定義代表三維笛卡爾坐標系上某個點的Point 類（包括x 、y 、z 三個屬性），為該類定義一個方法，可接收second 、third 、forth 三個參數，用于計算當前點、second 、third 組成的面與second 、third 、forth組成的面之間的夾角。
A,B,C,D分別對應于提示point1,point2,point3,point4,線段BC是面ABC與面DBC的公共邊，計算倆面空間夾角： cos （夾角） = （X·Y）/|X||Y|，其中X=AB×BC，Y=BC×CD，X·Y代表X與Y的點積，AB×BC代表AB與BC的叉乘

import mathclass Point():def __init__(self,x,y,z):self.x = xself.y = yself.z = zdef distance(self):xx = (self.x) ** 2yy = (self.y) ** 2zz = (self.z) ** 2return (xx + yy + zz) ** (0.5)def vector(self,other):xx = (self.x - other.x)yy = (self.y - other.y)zz = (self.z - other.z)return Point(xx,yy,zz)def cross(self,other):return Point(self.x*other.z-self.z*other.y , self.z*other.x-self.x*other.z , self.x*other.y-self.y*other.x)def dot(self,other):return (self.x*other.x + self.y*other.y + self.z*other.z)# def dot(self, other):# return Point((self.x * other.x),# (self.y * other.y),# (self.z * other.z))def angle(self,second,third,forth):vertor11 = point1.vector(point2)vertor12 = point1.vector(point3)vertor21 = point4.vector(point2)vertor22 = point4.vector(point3)vertor1 = vertor11.cross(vertor12)vertor2 = vertor21.cross(vertor22)return math.acos( (vertor1.dot(vertor2)) / ((vertor1.distance())*(vertor2.distance())) )point1 = Point(0,1,0) point2 = Point(1,0,0) point3 = Point(0,0,0) point4 = Point(0,0,1)angels = point1.angle(point2,point3,point4) print(math.degrees(angels))

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