# Instantiated by Slic3r::Print::Object->_support_material()
# only generate() and contact_distance() are called from the outside of this module.
package Slic3r::Print::SupportMaterial;
use Moo;

use List::Util qw(sum min max);
use Slic3r::ExtrusionPath ':roles';
use Slic3r::Flow ':roles';
use Slic3r::Geometry qw(epsilon scale scaled_epsilon PI rad2deg deg2rad convex_hull);
use Slic3r::Geometry::Clipper qw(offset diff union union_ex intersection offset_ex offset2
    intersection_pl offset2_ex diff_pl JT_MITER JT_ROUND);
use Slic3r::Surface ':types';

has 'print_config'      => (is => 'rw', required => 1);
has 'object_config'     => (is => 'rw', required => 1);
has 'flow'              => (is => 'rw', required => 1);
has 'first_layer_flow'  => (is => 'rw', required => 1);
has 'interface_flow'    => (is => 'rw', required => 1);

use constant DEBUG_CONTACT_ONLY => 0;

# increment used to reach MARGIN in steps to avoid trespassing thin objects
use constant MARGIN_STEP => MARGIN/3;

# generate a tree-like structure to save material
use constant PILLAR_SIZE    => 2.5;
use constant PILLAR_SPACING => 10;

sub generate {
    # $object is Slic3r::Print::Object
    my ($self, $object) = @_;
    
    # Determine the top surfaces of the support, defined as:
    # contact = overhangs - clearance + margin
    # This method is responsible for identifying what contact surfaces
    # should the support material expose to the object in order to guarantee
    # that it will be effective, regardless of how it's built below.
    my ($contact, $overhang) = $self->contact_area($object);
    
    # Determine the top surfaces of the object. We need these to determine 
    # the layer heights of support material and to clip support to the object
    # silhouette.
    my ($top) = $self->object_top($object, $contact);

    # We now know the upper and lower boundaries for our support material object
    # (@$contact_z and @$top_z), so we can generate intermediate layers.
    my $support_z = $self->support_layers_z(
        [ sort keys %$contact ],
        [ sort keys %$top ],
        max(map $_->height, @{$object->layers})
    );
    
    # If we wanted to apply some special logic to the first support layers lying on
    # object's top surfaces this is the place to detect them
    
    my $shape = [];
    if ($self->object_config->support_material_pattern eq 'pillars') {
        $self->generate_pillars_shape($contact, $support_z, $shape);
    }
    
    # Propagate contact layers downwards to generate interface layers
    my ($interface) = $self->generate_top_interface_layers($support_z, $contact, $top);
    $self->clip_with_object($interface, $support_z, $object);
    $self->clip_with_shape($interface, $shape) if @$shape;
    
    # Propagate contact layers and interface layers downwards to generate
    # the main support layers.
    my ($base) = $self->generate_base_layers($support_z, $contact, $interface, $top);
    $self->clip_with_object($base, $support_z, $object);
    $self->clip_with_shape($base, $shape) if @$shape;
    
    # Detect what part of base support layers are "reverse interfaces" because they
    # lie above object's top surfaces.
    $self->generate_bottom_interface_layers($support_z, $base, $top, $interface);
    
    # Install support layers into object.
    for my $i (0 .. $#$support_z) {
        $object->add_support_layer(
            $i, # id
            ($i == 0) ? $support_z->[$i] : ($support_z->[$i] - $support_z->[$i-1]), # height
            $support_z->[$i], # print_z
        );
        if ($i >= 1) {
            $object->support_layers->[-2]->set_upper_layer($object->support_layers->[-1]);
            $object->support_layers->[-1]->set_lower_layer($object->support_layers->[-2]);
        }
    }
    
    # Generate the actual toolpaths and save them into each layer.
    $self->generate_toolpaths($object, $overhang, $contact, $interface, $base);
}

sub contact_area {
    # $object is Slic3r::Print::Object
    my ($self, $object) = @_;
    
    # if user specified a custom angle threshold, convert it to radians
    my $threshold_rad;
    if ($self->object_config->support_material_threshold) {
        $threshold_rad = deg2rad($self->object_config->support_material_threshold + 1);  # +1 makes the threshold inclusive
        Slic3r::debugf "Threshold angle = %d°\n", rad2deg($threshold_rad);
    }
    
    # Build support on a build plate only? If so, then collect top surfaces into $buildplate_only_top_surfaces
    # and subtract $buildplate_only_top_surfaces from the contact surfaces, so
    # there is no contact surface supported by a top surface.
    my $buildplate_only = $self->object_config->support_material && $self->object_config->support_material_buildplate_only;
    my $buildplate_only_top_surfaces = [];

