else
                    original_box = get_full_unscaled_instance_local_bounding_box();

                relative_scale = original_box.size().cwiseProduct(scale).cwiseQuotient(current_box.size());
            }
        }
        transformation_type.set_relative();
    }

    for (unsigned int i : m_list) {
        GLVolume& v = *(*m_volumes)[i];
        const VolumeCache& volume_data = m_cache.volumes_data[i];
        const Geometry::Transformation& inst_trafo = volume_data.get_instance_transform();

        if (m_mode == Instance) {
            if (transformation_type.instance()) {
                const Vec3d world_inst_pivot = m_cache.dragging_center - inst_trafo.get_offset();
                const Vec3d local_inst_pivot = inst_trafo.get_matrix_no_offset().inverse() * world_inst_pivot;
                Matrix3d inst_rotation, inst_scale;
                inst_trafo.get_matrix().computeRotationScaling(&inst_rotation, &inst_scale);
                const Transform3d offset_trafo = Geometry::translation_transform(inst_trafo.get_offset() + world_translation);
                const Transform3d scale_trafo = Transform3d(inst_scale) * Geometry::scale_transform(relative_scale);
                v.set_instance_transformation(Geometry::translation_transform(world_inst_pivot) * offset_trafo * Transform3d(inst_rotation) * scale_trafo * Geometry::translation_transform(-local_inst_pivot));
            }
            else
                transform_instance_relative(v, volume_data, transformation_type, Geometry::translation_transform(world_translation) * Geometry::scale_transform(relative_scale), m_cache.dragging_center);
        }
        else {
            if (!is_single_volume_or_modifier()) {
                assert(transformation_type.world());
                transform_volume_relative(v, volume_data, transformation_type, Geometry::translation_transform(world_translation) * Geometry::scale_transform(scale), m_cache.dragging_center);
            }
            else {
                transformation_type.set_independent();
                Vec3d translation;
                if (transformation_type.local())
                    translation = volume_data.get_volume_transform().get_matrix_no_offset().inverse() * inst_trafo.get_matrix_no_offset().inverse() * world_translation;
                else if (transformation_type.instance())
                    translation = inst_trafo.get_matrix_no_offset().inverse() * world_translation;
                else
                    translation = world_translation;
                transform_volume_relative(v, volume_data, transformation_type, Geometry::translation_transform(translation) * Geometry::scale_transform(scale), m_cache.dragging_center);
            }
        }
    }

#if !DISABLE_INSTANCES_SYNCH
    if (m_mode == Instance)
        // even if there is no rotation, we pass SyncRotationType::GENERAL to force 
        // synchronize_unselected_instances() to apply the scale to the other instances
        synchronize_unselected_instances(SyncRotationType::GENERAL);
    else if (m_mode == Volume)
        synchronize_unselected_volumes();
#endif // !DISABLE_INSTANCES_SYNCH

    if (m_mode == EMode::Instance)
        ensure_on_bed();
    set_bounding_boxes_dirty();
    wxGetApp().plater()->canvas3D()->requires_check_outside_state();
}

void Selection::reset_skew()
{
    if (!m_valid)
        return;

    for (unsigned int i : m_list) {
        GLVolume& v = *(*m_volumes)[i];
        const VolumeCache& volume_data = m_cache.volumes_data[i];
        Geometry::Transformation inst_trafo = volume_data.get_instance_transform();
        Geometry::Transformation vol_trafo = volume_data.get_volume_transform();
        Geometry::Transformation world_trafo = inst_trafo * vol_trafo;
        if (world_trafo.has_skew()) {
            if (!inst_trafo.has_skew() && !vol_trafo.has_skew()) {
                // <W> = [I][V]
                world_trafo.reset_offset();
                world_trafo.reset_skew();
                v.set_volume_transformation(vol_trafo.get_offset_matrix() * inst_trafo.get_matrix_no_offset().inverse() * world_trafo.get_matrix());
            }
            else {
                // <W> = <I><V>
                // <W> = <I>[V]
                // <W> = [I]<V>
                if (inst_trafo.has_skew()) {
                    inst_trafo.reset_skew();
                    v.set_instance_transformation(inst_trafo);
                }
                if (vol_trafo.has_skew()) {
                    vol_trafo.reset_skew();
                    v.set_volume_transformation(vol_trafo);
                }
            }
        }
        else {
            // [W] = [I][V]
            // [W] = <I><V>
            if (inst_trafo.has_skew()) {
                inst_trafo.reset_skew();
                v.set_instance_transformation(inst_trafo);
            }
            if (vol_trafo.has_skew()) {
                vol_trafo.reset_skew();
                v.set_volume_transformation(vol_trafo);
            }
        }
    }

#if !DISABLE_INSTANCES_SYNCH
    if (m_mode == Instance)
        // even if there is no rotation, we pass SyncRotationType::GENERAL to force 
        // synchronize_unselected_instances() to remove skew from the other instances
        synchronize_unselected_instances(SyncRotationType::GENERAL);
    else if (m_mode == Volume)
        synchronize_unselected_volumes();
#endif // !DISABLE_INSTANCES_SYNCH

    ensure_on_bed();
    set_bounding_boxes_dirty();
    wxGetApp().plater()->canvas3D()->requires_check_outside_state();
}

void Selection::translate(unsigned int object_idx, unsigned int instance_idx, const Vec3d& displacement)
{
    if (!m_valid)
        return;

    for (unsigned int i : m_list) {
        GLVolume& v = *(*m_volumes)[i];
        if (v.object_idx() == (int)object_idx && v.instance_idx() == (int)instance_idx)
            v.set_instance_transformation(Geometry::translation_transform(displacement) * v.get_instance_transformation().get_matrix());
    }

    std::set<unsigned int> done;  // prevent processing volumes twice
    done.insert(m_list.begin(), m_list.end());

    for (unsigned int i : m_list) {
        if (done.size() == m_volumes->size())
            break;

        if ((*m_volumes)[i]->is_wipe_tower)
            continue;

        const int object_idx = (*m_volumes)[i]->object_idx();

        // Process unselected volumes of the object.
        for (unsigned int j = 0; j < (unsigned int)m_volumes->size(); ++j) {
            if (done.size() == m_volumes->size())
                break;

            if (done.find(j) != done.end())
                continue;

            GLVolume& v = *(*m_volumes)[j];
            if (v.object_idx() != object_idx || v.instance_idx() != (int)instance_idx)
                continue;

            v.set_instance_transformation(Geometry::translation_transform(displacement) * v.get_instance_transformation().get_matrix());
            done.insert(j);
        }
    }

    this->set_bounding_boxes_dirty();
}

int Selection::bake_transform_if_needed() const
{
    if ((is_single_full_instance() && wxGetApp().obj_manipul()->is_world_coordinates()) ||
        (is_single_volume_or_modifier() && !wxGetApp().obj_manipul()->is_local_coordinates())) {
        // Verify whether the instance rotation is multiples of 90 degrees, so that the scaling in world coordinates is possible.
        // all volumes in the selection belongs to the same instance, any of them contains the needed instance data, so we take the first one
        const GLVolume& volume = *get_first_volume();
        bool needs_baking = false;
        if (is_single_full_instance()) {
            // Is the instance angle close to a multiple of 90 degrees?
            needs_baking |= !Geometry::is_rotation_ninety_degrees(volume.get_instance_rotation());
            // Are all volumes angles close to a multiple of 90 degrees?
            for (unsigned int id : get_volume_idxs()) {
                if (needs_baking)
                    break;
                needs_baking |= !Geometry::is_rotation_ninety_degrees(get_volume(id)->get_volume_rotation());
            }
        }
        else if (is_single_volume_or_modifier()) {
            // is the volume angle close to a multiple of 90 degrees?
            needs_baking |= !Geometry::is_rotation_ninety_degrees(volume.get_volume_rotation());
            if (wxGetApp().obj_manipul()->is_world_coordinates())
                // Is the instance angle close to a multiple of 90 degrees?
                needs_baking |= !Geometry::is_rotation_ninety_degrees(volume.get_instance_rotation());
        }

        if (needs_baking) {
            MessageDialog dlg((wxWindow*)wxGetApp().mainframe,
                _L("The currently manipulated object is tilted or contains tilted parts (rotation angles are not multiples of 90°). "
                    "Non-uniform scaling of tilted objects is only possible in non-local coordinate systems, "
                    "once the rotation is embedded into the object coordinates.") + "\n" +
                _L("This operation is irreversible.") + "\n" +
                _L("Do you want to proceed?"),
                SLIC3R_APP_NAME,
                wxYES_NO | wxNO_DEFAULT | wxICON_QUESTION);
            if (dlg.ShowModal() != wxID_YES)
                return -1;

            wxGetApp().plater()->take_snapshot(_("Bake transform"));

