def add_polygons(self, polygons, color = '#A8F22A', alpha = 1):
        qcolor = QColor()
        qcolor.setNamedColor(color)
        qcolor.setAlphaF(alpha)
        for points in polygons:
            qpoly = QPolygonF( [QPointF(p[0], p[1]) for p in points] )
            scene_poly = self.scene.addPolygon(qpoly)
            scene_poly.setBrush(qcolor)
            scene_poly.setPen(self.pen)
            self.scene_polys.append(scene_poly)
            # Update custom bounding box
            sr = scene_poly.sceneBoundingRect()
            if len(self.scene_polys) == 1:
                self.scene_xmin = sr.left()
                self.scene_xmax = sr.right()
                self.scene_ymin = sr.top()
                self.scene_ymax = sr.bottom()
            else:
                self.scene_xmin = min(self.scene_xmin, sr.left())
                self.scene_xmax = max(self.scene_xmax, sr.right())
                self.scene_ymin = min(self.scene_ymin, sr.top())
                self.scene_ymax = max(self.scene_ymax, sr.bottom()) 

def __init__(self, geometry=QtGui.QPolygonF(),
         brush=QtGui.QBrush(QtCore.Qt.NoBrush),
         pen=QtGui.QPen(QtCore.Qt.NoPen)):
        """
        Initialize the polygon.
        :type geometry: T <= QRectF|QtGui.QPolygonF|QPainterPath
        :type brush: QBrush
        :type pen: QPen
        """
        self._geometry = geometry
        self._brush = brush
        self._pen = pen

    #############################################
    #   INTERFACE
    ################################# 

def draw_polygons(self):
        sf = shapefile.Reader(self.shapefile)       
        polygons = sf.shapes() 
        for polygon in polygons:
            # convert shapefile geometries into shapely geometries
            # to extract the polygons of a multipolygon
            polygon = shapely.geometry.shape(polygon)
            # if it is a polygon, we use a list to make it iterable
            if polygon.geom_type == 'Polygon':
                polygon = [polygon]
            for land in polygon:
                qt_polygon = QtGui.QPolygonF() 
                longitudes, latitudes = land.exterior.coords.xy
                for lon, lat in zip(longitudes, latitudes):
                    px, py = self.to_canvas_coordinates(lon, lat)
                    if px > 1e+10:
                        continue
                    qt_polygon.append(QtCore.QPointF(px, py))
                polygon_item = QtWidgets.QGraphicsPolygonItem(qt_polygon)
                polygon_item.setBrush(self.land_brush)
                polygon_item.setPen(self.land_pen)
                polygon_item.setZValue(1)
                yield polygon_item 

def __init__(self, y, x):
        hex_center_x, hex_center_y = indextoHex(y, x)
        center = QtCore.QPointF(hex_center_x, hex_center_y)
        points = [
            HEX_SCALE * HEX_SIDE_HALF * QtCore.QPointF(-1, 0) + center,
            HEX_SCALE * HEX_SIDE_HALF * QtCore.QPointF(-0.5, sqrt(3) / 2)
            + center,
            HEX_SCALE * HEX_SIDE_HALF * QtCore.QPointF(0.5, sqrt(3) / 2)
            + center,
            HEX_SCALE * HEX_SIDE_HALF * QtCore.QPointF(1, 0) + center,
            HEX_SCALE * HEX_SIDE_HALF * QtCore.QPointF(0.5, -sqrt(3) / 2)
            + center,
            HEX_SCALE * HEX_SIDE_HALF * QtCore.QPointF(-0.5, -sqrt(3) / 2)
            + center,
        ]

        hexagonPointsF = QtGui.QPolygonF(points)
        super().__init__(hexagonPointsF)
        self.setPen(HEX_PEN)
        self.setBrush(defaultcolor)  # initialize all as grey 

def draw_food_contour(self, image):
        if self.food_coordinates is None or not self.ui.checkBox_showFood.isChecked():
            return

        painter = QPainter()
        painter.begin(image)

        penwidth = max(1, max(image.height(), image.width()) // 800)
        col = Qt.darkMagenta
        p = QPolygonF()
        for x,y in self.food_coordinates:
            p.append(QPointF(x,y))
            
        pen = QPen()
        pen.setWidth(penwidth)
        pen.setColor(col)
        painter.setPen(pen)

        painter.drawPolyline(p)
        painter.end() 