    # determine contact areas
    my %contact  = ();  # contact_z => [ polygons ]
    my %overhang = ();  # contact_z => [ polygons ] - this stores the actual overhang supported by each contact layer
    for my $layer_id (0 .. $#{$object->layers}) {
        # note $layer_id might != $layer->id when raft_layers > 0
        # so $layer_id == 0 means first object layer
        # and $layer->id == 0 means first print layer (including raft)
        
        if ($self->object_config->raft_layers == 0) {
            next if $layer_id == 0;
        } elsif (!$self->object_config->support_material) {
            # if we are only going to generate raft just check 
            # the 'overhangs' of the first object layer
            last if $layer_id > 0;
        }
        my $layer = $object->get_layer($layer_id);

        if ($buildplate_only) {
            # Collect the top surfaces up to this layer and merge them.
            my $projection_new = [];
            push @$projection_new, ( map $_->p, map @{$_->slices->filter_by_type(S_TYPE_TOP)}, @{$layer->regions} );
            if (@$projection_new) {
                # Merge the new top surfaces with the preceding top surfaces.
                # Apply the safety offset to the newly added polygons, so they will connect
                # with the polygons collected before,
                # but don't apply the safety offset during the union operation as it would
                # inflate the polygons over and over.
                push @$buildplate_only_top_surfaces, @{ offset($projection_new, scale(0.01)) };
                $buildplate_only_top_surfaces = union($buildplate_only_top_surfaces, 0);
            }
        }

        # detect overhangs and contact areas needed to support them
        my (@overhang, @contact) = ();
        if ($layer_id == 0) {
            # this is the first object layer, so we're here just to get the object
            # footprint for the raft
            # we only consider contours and discard holes to get a more continuous raft
            push @overhang, map $_->clone, map $_->contour, @{$layer->slices};
            # Extend by SUPPORT_MATERIAL_MARGIN, which is 1.5mm
            # MARGIN is the C++ Slic3r::SUPPORT_MATERIAL_MARGIN constant.
            push @contact, @{offset(\@overhang, scale +MARGIN)};
        } else {
            my $lower_layer = $object->get_layer($layer_id-1);
            foreach my $layerm (@{$layer->regions}) {
                # Extrusion width accounts for the roundings of the extrudates.
                # It is the maximum widh of the extrudate.
                my $fw = $layerm->flow(FLOW_ROLE_EXTERNAL_PERIMETER)->scaled_width;
                my $diff;
            
                # If a threshold angle was specified, use a different logic for detecting overhangs.
                if (defined $threshold_rad
                    || $layer_id < $self->object_config->support_material_enforce_layers
                    || ($self->object_config->raft_layers > 0 && $layer_id == 0)) {
                    my $d = defined $threshold_rad
                        ? scale $lower_layer->height * ((cos $threshold_rad) / (sin $threshold_rad))
                        : 0;
                
                    # Shrinking the supported layer by layer_height/atan(threshold_rad).
                    $diff = diff(
                        offset([ map $_->p, @{$layerm->slices} ], -$d),
                        [ map @$_, @{$lower_layer->slices} ],
                    );
                
                    # only enforce spacing from the object ($fw/2) if the threshold angle
                    # is not too high: in that case, $d will be very small (as we need to catch
                    # very short overhangs), and such contact area would be eaten by the
                    # enforced spacing, resulting in high threshold angles to be almost ignored
                    $diff = diff(
                        offset($diff, $d - $fw/2),
                        [ map @$_, @{$lower_layer->slices} ],
                    ) if $d > $fw/2;
                } else {
                    # Automatic overhang detection.
                    $diff = diff(
                        [ map $_->p, @{$layerm->slices} ],
                        offset([ map @$_, @{$lower_layer->slices} ], 
                            #FIXME Vojtech: Why 2x extrusion width? Isn't this too much? Should it not be /2?
                            +$fw/2),
                    );
                
                    # collapse very tiny spots
                    $diff = offset2($diff, -$fw/10, +$fw/10);
                
                    # $diff now contains the ring or stripe comprised between the boundary of 
                    # lower slices and the centerline of the last perimeter in this overhanging layer.
                    # Void $diff means that there's no upper perimeter whose centerline is
                    # outside the lower slice boundary, thus no overhang
                }
                
                if ($self->object_config->dont_support_bridges) {
                    # compute the area of bridging perimeters
                    # Note: this is duplicate code from GCode.pm, we need to refactor
                    
                    my $bridged_perimeters;  # Polygons
                    {
                        my $bridge_flow = $layerm->flow(FLOW_ROLE_PERIMETER, 1);
                        
                        my $nozzle_diameter = $self->print_config->get_at('nozzle_diameter', $layerm->region->config->perimeter_extruder-1);
                        my $lower_grown_slices = offset([ map @$_, @{$lower_layer->slices} ], +scale($nozzle_diameter/2));
                        
                        # TODO: split_at_first_point() could split a bridge mid-way
                        my @overhang_perimeters =
                            map { $_->isa('Slic3r::ExtrusionLoop') ? $_->polygon->split_at_first_point : $_->polyline->clone }
                            map @$_, @{$layerm->perimeters};
                        
                        # workaround for Clipper bug, see Slic3r::Polygon::clip_as_polyline()
                        $_->[0]->translate(1,0) for @overhang_perimeters;
                        @overhang_perimeters = @{diff_pl(
                            \@overhang_perimeters,
                            $lower_grown_slices,
                        )};
                        
                        # only consider straight overhangs
                        @overhang_perimeters = grep $_->is_straight, @overhang_perimeters;
                        