            // Bake the rotation into the meshes of the object.
            wxGetApp().model().objects[volume.composite_id.object_id]->bake_xy_rotation_into_meshes(volume.composite_id.instance_id);
            // Update the 3D scene, selections etc.
            wxGetApp().plater()->update();
            return 0;
        }
    }

    return 1;
}

void Selection::erase()
{
    if (!m_valid)
        return;

    if (is_single_full_object())
        wxGetApp().obj_list()->delete_from_model_and_list(ItemType::itObject, get_object_idx(), 0);
    else if (is_multiple_full_object()) {
        std::vector<ItemForDelete> items;
        items.reserve(m_cache.content.size());
        for (ObjectIdxsToInstanceIdxsMap::iterator it = m_cache.content.begin(); it != m_cache.content.end(); ++it) {
            items.emplace_back(ItemType::itObject, it->first, 0);
        }
        wxGetApp().obj_list()->delete_from_model_and_list(items);
    }
    else if (is_multiple_full_instance()) {
        std::set<std::pair<int, int>> instances_idxs;
        for (ObjectIdxsToInstanceIdxsMap::iterator obj_it = m_cache.content.begin(); obj_it != m_cache.content.end(); ++obj_it) {
            for (InstanceIdxsList::reverse_iterator inst_it = obj_it->second.rbegin(); inst_it != obj_it->second.rend(); ++inst_it) {
                instances_idxs.insert(std::make_pair(obj_it->first, *inst_it));
            }
        }

        std::vector<ItemForDelete> items;
        items.reserve(instances_idxs.size());
        for (const std::pair<int, int>& i : instances_idxs) {
            items.emplace_back(ItemType::itInstance, i.first, i.second);
        }
        wxGetApp().obj_list()->delete_from_model_and_list(items);
    }
    else if (is_single_full_instance())
        wxGetApp().obj_list()->delete_from_model_and_list(ItemType::itInstance, get_object_idx(), get_instance_idx());
    else if (is_mixed()) {
        std::set<ItemForDelete> items_set;
        std::map<int, int> volumes_in_obj;

        for (auto i : m_list) {
            const auto gl_vol = (*m_volumes)[i];
            const auto glv_obj_idx = gl_vol->object_idx();
            const auto model_object = m_model->objects[glv_obj_idx];

            if (model_object->instances.size() == 1) {
                if (model_object->volumes.size() == 1)
                    items_set.insert(ItemForDelete(ItemType::itObject, glv_obj_idx, -1));
                else {
                    items_set.insert(ItemForDelete(ItemType::itVolume, glv_obj_idx, gl_vol->volume_idx()));
                    int idx = (volumes_in_obj.find(glv_obj_idx) == volumes_in_obj.end()) ? 0 : volumes_in_obj.at(glv_obj_idx);
                    volumes_in_obj[glv_obj_idx] = ++idx;
                }
                continue;
            }

            const auto glv_ins_idx = gl_vol->instance_idx();

            for (auto obj_ins : m_cache.content) {
                if (obj_ins.first == glv_obj_idx) {
                    if (obj_ins.second.find(glv_ins_idx) != obj_ins.second.end()) {
                        if (obj_ins.second.size() == model_object->instances.size())
                            items_set.insert(ItemForDelete(ItemType::itObject, glv_obj_idx, -1));
                        else
                            items_set.insert(ItemForDelete(ItemType::itInstance, glv_obj_idx, glv_ins_idx));

                        break;
                    }
                }
            }
        }

        std::vector<ItemForDelete> items;
        items.reserve(items_set.size());
        for (const ItemForDelete& i : items_set) {
            if (i.type == ItemType::itVolume) {
                const int vol_in_obj_cnt = volumes_in_obj.find(i.obj_idx) == volumes_in_obj.end() ? 0 : volumes_in_obj.at(i.obj_idx);
                if (vol_in_obj_cnt == (int)m_model->objects[i.obj_idx]->volumes.size()) {
                    if (i.sub_obj_idx == vol_in_obj_cnt - 1)
                        items.emplace_back(ItemType::itObject, i.obj_idx, 0);
                    continue;
                }
            }
            items.emplace_back(i.type, i.obj_idx, i.sub_obj_idx);
        }

        wxGetApp().obj_list()->delete_from_model_and_list(items);
    }
    else {
        std::set<std::pair<int, int>> volumes_idxs;
        for (unsigned int i : m_list) {
            const GLVolume* v = (*m_volumes)[i];
            // Only remove volumes associated with ModelVolumes from the object list.
            // Temporary meshes (SLA supports or pads) are not managed by the object list.
            if (v->volume_idx() >= 0)
                volumes_idxs.insert(std::make_pair(v->object_idx(), v->volume_idx()));
        }

        std::vector<ItemForDelete> items;
        items.reserve(volumes_idxs.size());
        for (const std::pair<int, int>& v : volumes_idxs) {
            items.emplace_back(ItemType::itVolume, v.first, v.second);
        }

        wxGetApp().obj_list()->delete_from_model_and_list(items);
        ensure_not_below_bed();
    }

    wxGetApp().plater()->canvas3D()->set_sequential_clearance_as_evaluating();
}

void Selection::render(float scale_factor)
{
    if (!m_valid || is_empty())
        return;

    m_scale_factor = scale_factor;
    // render cumulative bounding box of selected volumes
    const auto& [box, trafo] = get_bounding_box_in_current_reference_system();
    render_bounding_box(box, trafo, ColorRGB::WHITE());
    render_synchronized_volumes();
}

#if ENABLE_RENDER_SELECTION_CENTER
void Selection::render_center(bool gizmo_is_dragging)
{
    if (!m_valid || is_empty())
        return;

    GLShaderProgram* shader = wxGetApp().get_shader("flat");
    if (shader == nullptr)
        return;

    shader->start_using();

    const Vec3d center = gizmo_is_dragging ? m_cache.dragging_center : get_bounding_box().center();

    glsafe(::glDisable(GL_DEPTH_TEST));

    const Camera& camera = wxGetApp().plater()->get_camera();
    Transform3d view_model_matrix = camera.get_view_matrix() * Geometry::assemble_transform(center);

    shader->set_uniform("view_model_matrix", view_model_matrix);
    shader->set_uniform("projection_matrix", camera.get_projection_matrix());
    m_vbo_sphere.set_color(ColorRGBA::WHITE());

    m_vbo_sphere.render();

    shader->stop_using();
}
#endif // ENABLE_RENDER_SELECTION_CENTER

void Selection::render_sidebar_hints(const std::string& sidebar_field)
{
    if (sidebar_field.empty())
        return;

    GLShaderProgram* shader = wxGetApp().get_shader(boost::starts_with(sidebar_field, "layer") ? "flat" : "gouraud_light");
    if (shader == nullptr)
        return;

    shader->start_using();

    glsafe(::glEnable(GL_DEPTH_TEST));
    glsafe(::glDisable(GL_CULL_FACE));

    const Transform3d base_matrix = Geometry::translation_transform(get_bounding_box().center());
    Transform3d orient_matrix = Transform3d::Identity();

    const Vec3d center = get_bounding_box().center();
    Vec3d axes_center = center;

    if (!boost::starts_with(sidebar_field, "layer")) {
        shader->set_uniform("emission_factor", 0.05f);
        if (is_single_full_instance() && !wxGetApp().obj_manipul()->is_world_coordinates()) {
            orient_matrix = (*m_volumes)[*m_list.begin()]->get_instance_transformation().get_rotation_matrix();
            axes_center = (*m_volumes)[*m_list.begin()]->get_instance_offset();
        }
        else if (is_single_volume_or_modifier()) {
            if (!wxGetApp().obj_manipul()->is_world_coordinates()) {
                if (wxGetApp().obj_manipul()->is_local_coordinates()) {
                    orient_matrix = get_bounding_box_in_current_reference_system().second;
                    orient_matrix.translation() = Vec3d::Zero();
                }
                else {
                    orient_matrix = (*m_volumes)[*m_list.begin()]->get_instance_transformation().get_rotation_matrix();
                    axes_center = (*m_volumes)[*m_list.begin()]->get_instance_offset();
                }
            }
        }
        else {
            if (requires_local_axes())
                orient_matrix = (*m_volumes)[*m_list.begin()]->get_instance_transformation().get_rotation_matrix();
        }
    }

    if (!boost::starts_with(sidebar_field, "layer"))
        glsafe(::glClear(GL_DEPTH_BUFFER_BIT));

    if (!boost::starts_with(sidebar_field, "layer"))
        shader->set_uniform("emission_factor", 0.1f);

    if (boost::starts_with(sidebar_field, "position"))
        render_sidebar_position_hints(sidebar_field, *shader, base_matrix * orient_matrix);
    else if (boost::starts_with(sidebar_field, "rotation"))
        render_sidebar_rotation_hints(sidebar_field, *shader, base_matrix * orient_matrix);
    else if (boost::starts_with(sidebar_field, "scale") || boost::starts_with(sidebar_field, "size"))
        render_sidebar_scale_hints(sidebar_field, *shader, base_matrix * orient_matrix);
    else if (boost::starts_with(sidebar_field, "layer"))
        render_sidebar_layers_hints(sidebar_field, *shader);

    if (!boost::starts_with(sidebar_field, "layer")) {
        if (wxGetApp().obj_manipul()->is_instance_coordinates())
            m_axes.render(Geometry::translation_transform(axes_center) * orient_matrix, 0.25f);
    }

    glsafe(::glEnable(GL_CULL_FACE));
    shader->stop_using();
}

bool Selection::requires_local_axes() const
{
    return m_mode == Volume && is_from_single_instance();
}

void Selection::copy_to_clipboard()
{
    if (!m_valid)
        return;

    m_clipboard.reset();

    for (const ObjectIdxsToInstanceIdxsMap::value_type& object : m_cache.content) {
        ModelObject* src_object = m_model->objects[object.first];
        ModelObject* dst_object = m_clipboard.add_object();
        dst_object->name                 = src_object->name;
        dst_object->input_file           = src_object->input_file;
		dst_object->config.assign_config(src_object->config);
        dst_object->sla_support_points   = src_object->sla_support_points;
        dst_object->sla_points_status    = src_object->sla_points_status;
        dst_object->sla_drain_holes      = src_object->sla_drain_holes;
        dst_object->layer_config_ranges  = src_object->layer_config_ranges;     // #ys_FIXME_experiment
        dst_object->layer_height_profile.assign(src_object->layer_height_profile);
        dst_object->origin_translation   = src_object->origin_translation;

