Task and Solution in Python - Find the Torsional Angle (HackerRank)

 

You are given four points  and  in a 3-dimensional Cartesian coordinate system. You are required to print the angle between the plane made by the points  and  in degrees(not radians). Let the angle be .

 where  x  and  x .

Here,  means the dot product of  and , and  x  means the cross product of vectors  and . Also, .

Input Format

One line of input containing the space separated floating number values of the  and  coordinates of a point.

Output Format

Output the angle correct up to two decimal places.

Sample Input

0 4 5
1 7 6
0 5 9
1 7 2

Sample Output

8.19

Solution

import math

class Points(object):

    def __init__(self, x, y, z):

        self.x = x

        self.y = y

        self.z = z

    def __sub__(self, no):

        return Points(self.x - no.x, self.y - no.y, self.z - no.z)

    def dot(self, no):

        return math.fsum((self.x * no.x, self.y * no.y, self.z * no.z))

    def cross(self, no):

        return Points(

            self.y * no.z - self.z * no.y,

            self.z * no.x - self.x * no.z,

            self.x * no.y - self.y * no.x,

        )

    def absolute(self):

        return pow((self.x**2 + self.y**2 + self.z**2), 0.5)

if __name__ == '__main__':

    points = list()

    for i in range(4):

        a = list(map(float, input().split()))

        points.append(a)

    a, b, c, d = Points(*points[0]), Points(*points[1]), Points(*points[2]), Points(*points[3])

    x = (b - a).cross(c - b)

    y = (c - b).cross(d - c)

    angle = math.acos(x.dot(y) / (x.absolute() * y.absolute()))

    print("%.2f" % math.degrees(angle))

Source : HackerRank