Cura/cura/BuildVolume.py

# Copyright (c) 2016 Ultimaker B.V.
# Cura is released under the terms of the AGPLv3 or higher.

from cura.Settings.ExtruderManager import ExtruderManager
from UM.i18n import i18nCatalog
from UM.Scene.Platform import Platform
from UM.Scene.Iterator.BreadthFirstIterator import BreadthFirstIterator
from UM.Scene.SceneNode import SceneNode
from UM.Application import Application
from UM.Resources import Resources
from UM.Mesh.MeshBuilder import MeshBuilder
from UM.Math.Vector import Vector
from UM.Math.Matrix import Matrix
from UM.Math.Color import Color
from UM.Math.AxisAlignedBox import AxisAlignedBox
from UM.Math.Polygon import Polygon
from UM.Message import Message
from UM.Signal import Signal
from PyQt5.QtCore import QTimer
from UM.View.RenderBatch import RenderBatch
from UM.View.GL.OpenGL import OpenGL
catalog = i18nCatalog("cura")

import numpy
import copy
import math

import UM.Settings.ContainerRegistry


# Setting for clearance around the prime
PRIME_CLEARANCE = 6.5


##  Build volume is a special kind of node that is responsible for rendering the printable area & disallowed areas.
class BuildVolume(SceneNode):
    VolumeOutlineColor = Color(12, 169, 227, 255)
    XAxisColor = Color(255, 0, 0, 255)
    YAxisColor = Color(0, 0, 255, 255)
    ZAxisColor = Color(0, 255, 0, 255)

    raftThicknessChanged = Signal()

    def __init__(self, parent = None):
        super().__init__(parent)

        self._width = 0
        self._height = 0
        self._depth = 0
        self._shape = ""

        self._shader = None

        self._origin_mesh = None
        self._origin_line_length = 20
        self._origin_line_width = 0.5

        self._grid_mesh = None
        self._grid_shader = None

        self._disallowed_areas = []
        self._disallowed_area_mesh = None

        self._error_areas = []
        self._error_mesh = None

        self.setCalculateBoundingBox(False)
        self._volume_aabb = None

        self._raft_thickness = 0.0
        self._adhesion_type = None
        self._platform = Platform(self)

        self._global_container_stack = None
        Application.getInstance().globalContainerStackChanged.connect(self._onStackChanged)
        self._onStackChanged()

        self._has_errors = False
        Application.getInstance().getController().getScene().sceneChanged.connect(self._onSceneChanged)

        #Objects loaded at the moment. We are connected to the property changed events of these objects.
        self._scene_objects = set()

        self._change_timer = QTimer()
        self._change_timer.setInterval(100)
        self._change_timer.setSingleShot(True)
        self._change_timer.timeout.connect(self._onChangeTimerFinished)

        self._build_volume_message = Message(catalog.i18nc("@info:status",
            "The build volume height has been reduced due to the value of the"
            " \"Print Sequence\" setting to prevent the gantry from colliding"
            " with printed models."))

        # Must be after setting _build_volume_message, apparently that is used in getMachineManager.
        # activeQualityChanged is always emitted after setActiveVariant, setActiveMaterial and setActiveQuality.
        # Therefore this works.
        Application.getInstance().getMachineManager().activeQualityChanged.connect(self._onStackChanged)
        # This should also ways work, and it is semantically more correct,
        # but it does not update the disallowed areas after material change
        Application.getInstance().getMachineManager().activeStackChanged.connect(self._onStackChanged)

    def _onSceneChanged(self, source):
        if self._global_container_stack:
            self._change_timer.start()

    def _onChangeTimerFinished(self):
        root = Application.getInstance().getController().getScene().getRoot()
        new_scene_objects = set(node for node in BreadthFirstIterator(root) if node.getMeshData() and type(node) is SceneNode)
        if new_scene_objects != self._scene_objects:
            for node in new_scene_objects - self._scene_objects: #Nodes that were added to the scene.
                node.decoratorsChanged.connect(self._onNodeDecoratorChanged)
            for node in self._scene_objects - new_scene_objects: #Nodes that were removed from the scene.
                per_mesh_stack = node.callDecoration("getStack")
                if per_mesh_stack:
                    per_mesh_stack.propertyChanged.disconnect(self._onSettingPropertyChanged)
                active_extruder_changed = node.callDecoration("getActiveExtruderChangedSignal")
                if active_extruder_changed is not None:
                    node.callDecoration("getActiveExtruderChangedSignal").disconnect(self._updateDisallowedAreasAndRebuild)
                node.decoratorsChanged.disconnect(self._onNodeDecoratorChanged)

            self._scene_objects = new_scene_objects
            self._onSettingPropertyChanged("print_sequence", "value")  # Create fake event, so right settings are triggered.