        for (int i : object.second) {
            dst_object->add_instance(*src_object->instances[i]);
        }

        for (unsigned int i : m_list) {
            // Copy the ModelVolumes only for the selected GLVolumes of the 1st selected instance.
            const GLVolume* volume = (*m_volumes)[i];
            if (volume->object_idx() == object.first && volume->instance_idx() == *object.second.begin()) {
                int volume_idx = volume->volume_idx();
                if (0 <= volume_idx && volume_idx < (int)src_object->volumes.size()) {
                    ModelVolume* src_volume = src_object->volumes[volume_idx];
                    ModelVolume* dst_volume = dst_object->add_volume(*src_volume);
                    dst_volume->set_new_unique_id();
                }
                else
                    assert(false);
            }
        }
    }

    m_clipboard.set_mode(m_mode);
}

void Selection::paste_from_clipboard()
{
    if (!m_valid || m_clipboard.is_empty())
        return;

    switch (m_clipboard.get_mode())
    {
    case Volume:
    {
        if (is_from_single_instance())
            paste_volumes_from_clipboard();

        break;
    }
    case Instance:
    {
        if (m_mode == Instance)
            paste_objects_from_clipboard();

        break;
    }
    }
}

std::vector<unsigned int> Selection::get_volume_idxs_from_object(unsigned int object_idx) const
{
    std::vector<unsigned int> idxs;

    const PrinterTechnology pt = wxGetApp().plater()->printer_technology();

    for (unsigned int i = 0; i < (unsigned int)m_volumes->size(); ++i) {
        const GLVolume* v = (*m_volumes)[i];
        if (v->object_idx() == (int)object_idx) {
            if (pt == ptSLA && v->is_modifier &&
                m_model->objects[object_idx]->volumes[v->volume_idx()]->is_modifier())
                continue;
            idxs.push_back(i);
        }
    }

    return idxs;
}

std::vector<unsigned int> Selection::get_volume_idxs_from_instance(unsigned int object_idx, unsigned int instance_idx) const
{
    std::vector<unsigned int> idxs;
    for (unsigned int i = 0; i < (unsigned int)m_volumes->size(); ++i) {
        const GLVolume* v = (*m_volumes)[i];
        if (v->object_idx() == (int)object_idx && v->instance_idx() == (int)instance_idx)
            idxs.push_back(i);
    }
    return idxs;
}

std::vector<unsigned int> Selection::get_volume_idxs_from_volume(unsigned int object_idx, unsigned int instance_idx, unsigned int volume_idx) const
{
    std::vector<unsigned int> idxs;

    for (unsigned int i = 0; i < (unsigned int)m_volumes->size(); ++i) {
        const GLVolume* v = (*m_volumes)[i];
        if (v->object_idx() == (int)object_idx && v->volume_idx() == (int)volume_idx) {
            if ((int)instance_idx != -1 && v->instance_idx() == (int)instance_idx)
                idxs.push_back(i);
        }
    }

    return idxs;
}

std::vector<unsigned int> Selection::get_missing_volume_idxs_from(const std::vector<unsigned int>& volume_idxs) const
{
    std::vector<unsigned int> idxs;

    for (unsigned int i : m_list) {
        std::vector<unsigned int>::const_iterator it = std::find(volume_idxs.begin(), volume_idxs.end(), i);
        if (it == volume_idxs.end())
            idxs.push_back(i);
    }

    return idxs;
}

std::vector<unsigned int> Selection::get_unselected_volume_idxs_from(const std::vector<unsigned int>& volume_idxs) const
{
    std::vector<unsigned int> idxs;

    for (unsigned int i : volume_idxs) {
        if (m_list.find(i) == m_list.end())
            idxs.push_back(i);
    }

    return idxs;
}

std::set<unsigned int> Selection::get_object_idxs() const
{
    std::set<unsigned int> idxs;

    for (unsigned int i : m_list)
        idxs.emplace((*m_volumes)[i]->object_idx());

    return idxs;
}

void Selection::update_valid()
{
    m_valid = (m_volumes != nullptr) && (m_model != nullptr);
}

void Selection::update_type()
{
    m_cache.content.clear();
    m_type = Mixed;

    for (unsigned int i : m_list) {
        const GLVolume* volume = (*m_volumes)[i];
        int obj_idx = volume->object_idx();
        int inst_idx = volume->instance_idx();
        ObjectIdxsToInstanceIdxsMap::iterator obj_it = m_cache.content.find(obj_idx);
        if (obj_it == m_cache.content.end())
            obj_it = m_cache.content.insert(ObjectIdxsToInstanceIdxsMap::value_type(obj_idx, InstanceIdxsList())).first;

        obj_it->second.insert(inst_idx);
    }

    bool requires_disable = false;

    if (!m_valid)
        m_type = Invalid;
    else {
        if (m_list.empty())
            m_type = Empty;
        else if (m_list.size() == 1) {
            const GLVolume* first = (*m_volumes)[*m_list.begin()];
            if (first->is_wipe_tower)
                m_type = WipeTower;
            else if (first->is_modifier) {
                m_type = SingleModifier;
                requires_disable = true;
            }
            else {
                const ModelObject* model_object = m_model->objects[first->object_idx()];
                unsigned int volumes_count = (unsigned int)model_object->volumes.size();
                unsigned int instances_count = (unsigned int)model_object->instances.size();
                if (volumes_count * instances_count == 1) {
                    m_type = SingleFullObject;
                    // ensures the correct mode is selected
                    m_mode = Instance;
                }
                else if (volumes_count == 1) { // instances_count > 1
                    m_type = SingleFullInstance;
                    // ensures the correct mode is selected
                    m_mode = Instance;
                }
                else {
                    m_type = SingleVolume;
                    requires_disable = true;
                }
            }
        }
        else {
            unsigned int sla_volumes_count = 0;
            // Note: sla_volumes_count is a count of the selected sla_volumes per object instead of per instance, like a model_volumes_count is
            for (unsigned int i : m_list) {
                if ((*m_volumes)[i]->volume_idx() < 0)
                    ++sla_volumes_count;
            }

            if (m_cache.content.size() == 1) // single object
            {
                const ModelObject* model_object = m_model->objects[m_cache.content.begin()->first];
                unsigned int model_volumes_count = (unsigned int)model_object->volumes.size();

                unsigned int instances_count = (unsigned int)model_object->instances.size();
                unsigned int selected_instances_count = (unsigned int)m_cache.content.begin()->second.size();
                if (model_volumes_count * instances_count + sla_volumes_count == (unsigned int)m_list.size()) {
                    m_type = SingleFullObject;
                    // ensures the correct mode is selected
                    m_mode = Instance;
                }
                else if (selected_instances_count == 1) {
                    if (model_volumes_count + sla_volumes_count == (unsigned int)m_list.size()) {
                        m_type = SingleFullInstance;
                        // ensures the correct mode is selected
                        m_mode = Instance;
                    }
                    else {
                        unsigned int modifiers_count = 0;
                        for (unsigned int i : m_list) {
                            if ((*m_volumes)[i]->is_modifier)
                                ++modifiers_count;
                        }

                        if (modifiers_count == 0)
                            m_type = MultipleVolume;
                        else if (modifiers_count == (unsigned int)m_list.size())
                            m_type = MultipleModifier;

                        requires_disable = true;
                    }
                }
                else if (selected_instances_count > 1 && selected_instances_count * model_volumes_count + sla_volumes_count == (unsigned int)m_list.size()) {
                    m_type = MultipleFullInstance;
                    // ensures the correct mode is selected
                    m_mode = Instance;
                }
            }
            else {
                unsigned int sels_cntr = 0;
                for (ObjectIdxsToInstanceIdxsMap::iterator it = m_cache.content.begin(); it != m_cache.content.end(); ++it) {
                    const ModelObject* model_object = m_model->objects[it->first];
                    unsigned int volumes_count = (unsigned int)model_object->volumes.size();
                    unsigned int instances_count = (unsigned int)model_object->instances.size();
                    sels_cntr += volumes_count * instances_count;
                }
                if (sels_cntr + sla_volumes_count == (unsigned int)m_list.size()) {
                    m_type = MultipleFullObject;
                    // ensures the correct mode is selected
                    m_mode = Instance;
                }
            }
        }
    }

    int object_idx = get_object_idx();
    int instance_idx = get_instance_idx();
    for (GLVolume* v : *m_volumes) {
        v->disabled = requires_disable ? (v->object_idx() != object_idx) || (v->instance_idx() != instance_idx) : false;
    }

