PrusaSlicer-NonPlainar/xs/src/libslic3r/TriangleMesh.cpp

#include "TriangleMesh.hpp"
#include "ClipperUtils.hpp"
#include "Geometry.hpp"
#include <cmath>
#include <queue>
#include <deque>
#include <set>
#include <vector>
#include <map>
#include <utility>
#include <algorithm>
#include <math.h>
#include <assert.h>

#ifdef SLIC3R_DEBUG
#include "SVG.hpp"
#endif

namespace Slic3r {

TriangleMesh::TriangleMesh()
    : repaired(false)
{
    stl_initialize(&this->stl);
}

TriangleMesh::TriangleMesh(const TriangleMesh &other)
    : stl(other.stl), repaired(other.repaired)
{
    this->stl.heads = NULL;
    this->stl.tail  = NULL;
    this->stl.error = other.stl.error;
    if (other.stl.facet_start != NULL) {
        this->stl.facet_start = (stl_facet*)calloc(other.stl.stats.number_of_facets, sizeof(stl_facet));
        std::copy(other.stl.facet_start, other.stl.facet_start + other.stl.stats.number_of_facets, this->stl.facet_start);
    }
    if (other.stl.neighbors_start != NULL) {
        this->stl.neighbors_start = (stl_neighbors*)calloc(other.stl.stats.number_of_facets, sizeof(stl_neighbors));
        std::copy(other.stl.neighbors_start, other.stl.neighbors_start + other.stl.stats.number_of_facets, this->stl.neighbors_start);
    }
    if (other.stl.v_indices != NULL) {
        this->stl.v_indices = (v_indices_struct*)calloc(other.stl.stats.number_of_facets, sizeof(v_indices_struct));
        std::copy(other.stl.v_indices, other.stl.v_indices + other.stl.stats.number_of_facets, this->stl.v_indices);
    }
    if (other.stl.v_shared != NULL) {
        this->stl.v_shared = (stl_vertex*)calloc(other.stl.stats.shared_vertices, sizeof(stl_vertex));
        std::copy(other.stl.v_shared, other.stl.v_shared + other.stl.stats.shared_vertices, this->stl.v_shared);
    }
}

TriangleMesh& TriangleMesh::operator= (TriangleMesh other)
{
    this->swap(other);
    return *this;
}

void
TriangleMesh::swap(TriangleMesh &other)
{
    std::swap(this->stl,                 other.stl);
    std::swap(this->repaired,            other.repaired);
    std::swap(this->stl.facet_start,     other.stl.facet_start);
    std::swap(this->stl.neighbors_start, other.stl.neighbors_start);
    std::swap(this->stl.v_indices,       other.stl.v_indices);
    std::swap(this->stl.v_shared,        other.stl.v_shared);
}

TriangleMesh::~TriangleMesh() {
    stl_close(&this->stl);
}

void
TriangleMesh::ReadSTLFile(char* input_file) {
    stl_open(&stl, input_file);
}

void
TriangleMesh::write_ascii(char* output_file)
{
    stl_write_ascii(&this->stl, output_file, "");
}

void
TriangleMesh::write_binary(char* output_file)
{
    stl_write_binary(&this->stl, output_file, "");
}

void
TriangleMesh::repair() {
    if (this->repaired) return;
    
    // admesh fails when repairing empty meshes
    if (this->stl.stats.number_of_facets == 0) return;
    
    // checking exact
    stl_check_facets_exact(&stl);
    stl.stats.facets_w_1_bad_edge = (stl.stats.connected_facets_2_edge - stl.stats.connected_facets_3_edge);
    stl.stats.facets_w_2_bad_edge = (stl.stats.connected_facets_1_edge - stl.stats.connected_facets_2_edge);
    stl.stats.facets_w_3_bad_edge = (stl.stats.number_of_facets - stl.stats.connected_facets_1_edge);
    
    // checking nearby
    //int last_edges_fixed = 0;
    float tolerance = stl.stats.shortest_edge;
    float increment = stl.stats.bounding_diameter / 10000.0;
    int iterations = 2;
    if (stl.stats.connected_facets_3_edge < stl.stats.number_of_facets) {
        for (int i = 0; i < iterations; i++) {
            if (stl.stats.connected_facets_3_edge < stl.stats.number_of_facets) {
                //printf("Checking nearby. Tolerance= %f Iteration=%d of %d...", tolerance, i + 1, iterations);
                stl_check_facets_nearby(&stl, tolerance);
                //printf("  Fixed %d edges.\n", stl.stats.edges_fixed - last_edges_fixed);
                //last_edges_fixed = stl.stats.edges_fixed;
                tolerance += increment;
            } else {
                break;
            }
        }
    }
    
    // remove_unconnected
    if (stl.stats.connected_facets_3_edge <  stl.stats.number_of_facets) {
        stl_remove_unconnected_facets(&stl);
    }
    
    // fill_holes
    if (stl.stats.connected_facets_3_edge < stl.stats.number_of_facets) {
        stl_fill_holes(&stl);
        stl_clear_error(&stl);
    }
    
    // normal_directions
    stl_fix_normal_directions(&stl);
    
    // normal_values
    stl_fix_normal_values(&stl);
    
    // always calculate the volume and reverse all normals if volume is negative
    stl_calculate_volume(&stl);
    
