如何计算QPolygon面积

Question

我正在尝试获取蓝色和绿色QPolygons的交叉点，以及它构成蓝色QPolygon的百分比(见下图)。

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我按如下方式创建了多边形：

import PyQt5
from PyQt5 import QtWidgets,QtGui,QtCore

from PyQt5.QtWidgets import *
from PyQt5.QtGui import *
from PyQt5.QtCore import *

import sys, math


class MyWidget(QtWidgets.QWidget):
    def __init__(self, parent=None):
        QtWidgets.QWidget.__init__(self, parent)
        self.pen1 = QtGui.QPen(QtGui.QColor(20,0,250))                      # set lineColor
        self.pen = QtGui.QPen(QtGui.QColor(0,0,0))                      # set lineColor
        self.pen2 = QtGui.QPen(QtGui.QColor(0,250,0))                      # set lineColor

        self.pen.setWidth(3)                                            # set lineWidth
        self.brush = QtGui.QBrush(QtGui.QColor(255,255,255,10))        # set fillColor
        
        coords = [PyQt5.QtCore.QPointF(640.0, 334.0), PyQt5.QtCore.QPointF(626.0, 462.0), PyQt5.QtCore.QPointF(782.0, 509.0), PyQt5.QtCore.QPointF(807.0, 373.0), PyQt5.QtCore.QPointF(807.0, 333.0)]
        greenpolygoncoords = [PyQt5.QtCore.QPointF(698.0, 373.0), PyQt5.QtCore.QPointF(690.0, 433.0), PyQt5.QtCore.QPointF(757.0, 376.0), PyQt5.QtCore.QPointF(713.0, 351.0), PyQt5.QtCore.QPointF(713.0, 351.0), PyQt5.QtCore.QPointF(698.0, 373.0)]
        self.bluepolygon = QPolygonF(coords)
        self.greenpolygon =QPolygonF(greenpolygoncoords)
        self.intersection = self.bluepolygon.intersected(self.greenpolygon)


        print("overlap = "+str(self.intersection.size()/self.bluepolygon.size()))


    def paintEvent(self, event):
        painter = QtGui.QPainter(self)
        painter.setPen(self.pen1)
        painter.setBrush(self.brush)
        painter.drawPolygon(self.bluepolygon) #bluepolygon = Blue
        painter.setPen(self.pen)
        painter.drawPolygon(self.intersection) #Intersection = black
        painter.setPen(self.pen2)
        painter.drawPolygon(self.greenpolygon) # greenpolygon = Green
app = QtWidgets.QApplication(sys.argv)

widget = MyWidget()
widget.show()

sys.exit(app.exec_())

然而，当我试图计算两个多边形之间的重叠时，我得到了一个错误的答案(它说重叠等于1，但是绿色多边形肯定不是蓝色多边形的100% )。

overlap = self.intersection.size()/self.bluepolygon.size()

在查看QPolygon.size()计算的大小时，很明显QPolygon.size()返回了不正确的多边形大小。

    print("size of blue polygon = "+str(self.bluepolygon.size()))
    print("size of greenpolygon = "+str(self.greenpolygon.size()))
    print("size of intersection = "+str(self.intersection.size()))

返回：

size of blue polygon = 5
size of greenpolygon = 6
size of intersection = 5

显然，由于PyQt5的某些原因，蓝色多边形比绿色多边形小。怎么会这样?

我做错了什么？

Answer 1

size()方法返回的不是多边形的面积，而是边数或顶点数。如果要计算面积，则必须使用the standard method实现它

def calculate_area(qpolygon):
    area = 0
    for i in range(qpolygon.size()):
        p1 = qpolygon[i]
        p2 = qpolygon[(i + 1) % qpolygon.size()]
        d = p1.x() * p2.y() - p2.x() * p1.y()
        area += d
    return abs(area) / 2

然后你评估你想要的东西：

print(
    "overlap = "
    + str(calculate_area(self.intersection) / calculate_area(self.bluepolygon))
)

输出：

overlap = 0.0962288941619438