#if ENABLE_SELECTION_DEBUG_OUTPUT
    std::cout << "Selection: ";
    std::cout << "mode: ";
    switch (m_mode)
    {
    case Volume:
    {
        std::cout << "Volume";
        break;
    }
    case Instance:
    {
        std::cout << "Instance";
        break;
    }
    }

    std::cout << " - type: ";

    switch (m_type)
    {
    case Invalid:
    {
        std::cout << "Invalid" << std::endl;
        break;
    }
    case Empty:
    {
        std::cout << "Empty" << std::endl;
        break;
    }
    case WipeTower:
    {
        std::cout << "WipeTower" << std::endl;
        break;
    }
    case SingleModifier:
    {
        std::cout << "SingleModifier" << std::endl;
        break;
    }
    case MultipleModifier:
    {
        std::cout << "MultipleModifier" << std::endl;
        break;
    }
    case SingleVolume:
    {
        std::cout << "SingleVolume" << std::endl;
        break;
    }
    case MultipleVolume:
    {
        std::cout << "MultipleVolume" << std::endl;
        break;
    }
    case SingleFullObject:
    {
        std::cout << "SingleFullObject" << std::endl;
        break;
    }
    case MultipleFullObject:
    {
        std::cout << "MultipleFullObject" << std::endl;
        break;
    }
    case SingleFullInstance:
    {
        std::cout << "SingleFullInstance" << std::endl;
        break;
    }
    case MultipleFullInstance:
    {
        std::cout << "MultipleFullInstance" << std::endl;
        break;
    }
    case Mixed:
    {
        std::cout << "Mixed" << std::endl;
        break;
    }
    }
#endif // ENABLE_SELECTION_DEBUG_OUTPUT
}

void Selection::set_caches()
{
    m_cache.volumes_data.clear();
    m_cache.sinking_volumes.clear();
    for (unsigned int i = 0; i < (unsigned int)m_volumes->size(); ++i) {
        const GLVolume& v = *(*m_volumes)[i];
        m_cache.volumes_data.emplace(i, VolumeCache(v.get_volume_transformation(), v.get_instance_transformation()));
        if (v.is_sinking())
            m_cache.sinking_volumes.push_back(i);
    }
    m_cache.dragging_center = get_bounding_box().center();
    m_cache.rotation_pivot = get_bounding_sphere().first;
}

void Selection::do_add_volume(unsigned int volume_idx)
{
    m_list.insert(volume_idx);
    GLVolume* v = (*m_volumes)[volume_idx];
    v->selected = true;
    if (v->hover == GLVolume::HS_Select || v->hover == GLVolume::HS_Deselect)
        v->hover = GLVolume::HS_Hover;
}

void Selection::do_add_volumes(const std::vector<unsigned int>& volume_idxs)
{
    for (unsigned int i : volume_idxs)
    {
        if (i < (unsigned int)m_volumes->size())
            do_add_volume(i);
    }
}

void Selection::do_remove_volume(unsigned int volume_idx)
{
    IndicesList::iterator v_it = m_list.find(volume_idx);
    if (v_it == m_list.end())
        return;

    m_list.erase(v_it);

    (*m_volumes)[volume_idx]->selected = false;
}

void Selection::do_remove_instance(unsigned int object_idx, unsigned int instance_idx)
{
    for (unsigned int i = 0; i < (unsigned int)m_volumes->size(); ++i) {
        GLVolume* v = (*m_volumes)[i];
        if (v->object_idx() == (int)object_idx && v->instance_idx() == (int)instance_idx)
            do_remove_volume(i);
    }
}

void Selection::do_remove_object(unsigned int object_idx)
{
    for (unsigned int i = 0; i < (unsigned int)m_volumes->size(); ++i) {
        GLVolume* v = (*m_volumes)[i];
        if (v->object_idx() == (int)object_idx)
            do_remove_volume(i);
    }
}

void Selection::render_synchronized_volumes()
{
    if (m_mode == Instance)
        return;

    const ECoordinatesType coordinates_type = wxGetApp().obj_manipul()->get_coordinates_type();
    BoundingBoxf3 box;
    Transform3d trafo;

    for (unsigned int i : m_list) {
        const GLVolume& volume = *(*m_volumes)[i];
        int object_idx = volume.object_idx();
        int volume_idx = volume.volume_idx();
        for (unsigned int j = 0; j < (unsigned int)m_volumes->size(); ++j) {
            if (i == j)
                continue;

            const GLVolume& v = *(*m_volumes)[j];
            if (v.object_idx() != object_idx || v.volume_idx() != volume_idx)
                continue;

            if (coordinates_type == ECoordinatesType::World) {
                box = v.transformed_convex_hull_bounding_box();
                trafo = Transform3d::Identity();
            }
            else if (coordinates_type == ECoordinatesType::Local) {
                box = v.bounding_box();
                trafo = v.world_matrix();
            }
            else {
                box = v.transformed_convex_hull_bounding_box(v.get_volume_transformation().get_matrix());
                trafo = v.get_instance_transformation().get_matrix();
            }
            render_bounding_box(box, trafo, ColorRGB::YELLOW());
        }
    }
}

void Selection::render_bounding_box(const BoundingBoxf3& box, const Transform3d& trafo, const ColorRGB& color)
{
    const BoundingBoxf3& curr_box = m_box.get_bounding_box();

    if (!m_box.is_initialized() || !is_approx(box.min, curr_box.min) || !is_approx(box.max, curr_box.max)) {
        m_box.reset();

        const Vec3f b_min = box.min.cast<float>();
        const Vec3f b_max = box.max.cast<float>();
        const Vec3f size = 0.2f * box.size().cast<float>();

        GLModel::Geometry init_data;
        init_data.format = { GLModel::Geometry::EPrimitiveType::Lines, GLModel::Geometry::EVertexLayout::P3 };
        init_data.reserve_vertices(48);
        init_data.reserve_indices(48);

        // vertices
        init_data.add_vertex(Vec3f(b_min.x(), b_min.y(), b_min.z()));
        init_data.add_vertex(Vec3f(b_min.x() + size.x(), b_min.y(), b_min.z()));
        init_data.add_vertex(Vec3f(b_min.x(), b_min.y(), b_min.z()));
        init_data.add_vertex(Vec3f(b_min.x(), b_min.y() + size.y(), b_min.z()));
        init_data.add_vertex(Vec3f(b_min.x(), b_min.y(), b_min.z()));
        init_data.add_vertex(Vec3f(b_min.x(), b_min.y(), b_min.z() + size.z()));

        init_data.add_vertex(Vec3f(b_max.x(), b_min.y(), b_min.z()));
        init_data.add_vertex(Vec3f(b_max.x() - size.x(), b_min.y(), b_min.z()));
        init_data.add_vertex(Vec3f(b_max.x(), b_min.y(), b_min.z()));
        init_data.add_vertex(Vec3f(b_max.x(), b_min.y() + size.y(), b_min.z()));
        init_data.add_vertex(Vec3f(b_max.x(), b_min.y(), b_min.z()));
        init_data.add_vertex(Vec3f(b_max.x(), b_min.y(), b_min.z() + size.z()));

        init_data.add_vertex(Vec3f(b_max.x(), b_max.y(), b_min.z()));
        init_data.add_vertex(Vec3f(b_max.x() - size.x(), b_max.y(), b_min.z()));
        init_data.add_vertex(Vec3f(b_max.x(), b_max.y(), b_min.z()));
        init_data.add_vertex(Vec3f(b_max.x(), b_max.y() - size.y(), b_min.z()));
        init_data.add_vertex(Vec3f(b_max.x(), b_max.y(), b_min.z()));
        init_data.add_vertex(Vec3f(b_max.x(), b_max.y(), b_min.z() + size.z()));

        init_data.add_vertex(Vec3f(b_min.x(), b_max.y(), b_min.z()));
        init_data.add_vertex(Vec3f(b_min.x() + size.x(), b_max.y(), b_min.z()));
        init_data.add_vertex(Vec3f(b_min.x(), b_max.y(), b_min.z()));
        init_data.add_vertex(Vec3f(b_min.x(), b_max.y() - size.y(), b_min.z()));
        init_data.add_vertex(Vec3f(b_min.x(), b_max.y(), b_min.z()));
        init_data.add_vertex(Vec3f(b_min.x(), b_max.y(), b_min.z() + size.z()));

        init_data.add_vertex(Vec3f(b_min.x(), b_min.y(), b_max.z()));
        init_data.add_vertex(Vec3f(b_min.x() + size.x(), b_min.y(), b_max.z()));
        init_data.add_vertex(Vec3f(b_min.x(), b_min.y(), b_max.z()));
        init_data.add_vertex(Vec3f(b_min.x(), b_min.y() + size.y(), b_max.z()));
        init_data.add_vertex(Vec3f(b_min.x(), b_min.y(), b_max.z()));
        init_data.add_vertex(Vec3f(b_min.x(), b_min.y(), b_max.z() - size.z()));

        init_data.add_vertex(Vec3f(b_max.x(), b_min.y(), b_max.z()));
        init_data.add_vertex(Vec3f(b_max.x() - size.x(), b_min.y(), b_max.z()));
        init_data.add_vertex(Vec3f(b_max.x(), b_min.y(), b_max.z()));
        init_data.add_vertex(Vec3f(b_max.x(), b_min.y() + size.y(), b_max.z()));
        init_data.add_vertex(Vec3f(b_max.x(), b_min.y(), b_max.z()));
        init_data.add_vertex(Vec3f(b_max.x(), b_min.y(), b_max.z() - size.z()));

        init_data.add_vertex(Vec3f(b_max.x(), b_max.y(), b_max.z()));
        init_data.add_vertex(Vec3f(b_max.x() - size.x(), b_max.y(), b_max.z()));
        init_data.add_vertex(Vec3f(b_max.x(), b_max.y(), b_max.z()));
        init_data.add_vertex(Vec3f(b_max.x(), b_max.y() - size.y(), b_max.z()));
        init_data.add_vertex(Vec3f(b_max.x(), b_max.y(), b_max.z()));
        init_data.add_vertex(Vec3f(b_max.x(), b_max.y(), b_max.z() - size.z()));

        init_data.add_vertex(Vec3f(b_min.x(), b_max.y(), b_max.z()));
        init_data.add_vertex(Vec3f(b_min.x() + size.x(), b_max.y(), b_max.z()));
        init_data.add_vertex(Vec3f(b_min.x(), b_max.y(), b_max.z()));
        init_data.add_vertex(Vec3f(b_min.x(), b_max.y() - size.y(), b_max.z()));
        init_data.add_vertex(Vec3f(b_min.x(), b_max.y(), b_max.z()));
        init_data.add_vertex(Vec3f(b_min.x(), b_max.y(), b_max.z() - size.z()));