    // neighbors
    stl_verify_neighbors(&stl);
    
    this->repaired = true;
}

void
TriangleMesh::reset_repair_stats() {
    this->stl.stats.degenerate_facets   = 0;
    this->stl.stats.edges_fixed         = 0;
    this->stl.stats.facets_removed      = 0;
    this->stl.stats.facets_added        = 0;
    this->stl.stats.facets_reversed     = 0;
    this->stl.stats.backwards_edges     = 0;
    this->stl.stats.normals_fixed       = 0;
}

bool
TriangleMesh::needed_repair() const
{
    return this->stl.stats.degenerate_facets    > 0
        || this->stl.stats.edges_fixed          > 0
        || this->stl.stats.facets_removed       > 0
        || this->stl.stats.facets_added         > 0
        || this->stl.stats.facets_reversed      > 0
        || this->stl.stats.backwards_edges      > 0;
}

size_t
TriangleMesh::facets_count() const
{
    return this->stl.stats.number_of_facets;
}

void
TriangleMesh::WriteOBJFile(char* output_file) {
    stl_generate_shared_vertices(&stl);
    stl_write_obj(&stl, output_file);
}

void TriangleMesh::scale(float factor)
{
    stl_scale(&(this->stl), factor);
    stl_invalidate_shared_vertices(&this->stl);
}

void TriangleMesh::scale(const Pointf3 &versor)
{
    float fversor[3];
    fversor[0] = versor.x;
    fversor[1] = versor.y;
    fversor[2] = versor.z;
    stl_scale_versor(&this->stl, fversor);
    stl_invalidate_shared_vertices(&this->stl);
}

void TriangleMesh::translate(float x, float y, float z)
{
    stl_translate_relative(&(this->stl), x, y, z);
    stl_invalidate_shared_vertices(&this->stl);
}

void TriangleMesh::rotate(float angle, const Axis &axis)
{
    // admesh uses degrees
    angle = Slic3r::Geometry::rad2deg(angle);
    
    if (axis == X) {
        stl_rotate_x(&(this->stl), angle);
    } else if (axis == Y) {
        stl_rotate_y(&(this->stl), angle);
    } else if (axis == Z) {
        stl_rotate_z(&(this->stl), angle);
    }
    stl_invalidate_shared_vertices(&this->stl);
}

void TriangleMesh::rotate_x(float angle)
{
    this->rotate(angle, X);
}

void TriangleMesh::rotate_y(float angle)
{
    this->rotate(angle, Y);
}

void TriangleMesh::rotate_z(float angle)
{
    this->rotate(angle, Z);
}

void TriangleMesh::mirror(const Axis &axis)
{
    if (axis == X) {
        stl_mirror_yz(&this->stl);
    } else if (axis == Y) {
        stl_mirror_xz(&this->stl);
    } else if (axis == Z) {
        stl_mirror_xy(&this->stl);
    }
    stl_invalidate_shared_vertices(&this->stl);
}

void TriangleMesh::mirror_x()
{
    this->mirror(X);
}

void TriangleMesh::mirror_y()
{
    this->mirror(Y);
}

void TriangleMesh::mirror_z()
{
    this->mirror(Z);
}

void TriangleMesh::align_to_origin()
{
    this->translate(
        -(this->stl.stats.min.x),
        -(this->stl.stats.min.y),
        -(this->stl.stats.min.z)
    );
}

void TriangleMesh::rotate(double angle, Point* center)
{
    this->translate(-center->x, -center->y, 0);
    stl_rotate_z(&(this->stl), (float)angle);
    this->translate(+center->x, +center->y, 0);
}

TriangleMeshPtrs
TriangleMesh::split() const
{
    TriangleMeshPtrs meshes;
    std::set<int> seen_facets;
    
    // we need neighbors
    if (!this->repaired) CONFESS("split() requires repair()");
    
    // loop while we have remaining facets
    while (1) {
        // get the first facet
        std::queue<int> facet_queue;
        std::deque<int> facets;
        for (int facet_idx = 0; facet_idx < this->stl.stats.number_of_facets; facet_idx++) {
            if (seen_facets.find(facet_idx) == seen_facets.end()) {
                // if facet was not seen put it into queue and start searching
                facet_queue.push(facet_idx);
                break;
            }
        }
        if (facet_queue.empty()) break;
        
        while (!facet_queue.empty()) {
            int facet_idx = facet_queue.front();
            facet_queue.pop();
            if (seen_facets.find(facet_idx) != seen_facets.end()) continue;
            facets.push_back(facet_idx);
            for (int j = 0; j <= 2; j++) {
                facet_queue.push(this->stl.neighbors_start[facet_idx].neighbor[j]);
            }
            seen_facets.insert(facet_idx);
        }
        
        TriangleMesh* mesh = new TriangleMesh;
        meshes.push_back(mesh);
        mesh->stl.stats.type = inmemory;
        mesh->stl.stats.number_of_facets = facets.size();
        mesh->stl.stats.original_num_facets = mesh->stl.stats.number_of_facets;
        stl_clear_error(&mesh->stl);
        stl_allocate(&mesh->stl);
        
        int first = 1;
        for (std::deque<int>::const_iterator facet = facets.begin(); facet != facets.end(); ++facet) {
            mesh->stl.facet_start[facet - facets.begin()] = this->stl.facet_start[*facet];
            stl_facet_stats(&mesh->stl, this->stl.facet_start[*facet], first);
            first = 0;
        }
    }
    
    return meshes;
}

void
TriangleMesh::merge(const TriangleMesh &mesh)
{
    // reset stats and metadata
    int number_of_facets = this->stl.stats.number_of_facets;
    stl_invalidate_shared_vertices(&this->stl);
    this->repaired = false;
    