def paintEvent(self, event):
        # 绘制默认的样式
        super(SplitterHandle, self).paintEvent(event)
        # 绘制顶部扩展按钮
        painter = QPainter(self)
        painter.setRenderHint(QPainter.Antialiasing, True)
        painter.setPen(Qt.red)
        # 画矩形
        painter.drawRect(0, 0, self.width(), 24)
        # 画三角形
        painter.setBrush(Qt.red)
        painter.drawPolygon(QPolygonF([
            QPointF(0, (24 - 8) / 2),
            QPointF(self.width() - 2, 24 / 2),
            QPointF(0, (24 + 8) / 2)
        ])) 

def add_port(self, port, is_subport = False):
        if (port.width is None) or (port.width == 0):
            x,y = port.midpoint
            cs = 1 # cross size
            pn = QPointF(x, y+cs)
            ps = QPointF(x, y-cs)
            pe = QPointF(x+cs, y)
            pw = QPointF(x-cs, y)
            qline1 = self.scene.addLine(QLineF(pn, ps))
            qline2 = self.scene.addLine(QLineF(pw, pe))
            port_shapes = [qline1,qline2]
        else:
            point1, point2 = port.endpoints
            point1 = QPointF(point1[0], point1[1])
            point2 = QPointF(point2[0], point2[1])
            qline = self.scene.addLine(QLineF(point1, point2))
            arrow_points = np.array([[0,0],[10,0],[6,4],[6,2],[0,2]])/(40)*port.width
            arrow_qpoly = QPolygonF( [QPointF(p[0], p[1]) for p in arrow_points] )
            port_scene_poly = self.scene.addPolygon(arrow_qpoly)
            port_scene_poly.setRotation(port.orientation)
            port_scene_poly.moveBy(port.midpoint[0], port.midpoint[1])
            port_shapes = [qline,port_scene_poly]
        qtext = self.scene.addText(str(port.name), self.portfont)
        port_items = port_shapes + [qtext]
        rad = port.orientation*np.pi/180
        x,y = port.endpoints[0]*1/4 +  port.endpoints[1]*3/4 + np.array([np.cos(rad), np.sin(rad)])*port.width/8
#        x,y = port.midpoint[0], port.midpoint[1]
#        x,y  = x - qtext.boundingRect().width()/2, y - qtext.boundingRect().height()/2
        qtext.setPos(QPointF(x,y))
        qtext.setFlag(QGraphicsItem.ItemIgnoresTransformations)

        if not is_subport:
            [shape.setPen(self.portpen) for shape in port_shapes]
            qtext.setDefaultTextColor(self.portfontcolor)
            self.portitems += port_items
        else:
            [shape.setPen(self.subportpen) for shape in port_shapes]
            qtext.setDefaultTextColor(self.subportfontcolor)
            self.subportitems += port_items
#        self.portlabels.append(qtext) 

def turn():
    global epi_x, epi_y, p1, p2, p3, p4, rect
    write_log()
    teta = math.radians(window.spin_deg.value())
    t_x = window.spin_turn_x.value()
    t_y = window.spin_turn_y.value()
    scene.clear()

    rect_t = QPolygonF(4)
    p1 = [t_x + (p1[0] - t_x) * math.cos(teta) + (p1[1] - t_y) * math.sin(teta),
          t_y - (p1[0] - t_x) * math.sin(teta) + (p1[1] - t_y) * math.cos(teta)]
    p2 = [t_x + (p2[0] - t_x) * math.cos(teta) + (p2[1] - t_y) * math.sin(teta),
          t_y - (p2[0] - t_x) * math.sin(teta) + (p2[1] - t_y) * math.cos(teta)]
    p3 = [t_x + (p3[0] - t_x) * math.cos(teta) + (p3[1] - t_y) * math.sin(teta),
          t_y - (p3[0] - t_x) * math.sin(teta) + (p3[1] - t_y) * math.cos(teta)]
    p4 = [t_x + (p4[0] - t_x) * math.cos(teta) + (p4[1] - t_y) * math.sin(teta),
          t_y - (p4[0] - t_x) * math.sin(teta) + (p4[1] - t_y) * math.cos(teta)]
    rect[0] = QPointF(p1[0], p1[1])
    rect[1] = QPointF(p2[0], p2[1])
    rect[2] = QPointF(p3[0], p3[1])
    rect[3] = QPointF(p4[0], p4[1])
    scene.addPolygon(rect, pen=p, brush=b)
    l = len(epi_x)
    for i in range(l):
        x1 = t_x + (epi_x[i] - t_x) * math.cos(teta) + (epi_y[i] - t_y) * math.sin(teta)
        y1 = t_y - (epi_x[i] - t_x) * math.sin(teta) + (epi_y[i] - t_y) * math.cos(teta)
        epi_x[i] = x1
        epi_y[i] = y1
        scene.addLine(epi_x[i], epi_y[i], epi_x[i] + 0.01, epi_y[i] + 0.01, pen=p) 