    ##  Updates the listeners that listen for changes in per-mesh stacks.
    #
    #   \param node The node for which the decorators changed.
    def _onNodeDecoratorChanged(self, node):
        per_mesh_stack = node.callDecoration("getStack")
        if per_mesh_stack:
            per_mesh_stack.propertyChanged.connect(self._onSettingPropertyChanged)
        active_extruder_changed = node.callDecoration("getActiveExtruderChangedSignal")
        if active_extruder_changed is not None:
            active_extruder_changed.connect(self._updateDisallowedAreasAndRebuild)
            self._updateDisallowedAreasAndRebuild()

    def setWidth(self, width):
        if width: self._width = width

    def setHeight(self, height):
        if height: self._height = height

    def setDepth(self, depth):
        if depth: self._depth = depth

    def setShape(self, shape):
        if shape: self._shape = shape

    def getDisallowedAreas(self):
        return self._disallowed_areas

    def setDisallowedAreas(self, areas):
        self._disallowed_areas = areas

    def render(self, renderer):
        if not self.getMeshData():
            return True

        if not self._shader:
            self._shader = OpenGL.getInstance().createShaderProgram(Resources.getPath(Resources.Shaders, "default.shader"))
            self._grid_shader = OpenGL.getInstance().createShaderProgram(Resources.getPath(Resources.Shaders, "grid.shader"))

        renderer.queueNode(self, mode = RenderBatch.RenderMode.Lines)
        renderer.queueNode(self, mesh = self._origin_mesh)
        renderer.queueNode(self, mesh = self._grid_mesh, shader = self._grid_shader, backface_cull = True)
        if self._disallowed_area_mesh:
            renderer.queueNode(self, mesh = self._disallowed_area_mesh, shader = self._shader, transparent = True, backface_cull = True, sort = -9)

        if self._error_mesh:
            renderer.queueNode(self, mesh=self._error_mesh, shader=self._shader, transparent=True,
                               backface_cull=True, sort=-8)

        return True

    ##  Recalculates the build volume & disallowed areas.
    def rebuild(self):
        if not self._width or not self._height or not self._depth:
            return

        min_w = -self._width / 2
        max_w = self._width / 2
        min_h = 0.0
        max_h = self._height
        min_d = -self._depth / 2
        max_d = self._depth / 2

        z_fight_distance = 0.2 # Distance between buildplate and disallowed area meshes to prevent z-fighting

        if self._shape != "elliptic":
            # Outline 'cube' of the build volume
            mb = MeshBuilder()
            mb.addLine(Vector(min_w, min_h, min_d), Vector(max_w, min_h, min_d), color = self.VolumeOutlineColor)
            mb.addLine(Vector(min_w, min_h, min_d), Vector(min_w, max_h, min_d), color = self.VolumeOutlineColor)
            mb.addLine(Vector(min_w, max_h, min_d), Vector(max_w, max_h, min_d), color = self.VolumeOutlineColor)
            mb.addLine(Vector(max_w, min_h, min_d), Vector(max_w, max_h, min_d), color = self.VolumeOutlineColor)

            mb.addLine(Vector(min_w, min_h, max_d), Vector(max_w, min_h, max_d), color = self.VolumeOutlineColor)
            mb.addLine(Vector(min_w, min_h, max_d), Vector(min_w, max_h, max_d), color = self.VolumeOutlineColor)
            mb.addLine(Vector(min_w, max_h, max_d), Vector(max_w, max_h, max_d), color = self.VolumeOutlineColor)
            mb.addLine(Vector(max_w, min_h, max_d), Vector(max_w, max_h, max_d), color = self.VolumeOutlineColor)

            mb.addLine(Vector(min_w, min_h, min_d), Vector(min_w, min_h, max_d), color = self.VolumeOutlineColor)
            mb.addLine(Vector(max_w, min_h, min_d), Vector(max_w, min_h, max_d), color = self.VolumeOutlineColor)
            mb.addLine(Vector(min_w, max_h, min_d), Vector(min_w, max_h, max_d), color = self.VolumeOutlineColor)
            mb.addLine(Vector(max_w, max_h, min_d), Vector(max_w, max_h, max_d), color = self.VolumeOutlineColor)

            self.setMeshData(mb.build())

            # Build plate grid mesh
            mb = MeshBuilder()
            mb.addQuad(
                Vector(min_w, min_h - z_fight_distance, min_d),
                Vector(max_w, min_h - z_fight_distance, min_d),
                Vector(max_w, min_h - z_fight_distance, max_d),
                Vector(min_w, min_h - z_fight_distance, max_d)
            )

            for n in range(0, 6):
                v = mb.getVertex(n)
                mb.setVertexUVCoordinates(n, v[0], v[2])
            self._grid_mesh = mb.build()

        else:
            # Bottom and top 'ellipse' of the build volume
            aspect = 1.0
            scale_matrix = Matrix()
            if self._width != 0:
                # Scale circular meshes by aspect ratio if width != height
                aspect = self._height / self._width
                scale_matrix.compose(scale = Vector(1, 1, aspect))
            mb = MeshBuilder()
            mb.addArc(max_w, Vector.Unit_Y, center = (0, min_h - z_fight_distance, 0), color = self.VolumeOutlineColor)
            mb.addArc(max_w, Vector.Unit_Y, center = (0, max_h, 0),  color = self.VolumeOutlineColor)
            self.setMeshData(mb.build().getTransformed(scale_matrix))