    // update facet count and allocate more memory
    this->stl.stats.number_of_facets = number_of_facets + mesh.stl.stats.number_of_facets;
    this->stl.stats.original_num_facets = this->stl.stats.number_of_facets;
    stl_reallocate(&this->stl);
    
    // copy facets
    for (int i = 0; i < mesh.stl.stats.number_of_facets; i++) {
        this->stl.facet_start[number_of_facets + i] = mesh.stl.facet_start[i];
    }
    
    // update size
    stl_get_size(&this->stl);
}

/* this will return scaled ExPolygons */
ExPolygons
TriangleMesh::horizontal_projection() const
{
    Polygons pp;
    pp.reserve(this->stl.stats.number_of_facets);
    for (int i = 0; i < this->stl.stats.number_of_facets; i++) {
        stl_facet* facet = &this->stl.facet_start[i];
        Polygon p;
        p.points.resize(3);
        p.points[0] = Point(facet->vertex[0].x / SCALING_FACTOR, facet->vertex[0].y / SCALING_FACTOR);
        p.points[1] = Point(facet->vertex[1].x / SCALING_FACTOR, facet->vertex[1].y / SCALING_FACTOR);
        p.points[2] = Point(facet->vertex[2].x / SCALING_FACTOR, facet->vertex[2].y / SCALING_FACTOR);
        p.make_counter_clockwise();  // do this after scaling, as winding order might change while doing that
        pp.push_back(p);
    }
    
    // the offset factor was tuned using groovemount.stl
    offset(pp, &pp, 0.01 / SCALING_FACTOR);
    ExPolygons retval;
    union_(pp, &retval, true);
    return retval;
}

Polygon
TriangleMesh::convex_hull()
{
    this->require_shared_vertices();
    Points pp;
    pp.reserve(this->stl.stats.shared_vertices);
    for (int i = 0; i < this->stl.stats.shared_vertices; i++) {
        stl_vertex* v = &this->stl.v_shared[i];
        pp.push_back(Point(v->x / SCALING_FACTOR, v->y / SCALING_FACTOR));
    }
    return Slic3r::Geometry::convex_hull(pp);
}

BoundingBoxf3
TriangleMesh::bounding_box() const
{
    BoundingBoxf3 bb;
    bb.min.x = this->stl.stats.min.x;
    bb.min.y = this->stl.stats.min.y;
    bb.min.z = this->stl.stats.min.z;
    bb.max.x = this->stl.stats.max.x;
    bb.max.y = this->stl.stats.max.y;
    bb.max.z = this->stl.stats.max.z;
    return bb;
}

void
TriangleMesh::require_shared_vertices()
{
    if (!this->repaired) this->repair();
    if (this->stl.v_shared == NULL) stl_generate_shared_vertices(&(this->stl));
}

void
TriangleMeshSlicer::slice(const std::vector<float> &z, std::vector<Polygons>* layers)
{
    /*
       This method gets called with a list of unscaled Z coordinates and outputs
       a vector pointer having the same number of items as the original list.
       Each item is a vector of polygons created by slicing our mesh at the 
       given heights.
       
       This method should basically combine the behavior of the existing
       Perl methods defined in lib/Slic3r/TriangleMesh.pm:
       
       - analyze(): this creates the 'facets_edges' and the 'edges_facets'
            tables (we don't need the 'edges' table)
       
       - slice_facet(): this has to be done for each facet. It generates 
            intersection lines with each plane identified by the Z list.
            The get_layer_range() binary search used to identify the Z range
            of the facet is already ported to C++ (see Object.xsp)
       
       - make_loops(): this has to be done for each layer. It creates polygons
            from the lines generated by the previous step.
        
        At the end, we free the tables generated by analyze() as we don't 
        need them anymore.
        FUTURE: parallelize slice_facet() and make_loops()
        
        NOTE: this method accepts a vector of floats because the mesh coordinate
        type is float.
    */
    
    std::vector<IntersectionLines> lines(z.size());
    
    for (int facet_idx = 0; facet_idx < this->mesh->stl.stats.number_of_facets; facet_idx++) {
        stl_facet* facet = &this->mesh->stl.facet_start[facet_idx];
        
        // find facet extents
        float min_z = fminf(facet->vertex[0].z, fminf(facet->vertex[1].z, facet->vertex[2].z));
        float max_z = fmaxf(facet->vertex[0].z, fmaxf(facet->vertex[1].z, facet->vertex[2].z));
        
        #if 0
        // #ifdef SLIC3R_DEBUG
        printf("\n==> FACET %d (%f,%f,%f - %f,%f,%f - %f,%f,%f):\n", facet_idx,
            facet->vertex[0].x, facet->vertex[0].y, facet->vertex[0].z,
            facet->vertex[1].x, facet->vertex[1].y, facet->vertex[1].z,
            facet->vertex[2].x, facet->vertex[2].y, facet->vertex[2].z);
        printf("z: min = %.2f, max = %.2f\n", min_z, max_z);
        #endif
        