def sutherland_hodgman(clip, pol, norm):
    # дублируем начальную вершину отсекателя в конец
    clip.append(clip[0])

    s = None
    f = None
    # цикл по вершинам отсекателя
    for i in range(len(clip) - 1):
        new = []  # новый массив вершин
        for j in range(len(pol)):    # цикл по вершинам многоугольника
            if j == 0:
                f = pol[j]
            else:
                t = is_intersection([s, pol[j]], [clip[i], clip[i + 1]], norm)
                if t:
                    new.append(t)

            s = pol[j]
            if is_visiable(s,  clip[i], clip[i + 1], norm):
                    new.append(s)

        if len(new) != 0:
            t = is_intersection([s, f], [clip[i], clip[i + 1]], norm)
            if t:
                new.append(t)

        pol = copy.deepcopy(new)

    if len(pol) == 0:
        return False
    else:
        return QPolygonF(pol) 

def createArea(p1, p2, degrees, size):
    """
    Creates an area between the given QPointF and according to the given angle and size.
    :type p1: QPointF
    :type p2: QPointF
    :type degrees: float
    :type size: int
    :rtype: QPolygonF
    """
    rad = math.radians(degrees)
    x = size / 2 * math.sin(rad)
    y = size / 2 * math.cos(rad)
    a = QtCore.QPointF(+x, +y)
    b = QtCore.QPointF(-x, -y)
    return QtGui.QPolygonF([p1 + a, p1 + b, p2 + b, p2 + a]) 

def __init__(self, **kwargs):
        """
        Initialize the edge.
        """
        super().__init__(**kwargs)
        self.tail = Polygon(QtGui.QPolygonF())

    #############################################
    #   INTERFACE
    ################################# 

def createHead(p1, angle, size):
        """
        Create the head polygon.
        :type p1: QPointF
        :type angle: float
        :type size: int
        :rtype: QPolygonF
        """
        rad = radians(angle)
        p2 = p1 - QtCore.QPointF(sin(rad + M_PI / 3.0) * size, cos(rad + M_PI / 3.0) * size)
        p3 = p1 - QtCore.QPointF(sin(rad + M_PI - M_PI / 3.0) * size, cos(rad + M_PI - M_PI / 3.0) * size)
        return QtGui.QPolygonF([p1, p2, p3]) 

def createTail(p1, angle, size):
        """
        Create the tail polygon.
        :type p1: QPointF
        :type angle: float
        :type size: int
        :rtype: QPolygonF
        """
        rad = radians(angle)
        p2 = p1 + QtCore.QPointF(sin(rad + M_PI / 3.0) * size, cos(rad + M_PI / 3.0) * size)
        p3 = p1 + QtCore.QPointF(sin(rad + M_PI - M_PI / 3.0) * size, cos(rad + M_PI - M_PI / 3.0) * size)
        return QtGui.QPolygonF([p1, p2, p3]) 

def createHead(p1, angle, size):
        """
        Create the head polygon.
        :type p1: QPointF
        :type angle: float
        :type size: int
        :rtype: QPolygonF
        """
        rad = radians(angle)
        p2 = p1 - QtCore.QPointF(sin(rad + M_PI / 4.0) * size, cos(rad + M_PI / 4.0) * size)
        p3 = p2 - QtCore.QPointF(sin(rad + 3.0 / 4.0 * M_PI) * size, cos(rad + 3.0 / 4.0 * M_PI) * size)
        p4 = p3 - QtCore.QPointF(sin(rad - 3.0 / 4.0 * M_PI) * size, cos(rad - 3.0 / 4.0 * M_PI) * size)
        return QtGui.QPolygonF([p1, p2, p3, p4]) 

def __init__(self, source, target=None, breakpoints=None, **kwargs):
        """
        Initialize the edge.
        :type source: AbstractNode
        :type target: AbstractNode
        :type breakpoints: list
        """
        super().__init__(**kwargs)

        self.source = source
        self.target = target

        self.anchors = {} # {AbstractNode: Polygon}
        self.breakpoints = breakpoints or [] # [QtCore.QPointF]
        self.handles = [] # [Polygon]
        self.head = Polygon(QtGui.QPolygonF())
        self.path = Polygon(QtGui.QPainterPath())
        self.selection = Polygon(QtGui.QPainterPath())

        self.mp_AnchorNode = None
        self.mp_AnchorNodePos = None
        self.mp_BreakPoint = None
        self.mp_BreakPointPos = None
        self.mp_Pos = None

        self.setAcceptHoverEvents(True)
        self.setCacheMode(AbstractItem.DeviceCoordinateCache)
        self.setFlag(AbstractItem.ItemIsSelectable, True)

