Class 2 - Find the Torsional Angle python


Problem Statement :


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.


Solution :



title-img 


                            Solution in C :

import operator
import math

def cross(p1, p2):
  return [p1[1]*p2[2]-p1[2]*p2[1], p1[2]*p2[0]-p1[0]*p2[2], p1[0]*p2[1]-p1[1]*p2[0]]

def dot(p1, p2):
  return sum(map(operator.mul, p1, p2))
  
def subtract(a, b):
  return list(map(operator.sub, a, b))

def length(a):
  return math.sqrt(dot(a,a))

def parsePoint(str):
  components = str.split()
  return list(map(float, components))

A = parsePoint(input())
B = parsePoint(input())
C = parsePoint(input())
D = parsePoint(input())

AB = subtract(A,B)
BC = subtract(B,C)
CD = subtract(C,D)

X = cross(AB,BC)
Y = cross(BC,CD)

PHI = math.degrees(math.acos(dot(X,Y)/(length(X)*length(Y))))

print("{0:.2f}".format(PHI))








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