Angle between 3 points in 3d space

Question

I have 3 points containing X, Y, Z coordinates:

var A = {x: 100, y: 100, z: 80},
    B = {x: 100, y: 175, z: 80},
    C = {x: 100, y: 100, z: 120};
         


        

Answer 1

The same in python (with output in degrees):

import numpy as np
import math 
import time

def angle_2p_3d(a, b, c):       

    v1 = np.array([ a[0] - b[0], a[1] - b[1], a[2] - b[2] ])
    v2 = np.array([ c[0] - b[0], c[1] - b[1], c[2] - b[2] ])

    v1mag = np.sqrt([ v1[0] * v1[0] + v1[1] * v1[1] + v1[2] * v1[2] ])
    v1norm = np.array([ v1[0] / v1mag, v1[1] / v1mag, v1[2] / v1mag ])

    v2mag = np.sqrt(v2[0] * v2[0] + v2[1] * v2[1] + v2[2] * v2[2])
    v2norm = np.array([ v2[0] / v2mag, v2[1] / v2mag, v2[2] / v2mag ])
    res = v1norm[0] * v2norm[0] + v1norm[1] * v2norm[1] + v1norm[2] * v2norm[2]
    angle_rad = np.arccos(res)

    return math.degrees(angle_rad)


p1 = np.array([1,0,0])
p2 = np.array([0,0,0])
p3 = np.array([0,0,1])

start = time.time()
angle= angle_2p_3d(p1, p2, p3)
end = time.time()

print("angle: ", angle)
print("elapsed in: ", end - start)

Output:

angle: 90.0

elapsed in: 8.392333984375e-05