# -*- coding: utf-8 -*-
"""
Functions for calculating Basic Transformation Matrices in 3D space.
"""
from math import cos, radians, sin
from numpy import matrix
def rotate(axis, theta, angular_units='radians'):
'''Compute Basic Homogeneous Transform Matrix for
rotation of "theta" about specified axis.'''
#Verify string arguments are lowercase
axis=axis.lower()
angular_units=angular_units.lower()
#Convert to radians if necessary
if angular_units=='degrees':
theta=radians(theta)
elif angular_units=='radians':
pass
else:
raise Exception('Unknown angular units. Please use radians or degrees.')
#Select appropriate basic homogenous matrix
if axis=='x':
rotation_matrix=matrix([[1, 0, 0, 0],
[0, cos(theta), -sin(theta), 0],
[0, sin(theta), cos(theta), 0],
[0, 0, 0, 1]])
elif axis=='y':
rotation_matrix=matrix([[cos(theta), 0, sin(theta), 0],
[0, 1, 0, 0],
[-sin(theta), 0, cos(theta), 0],
[0, 0, 0, 1]])
elif axis=='z':
rotation_matrix=matrix([[cos(theta), -sin(theta), 0, 0],
[sin(theta), cos(theta), 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1]])
else:
raise Exception('Unknown axis of rotation. Please use x, y, or z.')
return rotation_matrix
def translate(axis, d):
'''Calculate Basic Homogeneous Transform Matrix for
translation of "d" along specified axis.'''
#Verify axis is lowercase
axis=axis.lower()
#Select appropriate basic homogenous matrix
if axis=='x':
translation_matrix=matrix([[1, 0, 0, d],
[0, 1, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1]])
elif axis=='y':
translation_matrix=matrix([[1, 0, 0, 0],
[0, 1, 0, d],
[0, 0, 1, 0],
[0, 0, 0, 1]])
elif axis=='z':
translation_matrix=matrix([[1, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 1, d],
[0, 0, 0, 1]])
else:
raise Exception('Unknown axis of translation. Please use x, y, or z.')
return translation_matrix
if __name__=='__main__':
#Calculate arbitrary homogeneous transformation matrix for CF0 to CF3
H0_1=rotate('x', 10, 'degrees')*translate('y', 50)
H1_2=rotate('y', 30, 'degrees')*translate('z', 10)
H2_3=rotate('z', -20, 'degrees')*translate('z', 10)
H0_3=H0_1*H1_2*H2_3
print(H0_3)

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