            # Build plate grid mesh
            mb = MeshBuilder()
            mb.addArc(max_w, Vector.Unit_Y, center = Vector(0, min_h - z_fight_distance, 0))
            sections = mb.getVertexCount()
            mb.addVertex(0, min_h - z_fight_distance, 0)
            for n in range(0, sections-1):
                mb.addIndices([sections, n + 1, n])

            for n in range(0, mb.getVertexCount()):
                v = mb.getVertex(n)
                mb.setVertexUVCoordinates(n, v[0], v[2] * aspect)
            self._grid_mesh = mb.build().getTransformed(scale_matrix)

        # Indication of the machine origin
        if self._global_container_stack.getProperty("machine_center_is_zero", "value"):
            origin = (Vector(min_w, min_h, min_d) + Vector(max_w, min_h, max_d)) / 2
        else:
            origin = Vector(min_w, min_h, max_d)

        mb = MeshBuilder()
        mb.addCube(
            width = self._origin_line_length,
            height = self._origin_line_width,
            depth = self._origin_line_width,
            center = origin + Vector(self._origin_line_length / 2, 0, 0),
            color = self.XAxisColor
        )
        mb.addCube(
            width = self._origin_line_width,
            height = self._origin_line_length,
            depth = self._origin_line_width,
            center = origin + Vector(0, self._origin_line_length / 2, 0),
            color = self.YAxisColor
        )
        mb.addCube(
            width = self._origin_line_width,
            height = self._origin_line_width,
            depth = self._origin_line_length,
            center = origin - Vector(0, 0, self._origin_line_length / 2),
            color = self.ZAxisColor
        )
        self._origin_mesh = mb.build()

        disallowed_area_height = 0.1
        disallowed_area_size = 0
        if self._disallowed_areas:
            mb = MeshBuilder()
            color = Color(0.0, 0.0, 0.0, 0.15)
            for polygon in self._disallowed_areas:
                points = polygon.getPoints()
                first = Vector(self._clamp(points[0][0], min_w, max_w), disallowed_area_height, self._clamp(points[0][1], min_d, max_d))
                previous_point = Vector(self._clamp(points[0][0], min_w, max_w), disallowed_area_height, self._clamp(points[0][1], min_d, max_d))
                for point in points:
                    new_point = Vector(self._clamp(point[0], min_w, max_w), disallowed_area_height, self._clamp(point[1], min_d, max_d))
                    mb.addFace(first, previous_point, new_point, color = color)
                    previous_point = new_point

                # Find the largest disallowed area to exclude it from the maximum scale bounds.
                # This is a very nasty hack. This pretty much only works for UM machines.
                # This disallowed area_size needs a -lot- of rework at some point in the future: TODO
                if numpy.min(points[:, 1]) >= 0: # This filters out all areas that have points to the left of the centre. This is done to filter the skirt area.
                    size = abs(numpy.max(points[:, 1]) - numpy.min(points[:, 1]))
                else:
                    size = 0
                disallowed_area_size = max(size, disallowed_area_size)

            self._disallowed_area_mesh = mb.build()
        else:
            self._disallowed_area_mesh = None

        if self._error_areas:
            mb = MeshBuilder()
            for error_area in self._error_areas:
                color = Color(1.0, 0.0, 0.0, 0.5)
                points = error_area.getPoints()
                first = Vector(self._clamp(points[0][0], min_w, max_w), disallowed_area_height,
                               self._clamp(points[0][1], min_d, max_d))
                previous_point = Vector(self._clamp(points[0][0], min_w, max_w), disallowed_area_height,
                                        self._clamp(points[0][1], min_d, max_d))
                for point in points:
                    new_point = Vector(self._clamp(point[0], min_w, max_w), disallowed_area_height,
                                       self._clamp(point[1], min_d, max_d))
                    mb.addFace(first, previous_point, new_point, color=color)
                    previous_point = new_point
            self._error_mesh = mb.build()
        else:
            self._error_mesh = None

        self._volume_aabb = AxisAlignedBox(
            minimum = Vector(min_w, min_h - 1.0, min_d),
            maximum = Vector(max_w, max_h - self._raft_thickness, max_d))

        bed_adhesion_size = self._getEdgeDisallowedSize()

        # As this works better for UM machines, we only add the disallowed_area_size for the z direction.
        # This is probably wrong in all other cases. TODO!
        # The +1 and -1 is added as there is always a bit of extra room required to work properly.
        scale_to_max_bounds = AxisAlignedBox(
            minimum = Vector(min_w + bed_adhesion_size + 1, min_h, min_d + disallowed_area_size - bed_adhesion_size + 1),
            maximum = Vector(max_w - bed_adhesion_size - 1, max_h - self._raft_thickness, max_d - disallowed_area_size + bed_adhesion_size - 1)
        )