        // find layer extents
        std::vector<float>::const_iterator min_layer, max_layer;
        min_layer = std::lower_bound(z.begin(), z.end(), min_z); // first layer whose slice_z is >= min_z
        max_layer = std::upper_bound(z.begin() + (min_layer - z.begin()), z.end(), max_z) - 1; // last layer whose slice_z is <= max_z
        #if 0
        // #ifdef SLIC3R_DEBUG
        printf("layers: min = %d, max = %d\n", (int)(min_layer - z.begin()), (int)(max_layer - z.begin()));
        #endif
        
        for (std::vector<float>::const_iterator it = min_layer; it != max_layer + 1; ++it) {
            std::vector<float>::size_type layer_idx = it - z.begin();
            this->slice_facet(*it / SCALING_FACTOR, *facet, facet_idx, min_z, max_z, &lines[layer_idx]);
        }
    }
    
    // v_scaled_shared could be freed here
    
    // build loops
    layers->resize(z.size());
    for (std::vector<IntersectionLines>::iterator it = lines.begin(); it != lines.end(); ++it) {
        size_t layer_idx = it - lines.begin();
        #if 0
        // #ifdef SLIC3R_DEBUG
        printf("Layer %zu:\n", layer_idx);
        #endif
        this->make_loops(*it, &(*layers)[layer_idx]);
    }
}

void
TriangleMeshSlicer::slice(const std::vector<float> &z, std::vector<ExPolygons>* layers)
{
    std::vector<Polygons> layers_p;
    this->slice(z, &layers_p);
    
    layers->resize(z.size());
    for (std::vector<Polygons>::const_iterator loops = layers_p.begin(); loops != layers_p.end(); ++loops) {
        #if 0
        // #ifdef SLIC3R_DEBUG
        size_t layer_id = loops - layers_p.begin();
        printf("Layer %zu (slice_z = %.2f):\n", layer_id, z[layer_id]);
        #endif
        
        this->make_expolygons(*loops, &(*layers)[ loops - layers_p.begin() ]);
    }
}

void
TriangleMeshSlicer::slice_facet(float slice_z, const stl_facet &facet, const int &facet_idx, const float &min_z, const float &max_z, std::vector<IntersectionLine>* lines) const
{
    std::vector<IntersectionPoint> points;
    std::vector< std::vector<IntersectionPoint>::size_type > points_on_layer;
    bool found_horizontal_edge = false;
    
    /* reorder vertices so that the first one is the one with lowest Z
       this is needed to get all intersection lines in a consistent order
       (external on the right of the line) */
    int i = 0;
    if (facet.vertex[1].z == min_z) {
        // vertex 1 has lowest Z
        i = 1;
    } else if (facet.vertex[2].z == min_z) {
        // vertex 2 has lowest Z
        i = 2;
    }
    for (int j = i; (j-i) < 3; j++) {  // loop through facet edges
        int edge_id = this->facets_edges[facet_idx][j % 3];
        int a_id = this->mesh->stl.v_indices[facet_idx].vertex[j % 3];
        int b_id = this->mesh->stl.v_indices[facet_idx].vertex[(j+1) % 3];
        stl_vertex* a = &this->v_scaled_shared[a_id];
        stl_vertex* b = &this->v_scaled_shared[b_id];
        
        if (a->z == b->z && a->z == slice_z) {
            // edge is horizontal and belongs to the current layer
            
            stl_vertex &v0 = this->v_scaled_shared[ this->mesh->stl.v_indices[facet_idx].vertex[0] ];
            stl_vertex &v1 = this->v_scaled_shared[ this->mesh->stl.v_indices[facet_idx].vertex[1] ];
            stl_vertex &v2 = this->v_scaled_shared[ this->mesh->stl.v_indices[facet_idx].vertex[2] ];
            IntersectionLine line;
            if (min_z == max_z) {
                line.edge_type = feHorizontal;
                if (this->mesh->stl.facet_start[facet_idx].normal.z < 0) {
                    /*  if normal points downwards this is a bottom horizontal facet so we reverse
                        its point order */
                    std::swap(a, b);
                    std::swap(a_id, b_id);
                }
            } else if (v0.z < slice_z || v1.z < slice_z || v2.z < slice_z) {
                line.edge_type = feTop;
                std::swap(a, b);
                std::swap(a_id, b_id);
            } else {
                line.edge_type = feBottom;
            }
            line.a.x    = a->x;
            line.a.y    = a->y;
            line.b.x    = b->x;
            line.b.y    = b->y;
            line.a_id   = a_id;
            line.b_id   = b_id;
            lines->push_back(line);
            
            found_horizontal_edge = true;
            
            // if this is a top or bottom edge, we can stop looping through edges
            // because we won't find anything interesting
            
            if (line.edge_type != feHorizontal) return;
        } else if (a->z == slice_z) {
            IntersectionPoint point;
            point.x         = a->x;
            point.y         = a->y;
            point.point_id  = a_id;
            points.push_back(point);
            points_on_layer.push_back(points.size()-1);
        } else if (b->z == slice_z) {
            IntersectionPoint point;
            point.x         = b->x;
            point.y         = b->y;
            point.point_id  = b_id;
            points.push_back(point);
            points_on_layer.push_back(points.size()-1);
        } else if ((a->z < slice_z && b->z > slice_z) || (b->z < slice_z && a->z > slice_z)) {
            // edge intersects the current layer; calculate intersection
            