                        # only consider overhangs having endpoints inside layer's slices
                        foreach my $polyline (@overhang_perimeters) {
                            $polyline->extend_start($fw);
                            $polyline->extend_end($fw);
                        }
                        @overhang_perimeters = grep {
                            $layer->slices->contains_point($_->first_point) && $layer->slices->contains_point($_->last_point)
                        } @overhang_perimeters;
                        
                        # convert bridging polylines into polygons by inflating them with their thickness
                        {
                            # since we're dealing with bridges, we can't assume width is larger than spacing,
                            # so we take the largest value and also apply safety offset to be ensure no gaps
                            # are left in between
                            my $w = max($bridge_flow->scaled_width, $bridge_flow->scaled_spacing);
                            $bridged_perimeters = union([
                                map @{$_->grow($w/2 + 10)}, @overhang_perimeters
                            ]);
                        }
                    }
                    
                    if (1) {
                        # remove the entire bridges and only support the unsupported edges
                        my @bridges = map $_->expolygon,
                            grep $_->bridge_angle != -1,
                            @{$layerm->fill_surfaces->filter_by_type(S_TYPE_BOTTOMBRIDGE)};
                            
                        $diff = diff(
                            $diff,
                            [
                                (map @$_, @bridges),
                                @$bridged_perimeters,
                            ],
                            1,
                        );
                        
                        push @$diff, @{intersection(
                            [ map @{$_->grow(+scale MARGIN)}, @{$layerm->unsupported_bridge_edges} ],
                            [ map @$_, @bridges ],
                        )};
                    
                    } else {
                        # just remove bridged areas
                        $diff = diff(
                            $diff,
                            $layerm->bridged,
                            1,
                        );
                    }
                } # if ($self->object_config->dont_support_bridges)

                if ($buildplate_only) {
                    # Don't support overhangs above the top surfaces.
                    # This step is done before the contact surface is calcuated by growing the overhang region.
                    $diff = diff($diff, $buildplate_only_top_surfaces);
                }

                next if !@$diff;
                push @overhang, @$diff;  # NOTE: this is not the full overhang as it misses the outermost half of the perimeter width!
            
                # Let's define the required contact area by using a max gap of half the upper 
                # extrusion width and extending the area according to the configured margin.
                # We increment the area in steps because we don't want our support to overflow
                # on the other side of the object (if it's very thin).
                {
                    my $slices_margin = offset([ map @$_, @{$lower_layer->slices} ], +$fw/2);
                    if ($buildplate_only) {
                        # Trim the inflated contact surfaces by the top surfaces as well.
                        push @$slices_margin, map $_->clone, @{$buildplate_only_top_surfaces};
                        $slices_margin = union($slices_margin);
                    }
                    for ($fw/2, map {scale MARGIN_STEP} 1..(MARGIN / MARGIN_STEP)) {
                        $diff = diff(
                            offset(
                                $diff, 
                                $_,
                                JT_ROUND,
                                scale(0.05)),
                            $slices_margin
                        );
                    }
                }
                push @contact, @$diff;
            }
        }
        next if !@contact;
        
        # now apply the contact areas to the layer were they need to be made
        {
            # get the average nozzle diameter used on this layer
            my @nozzle_diameters = map $self->print_config->get_at('nozzle_diameter', $_),
                map { $_->config->perimeter_extruder-1, $_->config->infill_extruder-1, $_->config->solid_infill_extruder-1 }
                map $_->region, @{$layer->regions};
            my $nozzle_diameter = sum(@nozzle_diameters)/@nozzle_diameters;
            
            my $contact_z = $layer->print_z - $self->contact_distance($layer->height, $nozzle_diameter);
            
            # Ignore this contact area if it's too low.
            #FIXME Better to control the thickness of the interface layer printed, but that would
            # require having attributes (extrusion width / height, bridge flow etc) per island.
            next if $contact_z < $self->object_config->get_value('first_layer_height') - epsilon;
            
            $contact{$contact_z}  = [ @contact ];
            $overhang{$contact_z} = [ @overhang ];
            
            if (0) {
                require "Slic3r/SVG.pm";
                Slic3r::SVG::output(Slic3r::DEBUG_OUT_PATH_PREFIX . "contact_" . $contact_z . ".svg",
                    green_expolygons => union_ex($buildplate_only_top_surfaces),
                    blue_expolygons  => union_ex(\@contact),
                    red_expolygons   => union_ex(\@overhang),
                );
            }
        }
    }

    return (\%contact, \%overhang);
}

sub object_top {
    my ($self, $object, $contact) = @_;
    
    # find object top surfaces
    # we'll use them to clip our support and detect where does it stick
    my %top = ();  # print_z => [ expolygons ]
    return \%top if ($self->object_config->support_material_buildplate_only);