        Application.getInstance().getController().getScene()._maximum_bounds = scale_to_max_bounds

    def getBoundingBox(self):
        return self._volume_aabb

    def getRaftThickness(self):
        return self._raft_thickness

    def _updateRaftThickness(self):
        old_raft_thickness = self._raft_thickness
        self._adhesion_type = self._global_container_stack.getProperty("adhesion_type", "value")
        self._raft_thickness = 0.0
        if self._adhesion_type == "raft":
            self._raft_thickness = (
                self._global_container_stack.getProperty("raft_base_thickness", "value") +
                self._global_container_stack.getProperty("raft_interface_thickness", "value") +
                self._global_container_stack.getProperty("raft_surface_layers", "value") *
                    self._global_container_stack.getProperty("raft_surface_thickness", "value") +
                self._global_container_stack.getProperty("raft_airgap", "value"))

        # Rounding errors do not matter, we check if raft_thickness has changed at all
        if old_raft_thickness != self._raft_thickness:
            self.setPosition(Vector(0, -self._raft_thickness, 0), SceneNode.TransformSpace.World)
            self.raftThicknessChanged.emit()

    ##  Update the build volume visualization
    def _onStackChanged(self):
        if self._global_container_stack:
            self._global_container_stack.propertyChanged.disconnect(self._onSettingPropertyChanged)
            extruders = ExtruderManager.getInstance().getMachineExtruders(self._global_container_stack.getId())
            for extruder in extruders:
                extruder.propertyChanged.disconnect(self._onSettingPropertyChanged)

        self._global_container_stack = Application.getInstance().getGlobalContainerStack()

        if self._global_container_stack:
            self._global_container_stack.propertyChanged.connect(self._onSettingPropertyChanged)
            extruders = ExtruderManager.getInstance().getMachineExtruders(self._global_container_stack.getId())
            for extruder in extruders:
                extruder.propertyChanged.connect(self._onSettingPropertyChanged)

            self._width = self._global_container_stack.getProperty("machine_width", "value")
            machine_height = self._global_container_stack.getProperty("machine_height", "value")
            if self._global_container_stack.getProperty("print_sequence", "value") == "one_at_a_time" and len(self._scene_objects) > 1:
                self._height = min(self._global_container_stack.getProperty("gantry_height", "value"), machine_height)
                if self._height < machine_height:
                    self._build_volume_message.show()
                else:
                    self._build_volume_message.hide()
            else:
                self._height = self._global_container_stack.getProperty("machine_height", "value")
                self._build_volume_message.hide()
            self._depth = self._global_container_stack.getProperty("machine_depth", "value")
            self._shape = self._global_container_stack.getProperty("machine_shape", "value")

            self._updateDisallowedAreas()
            self._updateRaftThickness()

            self.rebuild()

    def _onSettingPropertyChanged(self, setting_key, property_name):
        if property_name != "value":
            return

        rebuild_me = False
        if setting_key == "print_sequence":
            machine_height = self._global_container_stack.getProperty("machine_height", "value")
            if Application.getInstance().getGlobalContainerStack().getProperty("print_sequence", "value") == "one_at_a_time" and len(self._scene_objects) > 1:
                self._height = min(self._global_container_stack.getProperty("gantry_height", "value"), machine_height)
                if self._height < machine_height:
                    self._build_volume_message.show()
                else:
                    self._build_volume_message.hide()
            else:
                self._height = self._global_container_stack.getProperty("machine_height", "value")
                self._build_volume_message.hide()
            rebuild_me = True

        if setting_key in self._skirt_settings or setting_key in self._prime_settings or setting_key in self._tower_settings or setting_key == "print_sequence" or setting_key in self._ooze_shield_settings or setting_key in self._distance_settings or setting_key in self._extruder_settings:
            self._updateDisallowedAreas()
            rebuild_me = True

        if setting_key in self._raft_settings:
            self._updateRaftThickness()
            rebuild_me = True

        if rebuild_me:
            self.rebuild()

    def hasErrors(self):
        return self._has_errors

    ##  Calls _updateDisallowedAreas and makes sure the changes appear in the
    #   scene.
    #
    #   This is required for a signal to trigger the update in one go. The
    #   ``_updateDisallowedAreas`` method itself shouldn't call ``rebuild``,
    #   since there may be other changes before it needs to be rebuilt, which
    #   would hit performance.
    def _updateDisallowedAreasAndRebuild(self):
        self._updateDisallowedAreas()
        self.rebuild()

    def _updateDisallowedAreas(self):
        if not self._global_container_stack:
            return

        self._error_areas = []

        extruder_manager = ExtruderManager.getInstance()
        used_extruders = extruder_manager.getUsedExtruderStacks()
        disallowed_border_size = self._getEdgeDisallowedSize()

        result_areas = self._computeDisallowedAreasStatic(disallowed_border_size, used_extruders) #Normal machine disallowed areas can always be added.
        prime_areas = self._computeDisallowedAreasPrime(disallowed_border_size, used_extruders)
        prime_disallowed_areas = self._computeDisallowedAreasStatic(0, used_extruders) #Where the priming is not allowed to happen. This is not added to the result, just for collision checking.

