数学解决方法:

# -*- 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()