    # Sum of unsupported contact areas above the current $layer->print_z.
    my $projection = [];
    foreach my $layer (reverse @{$object->layers}) {
        if (my @top = map @{$_->slices->filter_by_type(S_TYPE_TOP)}, @{$layer->regions}) {
            # compute projection of the contact areas above this top layer
            # first add all the 'new' contact areas to the current projection
            # ('new' means all the areas that are lower than the last top layer
            # we considered)
            my $min_top = min(keys %top) // max(keys %$contact);
            # use <= instead of just < because otherwise we'd ignore any contact regions
            # having the same Z of top layers
            push @$projection, map @{$contact->{$_}}, grep { $_ > $layer->print_z && $_ <= $min_top } keys %$contact;
            
            # Now find whether any projection of the contact surfaces above $layer->print_z not yet supported by any top surfaces above $layer->z falls onto this top surface. 
            # $touching are the contact surfaces supported exclusively by this @top surfaaces.
            my $touching = intersection($projection, [ map $_->p, @top ]);
            if (@$touching) {
                # grow top surfaces so that interface and support generation are generated
                # with some spacing from object - it looks we don't need the actual
                # top shapes so this can be done here
                $top{ $layer->print_z } = offset($touching, $self->flow->scaled_width);
            }
            
            # remove the areas that touched from the projection that will continue on 
            # next, lower, top surfaces
            $projection = diff($projection, $touching);
        }
    }
    
    return \%top;
}

sub support_layers_z {
    my ($self, $contact_z, $top_z, $max_object_layer_height) = @_;
    
    # quick table to check whether a given Z is a top surface
    my %top = map { $_ => 1 } @$top_z;
    
    # determine layer height for any non-contact layer
    # we use max() to prevent many ultra-thin layers to be inserted in case
    # layer_height > nozzle_diameter * 0.75
    my $nozzle_diameter = $self->print_config->get_at('nozzle_diameter', $self->object_config->support_material_extruder-1);
    my $support_material_height = max($max_object_layer_height, $nozzle_diameter * 0.75);
    my $contact_distance = $self->contact_distance($support_material_height, $nozzle_diameter);
    
    # initialize known, fixed, support layers
    my @z = sort { $a <=> $b }
        @$contact_z,
        # TODO: why we have this?
        # Vojtech: To detect the bottom interface layers by finding a Z value in the $top_z.
        @$top_z,
        # Top surfaces of the bottom interface layers.
        (map $_ + $contact_distance, @$top_z);
    
    # enforce first layer height
    my $first_layer_height = $self->object_config->get_value('first_layer_height');
    shift @z while @z && $z[0] <= $first_layer_height;
    unshift @z, $first_layer_height;
    
    # add raft layers by dividing the space between first layer and
    # first contact layer evenly
    if ($self->object_config->raft_layers > 1 && @z >= 2) {
        # $z[1] is last raft layer (contact layer for the first layer object)
        my $height = ($z[1] - $z[0]) / ($self->object_config->raft_layers - 1);
        # since we already have two raft layers ($z[0] and $z[1]) we need to insert
        # raft_layers-2 more
        splice @z, 1, 0,
            map { sprintf "%.2f", $_ }
            map { $z[0] + $height * $_ }
            1..($self->object_config->raft_layers - 2);
    }
    
    # create other layers (skip raft layers as they're already done and use thicker layers)
    for (my $i = $#z; $i >= $self->object_config->raft_layers; $i--) {
        my $target_height = $support_material_height;
        if ($i > 0 && $top{ $z[$i-1] }) {
            # Bridge flow?
            #FIXME We want to enforce not only the bridge flow height, but also the interface gap!
            # This will introduce an additional layer if the gap is set to an extreme value!
            $target_height = $nozzle_diameter;
        }
        
        # enforce first layer height
        #FIXME better to split the layers regularly, than to bite a constant height one at a time, 
        # and then be left with a very thin layer at the end.
        if (($i == 0 && $z[$i] > $target_height + $first_layer_height)
            || ($z[$i] - $z[$i-1] > $target_height + Slic3r::Geometry::epsilon)) {
            splice @z, $i, 0, ($z[$i] - $target_height);
            $i++;
        }
    }
    
    # remove duplicates and make sure all 0.x values have the leading 0
    {
        my %sl = map { 1 * $_ => 1 } @z;
        @z = sort { $a <=> $b } keys %sl;
    }
    
    return \@z;
}

sub generate_top_interface_layers {
    my ($self, $support_z, $contact, $top) = @_;

    # If no interface layers are allowed, don't generate top interface layers.
    return if $self->object_config->support_material_interface_layers == 0;
    
    # let's now generate interface layers below contact areas
    my %interface = ();  # layer_id => [ polygons ]
    my $interface_layers_num = $self->object_config->support_material_interface_layers;
    for my $layer_id (0 .. $#$support_z) {
        my $z = $support_z->[$layer_id];
        my $this = $contact->{$z} // next;
        
        # count contact layer as interface layer
        for (my $i = $layer_id-1; $i >= 0 && $i > $layer_id-$interface_layers_num; $i--) {
            $z = $support_z->[$i];
            my @overlapping_layers = $self->overlapping_layers($i, $support_z);
            my @overlapping_z = map $support_z->[$_], @overlapping_layers;
            