        #Check if prime positions intersect with disallowed areas.
        for extruder in used_extruders:
            extruder_id = extruder.getId()

            collision = False
            for prime_polygon in prime_areas[extruder_id]:
                for disallowed_polygon in prime_disallowed_areas[extruder_id]:
                    if prime_polygon.intersectsPolygon(disallowed_polygon) is not None:
                        collision = True
                        break
                if collision:
                    break

                #Also check other prime positions (without additional offset).
                for other_extruder_id in prime_areas:
                    if extruder_id == other_extruder_id: #It is allowed to collide with itself.
                        continue
                    for other_prime_polygon in prime_areas[other_extruder_id]:
                        if prime_polygon.intersectsPolygon(other_prime_polygon):
                            collision = True
                            break
                    if collision:
                        break
                if collision:
                    break

            result_areas[extruder_id].extend(prime_areas[extruder_id])

            nozzle_disallowed_areas = extruder.getProperty("nozzle_disallowed_areas", "value")
            for area in nozzle_disallowed_areas:
                polygon = Polygon(numpy.array(area, numpy.float32))
                polygon = polygon.getMinkowskiHull(Polygon.approximatedCircle(disallowed_border_size))
                result_areas[extruder_id].append(polygon) #Don't perform the offset on these.

        # Add prime tower location as disallowed area.
        prime_tower_collision = False
        prime_tower_areas = self._computeDisallowedAreasPrinted(used_extruders)
        for extruder_id in prime_tower_areas:
            for prime_tower_area in prime_tower_areas[extruder_id]:
                for area in result_areas[extruder_id]:
                    if prime_tower_area.intersectsPolygon(area) is not None:
                        prime_tower_collision = True
                        break
                if prime_tower_collision: #Already found a collision.
                    break
            if not prime_tower_collision:
                result_areas[extruder_id].extend(prime_tower_areas[extruder_id])
            else:
                self._error_areas.extend(prime_tower_areas[extruder_id])

        self._has_errors = len(self._error_areas) > 0

        self._disallowed_areas = []
        for extruder_id in result_areas:
            self._disallowed_areas.extend(result_areas[extruder_id])

    ##  Computes the disallowed areas for objects that are printed with print
    #   features.
    #
    #   This means that the brim, travel avoidance and such will be applied to
    #   these features.
    #
    #   \return A dictionary with for each used extruder ID the disallowed areas
    #   where that extruder may not print.
    def _computeDisallowedAreasPrinted(self, used_extruders):
        result = {}
        for extruder in used_extruders:
            result[extruder.getId()] = []

        #Currently, the only normally printed object is the prime tower.
        if ExtruderManager.getInstance().getResolveOrValue("prime_tower_enable") == True:
            prime_tower_size = self._global_container_stack.getProperty("prime_tower_size", "value")
            machine_width = self._global_container_stack.getProperty("machine_width", "value")
            machine_depth = self._global_container_stack.getProperty("machine_depth", "value")
            prime_tower_x = self._global_container_stack.getProperty("prime_tower_position_x", "value") - machine_width / 2 #Offset by half machine_width and _depth to put the origin in the front-left.
            prime_tower_y = - self._global_container_stack.getProperty("prime_tower_position_y", "value") + machine_depth / 2

            prime_tower_area = Polygon([
                [prime_tower_x - prime_tower_size, prime_tower_y - prime_tower_size],
                [prime_tower_x, prime_tower_y - prime_tower_size],
                [prime_tower_x, prime_tower_y],
                [prime_tower_x - prime_tower_size, prime_tower_y],
            ])
            prime_tower_area = prime_tower_area.getMinkowskiHull(Polygon.approximatedCircle(0))
            for extruder in used_extruders:
                result[extruder.getId()].append(prime_tower_area) #The prime tower location is the same for each extruder, regardless of offset.

        return result

    ##  Computes the disallowed areas for the prime locations.
    #
    #   These are special because they are not subject to things like brim or
    #   travel avoidance. They do get a dilute with the border size though
    #   because they may not intersect with brims and such of other objects.
    #
    #   \param border_size The size with which to offset the disallowed areas
    #   due to skirt, brim, travel avoid distance, etc.
    #   \param used_extruders The extruder stacks to generate disallowed areas
    #   for.
    #   \return A dictionary with for each used extruder ID the prime areas.
    def _computeDisallowedAreasPrime(self, border_size, used_extruders):
        result = {}