        // indices
        for (unsigned int i = 0; i < 48; ++i) {
            init_data.add_index(i);
        }

        m_box.init_from(std::move(init_data));
    }

    glsafe(::glEnable(GL_DEPTH_TEST));

#if SLIC3R_OPENGL_ES
    GLShaderProgram* shader = wxGetApp().get_shader("dashed_lines");
#else
    if (!OpenGLManager::get_gl_info().is_core_profile())
        glsafe(::glLineWidth(2.0f * m_scale_factor));

    GLShaderProgram* shader = OpenGLManager::get_gl_info().is_core_profile() ? wxGetApp().get_shader("dashed_thick_lines") : wxGetApp().get_shader("flat");
#endif // SLIC3R_OPENGL_ES
    if (shader == nullptr)
        return;

    shader->start_using();
    const Camera& camera = wxGetApp().plater()->get_camera();
    shader->set_uniform("view_model_matrix", camera.get_view_matrix() * trafo);
    shader->set_uniform("projection_matrix", camera.get_projection_matrix());
#if !SLIC3R_OPENGL_ES
    if (OpenGLManager::get_gl_info().is_core_profile()) {
#endif // !SLIC3R_OPENGL_ES
        const std::array<int, 4>& viewport = camera.get_viewport();
        shader->set_uniform("viewport_size", Vec2d(double(viewport[2]), double(viewport[3])));
        shader->set_uniform("width", 1.5f);
        shader->set_uniform("gap_size", 0.0f);
#if !SLIC3R_OPENGL_ES
    }
#endif // !SLIC3R_OPENGL_ES
    m_box.set_color(to_rgba(color));
    m_box.render();
    shader->stop_using();
}

static ColorRGBA get_color(Axis axis)
{
    return AXES_COLOR[axis];
}

void Selection::render_sidebar_position_hints(const std::string& sidebar_field, GLShaderProgram& shader, const Transform3d& matrix)
{
    const Camera& camera = wxGetApp().plater()->get_camera();
    const Transform3d& view_matrix = camera.get_view_matrix();
    shader.set_uniform("projection_matrix", camera.get_projection_matrix());

    if (boost::ends_with(sidebar_field, "x")) {
        const Transform3d model_matrix = matrix * Geometry::rotation_transform(-0.5 * PI * Vec3d::UnitZ());
        shader.set_uniform("view_model_matrix", view_matrix * model_matrix);
        const Matrix3d view_normal_matrix = view_matrix.matrix().block(0, 0, 3, 3) * model_matrix.matrix().block(0, 0, 3, 3).inverse().transpose();
        shader.set_uniform("view_normal_matrix", view_normal_matrix);
        m_arrow.set_color(get_color(X));
        m_arrow.render();
    }
    else if (boost::ends_with(sidebar_field, "y")) {
        shader.set_uniform("view_model_matrix", view_matrix * matrix);
        shader.set_uniform("view_normal_matrix", (Matrix3d)Matrix3d::Identity());
        m_arrow.set_color(get_color(Y));
        m_arrow.render();
    }
    else if (boost::ends_with(sidebar_field, "z")) {
        const Transform3d model_matrix = matrix * Geometry::rotation_transform(0.5 * PI * Vec3d::UnitX());
        shader.set_uniform("view_model_matrix", view_matrix * model_matrix);
        const Matrix3d view_normal_matrix = view_matrix.matrix().block(0, 0, 3, 3) * model_matrix.matrix().block(0, 0, 3, 3).inverse().transpose();
        shader.set_uniform("view_normal_matrix", view_normal_matrix);
        m_arrow.set_color(get_color(Z));
        m_arrow.render();
    }
}

void Selection::render_sidebar_rotation_hints(const std::string& sidebar_field, GLShaderProgram& shader, const Transform3d& matrix)
{
    auto render_sidebar_rotation_hint = [this](GLShaderProgram& shader, const Transform3d& view_matrix, const Transform3d& model_matrix) {
        shader.set_uniform("view_model_matrix", view_matrix * model_matrix);
        Matrix3d view_normal_matrix = view_matrix.matrix().block(0, 0, 3, 3) * model_matrix.matrix().block(0, 0, 3, 3).inverse().transpose();
        shader.set_uniform("view_normal_matrix", view_normal_matrix);
        m_curved_arrow.render();
        const Transform3d matrix = model_matrix * Geometry::rotation_transform(PI * Vec3d::UnitZ());
        shader.set_uniform("view_model_matrix", view_matrix * matrix);
        view_normal_matrix = view_matrix.matrix().block(0, 0, 3, 3) * matrix.matrix().block(0, 0, 3, 3).inverse().transpose();
        shader.set_uniform("view_normal_matrix", view_normal_matrix);
        m_curved_arrow.render();
    };

    const Camera& camera = wxGetApp().plater()->get_camera();
    const Transform3d& view_matrix = camera.get_view_matrix();
    shader.set_uniform("projection_matrix", camera.get_projection_matrix());

    if (boost::ends_with(sidebar_field, "x")) {
        m_curved_arrow.set_color(get_color(X));
        render_sidebar_rotation_hint(shader, view_matrix, matrix * Geometry::rotation_transform(0.5 * PI * Vec3d::UnitY()));
    }
    else if (boost::ends_with(sidebar_field, "y")) {
        m_curved_arrow.set_color(get_color(Y));
        render_sidebar_rotation_hint(shader, view_matrix, matrix * Geometry::rotation_transform(-0.5 * PI * Vec3d::UnitX()));
    }
    else if (boost::ends_with(sidebar_field, "z")) {
        m_curved_arrow.set_color(get_color(Z));
        render_sidebar_rotation_hint(shader, view_matrix, matrix);
    }
}

void Selection::render_sidebar_scale_hints(const std::string& sidebar_field, GLShaderProgram& shader, const Transform3d& matrix)
{
    const bool uniform_scale = wxGetApp().obj_manipul()->get_uniform_scaling();

    auto render_sidebar_scale_hint = [this, uniform_scale](Axis axis, GLShaderProgram& shader, const Transform3d& view_matrix, const Transform3d& model_matrix) {
        m_arrow.set_color(uniform_scale ? UNIFORM_SCALE_COLOR : get_color(axis));
        Transform3d matrix = model_matrix * Geometry::translation_transform(5.0 * Vec3d::UnitY());
        shader.set_uniform("view_model_matrix", view_matrix * matrix);
        Matrix3d view_normal_matrix = view_matrix.matrix().block(0, 0, 3, 3) * matrix.matrix().block(0, 0, 3, 3).inverse().transpose();
        shader.set_uniform("view_normal_matrix", view_normal_matrix);
        m_arrow.render();

        matrix = model_matrix * Geometry::translation_transform(-5.0 * Vec3d::UnitY()) * Geometry::rotation_transform(PI * Vec3d::UnitZ());
        shader.set_uniform("view_model_matrix", view_matrix * matrix);
        view_normal_matrix = view_matrix.matrix().block(0, 0, 3, 3) * matrix.matrix().block(0, 0, 3, 3).inverse().transpose();
        shader.set_uniform("view_normal_matrix", view_normal_matrix);
        m_arrow.render();
    };

    const Camera& camera = wxGetApp().plater()->get_camera();
    const Transform3d& view_matrix = camera.get_view_matrix();
    shader.set_uniform("projection_matrix", camera.get_projection_matrix());

    if (boost::ends_with(sidebar_field, "x") || uniform_scale)
      render_sidebar_scale_hint(X, shader, view_matrix, matrix * Geometry::rotation_transform(-0.5 * PI * Vec3d::UnitZ()));

    if (boost::ends_with(sidebar_field, "y") || uniform_scale)
        render_sidebar_scale_hint(Y, shader, view_matrix, matrix);

    if (boost::ends_with(sidebar_field, "z") || uniform_scale)
      render_sidebar_scale_hint(Z, shader, view_matrix, matrix * Geometry::rotation_transform(0.5 * PI * Vec3d::UnitX()));
}

void Selection::render_sidebar_layers_hints(const std::string& sidebar_field, GLShaderProgram& shader)
{
    static const float Margin = 10.0f;

    std::string field = sidebar_field;

    // extract max_z
    std::string::size_type pos = field.rfind("_");
    if (pos == std::string::npos)
        return;

    const float max_z = float(string_to_double_decimal_point(field.substr(pos + 1)));

    // extract min_z
    field = field.substr(0, pos);
    pos = field.rfind("_");
    if (pos == std::string::npos)
        return;

    const float min_z = float(string_to_double_decimal_point(field.substr(pos + 1)));

    // extract type
    field = field.substr(0, pos);
    pos = field.rfind("_");
    if (pos == std::string::npos)
        return;

    const int type = std::stoi(field.substr(pos + 1));

    const BoundingBoxf3& box = get_bounding_box();