            IntersectionPoint point;
            point.x         = b->x + (a->x - b->x) * (slice_z - b->z) / (a->z - b->z);
            point.y         = b->y + (a->y - b->y) * (slice_z - b->z) / (a->z - b->z);
            point.edge_id   = edge_id;
            points.push_back(point);
        }
    }
    if (found_horizontal_edge) return;
    
    if (!points_on_layer.empty()) {
        // we can't have only one point on layer because each vertex gets detected
        // twice (once for each edge), and we can't have three points on layer because
        // we assume this code is not getting called for horizontal facets
        assert(points_on_layer.size() == 2);
        assert( points[ points_on_layer[0] ].point_id == points[ points_on_layer[1] ].point_id );
        if (points.size() < 3) return;  // no intersection point, this is a V-shaped facet tangent to plane
        points.erase( points.begin() + points_on_layer[1] );
    }
    
    if (!points.empty()) {
        assert(points.size() == 2); // facets must intersect each plane 0 or 2 times
        IntersectionLine line;
        line.a          = (Point)points[1];
        line.b          = (Point)points[0];
        line.a_id       = points[1].point_id;
        line.b_id       = points[0].point_id;
        line.edge_a_id  = points[1].edge_id;
        line.edge_b_id  = points[0].edge_id;
        lines->push_back(line);
        return;
    }
}

void
TriangleMeshSlicer::make_loops(std::vector<IntersectionLine> &lines, Polygons* loops)
{
    /*
    SVG svg("lines.svg");
    svg.draw(lines);
    svg.Close();
    */
    
    // remove tangent edges
    for (IntersectionLines::iterator line = lines.begin(); line != lines.end(); ++line) {
        if (line->skip || line->edge_type == feNone) continue;
        
        /* if the line is a facet edge, find another facet edge
           having the same endpoints but in reverse order */
        for (IntersectionLines::iterator line2 = line + 1; line2 != lines.end(); ++line2) {
            if (line2->skip || line2->edge_type == feNone) continue;
            
            // are these facets adjacent? (sharing a common edge on this layer)
            if (line->a_id == line2->a_id && line->b_id == line2->b_id) {
                line2->skip = true;
                
                /* if they are both oriented upwards or downwards (like a 'V')
                   then we can remove both edges from this layer since it won't 
                   affect the sliced shape */
                /* if one of them is oriented upwards and the other is oriented
                   downwards, let's only keep one of them (it doesn't matter which
                   one since all 'top' lines were reversed at slicing) */
                if (line->edge_type == line2->edge_type) {
                    line->skip = true;
                    break;
                }
            } else if (line->a_id == line2->b_id && line->b_id == line2->a_id) {
                /* if this edge joins two horizontal facets, remove both of them */
                if (line->edge_type == feHorizontal && line2->edge_type == feHorizontal) {
                    line->skip = true;
                    line2->skip = true;
                    break;
                }
            }
        }
    }
    
    // build a map of lines by edge_a_id and a_id
    std::vector<IntersectionLinePtrs> by_edge_a_id, by_a_id;
    by_edge_a_id.resize(this->mesh->stl.stats.number_of_facets * 3);
    by_a_id.resize(this->mesh->stl.stats.shared_vertices);
    for (IntersectionLines::iterator line = lines.begin(); line != lines.end(); ++line) {
        if (line->skip) continue;
        if (line->edge_a_id != -1) by_edge_a_id[line->edge_a_id].push_back(&(*line));
        if (line->a_id != -1) by_a_id[line->a_id].push_back(&(*line));
    }
    
    CYCLE: while (1) {
        // take first spare line and start a new loop
        IntersectionLine* first_line = NULL;
        for (IntersectionLines::iterator line = lines.begin(); line != lines.end(); ++line) {
            if (line->skip) continue;
            first_line = &(*line);
            break;
        }
        if (first_line == NULL) break;
        first_line->skip = true;
        IntersectionLinePtrs loop;
        loop.push_back(first_line);
        
        /*
        printf("first_line edge_a_id = %d, edge_b_id = %d, a_id = %d, b_id = %d, a = %d,%d, b = %d,%d\n", 
            first_line->edge_a_id, first_line->edge_b_id, first_line->a_id, first_line->b_id,
            first_line->a.x, first_line->a.y, first_line->b.x, first_line->b.y);
        */
        
        while (1) {
            // find a line starting where last one finishes
            IntersectionLine* next_line = NULL;
            if (loop.back()->edge_b_id != -1) {
                IntersectionLinePtrs &candidates = by_edge_a_id[loop.back()->edge_b_id];
                for (IntersectionLinePtrs::iterator lineptr = candidates.begin(); lineptr != candidates.end(); ++lineptr) {
                    if ((*lineptr)->skip) continue;
                    next_line = *lineptr;
                    break;
                }
            }
            if (next_line == NULL && loop.back()->b_id != -1) {
                IntersectionLinePtrs &candidates = by_a_id[loop.back()->b_id];
                for (IntersectionLinePtrs::iterator lineptr = candidates.begin(); lineptr != candidates.end(); ++lineptr) {
                    if ((*lineptr)->skip) continue;
                    next_line = *lineptr;
                    break;
                }
            }
            
            if (next_line == NULL) {
                // check whether we closed this loop
                if ((loop.front()->edge_a_id != -1 && loop.front()->edge_a_id == loop.back()->edge_b_id)
                    || (loop.front()->a_id != -1 && loop.front()->a_id == loop.back()->b_id)) {
                    // loop is complete
                    Polygon p;
                    p.points.reserve(loop.size());
                    for (IntersectionLinePtrs::const_iterator lineptr = loop.begin(); lineptr != loop.end(); ++lineptr) {
                        p.points.push_back((*lineptr)->a);
                    }
                    loops->push_back(p);
                    