        machine_width = self._global_container_stack.getProperty("machine_width", "value")
        machine_depth = self._global_container_stack.getProperty("machine_depth", "value")
        for extruder in used_extruders:
            prime_x = extruder.getProperty("extruder_prime_pos_x", "value") - machine_width / 2 #Offset by half machine_width and _depth to put the origin in the front-left.
            prime_y = machine_depth / 2 - extruder.getProperty("extruder_prime_pos_y", "value")

            prime_polygon = Polygon.approximatedCircle(PRIME_CLEARANCE)
            prime_polygon = prime_polygon.translate(prime_x, prime_y)
            prime_polygon = prime_polygon.getMinkowskiHull(Polygon.approximatedCircle(border_size))
            result[extruder.getId()] = [prime_polygon]

        return result

    ##  Computes the disallowed areas that are statically placed in the machine.
    #
    #   It computes different disallowed areas depending on the offset of the
    #   extruder. The resulting dictionary will therefore have an entry for each
    #   extruder that is used.
    #
    #   \param border_size The size with which to offset the disallowed areas
    #   due to skirt, brim, travel avoid distance, etc.
    #   \param used_extruders The extruder stacks to generate disallowed areas
    #   for.
    #   \return A dictionary with for each used extruder ID the disallowed areas
    #   where that extruder may not print.
    def _computeDisallowedAreasStatic(self, border_size, used_extruders):
        #Convert disallowed areas to polygons and dilate them.
        machine_disallowed_polygons = []
        for area in self._global_container_stack.getProperty("machine_disallowed_areas", "value"):
            polygon = Polygon(numpy.array(area, numpy.float32))
            polygon = polygon.getMinkowskiHull(Polygon.approximatedCircle(border_size))
            machine_disallowed_polygons.append(polygon)

        result = {}
        for extruder in used_extruders:
            extruder_id = extruder.getId()
            offset_x = extruder.getProperty("machine_nozzle_offset_x", "value")
            if offset_x is None:
                offset_x = 0
            offset_y = extruder.getProperty("machine_nozzle_offset_y", "value")
            if offset_y is None:
                offset_y = 0
            result[extruder_id] = []

            for polygon in machine_disallowed_polygons:
                result[extruder_id].append(polygon.translate(offset_x, offset_y)) #Compensate for the nozzle offset of this extruder.

            #Add the border around the edge of the build volume.
            left_unreachable_border = 0
            right_unreachable_border = 0
            top_unreachable_border = 0
            bottom_unreachable_border = 0
            #The build volume is defined as the union of the area that all extruders can reach, so we need to know the relative offset to all extruders.
            for other_extruder in ExtruderManager.getInstance().getActiveExtruderStacks():
                other_offset_x = other_extruder.getProperty("machine_nozzle_offset_x", "value")
                other_offset_y = other_extruder.getProperty("machine_nozzle_offset_y", "value")
                left_unreachable_border = min(left_unreachable_border, other_offset_x - offset_x)
                right_unreachable_border = max(right_unreachable_border, other_offset_x - offset_x)
                top_unreachable_border = min(top_unreachable_border, other_offset_y - offset_y)
                bottom_unreachable_border = max(bottom_unreachable_border, other_offset_y - offset_y)
            half_machine_width = self._global_container_stack.getProperty("machine_width", "value") / 2
            half_machine_depth = self._global_container_stack.getProperty("machine_depth", "value") / 2

            if self._shape != "elliptic":
                if border_size - left_unreachable_border > 0:
                    result[extruder_id].append(Polygon(numpy.array([
                        [-half_machine_width, -half_machine_depth],
                        [-half_machine_width, half_machine_depth],
                        [-half_machine_width + border_size - left_unreachable_border, half_machine_depth - border_size - bottom_unreachable_border],
                        [-half_machine_width + border_size - left_unreachable_border, -half_machine_depth + border_size - top_unreachable_border]
                    ], numpy.float32)))
                if border_size + right_unreachable_border > 0:
                    result[extruder_id].append(Polygon(numpy.array([
                        [half_machine_width, half_machine_depth],
                        [half_machine_width, -half_machine_depth],
                        [half_machine_width - border_size - right_unreachable_border, -half_machine_depth + border_size - top_unreachable_border],
                        [half_machine_width - border_size - right_unreachable_border, half_machine_depth - border_size - bottom_unreachable_border]
                    ], numpy.float32)))
                if border_size + bottom_unreachable_border > 0:
                    result[extruder_id].append(Polygon(numpy.array([
                        [-half_machine_width, half_machine_depth],
                        [half_machine_width, half_machine_depth],
                        [half_machine_width - border_size - right_unreachable_border, half_machine_depth - border_size - bottom_unreachable_border],
                        [-half_machine_width + border_size - left_unreachable_border, half_machine_depth - border_size - bottom_unreachable_border]
                    ], numpy.float32)))
                if border_size - top_unreachable_border > 0:
                    result[extruder_id].append(Polygon(numpy.array([
                        [half_machine_width, -half_machine_depth],
                        [-half_machine_width, -half_machine_depth],
                        [-half_machine_width + border_size - left_unreachable_border, -half_machine_depth + border_size - top_unreachable_border],
                        [half_machine_width - border_size - right_unreachable_border, -half_machine_depth + border_size - top_unreachable_border]
                    ], numpy.float32)))
            else:
                sections = 32
                arc_vertex = [0, half_machine_depth - border_size]
                for i in range(0, sections):
                    quadrant = math.floor(4 * i / sections)
                    vertices = []
                    if quadrant == 0:
                        vertices.append([-half_machine_width, half_machine_depth])
                    elif quadrant == 1:
                        vertices.append([-half_machine_width, -half_machine_depth])
                    elif quadrant == 2:
                        vertices.append([half_machine_width, -half_machine_depth])
                    elif quadrant == 3:
                        vertices.append([half_machine_width, half_machine_depth])
                    vertices.append(arc_vertex)