            # Compute interface area on this layer as diff of upper contact area
            # (or upper interface area) and layer slices.
            # This diff is responsible of the contact between support material and
            # the top surfaces of the object. We should probably offset the top 
            # surfaces vertically before performing the diff, but this needs 
            # investigation.
            $this = $interface{$i} = diff(
                [
                    @$this,                         # clipped projection of the current contact regions
                    @{ $interface{$i} || [] },      # interface regions already applied to this layer
                ],
                [
                    (map @$_, map $top->{$_}, grep exists $top->{$_}, @overlapping_z),  # top slices on this layer
                    (map @$_, map $contact->{$_}, grep exists $contact->{$_}, @overlapping_z),  # contact regions on this layer
                ],
                1,
            );
        }
    }
    
    return \%interface;
}

sub generate_bottom_interface_layers {
    my ($self, $support_z, $base, $top, $interface) = @_;

    # If no interface layers are allowed, don't generate bottom interface layers.
    return if $self->object_config->support_material_interface_layers == 0;
    
    my $area_threshold = $self->interface_flow->scaled_spacing ** 2;
    
    # loop through object's top surfaces
    foreach my $top_z (sort keys %$top) {
        my $this = $top->{$top_z};
        
        # keep a count of the interface layers we generated for this top surface
        my $interface_layers = 0;
        
        # loop through support layers until we find the one(s) right above the top
        # surface
        foreach my $layer_id (0 .. $#$support_z) {
            my $z = $support_z->[$layer_id];
            next unless $z > $top_z;
            
            if ($base->{$layer_id}) {
                # get the support material area that should be considered interface
                my $interface_area = intersection(
                    $base->{$layer_id},
                    $this,
                );
            
                # discard too small areas
                $interface_area = [ grep abs($_->area) >= $area_threshold, @$interface_area ];
            
                # subtract new interface area from base
                $base->{$layer_id} = diff(
                    $base->{$layer_id},
                    $interface_area,
                );
            
                # add new interface area to interface
                push @{$interface->{$layer_id}}, @$interface_area;
            }
            
            $interface_layers++;
            last if $interface_layers == $self->object_config->support_material_interface_layers;
        }
    }
}

sub generate_base_layers {
    my ($self, $support_z, $contact, $interface, $top) = @_;
    
    # let's now generate support layers under interface layers
    my $base = {};  # layer_id => [ polygons ]
    {
        my $fillet_radius_scaled = scale($self->object_config->support_material_spacing);
        for my $i (reverse 0 .. $#$support_z-1) {
            my $z = $support_z->[$i];
            my @overlapping_layers = $self->overlapping_layers($i, $support_z);
            my @overlapping_z = map $support_z->[$_], @overlapping_layers;
            
            # in case we have no interface layers, look at upper contact
            # (1 interface layer means we only have contact layer, so $interface->{$i+1} is empty)
            my @upper_contact = ();
            if ($self->object_config->support_material_interface_layers <= 1) {
                @upper_contact = @{ $contact->{$support_z->[$i+1]} || [] };
            }
            
            my $trim_polygons = [
                    (map @$_, map $top->{$_}, grep exists $top->{$_}, @overlapping_z),  # top slices on this layer
                    (map @$_, map $interface->{$_}, grep exists $interface->{$_}, @overlapping_layers),  # interface regions on this layer
                    (map @$_, map $contact->{$_}, grep exists $contact->{$_}, @overlapping_z),  # contact regions on this layer
                ];

            $base->{$i} = diff(
                [
                    @{ $base->{$i+1} || [] },         # support regions on upper layer
                    @{ $interface->{$i+1} || [] },    # interface regions on upper layer
                    @upper_contact,                   # contact regions on upper layer
                ],
                $trim_polygons,
                1, # safety offset to merge the touching source polygons
            );

            if (0) {
                # Fillet the base polygons and trim them again with the top, interface and contact layers.
                $base->{$i} = diff(
                    offset2(
                        $base->{$i}, 
                        $fillet_radius_scaled, 
                        -$fillet_radius_scaled,
                        # Use a geometric offsetting for filleting.
                        JT_ROUND,
                        0.2*$fillet_radius_scaled),
                    $trim_polygons,
                    0); # don't apply the safety offset.
            }
        }
    }
    
    return $base;
}

# This method removes object silhouette from support material
# (it's used with interface and base only). It removes a bit more,
# leaving a thin gap between object and support in the XY plane.
sub clip_with_object {
    my ($self, $support, $support_z, $object) = @_;
    
    foreach my $i (keys %$support) {
        next if !@{$support->{$i}};
        
        my $zmax = $support_z->[$i];
        my $zmin = ($i == 0) ? 0 : $support_z->[$i-1];
        my @layers = grep { $_->print_z > $zmin && ($_->print_z - $_->height) < $zmax }
            @{$object->layers};
        
        # $layer->slices contains the full shape of layer, thus including
        # perimeter's width. $support contains the full shape of support
        # material, thus including the width of its foremost extrusion.
        # We leave a gap equal to a full extrusion width.
        $support->{$i} = diff(
            $support->{$i},
            offset([ map @$_, map @{$_->slices}, @layers ], +$self->flow->scaled_width),
        );
    }
}

sub generate_toolpaths {
    my ($self, $object, $overhang, $contact, $interface, $base) = @_;
    
    my $flow            = $self->flow;
    my $interface_flow  = $self->interface_flow;
    