    // view dependend order of rendering to keep correct transparency
    const bool camera_on_top = wxGetApp().plater()->get_camera().is_looking_downward();
    const float z1 = camera_on_top ? min_z : max_z;
    const float z2 = camera_on_top ? max_z : min_z;

    const Vec3f p1 = { float(box.min.x()) - Margin, float(box.min.y()) - Margin, z1 };
    const Vec3f p2 = { float(box.max.x()) + Margin, float(box.max.y()) + Margin, z2 };

    glsafe(::glEnable(GL_DEPTH_TEST));
    glsafe(::glDisable(GL_CULL_FACE));
    glsafe(::glEnable(GL_BLEND));
    glsafe(::glBlendFunc(GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA));

    if (!m_planes.models[0].is_initialized() || !is_approx(m_planes.check_points[0], p1)) {
        m_planes.check_points[0] = p1;
        m_planes.models[0].reset();

        GLModel::Geometry init_data;
        init_data.format = { GLModel::Geometry::EPrimitiveType::Triangles, GLModel::Geometry::EVertexLayout::P3 };
        init_data.reserve_vertices(4);
        init_data.reserve_indices(6);

        // vertices
        init_data.add_vertex(Vec3f(p1.x(), p1.y(), z1));
        init_data.add_vertex(Vec3f(p2.x(), p1.y(), z1));
        init_data.add_vertex(Vec3f(p2.x(), p2.y(), z1));
        init_data.add_vertex(Vec3f(p1.x(), p2.y(), z1));

        // indices
        init_data.add_triangle(0, 1, 2);
        init_data.add_triangle(2, 3, 0);

        m_planes.models[0].init_from(std::move(init_data));
    }

    if (!m_planes.models[1].is_initialized() || !is_approx(m_planes.check_points[1], p2)) {
        m_planes.check_points[1] = p2;
        m_planes.models[1].reset();

        GLModel::Geometry init_data;
        init_data.format = { GLModel::Geometry::EPrimitiveType::Triangles, GLModel::Geometry::EVertexLayout::P3 };
        init_data.reserve_vertices(4);
        init_data.reserve_indices(6);

        // vertices
        init_data.add_vertex(Vec3f(p1.x(), p1.y(), z2));
        init_data.add_vertex(Vec3f(p2.x(), p1.y(), z2));
        init_data.add_vertex(Vec3f(p2.x(), p2.y(), z2));
        init_data.add_vertex(Vec3f(p1.x(), p2.y(), z2));

        // indices
        init_data.add_triangle(0, 1, 2);
        init_data.add_triangle(2, 3, 0);

        m_planes.models[1].init_from(std::move(init_data));
    }

    const Camera& camera = wxGetApp().plater()->get_camera();
    shader.set_uniform("view_model_matrix", camera.get_view_matrix());
    shader.set_uniform("projection_matrix", camera.get_projection_matrix());

    m_planes.models[0].set_color((camera_on_top && type == 1) || (!camera_on_top && type == 2) ? SOLID_PLANE_COLOR : TRANSPARENT_PLANE_COLOR);
    m_planes.models[0].render();
    m_planes.models[1].set_color((camera_on_top && type == 2) || (!camera_on_top && type == 1) ? SOLID_PLANE_COLOR : TRANSPARENT_PLANE_COLOR);
    m_planes.models[1].render();

    glsafe(::glEnable(GL_CULL_FACE));
    glsafe(::glDisable(GL_BLEND));
}

#if ENABLE_MATRICES_DEBUG
void Selection::render_debug_window() const
{
    if (m_list.empty())
        return;

    if (get_first_volume()->is_wipe_tower)
        return;

    ImGuiWrapper& imgui = *wxGetApp().imgui();
    ImGui::SetNextWindowCollapsed(true, ImGuiCond_Once);
    imgui.begin(std::string("Selection matrices"), ImGuiWindowFlags_AlwaysAutoResize | ImGuiWindowFlags_NoResize);

    auto volume_name = [this](size_t id) {
        const GLVolume& v = *(*m_volumes)[id];
        return m_model->objects[v.object_idx()]->volumes[v.volume_idx()]->name;
    };

    static size_t current_cmb_idx = 0;
    static size_t current_vol_idx = *m_list.begin();

    if (m_list.find(current_vol_idx) == m_list.end())
        current_vol_idx = *m_list.begin();

    if (ImGui::BeginCombo("Volumes", volume_name(current_vol_idx).c_str())) {
        size_t count = 0;
        for (unsigned int id : m_list) {
            const GLVolume& v = *(*m_volumes)[id];
            const bool is_selected = (current_cmb_idx == count);
            if (ImGui::Selectable(volume_name(id).c_str(), is_selected)) {
                current_cmb_idx = count;
                current_vol_idx = id;
            }
            if (is_selected)
                ImGui::SetItemDefaultFocus();
            ++count;
        }
        ImGui::EndCombo();
    }

    static int current_method_idx = 0;
    ImGui::Combo("Decomposition method", &current_method_idx, "computeRotationScaling\0computeScalingRotation\0SVD\0");

    const GLVolume& v = *get_volume(current_vol_idx);

    auto add_matrix = [&imgui](const std::string& name, const Transform3d& m, unsigned int size) {
        ImGui::BeginGroup();
        imgui.text(name);
        if (ImGui::BeginTable(name.c_str(), size, ImGuiTableFlags_BordersOuter | ImGuiTableFlags_BordersInner)) {
            for (unsigned int r = 0; r < size; ++r) {
                ImGui::TableNextRow();
                for (unsigned int c = 0; c < size; ++c) {
                    ImGui::TableSetColumnIndex(c);
                    imgui.text(std::to_string(m(r, c)));
                }
            }
            ImGui::EndTable();
        }
        ImGui::EndGroup();
    };

    auto add_matrices_set = [&imgui, add_matrix](const std::string& name, const Transform3d& m, size_t method) {
        static unsigned int counter = 0;
        ++counter;
        if (ImGui::CollapsingHeader(name.c_str(), ImGuiTreeNodeFlags_DefaultOpen)) {
            add_matrix("Full", m, 4);

            if (method == 0 || method == 1) {
                Matrix3d rotation;
                Matrix3d scale;
                if (method == 0)
                    m.computeRotationScaling(&rotation, &scale);
                else
                    m.computeScalingRotation(&scale, &rotation);

                ImGui::SameLine();
                add_matrix("Rotation component", Transform3d(rotation), 3);
                ImGui::SameLine();
                add_matrix("Scale component", Transform3d(scale), 3);
            }
            else {
                const Geometry::TransformationSVD svd(m);

                ImGui::SameLine();
                add_matrix("U", Transform3d(svd.u), 3);
                ImGui::SameLine();
                add_matrix("S", Transform3d(svd.s), 3);
                ImGui::SameLine();
                add_matrix("V", Transform3d(svd.v), 3);
                ImGui::Dummy(ImVec2(0.0f, 0.0f));
                float spacing = 0.0f;
                if (svd.rotation) {
                    ImGui::SameLine(0.0f, spacing);
                    imgui.text_colored(ImGuiWrapper::COL_ORANGE_LIGHT, svd.rotation_90_degrees ? "Rotation 90 degs" : "Rotation");
                    spacing = 10.0f;
                }
                if (svd.scale) {
                    ImGui::SameLine(0.0f, spacing);
                    imgui.text_colored(ImGuiWrapper::COL_ORANGE_LIGHT, svd.anisotropic_scale ? "Anisotropic scale" : "Isotropic scale");
                    spacing = 10.0f;
                }
                if (svd.mirror) {
                    ImGui::SameLine(0.0f, spacing);
                    imgui.text_colored(ImGuiWrapper::COL_ORANGE_LIGHT, "Mirror");
                    spacing = 10.0f;
                }
                if (svd.skew) {
                    ImGui::SameLine(0.0f, spacing);
                    imgui.text_colored(ImGuiWrapper::COL_ORANGE_LIGHT, "Skew");
                }
            }
        }
    };

    add_matrices_set("World", v.world_matrix(), current_method_idx);
    add_matrices_set("Instance", v.get_instance_transformation().get_matrix(), current_method_idx);
    add_matrices_set("Volume", v.get_volume_transformation().get_matrix(), current_method_idx);

    imgui.end();
}
#endif // ENABLE_MATRICES_DEBUG

static bool is_left_handed(const Transform3d::ConstLinearPart& m)
{
    return m.determinant() < 0;
}

static bool is_left_handed(const Transform3d& m)
{
    return is_left_handed(m.linear());
}

#ifndef NDEBUG
static bool is_rotation_xy_synchronized(const Vec3d &rot_xyz_from, const Vec3d &rot_xyz_to)
{
    const Eigen::AngleAxisd angle_axis(Geometry::rotation_xyz_diff(rot_xyz_from, rot_xyz_to));
    const Vec3d  axis = angle_axis.axis();
    const double angle = angle_axis.angle();
    if (std::abs(angle) < 1e-8)
        return true;
    assert(std::abs(axis.x()) < 1e-8);
    assert(std::abs(axis.y()) < 1e-8);
    assert(std::abs(std::abs(axis.z()) - 1.) < 1e-8);
    return std::abs(axis.x()) < 1e-8 && std::abs(axis.y()) < 1e-8 && std::abs(std::abs(axis.z()) - 1.) < 1e-8;
}