                    angle = 2 * math.pi * (i + 1) / sections
                    arc_vertex = [-(half_machine_width - border_size) * math.sin(angle), (half_machine_depth - border_size) * math.cos(angle)]
                    vertices.append(arc_vertex)

                    result[extruder_id].append(Polygon(numpy.array(vertices, numpy.float32)))

                if border_size > 0:
                    result[extruder_id].append(Polygon(numpy.array([
                        [-half_machine_width, -half_machine_depth],
                        [-half_machine_width, half_machine_depth],
                        [-half_machine_width + border_size, 0]
                    ], numpy.float32)))
                    result[extruder_id].append(Polygon(numpy.array([
                        [-half_machine_width, half_machine_depth],
                        [ half_machine_width, half_machine_depth],
                        [ 0, half_machine_depth - border_size]
                    ], numpy.float32)))
                    result[extruder_id].append(Polygon(numpy.array([
                        [ half_machine_width, half_machine_depth],
                        [ half_machine_width, -half_machine_depth],
                        [ half_machine_width - border_size, 0]
                    ], numpy.float32)))
                    result[extruder_id].append(Polygon(numpy.array([
                        [ half_machine_width,-half_machine_depth],
                        [-half_machine_width,-half_machine_depth],
                        [ 0, -half_machine_depth + border_size]
                    ], numpy.float32)))

        return result

    ##  Private convenience function to get a setting from the adhesion
    #   extruder.
    #
    #   \param setting_key The key of the setting to get.
    #   \param property The property to get from the setting.
    #   \return The property of the specified setting in the adhesion extruder.
    def _getSettingFromAdhesionExtruder(self, setting_key, property = "value"):
        return self._getSettingFromExtruder(setting_key, "adhesion_extruder_nr", property)

    ##  Private convenience function to get a setting from every extruder.
    #
    #   For single extrusion machines, this gets the setting from the global
    #   stack.
    #
    #   \return A sequence of setting values, one for each extruder.
    def _getSettingFromAllExtruders(self, setting_key, property = "value"):
        return ExtruderManager.getInstance().getAllExtruderSettings(setting_key, property)

    ##  Private convenience function to get a setting from the support infill
    #   extruder.
    #
    #   \param setting_key The key of the setting to get.
    #   \param property The property to get from the setting.
    #   \return The property of the specified setting in the support infill
    #   extruder.
    def _getSettingFromSupportInfillExtruder(self, setting_key, property = "value"):
        return self._getSettingFromExtruder(setting_key, "support_infill_extruder_nr", property)

    ##  Helper function to get a setting from an extruder specified in another
    #   setting.
    #
    #   \param setting_key The key of the setting to get.
    #   \param extruder_setting_key The key of the setting that specifies from
    #   which extruder to get the setting, if there are multiple extruders.
    #   \param property The property to get from the setting.
    #   \return The property of the specified setting in the specified extruder.
    def _getSettingFromExtruder(self, setting_key, extruder_setting_key, property = "value"):
        multi_extrusion = self._global_container_stack.getProperty("machine_extruder_count", "value") > 1

        if not multi_extrusion:
            return self._global_container_stack.getProperty(setting_key, property)

        extruder_index = self._global_container_stack.getProperty(extruder_setting_key, "value")

        if extruder_index == "-1":  # If extruder index is -1 use global instead
            return self._global_container_stack.getProperty(setting_key, property)

        extruder_stack_id = ExtruderManager.getInstance().extruderIds[str(extruder_index)]
        stack = UM.Settings.ContainerRegistry.getInstance().findContainerStacks(id = extruder_stack_id)[0]
        return stack.getProperty(setting_key, property)

    ##  Convenience function to calculate the disallowed radius around the edge.
    #
    #   This disallowed radius is to allow for space around the models that is
    #   not part of the collision radius, such as bed adhesion (skirt/brim/raft)
    #   and travel avoid distance.
    def _getEdgeDisallowedSize(self):
        if not self._global_container_stack:
            return 0
        container_stack = self._global_container_stack

        # If we are printing one at a time, we need to add the bed adhesion size to the disallowed areas of the objects
        if container_stack.getProperty("print_sequence", "value") == "one_at_a_time":
            return 0.1  # Return a very small value, so we do draw disallowed area's near the edges.