                    #if 0
                    // #ifdef SLIC3R_DEBUG
                    printf("  Discovered %s polygon of %d points\n", (p.is_counter_clockwise() ? "ccw" : "cw"), (int)p.points.size());
                    #endif
                    
                    goto CYCLE;
                }
                
                // we can't close this loop!
                //// push @failed_loops, [@loop];
                //#ifdef SLIC3R_DEBUG
                printf("  Unable to close this loop having %d points\n", (int)loop.size());
                //#endif
                goto CYCLE;
            }
            /*
            printf("next_line edge_a_id = %d, edge_b_id = %d, a_id = %d, b_id = %d, a = %d,%d, b = %d,%d\n", 
                next_line->edge_a_id, next_line->edge_b_id, next_line->a_id, next_line->b_id,
                next_line->a.x, next_line->a.y, next_line->b.x, next_line->b.y);
            */
            loop.push_back(next_line);
            next_line->skip = true;
        }
    }
}

class _area_comp {
    public:
    _area_comp(std::vector<double>* _aa) : abs_area(_aa) {};
    bool operator() (const size_t &a, const size_t &b) {
        return (*this->abs_area)[a] > (*this->abs_area)[b];
    }
    
    private:
    std::vector<double>* abs_area;
};

void
TriangleMeshSlicer::make_expolygons_simple(std::vector<IntersectionLine> &lines, ExPolygons* slices)
{
    Polygons loops;
    this->make_loops(lines, &loops);
    
    Polygons cw;
    for (Polygons::const_iterator loop = loops.begin(); loop != loops.end(); ++loop) {
        if (loop->area() >= 0) {
            ExPolygon ex;
            ex.contour = *loop;
            slices->push_back(ex);
        } else {
            cw.push_back(*loop);
        }
    }
    
    // assign holes to contours
    for (Polygons::const_iterator loop = cw.begin(); loop != cw.end(); ++loop) {
        int slice_idx = -1;
        double current_contour_area = -1;
        for (ExPolygons::iterator slice = slices->begin(); slice != slices->end(); ++slice) {
            if (slice->contour.contains(loop->points.front())) {
                double area = slice->contour.area();
                if (area < current_contour_area || current_contour_area == -1) {
                    slice_idx = slice - slices->begin();
                    current_contour_area = area;
                }
            }
        }
        (*slices)[slice_idx].holes.push_back(*loop);
    }
}

void
TriangleMeshSlicer::make_expolygons(const Polygons &loops, ExPolygons* slices)
{
    /*
        Input loops are not suitable for evenodd nor nonzero fill types, as we might get
        two consecutive concentric loops having the same winding order - and we have to 
        respect such order. In that case, evenodd would create wrong inversions, and nonzero
        would ignore holes inside two concentric contours.
        So we're ordering loops and collapse consecutive concentric loops having the same 
        winding order.
        TODO: find a faster algorithm for this, maybe with some sort of binary search.
        If we computed a "nesting tree" we could also just remove the consecutive loops
        having the same winding order, and remove the extra one(s) so that we could just
        supply everything to offset() instead of performing several union/diff calls.
    
        we sort by area assuming that the outermost loops have larger area;
        the previous sorting method, based on $b->contains($a->[0]), failed to nest
        loops correctly in some edge cases when original model had overlapping facets
    */

    std::vector<double> area;
    std::vector<double> abs_area;
    std::vector<size_t> sorted_area;  // vector of indices
    for (Polygons::const_iterator loop = loops.begin(); loop != loops.end(); ++loop) {
        double a = loop->area();
        area.push_back(a);
        abs_area.push_back(std::fabs(a));
        sorted_area.push_back(loop - loops.begin());
    }
    
    std::sort(sorted_area.begin(), sorted_area.end(), _area_comp(&abs_area));  // outer first

    // we don't perform a safety offset now because it might reverse cw loops
    Polygons p_slices;
    for (std::vector<size_t>::const_iterator loop_idx = sorted_area.begin(); loop_idx != sorted_area.end(); ++loop_idx) {
        /* we rely on the already computed area to determine the winding order
           of the loops, since the Orientation() function provided by Clipper
           would do the same, thus repeating the calculation */
        Polygons::const_iterator loop = loops.begin() + *loop_idx;
        if (area[*loop_idx] > +EPSILON) {
            p_slices.push_back(*loop);
        } else if (area[*loop_idx] < -EPSILON) {
            diff(p_slices, *loop, &p_slices);
        }
    }

    // perform a safety offset to merge very close facets (TODO: find test case for this)
    double safety_offset = scale_(0.0499);
    ExPolygons ex_slices;
    offset2(p_slices, &ex_slices, +safety_offset, -safety_offset);
    