#if 0
static void verify_instances_rotation_synchronized(const Model &model, const GLVolumePtrs &volumes)
{
    for (int idx_object = 0; idx_object < int(model.objects.size()); ++idx_object) {
        int idx_volume_first = -1;
        for (int i = 0; i < (int)volumes.size(); ++i) {
            if (volumes[i]->object_idx() == idx_object) {
                idx_volume_first = i;
                break;
            }
        }
        assert(idx_volume_first != -1); // object without instances?
        if (idx_volume_first == -1)
            continue;
        const Vec3d &rotation0 = volumes[idx_volume_first]->get_instance_rotation();
        for (int i = idx_volume_first + 1; i < (int)volumes.size(); ++i)
            if (volumes[i]->object_idx() == idx_object) {
                const Vec3d &rotation = volumes[i]->get_instance_rotation();
                assert(is_rotation_xy_synchronized(rotation, rotation0));
            }
    }
}
#endif

static bool is_rotation_xy_synchronized(const Transform3d::ConstLinearPart &trafo_from, const Transform3d::ConstLinearPart &trafo_to)
{
    auto rot = trafo_to * trafo_from.inverse();
    static constexpr const double eps = EPSILON;
    return 
           // Looks like a rotation around Z: block(0..1, 0..1) + no change of Z component.
           is_approx(rot(0, 0),   rot(1, 1), eps) &&
           is_approx(rot(0, 1), - rot(1, 0), eps) &&
           is_approx(rot(2, 2),          1., eps) &&
           // Rest should be zeros.
           is_approx(rot(0, 2),          0., eps) &&
           is_approx(rot(1, 2),          0., eps) &&
           is_approx(rot(2, 0),          0., eps) &&
           is_approx(rot(2, 1),          0., eps) &&
           // Determinant equals 1
           is_approx(rot.determinant(),  1., eps) &&
           // and finally the rotated X and Y axes shall be perpendicular.
           is_approx(rot(0, 0) * rot(0, 1) + rot(1, 0) * rot(1, 1), 0., eps);
}

static bool is_rotation_xy_synchronized(const Transform3d& trafo_from, const Transform3d& trafo_to)
{
    return is_rotation_xy_synchronized(trafo_from.linear(), trafo_to.linear());
}

static void verify_instances_rotation_synchronized(const Model &model, const GLVolumePtrs &volumes)
{
    for (int idx_object = 0; idx_object < int(model.objects.size()); ++idx_object) {
        int idx_volume_first = -1;
        for (int i = 0; i < (int)volumes.size(); ++i) {
            if (volumes[i]->object_idx() == idx_object) {
                idx_volume_first = i;
                break;
            }
        }
        assert(idx_volume_first != -1); // object without instances?
        if (idx_volume_first == -1)
            continue;
        const Transform3d::ConstLinearPart& rotation0 = volumes[idx_volume_first]->get_instance_transformation().get_matrix().linear();
        for (int i = idx_volume_first + 1; i < (int)volumes.size(); ++i)
            if (volumes[i]->object_idx() == idx_object && volumes[i]->volume_idx() >= 0) {
                const Transform3d::ConstLinearPart& rotation = volumes[i]->get_instance_transformation().get_matrix().linear();
                assert(is_rotation_xy_synchronized(rotation, rotation0));
            }
    }
}

#endif /* NDEBUG */

void Selection::synchronize_unselected_instances(SyncRotationType sync_rotation_type)
{
    std::set<unsigned int> done;  // prevent processing volumes twice
    done.insert(m_list.begin(), m_list.end());
    for (unsigned int i : m_list) {
        if (done.size() == m_volumes->size())
            break;
        const GLVolume* volume_i = (*m_volumes)[i];
        if (volume_i->is_wipe_tower)
            continue;

        const int object_idx = volume_i->object_idx();
        const int instance_idx = volume_i->instance_idx();
        const Transform3d& curr_inst_trafo_i = volume_i->get_instance_transformation().get_matrix();
        const Transform3d& old_inst_trafo_i = m_cache.volumes_data[i].get_instance_transform().get_matrix();
        bool               mirrored = is_left_handed(curr_inst_trafo_i) != is_left_handed(old_inst_trafo_i);
//        bool               mirrored = curr_inst_trafo_i.linear().determinant() * old_inst_trafo_i.linear().determinant() < 0;

        // Process unselected instances.
        for (unsigned int j = 0; j < (unsigned int)m_volumes->size(); ++j) {
            if (done.size() == m_volumes->size())
                break;
            if (done.find(j) != done.end())
                continue;
            GLVolume* volume_j = (*m_volumes)[j];
            if (volume_j->object_idx() != object_idx || volume_j->instance_idx() == instance_idx)
                continue;
            const Transform3d& old_inst_trafo_j = m_cache.volumes_data[j].get_instance_transform().get_matrix();
            assert(is_rotation_xy_synchronized(old_inst_trafo_i, old_inst_trafo_j));
            Transform3d        new_inst_trafo_j = volume_j->get_instance_transformation().get_matrix();
            if (sync_rotation_type == SyncRotationType::RESET) {
                Geometry::Transformation new_inst_trafo_j_no_rotation(new_inst_trafo_j);
                new_inst_trafo_j_no_rotation.reset_rotation();
                new_inst_trafo_j = new_inst_trafo_j_no_rotation.get_matrix();
            }
            else if (sync_rotation_type != SyncRotationType::NONE || mirrored)
                new_inst_trafo_j.linear() = (old_inst_trafo_j.linear() * old_inst_trafo_i.linear().inverse()) * curr_inst_trafo_i.linear();
            if (wxGetApp().preset_bundle->printers.get_edited_preset().printer_technology() != ptSLA)
                new_inst_trafo_j.translation().z() = curr_inst_trafo_i.translation().z();
            assert(is_rotation_xy_synchronized(curr_inst_trafo_i, new_inst_trafo_j));
            volume_j->set_instance_transformation(new_inst_trafo_j);
            done.insert(j);
        }
    }
#ifndef NDEBUG
    verify_instances_rotation_synchronized(*m_model, *m_volumes);
#endif /* NDEBUG */
}

void Selection::synchronize_unselected_volumes()
{
    for (unsigned int i : m_list) {
        const GLVolume* volume = (*m_volumes)[i];
        if (volume->is_wipe_tower)
            continue;

        const int object_idx = volume->object_idx();
        const int volume_idx = volume->volume_idx();
        const Geometry::Transformation& trafo = volume->get_volume_transformation();

        // Process unselected volumes.
        for (unsigned int j = 0; j < (unsigned int)m_volumes->size(); ++j) {
            if (j == i)
                continue;

            GLVolume* v = (*m_volumes)[j];
            if (v->object_idx() != object_idx || v->volume_idx() != volume_idx)
                continue;

            v->set_volume_transformation(trafo);
        }
    }
}

void Selection::ensure_on_bed()
{
    typedef std::map<std::pair<int, int>, double> InstancesToZMap;
    InstancesToZMap instances_min_z;

    for (size_t i = 0; i < m_volumes->size(); ++i) {
        GLVolume* volume = (*m_volumes)[i];
        if (!volume->is_wipe_tower && !volume->is_modifier && 
            std::find(m_cache.sinking_volumes.begin(), m_cache.sinking_volumes.end(), i) == m_cache.sinking_volumes.end()) {
            const double min_z = volume->transformed_convex_hull_bounding_box().min.z();
            std::pair<int, int> instance = std::make_pair(volume->object_idx(), volume->instance_idx());
            InstancesToZMap::iterator it = instances_min_z.find(instance);
            if (it == instances_min_z.end())
                it = instances_min_z.insert(InstancesToZMap::value_type(instance, DBL_MAX)).first;

            it->second = std::min(it->second, min_z);
        }
    }

    for (GLVolume* volume : *m_volumes) {
        std::pair<int, int> instance = std::make_pair(volume->object_idx(), volume->instance_idx());
        InstancesToZMap::iterator it = instances_min_z.find(instance);
        if (it != instances_min_z.end())
            volume->set_instance_offset(Z, volume->get_instance_offset(Z) - it->second);
    }
}

void Selection::ensure_not_below_bed()
{
    typedef std::map<std::pair<int, int>, double> InstancesToZMap;
    InstancesToZMap instances_max_z;

    for (size_t i = 0; i < m_volumes->size(); ++i) {
        GLVolume* volume = (*m_volumes)[i];
        if (!volume->is_wipe_tower && !volume->is_modifier) {
            const double max_z = volume->transformed_convex_hull_bounding_box().max.z();
            const std::pair<int, int> instance = std::make_pair(volume->object_idx(), volume->instance_idx());
            InstancesToZMap::iterator it = instances_max_z.find(instance);
            if (it == instances_max_z.end())
                it = instances_max_z.insert({ instance, -DBL_MAX }).first;

            it->second = std::max(it->second, max_z);
        }
    }

    if (is_any_volume()) {
        for (unsigned int i : m_list) {
            GLVolume& volume = *(*m_volumes)[i];
            const std::pair<int, int> instance = std::make_pair(volume.object_idx(), volume.instance_idx());
            InstancesToZMap::const_iterator it = instances_max_z.find(instance);
            const double z_shift = SINKING_MIN_Z_THRESHOLD - it->second;
            if (it != instances_max_z.end() && z_shift > 0.0)
                volume.set_volume_offset(Z, volume.get_volume_offset(Z) + z_shift);
        }
    }
    else {
        for (GLVolume* volume : *m_volumes) {
            const std::pair<int, int> instance = std::make_pair(volume->object_idx(), volume->instance_idx());
            InstancesToZMap::const_iterator it = instances_max_z.find(instance);
            if (it != instances_max_z.end() && it->second < SINKING_MIN_Z_THRESHOLD)
                volume->set_instance_offset(Z, volume->get_instance_offset(Z) + SINKING_MIN_Z_THRESHOLD - it->second);
        }
    }
}

bool Selection::is_from_fully_selected_instance(unsigned int volume_idx) const
{
    struct SameInstance
    {
        int obj_idx;
        int inst_idx;
        GLVolumePtrs& volumes;