    # shape of contact area
    my $contact_loops   = 1;
    my $circle_radius   = 1.5 * $interface_flow->scaled_width;
    my $circle_distance = 3 * $circle_radius;
    my $circle          = Slic3r::Polygon->new(map [ $circle_radius * cos $_, $circle_radius * sin $_ ],
                            (5*PI/3, 4*PI/3, PI, 2*PI/3, PI/3, 0));
    
    Slic3r::debugf "Generating patterns\n";
    
    # prepare fillers
    my $pattern = $self->object_config->support_material_pattern;
    my $with_sheath = $self->object_config->support_material_with_sheath;
    my @angles = ($self->object_config->support_material_angle);
    if ($pattern eq 'rectilinear-grid') {
        $pattern = 'rectilinear';
        push @angles, $angles[0] + 90;
    } elsif ($pattern eq 'pillars') {
        $pattern = 'honeycomb';
    }
    
    my $interface_angle = $self->object_config->support_material_angle + 90;
    my $interface_spacing = $self->object_config->support_material_interface_spacing + $interface_flow->spacing;
    my $interface_density = $interface_spacing == 0 ? 1 : $interface_flow->spacing / $interface_spacing;
    my $support_spacing = $self->object_config->support_material_spacing + $flow->spacing;
    my $support_density = $support_spacing == 0 ? 1 : $flow->spacing / $support_spacing;
    
    my $process_layer = sub {
        my ($layer_id) = @_;
        my $layer = $object->support_layers->[$layer_id];
        my $z = $layer->print_z;
        
        # we redefine flows locally by applying this layer's height
        my $_flow           = $flow->clone;
        my $_interface_flow = $interface_flow->clone;
        $_flow->set_height($layer->height);
        $_interface_flow->set_height($layer->height);
        
        my $overhang    = $overhang->{$z}           || [];
        my $contact     = $contact->{$z}            || [];
        my $interface   = $interface->{$layer_id}   || [];
        my $base        = $base->{$layer_id}        || [];
        
        if (DEBUG_CONTACT_ONLY) {
            $interface = [];
            $base = [];
        }
        
        if (0) {
            require "Slic3r/SVG.pm";
            Slic3r::SVG::output(Slic3r::DEBUG_OUT_PATH_PREFIX . "layer_" . $z . ".svg",
                blue_expolygons     => union_ex($base),
                red_expolygons      => union_ex($contact),
                green_expolygons    => union_ex($interface),
            );
        }
        
        # islands
        $layer->support_islands->append(@{union_ex([ @$interface, @$base, @$contact ])});
        
        # contact
        my $contact_infill = [];
        if ($self->object_config->support_material_interface_layers == 0) {
            # if no interface layers were requested we treat the contact layer
            # exactly as a generic base layer
            push @$base, @$contact;
        } elsif (@$contact && $contact_loops > 0) {
            # generate the outermost loop
            
            # find centerline of the external loop (or any other kind of extrusions should the loop be skipped)
            $contact = offset($contact, -$_interface_flow->scaled_width/2);
            
            my @loops0 = ();
            {
                # find centerline of the external loop of the contours
                my @external_loops = @$contact;
                
                # only consider the loops facing the overhang
                {
                    my $overhang_with_margin = offset($overhang, +$_interface_flow->scaled_width/2);
                    @external_loops = grep {
                        @{intersection_pl(
                            [ $_->split_at_first_point ],
                            $overhang_with_margin,
                        )}
                    } @external_loops;
                }
                
                # apply a pattern to the loop
                my @positions = map @{Slic3r::Polygon->new(@$_)->equally_spaced_points($circle_distance)}, @external_loops;
                @loops0 = @{diff(
                    [ @external_loops ],
                    [ map { my $c = $circle->clone; $c->translate(@$_); $c } @positions ],
                )};
            }
            
            # make more loops
            my @loops = @loops0;
            for my $i (2..$contact_loops) {
                my $d = ($i-1) * $_interface_flow->scaled_spacing;
                push @loops, @{offset2(\@loops0, -$d -0.5*$_interface_flow->scaled_spacing, +0.5*$_interface_flow->scaled_spacing)};
            }
            
            # clip such loops to the side oriented towards the object
            @loops = @{intersection_pl(
                [ map $_->split_at_first_point, @loops ],
                offset($overhang, +scale MARGIN),
            )};
            
            # add the contact infill area to the interface area
            # note that growing loops by $circle_radius ensures no tiny
            # extrusions are left inside the circles; however it creates
            # a very large gap between loops and contact_infill, so maybe another
            # solution should be found to achieve both goals
            $contact_infill = diff(
                $contact,
                [ map @{$_->grow($circle_radius*1.1)}, @loops ],
            );
            
            # transform loops into ExtrusionPath objects
            my $mm3_per_mm = $_interface_flow->mm3_per_mm;
            @loops = map Slic3r::ExtrusionPath->new(
                polyline    => $_,
                role        => EXTR_ROLE_SUPPORTMATERIAL_INTERFACE,
                mm3_per_mm  => $mm3_per_mm,
                width       => $_interface_flow->width,
                height      => $layer->height,
            ), @loops;
            