    #############################################
    #   INTERFACE
    ################################# 

def createHead(p1, angle, size):
        """
        Create the head polygon.
        :type p1: QPointF
        :type angle: float
        :type size: int
        :rtype: QPolygonF
        """
        rad = radians(angle)
        p2 = p1 - QtCore.QPointF(sin(rad + M_PI / 3.0) * size, cos(rad + M_PI / 3.0) * size)
        p3 = p1 - QtCore.QPointF(sin(rad + M_PI - M_PI / 3.0) * size, cos(rad + M_PI - M_PI / 3.0) * size)
        return QtGui.QPolygonF([p1, p2, p3]) 

def __init__(self, width=60, height=60, brush=None, **kwargs):
        """
        Initialize the node.
        :type width: int
        :type height: int
        :type brush: QBrush
        """
        super().__init__(**kwargs)

        w = max(width, 60)
        h = max(height, 60)
        brush = brush or IndividualNode.DefaultBrush
        pen = IndividualNode.DefaultPen

        createPolygon = lambda x, y: QtGui.QPolygonF([
            QtCore.QPointF(-(x / 2), -((y / (1 + math.sqrt(2))) / 2)),
            QtCore.QPointF(-(x / 2), +((y / (1 + math.sqrt(2))) / 2)),
            QtCore.QPointF(-((x / (1 + math.sqrt(2))) / 2), +(y / 2)),
            QtCore.QPointF(+((x / (1 + math.sqrt(2))) / 2), +(y / 2)),
            QtCore.QPointF(+(x / 2), +((y / (1 + math.sqrt(2))) / 2)),
            QtCore.QPointF(+(x / 2), -((y / (1 + math.sqrt(2))) / 2)),
            QtCore.QPointF(+((x / (1 + math.sqrt(2))) / 2), -(y / 2)),
            QtCore.QPointF(-((x / (1 + math.sqrt(2))) / 2), -(y / 2)),
            QtCore.QPointF(-(x / 2), -((y / (1 + math.sqrt(2))) / 2)),
        ])

        self.background = Polygon(createPolygon(w + 8, h + 8))
        self.selection = Polygon(createPolygon(w + 8, h + 8))
        self.polygon = Polygon(createPolygon(w, h), brush, pen)
        self.label = NodeLabel(template='individual', pos=self.center, parent=self)
        self.label.setAlignment(QtCore.Qt.AlignCenter)
        self.updateNode()
        self.updateTextPos()

    #############################################
    #   PROPERTIES
    ################################# 

def __init__(self, width=70, height=50, brush=None, **kwargs):
        """
        Initialize the node.
        :type width: int
        :type height: int
        :type brush: QBrush
        """
        super().__init__(**kwargs)
        
        w = max(width, 70)
        h = max(height, 50)
        brush = brush or RoleNode.DefaultBrush
        pen = RoleNode.DefaultPen

        createPolygon = lambda x, y: QtGui.QPolygonF([
            QtCore.QPointF(-x / 2, 0),
            QtCore.QPointF(0, +y / 2),
            QtCore.QPointF(+x / 2, 0),
            QtCore.QPointF(0, -y / 2),
            QtCore.QPointF(-x / 2, 0)
        ])

        self.fpolygon = Polygon(QtGui.QPainterPath())
        self.ipolygon = Polygon(QtGui.QPainterPath())
        self.background = Polygon(createPolygon(w + 8, h + 8))
        self.selection = Polygon(createPolygon(w + 8, h + 8))
        self.polygon = Polygon(createPolygon(w, h), brush, pen)
        self.label = NodeLabel(template='role', pos=self.center, parent=self)
        self.label.setAlignment(QtCore.Qt.AlignCenter)
        self.updateNode()
        self.updateTextPos()

