This Python program is designed to calculate the torsional angle between four points in a 3D space. The points are represented as instances of a class 'Points', which has methods for subtraction, dot product, cross product, and calculating the absolute value of a point.
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The solution works by first creating instances of the 'Points' class for each of the four points. It then calculates the cross product of the vectors formed by these points, and uses these to calculate the dot product. The torsional angle is then calculated using the dot product and the absolute values of the cross products, and is converted to degrees before being printed.
import math
class Points:
def __init__(self, x, y, z):
self.x = x
self.y = y
self.z = z
def __sub__(self, other):
return Points(self.x - other.x, self.y - other.y, self.z - other.z)
def dot(self, other):
return self.x * other.x + self.y * other.y + self.z * other.z
def absolute(self):
return math.sqrt(self.x * self.x + self.y * self.y + self.z * self.z)
def cross(self, other):
return Points(
self.y * other.z - self.z * other.y,
self.z * other.x - self.x * other.z,
self.x * other.y - self.y * other.x,
)
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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