Angle θ is in radians. Pi radians equal 180 degrees (2
| Description | Transformation Matrix | numpy array |
|---|---|---|
| Point Coordinates |
xyz = numpy.array([x, y, z, 1]) | |
| Identity |
1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 |
m = numpy.array([ [1, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1] ])
|
| Scaling |
cx 0 0 0 0 cy 0 0 0 0 cz 0 0 0 0 1 |
m = numpy.array([ [cx, 0, 0, 0],
[0, cy, 0, 0],
[0, 0, cz, 0],
[0, 0, 0, 1] ])
|
| Translation |
1 0 0 tx 0 1 0 ty 0 0 1 tz 0 0 0 1 |
m = numpy.array([ [1, 0, 0, tx],
[0, 1, 0, ty],
[0, 0, 1, tz],
[0, 0, 0, 1] ])
|
| Rotate About The Z Axis |
cos(θ) -sin(θ) 0 0 sin(θ) cos(θ) 0 0 0 0 1 0 0 0 0 1 |
m = numpy.array([ [cos(θ), -sin(θ), 0, 0],
[sin(θ), cos(θ), 0, 0],
[ 0, 0, 1, 0],
[ 0, 0, 0, 1] ])
|
| Rotate About The Y Axis |
cos(θ) 0 sin(θ) 0 0 1 0 0 -sin(θ) 0 cos(θ) 0 0 0 0 1 |
m = numpy.array([ [ cos(θ), 0, sin(θ), 0],
[ 0, 1, 0, 0],
[-sin(θ), 0, cos(θ), 0],
[ 0, 0, 0, 1] ])
|
| Rotate About The X Axis |
1 0 0 0 0 cos(θ) -sin(θ) 0 0 sin(θ) cos(θ) 0 0 0 0 1 |
m = numpy.array([ [1, 0, 0, 0],
[0, cos(θ), -sin(θ), 0],
[0, sin(θ), cos(θ), 0],
[0 0, 0, 1] ])
|
Code examples: convert degrees to radians, radians to degrees
import numpy as np
rad = np.deg2rad(deg)
deg = np.rad2deg(rad)