    #############################################
    #   INTERFACE
    ################################# 

def createPolygon(w, h):
        """
        Returns the initialized polygon according to the given width/height.
        :type w: int
        :type h: int
        :rtype: QtGui.QPolygonF
        """
        return QtGui.QPolygonF([
            QtCore.QPointF(-w / 2 + 10, -h / 2),
            QtCore.QPointF(+w / 2, -h / 2),
            QtCore.QPointF(+w / 2 - 10, +h / 2),
            QtCore.QPointF(-w / 2, +h / 2),
            QtCore.QPointF(-w / 2 + 10, -h / 2),
        ]) 

def createPolygonB(w, h):
        """
        Returns the initialized bottom-half polygon according to the given width/height.
        :type w: int
        :type h: int
        :rtype: QtGui.QPolygonF
        """
        return QtGui.QPolygonF([
            QtCore.QPointF(-w / 2 + 10 / 2, 0),
            QtCore.QPointF(+w / 2 - 10 / 2, 0),
            QtCore.QPointF(+w / 2 - 10, +h / 2),
            QtCore.QPointF(-w / 2, +h / 2),
            QtCore.QPointF(-w / 2 + 10 / 2, 0),
        ]) 

def geometryA(self):
        """
        Returns the geometry of the shape A of this node.
        :rtype: QtGui.QPolygonF
        """
        return self.polygonA.geometry() 

def geometryB(self):
        """
        Returns the geometry of the shape B of this node.
        :rtype: QtGui.QPolygonF
        """
        return self.polygonB.geometry() 

def __init__(self, width=50, height=30, brush=None, **kwargs):
        """
        Initialize the node.
        :type width: int
        :type height: int
        :type brush: QBrush
        """
        super().__init__(**kwargs)

        createPolygon = lambda x, y: QtGui.QPolygonF([
            QtCore.QPointF(-x / 2, 0),
            QtCore.QPointF(-x / 2 + 6, +y / 2),
            QtCore.QPointF(+x / 2 - 6, +y / 2),
            QtCore.QPointF(+x / 2, 0),
            QtCore.QPointF(+x / 2 - 6, -y / 2),
            QtCore.QPointF(-x / 2 + 6, -y / 2),
            QtCore.QPointF(-x / 2, 0),
        ])

        self.background = Polygon(createPolygon(58, 38))
        self.selection = Polygon(createPolygon(58, 38))
        self.polygon = Polygon(createPolygon(50, 30), brush or OperatorNode.DefaultBrush, OperatorNode.DefaultPen)

    #############################################
    #   INTERFACE
    ################################# 

def geometry(self):
        """
        Returns the geometry of the shape of this node.
        :rtype: QtGui.QPolygonF
        """
        return self.polygon.geometry() 

def geometry(self):
        """
        Returns the polygon geometry.
        :rtype: T <= QRectF | QPolygonF | QPainterPath
        """
        return self._geometry 

def setGeometry(self, geometry):
        """
        Set the shape polygon.
        :type geometry: T <= QRectF | QPolygonF | QPainterPath
        """
        self._geometry = geometry 

def addPoint(self, p):
        self._points.append(p)
        item = EditablePolygonPoint(len(self._points) - 1)
        item.brush_color = self._brush_color
        item.pen_color = self._pen_color
        item.pen_width = self._pen_width
        item.signals.moved.connect(self.point_moved_slot)
        item.signals.deleted.connect(self.point_deleted_slot)
        item.signals.doubleClicked.connect(self.point_double_clicked)
        self.scene().addItem(item)
        item.setPos(p)
        self._controls.append(item)
        self.setPolygon(QtGui.QPolygonF(self.points)) 

def insertPoint(self, index, p):
        self.points.insert(index, p)
        item = EditablePolygonPoint(index)
        item.brush_color = self._brush_color
        item.pen_color = self._pen_color
        item.signals.moved.connect(self.point_moved_slot)
        item.signals.deleted.connect(self.point_deleted_slot)
        item.signals.doubleClicked.connect(self.point_double_clicked)
        self.scene().addItem(item)
        item.setPos(p)
        self.controls.insert(index, item)
        self.setPolygon(QtGui.QPolygonF(self.points)) 

def point_moved_slot(self, item: EditablePolygonPoint, pos: QPointF):
        self.points[item.index] = self.mapFromScene(pos)
        self.setPolygon(QtGui.QPolygonF(self.points)) 

def point_deleted_slot(self, index: int):
        del self.points[index]
        del self.controls[index]
        self.setPolygon(QtGui.QPolygonF(self.points))
        self.update_indexes()