codingcircle » Class 2 - Find the Torsional Angle

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 = AB x BC and Y = BC x CD.

Here, X.Y means the dot product of X and Y, and AB x BC means the cross product of vectors AB and BC. 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 Implementation


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 (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))

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Class 2 – Find the Torsional Angle

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