    #if 0
    // #ifdef SLIC3R_DEBUG
    size_t holes_count = 0;
    for (ExPolygons::const_iterator e = ex_slices.begin(); e != ex_slices.end(); ++e) {
        holes_count += e->holes.size();
    }
    printf("%zu surface(s) having %zu holes detected from %zu polylines\n",
        ex_slices.size(), holes_count, loops.size());
    #endif
    
    // append to the supplied collection
    slices->insert(slices->end(), ex_slices.begin(), ex_slices.end());
}

void
TriangleMeshSlicer::make_expolygons(std::vector<IntersectionLine> &lines, ExPolygons* slices)
{
    Polygons pp;
    this->make_loops(lines, &pp);
    this->make_expolygons(pp, slices);
}

void
TriangleMeshSlicer::cut(float z, TriangleMesh* upper, TriangleMesh* lower)
{
    IntersectionLines upper_lines, lower_lines;
    
    float scaled_z = scale_(z);
    for (int facet_idx = 0; facet_idx < this->mesh->stl.stats.number_of_facets; facet_idx++) {
        stl_facet* facet = &this->mesh->stl.facet_start[facet_idx];
        
        // find facet extents
        float min_z = fminf(facet->vertex[0].z, fminf(facet->vertex[1].z, facet->vertex[2].z));
        float max_z = fmaxf(facet->vertex[0].z, fmaxf(facet->vertex[1].z, facet->vertex[2].z));
        
        // intersect facet with cutting plane
        IntersectionLines lines;
        this->slice_facet(scaled_z, *facet, facet_idx, min_z, max_z, &lines);
        
        // save intersection lines for generating correct triangulations
        for (IntersectionLines::const_iterator it = lines.begin(); it != lines.end(); ++it) {
            if (it->edge_type == feTop) {
                lower_lines.push_back(*it);
            } else if (it->edge_type == feBottom) {
                upper_lines.push_back(*it);
            } else if (it->edge_type != feHorizontal) {
                lower_lines.push_back(*it);
                upper_lines.push_back(*it);
            }
        }
        
        if (min_z > z || (min_z == z && max_z > min_z)) {
            // facet is above the cut plane and does not belong to it
            if (upper != NULL) stl_add_facet(&upper->stl, facet);
        } else if (max_z < z || (max_z == z && max_z > min_z)) {
            // facet is below the cut plane and does not belong to it
            if (lower != NULL) stl_add_facet(&lower->stl, facet);
        } else if (min_z < z && max_z > z) {
            // facet is cut by the slicing plane
            
            // look for the vertex on whose side of the slicing plane there are no other vertices
            int isolated_vertex;
            if ( (facet->vertex[0].z > z) == (facet->vertex[1].z > z) ) {
                isolated_vertex = 2;
            } else if ( (facet->vertex[1].z > z) == (facet->vertex[2].z > z) ) {
                isolated_vertex = 0;
            } else {
                isolated_vertex = 1;
            }
            
            // get vertices starting from the isolated one
            stl_vertex* v0 = &facet->vertex[isolated_vertex];
            stl_vertex* v1 = &facet->vertex[(isolated_vertex+1) % 3];
            stl_vertex* v2 = &facet->vertex[(isolated_vertex+2) % 3];
            
            // intersect v0-v1 and v2-v0 with cutting plane and make new vertices
            stl_vertex v0v1, v2v0;
            v0v1.x = v1->x + (v0->x - v1->x) * (z - v1->z) / (v0->z - v1->z);
            v0v1.y = v1->y + (v0->y - v1->y) * (z - v1->z) / (v0->z - v1->z);
            v0v1.z = z;
            v2v0.x = v2->x + (v0->x - v2->x) * (z - v2->z) / (v0->z - v2->z);
            v2v0.y = v2->y + (v0->y - v2->y) * (z - v2->z) / (v0->z - v2->z);
            v2v0.z = z;
            
            // build the triangular facet
            stl_facet triangle;
            triangle.normal = facet->normal;
            triangle.vertex[0] = *v0;
            triangle.vertex[1] = v0v1;
            triangle.vertex[2] = v2v0;
            
            // build the facets forming a quadrilateral on the other side
            stl_facet quadrilateral[2];
            quadrilateral[0].normal = facet->normal;
            quadrilateral[0].vertex[0] = *v1;
            quadrilateral[0].vertex[1] = *v2;
            quadrilateral[0].vertex[2] = v0v1;
            quadrilateral[1].normal = facet->normal;
            quadrilateral[1].vertex[0] = *v2;
            quadrilateral[1].vertex[1] = v2v0;
            quadrilateral[1].vertex[2] = v0v1;
            
            if (v0->z > z) {
                if (upper != NULL) stl_add_facet(&upper->stl, &triangle);
                if (lower != NULL) {
                    stl_add_facet(&lower->stl, &quadrilateral[0]);
                    stl_add_facet(&lower->stl, &quadrilateral[1]);
                }
            } else {
                if (upper != NULL) {
                    stl_add_facet(&upper->stl, &quadrilateral[0]);
                    stl_add_facet(&upper->stl, &quadrilateral[1]);
                }
                if (lower != NULL) stl_add_facet(&lower->stl, &triangle);
            }
        }
    }
    