        adhesion_type = container_stack.getProperty("adhesion_type", "value")
        if adhesion_type == "skirt":
            skirt_distance = self._getSettingFromAdhesionExtruder("skirt_gap")
            skirt_line_count = self._getSettingFromAdhesionExtruder("skirt_line_count")
            bed_adhesion_size = skirt_distance + (skirt_line_count * self._getSettingFromAdhesionExtruder("skirt_brim_line_width"))
            if self._global_container_stack.getProperty("machine_extruder_count", "value") > 1:
                adhesion_extruder_nr = int(self._global_container_stack.getProperty("adhesion_extruder_nr", "value"))
                extruder_values = ExtruderManager.getInstance().getAllExtruderValues("skirt_brim_line_width")
                del extruder_values[adhesion_extruder_nr]  # Remove the value of the adhesion extruder nr.
                for value in extruder_values:
                    bed_adhesion_size += value
        elif adhesion_type == "brim":
            bed_adhesion_size = self._getSettingFromAdhesionExtruder("brim_line_count") * self._getSettingFromAdhesionExtruder("skirt_brim_line_width")
            if self._global_container_stack.getProperty("machine_extruder_count", "value") > 1:
                adhesion_extruder_nr = int(self._global_container_stack.getProperty("adhesion_extruder_nr", "value"))
                extruder_values = ExtruderManager.getInstance().getAllExtruderValues("skirt_brim_line_width")
                del extruder_values[adhesion_extruder_nr]  # Remove the value of the adhesion extruder nr.
                for value in extruder_values:
                    bed_adhesion_size += value
        elif adhesion_type == "raft":
            bed_adhesion_size = self._getSettingFromAdhesionExtruder("raft_margin")
        elif adhesion_type == "none":
            bed_adhesion_size = 0
        else:
            raise Exception("Unknown bed adhesion type. Did you forget to update the build volume calculations for your new bed adhesion type?")

        support_expansion = 0
        if self._getSettingFromSupportInfillExtruder("support_offset") and self._global_container_stack.getProperty("support_enable", "value"):
            support_expansion += self._getSettingFromSupportInfillExtruder("support_offset")

        farthest_shield_distance = 0
        if container_stack.getProperty("draft_shield_enabled", "value"):
            farthest_shield_distance = max(farthest_shield_distance, container_stack.getProperty("draft_shield_dist", "value"))
        if container_stack.getProperty("ooze_shield_enabled", "value"):
            farthest_shield_distance = max(farthest_shield_distance, container_stack.getProperty("ooze_shield_dist", "value"))

        move_from_wall_radius = 0  # Moves that start from outer wall.
        move_from_wall_radius = max(move_from_wall_radius, max(self._getSettingFromAllExtruders("infill_wipe_dist")))
        avoid_enabled_per_extruder = self._getSettingFromAllExtruders(("travel_avoid_other_parts"))
        avoid_distance_per_extruder = self._getSettingFromAllExtruders("travel_avoid_distance")
        for index, avoid_other_parts_enabled in enumerate(avoid_enabled_per_extruder): #For each extruder (or just global).
            if avoid_other_parts_enabled:
                move_from_wall_radius = max(move_from_wall_radius, avoid_distance_per_extruder[index]) #Index of the same extruder.

        #Now combine our different pieces of data to get the final border size.
        #Support expansion is added to the bed adhesion, since the bed adhesion goes around support.
        #Support expansion is added to farthest shield distance, since the shields go around support.
        border_size = max(move_from_wall_radius, support_expansion + farthest_shield_distance, support_expansion + bed_adhesion_size)
        return border_size

    def _clamp(self, value, min_value, max_value):
        return max(min(value, max_value), min_value)

    _skirt_settings = ["adhesion_type", "skirt_gap", "skirt_line_count", "skirt_brim_line_width", "brim_width", "brim_line_count", "raft_margin", "draft_shield_enabled", "draft_shield_dist"]
    _raft_settings = ["adhesion_type", "raft_base_thickness", "raft_interface_thickness", "raft_surface_layers", "raft_surface_thickness", "raft_airgap"]
    _prime_settings = ["extruder_prime_pos_x", "extruder_prime_pos_y", "extruder_prime_pos_z"]
    _tower_settings = ["prime_tower_enable", "prime_tower_size", "prime_tower_position_x", "prime_tower_position_y"]
    _ooze_shield_settings = ["ooze_shield_enabled", "ooze_shield_dist"]
    _distance_settings = ["infill_wipe_dist", "travel_avoid_distance", "support_offset", "support_enable", "travel_avoid_other_parts"]
    _extruder_settings = ["support_enable", "support_interface_enable", "support_infill_extruder_nr", "support_extruder_nr_layer_0", "support_interface_extruder_nr", "brim_line_count", "adhesion_extruder_nr", "adhesion_type"] #Settings that can affect which extruders are used.