        SameInstance(int obj_idx, int inst_idx, GLVolumePtrs& volumes) : obj_idx(obj_idx), inst_idx(inst_idx), volumes(volumes) {}
        bool operator () (unsigned int i) { return (volumes[i]->volume_idx() >= 0) && (volumes[i]->object_idx() == obj_idx) && (volumes[i]->instance_idx() == inst_idx); }
    };

    if ((unsigned int)m_volumes->size() <= volume_idx)
        return false;

    GLVolume* volume = (*m_volumes)[volume_idx];
    int object_idx = volume->object_idx();
    if ((int)m_model->objects.size() <= object_idx)
        return false;

    unsigned int count = (unsigned int)std::count_if(m_list.begin(), m_list.end(), SameInstance(object_idx, volume->instance_idx(), *m_volumes));

    PrinterTechnology pt = wxGetApp().plater()->printer_technology();
    const ModelVolumePtrs& volumes = m_model->objects[object_idx]->volumes;
    const unsigned int vol_cnt = (unsigned int)std::count_if(volumes.begin(), volumes.end(), [pt](const ModelVolume* volume) { return pt == ptFFF || !volume->is_modifier(); });

    return count == vol_cnt;
}

void Selection::paste_volumes_from_clipboard()
{
#ifdef _DEBUG
    check_model_ids_validity(*m_model);
#endif /* _DEBUG */

    int dst_obj_idx = get_object_idx();
    if ((dst_obj_idx < 0) || ((int)m_model->objects.size() <= dst_obj_idx))
        return;

    ModelObject* dst_object = m_model->objects[dst_obj_idx];

    int dst_inst_idx = get_instance_idx();
    if ((dst_inst_idx < 0) || ((int)dst_object->instances.size() <= dst_inst_idx))
        return;

    ModelObject* src_object = m_clipboard.get_object(0);
    if (src_object != nullptr)
    {
        ModelInstance* dst_instance = dst_object->instances[dst_inst_idx];
        BoundingBoxf3 dst_instance_bb = dst_object->instance_bounding_box(dst_inst_idx);
        Transform3d src_matrix = src_object->instances[0]->get_transformation().get_matrix_no_offset();
        Transform3d dst_matrix = dst_instance->get_transformation().get_matrix_no_offset();
        bool from_same_object = (src_object->input_file == dst_object->input_file) && src_matrix.isApprox(dst_matrix);

        // used to keep relative position of multivolume selections when pasting from another object
        BoundingBoxf3 total_bb;

        ModelVolumePtrs volumes;
        for (ModelVolume* src_volume : src_object->volumes)
        {
            ModelVolume* dst_volume = dst_object->add_volume(*src_volume);
            dst_volume->set_new_unique_id();
            if (from_same_object)
            {
//                // if the volume comes from the same object, apply the offset in world system
//                double offset = wxGetApp().plater()->canvas3D()->get_size_proportional_to_max_bed_size(0.05);
//                dst_volume->translate(dst_matrix.inverse() * Vec3d(offset, offset, 0.0));
            }
            else
            {
                // if the volume comes from another object, apply the offset as done when adding modifiers
                // see ObjectList::load_generic_subobject()
                total_bb.merge(dst_volume->mesh().bounding_box().transformed(src_volume->get_matrix()));
            }

            volumes.push_back(dst_volume);
#ifdef _DEBUG
		    check_model_ids_validity(*m_model);
#endif /* _DEBUG */
        }

        // keeps relative position of multivolume selections
        if (!from_same_object)
        {
            for (ModelVolume* v : volumes)
            {
                v->set_offset((v->get_offset() - total_bb.center()) + dst_matrix.inverse() * (Vec3d(dst_instance_bb.max(0), dst_instance_bb.min(1), dst_instance_bb.min(2)) + 0.5 * total_bb.size() - dst_instance->get_transformation().get_offset()));
            }
        }

        wxGetApp().obj_list()->paste_volumes_into_list(dst_obj_idx, volumes);
    }

#ifdef _DEBUG
    check_model_ids_validity(*m_model);
#endif /* _DEBUG */
}

void Selection::paste_objects_from_clipboard()
{
#ifdef _DEBUG
    check_model_ids_validity(*m_model);
#endif /* _DEBUG */

    std::vector<size_t> object_idxs;
    const ModelObjectPtrs& src_objects = m_clipboard.get_objects();
    for (const ModelObject* src_object : src_objects)
    {
        ModelObject* dst_object = m_model->add_object(*src_object);
        double offset = wxGetApp().plater()->canvas3D()->get_size_proportional_to_max_bed_size(0.05);
        Vec3d displacement(offset, offset, 0.0);
        for (ModelInstance* inst : dst_object->instances)
        {
            inst->set_offset(inst->get_offset() + displacement);
        }

        object_idxs.push_back(m_model->objects.size() - 1);
#ifdef _DEBUG
	    check_model_ids_validity(*m_model);
#endif /* _DEBUG */
    }

    wxGetApp().obj_list()->paste_objects_into_list(object_idxs);

#ifdef _DEBUG
    check_model_ids_validity(*m_model);
#endif /* _DEBUG */
}

void Selection::transform_instance_relative(GLVolume& volume, const VolumeCache& volume_data, TransformationType transformation_type,
    const Transform3d& transform, const Vec3d& world_pivot)
{
    assert(transformation_type.relative());

    const Geometry::Transformation& inst_trafo = volume_data.get_instance_transform();
    if (transformation_type.world()) {
        const Vec3d inst_pivot = transformation_type.independent() && !is_from_single_instance() ? inst_trafo.get_offset() : world_pivot;
        const Transform3d trafo = Geometry::translation_transform(inst_pivot) * transform * Geometry::translation_transform(-inst_pivot);
        volume.set_instance_transformation(trafo * inst_trafo.get_matrix());
    }
    else if (transformation_type.instance())
        volume.set_instance_transformation(inst_trafo.get_matrix() * transform);
    else
        assert(false);
}

void Selection::transform_volume_relative(GLVolume& volume, const VolumeCache& volume_data, TransformationType transformation_type,
    const Transform3d& transform, const Vec3d& world_pivot)
{
    assert(transformation_type.relative());

    const Geometry::Transformation& vol_trafo = volume_data.get_volume_transform();
    const Geometry::Transformation& inst_trafo = volume_data.get_instance_transform();

    if (transformation_type.world()) {
        const Vec3d inst_pivot = transformation_type.independent() ? vol_trafo.get_offset() : (Vec3d)(inst_trafo.get_matrix().inverse() * world_pivot);
        const Transform3d inst_matrix_no_offset = inst_trafo.get_matrix_no_offset();
        const Transform3d trafo = Geometry::translation_transform(inst_pivot) * inst_matrix_no_offset.inverse() * transform * inst_matrix_no_offset * Geometry::translation_transform(-inst_pivot);
        volume.set_volume_transformation(trafo * vol_trafo.get_matrix());
    }
    else if (transformation_type.instance()) {
        const Vec3d inst_pivot = transformation_type.independent() ? vol_trafo.get_offset() : (Vec3d)(inst_trafo.get_matrix().inverse() * world_pivot);
        const Transform3d trafo = Geometry::translation_transform(inst_pivot) * transform * Geometry::translation_transform(-inst_pivot);
        volume.set_volume_transformation(trafo * vol_trafo.get_matrix());
    }
    else if (transformation_type.local())
        volume.set_volume_transformation(vol_trafo.get_matrix() * transform);
    else
        assert(false);
}

ModelVolume *get_selected_volume(const Selection &selection)
{
    const GLVolume *gl_volume = get_selected_gl_volume(selection);
    if (gl_volume == nullptr)
        return nullptr;
    const ModelObjectPtrs &objects = selection.get_model()->objects;
    return get_model_volume(*gl_volume, objects);
}

const GLVolume *get_selected_gl_volume(const Selection &selection)
{
    int object_idx = selection.get_object_idx();
    // is more object selected?
    if (object_idx == -1)
        return nullptr;

    const auto &list = selection.get_volume_idxs();
    // is more volumes selected?
    if (list.size() != 1)
        return nullptr;

    unsigned int volume_idx = *list.begin();
    return selection.get_volume(volume_idx);
}

ModelVolume *get_selected_volume(const ObjectID &volume_id, const Selection &selection) {
    const Selection::IndicesList &volume_ids = selection.get_volume_idxs();
    const ModelObjectPtrs &model_objects     = selection.get_model()->objects;
    for (auto id : volume_ids) {
        const GLVolume *selected_volume = selection.get_volume(id);
        const GLVolume::CompositeID &cid = selected_volume->composite_id;
        ModelObject *obj    = model_objects[cid.object_id];
        ModelVolume *volume = obj->volumes[cid.volume_id];
        if (volume_id == volume->id())
            return volume;
    }
    return nullptr;
}

ModelVolume *get_volume(const ObjectID &volume_id, const Selection &selection) {
    const ModelObjectPtrs &objects = selection.get_model()->objects;
    for (const ModelObject *object : objects) {
        for (ModelVolume *volume : object->volumes) {
            if (volume->id() == volume_id)
                return volume;
        }        
    }
    return nullptr;
}

} // namespace GUI
} // namespace Slic3r