    // triangulate holes of upper mesh
    if (upper != NULL) {
        // compute shape of section
        ExPolygons section;
        this->make_expolygons_simple(upper_lines, &section);
        
        // triangulate section
        Polygons triangles;
        for (ExPolygons::const_iterator expolygon = section.begin(); expolygon != section.end(); ++expolygon)
            expolygon->triangulate_p2t(&triangles);
        
        // convert triangles to facets and append them to mesh
        for (Polygons::const_iterator polygon = triangles.begin(); polygon != triangles.end(); ++polygon) {
            Polygon p = *polygon;
            p.reverse();
            stl_facet facet;
            facet.normal.x = 0;
            facet.normal.y = 0;
            facet.normal.z = -1;
            for (size_t i = 0; i <= 2; ++i) {
                facet.vertex[i].x = unscale(p.points[i].x);
                facet.vertex[i].y = unscale(p.points[i].y);
                facet.vertex[i].z = z;
            }
            stl_add_facet(&upper->stl, &facet);
        }
    }
    
    // triangulate holes of lower mesh
    if (lower != NULL) {
        // compute shape of section
        ExPolygons section;
        this->make_expolygons_simple(lower_lines, &section);
        
        // triangulate section
        Polygons triangles;
        for (ExPolygons::const_iterator expolygon = section.begin(); expolygon != section.end(); ++expolygon)
            expolygon->triangulate_p2t(&triangles);
        
        // convert triangles to facets and append them to mesh
        for (Polygons::const_iterator polygon = triangles.begin(); polygon != triangles.end(); ++polygon) {
            stl_facet facet;
            facet.normal.x = 0;
            facet.normal.y = 0;
            facet.normal.z = 1;
            for (size_t i = 0; i <= 2; ++i) {
                facet.vertex[i].x = unscale(polygon->points[i].x);
                facet.vertex[i].y = unscale(polygon->points[i].y);
                facet.vertex[i].z = z;
            }
            stl_add_facet(&lower->stl, &facet);
        }
    }
    
    
    stl_get_size(&(upper->stl));
    stl_get_size(&(lower->stl));
    
}

TriangleMeshSlicer::TriangleMeshSlicer(TriangleMesh* _mesh) : mesh(_mesh), v_scaled_shared(NULL)
{
    // build a table to map a facet_idx to its three edge indices
    this->mesh->require_shared_vertices();
    typedef std::pair<int,int>              t_edge;
    typedef std::vector<t_edge>             t_edges;  // edge_idx => a_id,b_id
    typedef std::map<t_edge,int>            t_edges_map;  // a_id,b_id => edge_idx
    
    this->facets_edges.resize(this->mesh->stl.stats.number_of_facets);
    
    {
        t_edges edges;
        // reserve() instad of resize() because otherwise we couldn't read .size() below to assign edge_idx
        edges.reserve(this->mesh->stl.stats.number_of_facets * 3);  // number of edges = number of facets * 3
        t_edges_map edges_map;
        for (int facet_idx = 0; facet_idx < this->mesh->stl.stats.number_of_facets; facet_idx++) {
            this->facets_edges[facet_idx].resize(3);
            for (int i = 0; i <= 2; i++) {
                int a_id = this->mesh->stl.v_indices[facet_idx].vertex[i];
                int b_id = this->mesh->stl.v_indices[facet_idx].vertex[(i+1) % 3];
                
                int edge_idx;
                t_edges_map::const_iterator my_edge = edges_map.find(std::make_pair(b_id,a_id));
                if (my_edge != edges_map.end()) {
                    edge_idx = my_edge->second;
                } else {
                    /* admesh can assign the same edge ID to more than two facets (which is 
                       still topologically correct), so we have to search for a duplicate of 
                       this edge too in case it was already seen in this orientation */
                    my_edge = edges_map.find(std::make_pair(a_id,b_id));
                    
                    if (my_edge != edges_map.end()) {
                        edge_idx = my_edge->second;
                    } else {
                        // edge isn't listed in table, so we insert it
                        edge_idx = edges.size();
                        edges.push_back(std::make_pair(a_id,b_id));
                        edges_map[ edges[edge_idx] ] = edge_idx;
                    }
                }
                this->facets_edges[facet_idx][i] = edge_idx;
                
                #if 0
                // #ifdef SLIC3R_DEBUG
                printf("  [facet %d, edge %d] a_id = %d, b_id = %d   --> edge %d\n", facet_idx, i, a_id, b_id, edge_idx);
                #endif
            }
        }
    }
    
    // clone shared vertices coordinates and scale them
    this->v_scaled_shared = (stl_vertex*)calloc(this->mesh->stl.stats.shared_vertices, sizeof(stl_vertex));
    std::copy(this->mesh->stl.v_shared, this->mesh->stl.v_shared + this->mesh->stl.stats.shared_vertices, this->v_scaled_shared);
    for (int i = 0; i < this->mesh->stl.stats.shared_vertices; i++) {
        this->v_scaled_shared[i].x /= SCALING_FACTOR;
        this->v_scaled_shared[i].y /= SCALING_FACTOR;
        this->v_scaled_shared[i].z /= SCALING_FACTOR;
    }
}

TriangleMeshSlicer::~TriangleMeshSlicer()
{
    if (this->v_scaled_shared != NULL) free(this->v_scaled_shared);
}

}