            $layer->support_interface_fills->append(@loops);
        }

        # Allocate the fillers exclusively in the worker threads! Don't allocate them at the main thread,
        # as Perl copies the C++ pointers by default, so then the C++ objects are shared between threads!
        my %fillers = (
            interface   => Slic3r::Filler->new_from_type('rectilinear'),
            support     => Slic3r::Filler->new_from_type($pattern),
        );
        my $bounding_box = $object->bounding_box;
        $fillers{interface}->set_bounding_box($object->bounding_box);
        $fillers{support}->set_bounding_box($object->bounding_box);

        # interface and contact infill
        if (@$interface || @$contact_infill) {
            $fillers{interface}->set_angle($interface_angle);
            $fillers{interface}->set_spacing($_interface_flow->spacing);
            
            # find centerline of the external loop
            $interface = offset2($interface, +scaled_epsilon, -(scaled_epsilon + $_interface_flow->scaled_width/2));
            
            # join regions by offsetting them to ensure they're merged
            $interface = offset([ @$interface, @$contact_infill ], scaled_epsilon);
            
            # turn base support into interface when it's contained in our holes
            # (this way we get wider interface anchoring)
            {
                my @p = @$interface;
                @$interface = ();
                foreach my $p (@p) {
                    if ($p->is_clockwise) {
                        my $p2 = $p->clone;
                        $p2->make_counter_clockwise;
                        next if !@{diff([$p2], $base, 1)};
                    }
                    push @$interface, $p;
                }
            }
            $base = diff($base, $interface);
            
            my @paths = ();
            foreach my $expolygon (@{union_ex($interface)}) {
                my $polylines = $fillers{interface}->fill_surface(
                    Slic3r::Surface->new(expolygon => $expolygon, surface_type => S_TYPE_INTERNAL),
                    density      => $interface_density,
                    layer_height => $layer->height,
                    complete     => 1,
                );
                my $mm3_per_mm = $_interface_flow->mm3_per_mm;
                
                push @paths, map Slic3r::ExtrusionPath->new(
                    polyline    => Slic3r::Polyline->new(@$_),
                    role        => EXTR_ROLE_SUPPORTMATERIAL_INTERFACE,
                    mm3_per_mm  => $mm3_per_mm,
                    width       => $_interface_flow->width,
                    height      => $layer->height,
                ), @$polylines,
            }
            
            $layer->support_interface_fills->append(@paths);
        }
        
        # support or flange
        if (@$base) {
            my $filler = $fillers{support};
            $filler->set_angle($angles[ ($layer_id) % @angles ]);
            
            # We don't use $base_flow->spacing because we need a constant spacing
            # value that guarantees that all layers are correctly aligned.
            $filler->set_spacing($flow->spacing);
            
            my $density     = $support_density;
            my $base_flow   = $_flow;
            
            # find centerline of the external loop/extrusions
            my $to_infill = offset2_ex($base, +scaled_epsilon, -(scaled_epsilon + $_flow->scaled_width/2));

            if (0) {
                require "Slic3r/SVG.pm";
                Slic3r::SVG::output(Slic3r::DEBUG_OUT_PATH_PREFIX . "to_infill_base" . $z . ".svg",
                    red_expolygons      => union_ex($contact),
                    green_expolygons    => union_ex($interface),
                    blue_expolygons     => $to_infill,
                );
            }
            
            my @paths = ();
            
            # base flange
            if ($layer_id == 0) {
                $filler = $fillers{interface};
                $filler->set_angle($self->object_config->support_material_angle + 90);
                $density        = 0.5;
                $base_flow      = $self->first_layer_flow;
                
                # use the proper spacing for first layer as we don't need to align
                # its pattern to the other layers
                $filler->set_spacing($base_flow->spacing);
            } elsif ($with_sheath) {
                # draw a perimeter all around support infill
                # TODO: use brim ordering algorithm
                my $mm3_per_mm = $_flow->mm3_per_mm;
                push @paths, map Slic3r::ExtrusionPath->new(
                    polyline    => $_->split_at_first_point,
                    role        => EXTR_ROLE_SUPPORTMATERIAL,
                    mm3_per_mm  => $mm3_per_mm,
                    width       => $_flow->width,
                    height      => $layer->height,
                ), map @$_, @$to_infill;
                
                # TODO: use offset2_ex()
                $to_infill = offset_ex([ map @$_, @$to_infill ], -$_flow->scaled_spacing);
            }
            
            foreach my $expolygon (@$to_infill) {
                my $polylines = $filler->fill_surface(
                    Slic3r::Surface->new(expolygon => $expolygon, surface_type => S_TYPE_INTERNAL),
                    density     => $density,
                    layer_height => $layer->height,
                    complete    => 1,
                );
                
                push @paths, map Slic3r::ExtrusionPath->new(
                    polyline    => Slic3r::Polyline->new(@$_),
                    role        => EXTR_ROLE_SUPPORTMATERIAL,
                    mm3_per_mm  => $base_flow->mm3_per_mm,
                    width       => $base_flow->width,
                    height      => $layer->height,
                ), @$polylines;
            }
            
