数学解决方法:
多边形外选取一点,连接各点构成三角形,计算求和...... 详细链接 http://blog.csdn.net/hemmingway/article/details/7814494
已知三角形三边长,求三角形面积 ------> 海伦公式 链接: http://www.zybang.com/question/29d209e9732d1f1f6a6de35b94edd3ba.html
由上实现下面 python 代码 源代码出处 链接: http://blog.csdn.net/zfq43/article/details/8595288
- # -*- coding: cp936 -*-
- import math
- class Point():
- def __init__(self,x,y):
- self.x = x
- self.y = y
- def GetAreaOfPolyGon(points):
- area = 0
- if(len(points)<3):
- raise Exception("error")
- p1 = points[0]
- for i in range(1,len(points)-1):
- p2 = points[1]
- p3 = points[2]
- #计算向量
- vecp1p2 = Point(p2.x-p1.x,p2.y-p1.y)
- vecp2p3 = Point(p3.x-p2.x,p3.y-p2.y)
- #判断顺时针还是逆时针,顺时针面积为正,逆时针面积为负
- vecMult = vecp1p2.x*vecp2p3.y - vecp1p2.y*vecp2p3.x #判断正负方向比较有意思
- sign = 0
- if(vecMult>0):
- sign = 1
- elif(vecMult<0):
- sign = -1
- triArea = GetAreaOfTriangle(p1,p2,p3)*sign
- area += triArea
- return abs(area)
- def GetAreaOfTriangle(p1,p2,p3):
- '''计算三角形面积 海伦公式'''
- area = 0
- p1p2 = GetLineLength(p1,p2)
- p2p3 = GetLineLength(p2,p3)
- p3p1 = GetLineLength(p3,p1)
- s = (p1p2 + p2p3 + p3p1)/2
- area = s*(s-p1p2)*(s-p2p3)*(s-p3p1) #海伦公式
- area = math.sqrt(area)
- return area
- def GetLineLength(p1,p2):
- '''计算边长'''
- length = math.pow((p1.x-p2.x),2) + math.pow((p1.y-p2.y),2) #pow 次方
- length = math.sqrt(length)
- return length
- def main():
- p1 = Point(1,1)
- p2 = Point(2,1)
- p3 = Point(2,2)
- p4 = Point(1,2)
- points = [p1,p2,p3,p4]
- area = GetAreaOfPolyGon(points)
- print(math.ceil(area))
- assert math.ceil(area)==1
- if __name__ == '__main__':
- main()
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