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rotor.py

Simple 2D/3D point rotation module written in pure python.

Installation

No installation required. Copy the script to the working directory.

Dependencies

rotor.py utilizes the standard math.py library

License

The project has been released with the MIT license

Author

Jaime Ortiz ( jimijimi ) email: jim2o at hotmail.com

Detailed description

rotor.py is a collection of functions. There are four main functions. The first three: rotateX( point, angle ), rotateY( point, angle ), rotateZ( point, angle ) are used to rotate a given point around any of the cartesian coordinate axes. The last function is rotate( point, angle, vector ) this allows the rotation around any arbitrary axis represented by vector.

A point is a list of three elements. [ x, y, z ] A vector is a list of three real numbers of the form [ vx, vy, vz ]. The vector can be normalized or unnormalized. An angle is specified in degrees.

Additionally the script contains functions handling vectors and quaternions. However rotor.py shuldn't be seen as a vector/quartenion library.

rotor.py can be used in python 2.XX and python 3.XX

Example:

Rotate an arbitrary point around the z axys:

  import rotor as r
  
  p0 = [ 1, 0, 0 ]
  angle = 90
  p1 = r.rotateZ( p0, angle )

  print( "%.3f %.3f %.3f " % ( p0[0], p0[1], p0[2] ) )
  print( "%.3f %.3f %.3f " % ( p1[0], p1[1], p1[2] ) )

Output:

  1.000 0.000 0.000
  0.000 1.000 0.000

Picture

The red square is the origin. The black square over the x axys is the initial position. The black square over the y axys is the final position. The background mesh is not to scale.

Example:

Rotate an arbitrary point around the axys defined by the vector v = [ 1, 1, 1 ]:

  import rotor as r
  
  p0 = [ 1, 0, 0 ]
  angle = 90
  v = [ 1, 1, 1 ]
  p1 = r.rotate( p0, angle, v )

  print( "%.3f %.3f %.3f " % ( p0[0], p0[1], p0[2] ) )
  print( "%.3f %.3f %.3f " % ( p1[0], p1[1], p1[2] ) )

Output:

  1.000 0.000 0.000
  0.333 0.911 -0.244

Example:

Create 8 points over the circuference defined around the vector v = [ 1, 1, 1 ] and starting at point p0 = [ 1, 0, 0 ]

  import rotor as r

  p0 = [ 1, 0, 0 ]
  v = [ 1, 1, 1 ]
  
  for angle in range( 0, 360, 45 ):
	  p1 = r.rotate( p0, angle, v )
	  print( "%.3f,%.3f,%.3f " % ( p1[0], p1[1], p1[2] ) )

Output:

  1.000,0.000,0.000      #0 deg ( initial point )
  0.805,0.506,-0.311     #45 deg
  0.333,0.911,-0.244     #90 deg
  -0.138,0.977,0.161
  -0.333,0.667,0.667
  -0.138,0.161,0.977
  0.333,-0.244,0.911
  0.805,-0.311,0.506     #315 deg