Class 2 - Find the Torsional Angle in Python - HackerRank Solution

CodeWorld19

8 Dec, 2020

Class 2 - Find the Torsional Angle in Python - HackerRank Solution

Problem :

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

Cos(PHI) = (X*Y) / |X| |Y| where X = ABxBC and Y = BC x CD.

Here, X.Y means the dot product of X and Y, and ABxBC means the cross product of vectors and . Also, AB = B - A.

Input Format :

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

Output Format :

Output the angle correct up to two decimal places.

Sample Input :

Sample Output :

8.19

Solution :

# Class 2 - Find the Torsional Angle in Python - HackerRank Solution
# Python 3
import math

class Points(object):
# Class 2 - Find the Torsional Angle in Python - HackerRank Solution START
    def __init__(self, x, y, z):
        self.x = x
        self.y = y
        self.z = z

    def __sub__(self, no):
        x = self.x - no.x
        y = self.y - no.y
        z = self.z - no.z
        return Points(x, y, z)

    def dot(self, no):
        x = self.x * no.x
        y = self.y * no.y
        z = self.z * no.z
        return x + y + z

    def cross(self, no):
        x = self.y * no.z - self.z * no.y
        y = self.z * no.x - self.x * no.z
        z = self.x * no.y - self.y * no.x
        return Points(x, y, z)

# Class 2 - Find the Torsional Angle in Python - HackerRank Solution END
    
    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))

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