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Python NumPy (Page: 6)
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 NumPy creating;
 NumPy array reshaping;
 Images with NumPy;
 NumPy copy;
 NumPy mask;
 Geometry;
Please note, that some of these operation are much easier to perform with SciPy module
NumPy is a powerfull tool for algebra and geomentry calculations. I will try to make a very small but usefull library for vector manipulations
Angle between two vectors
This function use formula cos(α) = a·b/a·b => α = arccos(a·b/a·b). In this format this function do not count the sign of the angle and give only absoluyte value.
import numpy as np
def unit_vector(vector):
""" Calculate Unit Vector """
return vector / np.linalg.norm(vector)
def angle_between(v1, v2, radian = True):
""" Angle between vectors is arrcos from scalar (dot) product
of tweo unit vectors """
v1_u = unit_vector(v1)
v2_u = unit_vector(v2)
ang = np.arccos(np.clip(np.dot(v1_u, v2_u), 1.0, 1.0))
if radian: return ang
return np.rad2deg(ang)
v1 = (1, 0, 0)
v2 = (0, 1, 0)
print(angle_between(v1, v2, False)) # 90.0
Rotate 2D vector
Rotation of 2D vector in the plane is very easy task. It is nesessary no make dot product of rotation matrix and our vector.
Rotation matrics is R=[[cosθ, sinθ], [sinθ, cosθ]].
import numpy as np
def rotate_2d(vector, theta, radian = True):
"""Rotate vector by given angle"""
if not radian: theta = np.deg2rad(theta)
c, s = np.cos(theta), np.sin(theta)
rot = np.array([[c, s],
[s, c]
])
return np.dot(rot, vector)
print(rotate_2d([1, 0], 45, False)) # [ 0.70710678 0.70710678]
Rotate 3D vector
Find the rotation between two vectors
How to find the rotation matrix between 2 vectors in 3D space.
r = I + k + np.square(k) * ((1 c)/(s**2)), np.square(k) squares each element of the matrix. You want np.matmul(k,k) or k @ k which is the matrix multiplied by itself.
def rotation_matrix_from_vectors(v1, v2):
""" Find the rotation matrix that aligns 3D v1 to v2
:return mat: A transform matrix (3x3) which when applied to v1, aligns it with v2.
"""
a = v1 / np.linalg.norm(v1)
b = v2 / np.linalg.norm(v2)
v = np.cross(a, b)
if not any(v): return np.eye(3) #vectors are parallel
c = np.dot(a, b)
s = np.linalg.norm(v)
kmat = np.array([[0, v[2], v[1]], [v[2], 0, v[0]], [v[1], v[0], 0]])
rotation_matrix = np.eye(3) + kmat + kmat.dot(kmat) * ((1  c) / (s ** 2))
return rotation_matrix
# TESTS
vec1 = [1, 0, 0]
vec2 = [0, 2, 0]
mat = rotation_matrix_from_vectors(vec1, vec2)
vec1_rot = mat.dot(vec1)
print( mat ) # [[ 0. 1. 0.] [ 1. 0. 0.] [ 0. 0. 1.]]
print(vec1_rot) # [0. 1. 0.]
How to rotate 3D vector agains another vector
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Published: 20211004 11:48:19 Updated: 20211114 08:41:55

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