            $layer->support_fills->append(@paths);
        }
        
        if (0) {
            require "Slic3r/SVG.pm";
            Slic3r::SVG::output("islands_" . $z . ".svg",
                red_expolygons      => union_ex($contact),
                green_expolygons    => union_ex($interface),
                green_polylines     => [ map $_->unpack->polyline, @{$layer->support_contact_fills} ],
                polylines           => [ map $_->unpack->polyline, @{$layer->support_fills} ],
            );
        }
    };
    
    Slic3r::parallelize(
        threads => $self->print_config->threads,
        items => [ 0 .. $#{$object->support_layers} ],
        thread_cb => sub {
            my $q = shift;
            while (defined (my $layer_id = $q->dequeue)) {
                $process_layer->($layer_id);
            }
        },
        no_threads_cb => sub {
            $process_layer->($_) for 0 .. $#{$object->support_layers};
        },
    );
}

sub generate_pillars_shape {
    my ($self, $contact, $support_z, $shape) = @_;
    
    # this prevents supplying an empty point set to BoundingBox constructor
    return if !%$contact;
    
    my $pillar_size     = scale PILLAR_SIZE;
    my $pillar_spacing  = scale PILLAR_SPACING;
    
    # A regular grid of pillars, filling the 2D bounding box.
    # arrayref of polygons
    my $grid;  # arrayref of polygons
    {
        # Rectangle with a side of 2.5x2.5mm.
        my $pillar = Slic3r::Polygon->new(
            [0,0],
            [$pillar_size, 0],
            [$pillar_size, $pillar_size],
            [0, $pillar_size],
        );
        
        # A regular grid of pillars, filling the 2D bounding box.
        my @pillars = ();
        # 2D bounding box of the projection of all contact polygons.
        my $bb = Slic3r::Geometry::BoundingBox->new_from_points([ map @$_, map @$_, values %$contact ]);
        for (my $x = $bb->x_min; $x <= $bb->x_max-$pillar_size; $x += $pillar_spacing) {
            for (my $y = $bb->y_min; $y <= $bb->y_max-$pillar_size; $y += $pillar_spacing) {
                push @pillars, my $p = $pillar->clone;
                $p->translate($x, $y);
            }
        }
        $grid = union(\@pillars);
    }
    
    # add pillars to every layer
    for my $i (0..$#$support_z) {
        $shape->[$i] = [ @$grid ];
    }
    
    # build capitals
    for my $i (0..$#$support_z) {
        my $z = $support_z->[$i];
        
        my $capitals = intersection(
            $grid,
            $contact->{$z} // [],
        );
        
        # work on one pillar at time (if any) to prevent the capitals from being merged
        # but store the contact area supported by the capital because we need to make 
        # sure nothing is left
        my $contact_supported_by_capitals = [];
        foreach my $capital (@$capitals) {
            # enlarge capital tops
            $capital = offset([$capital], +($pillar_spacing - $pillar_size)/2);
            push @$contact_supported_by_capitals, @$capital;
            
            for (my $j = $i-1; $j >= 0; $j--) {
                my $jz = $support_z->[$j];
                $capital = offset($capital, -$self->interface_flow->scaled_width/2);
                last if !@$capitals;
                push @{ $shape->[$j] }, @$capital;
            }
        }
        
        # Capitals will not generally cover the whole contact area because there will be
        # remainders. For now we handle this situation by projecting such unsupported
        # areas to the ground, just like we would do with a normal support.
        my $contact_not_supported_by_capitals = diff(
            $contact->{$z} // [],
            $contact_supported_by_capitals,
        );
        if (@$contact_not_supported_by_capitals) {
            for (my $j = $i-1; $j >= 0; $j--) {
                push @{ $shape->[$j] }, @$contact_not_supported_by_capitals;
            }
        }
    }
}

sub clip_with_shape {
    my ($self, $support, $shape) = @_;
    
    foreach my $i (keys %$support) {
        # don't clip bottom layer with shape so that we 
        # can generate a continuous base flange
        # also don't clip raft layers
        next if $i == 0;
        next if $i < $self->object_config->raft_layers;
        $support->{$i} = intersection(
            $support->{$i},
            $shape->[$i],
        );
    }
}

# this method returns the indices of the layers overlapping with the given one
sub overlapping_layers {
    my ($self, $i, $support_z) = @_;
    
    my $zmax = $support_z->[$i];
    my $zmin = ($i == 0) ? 0 : $support_z->[$i-1];
    
    return grep {
        my $zmax2 = $support_z->[$_];
        my $zmin2 = ($_ == 0) ? 0 : $support_z->[$_-1];
        $zmax > $zmin2 && $zmin < $zmax2;
    } 0..$#$support_z;
}

sub contact_distance {
    my ($self, $layer_height, $nozzle_diameter) = @_;

    my $extra = $self->object_config->support_material_contact_distance;
    if ($extra == 0) {
        return $layer_height;
    } else {
        return $nozzle_diameter + $extra;
    }
}

1;