andrewadare / spatial-effects

Geometry for vision and robotics

This is a Python package for working with coordinate transforms in three dimensions. It provides the following:

• Conversion between common spatial rotation representations
• The SE3 class for applying rigid translations and rotations to points and vectors
• TransformTree and TransformForest types for handling named coordinate frames and frame hierarchies

Dependencies

Numpy is the only dependency. It is installed automatically with this package.

Installation

Clone this repo and do pip install -e /path/to/spatial-effects.

Verify the installation by running the tests:

python -m unittest discover

Usage of SE(3) type:

    x = [1, 0, 0]              # Define a point/translation
    r = [0, 0, pi/2]           # Define an orientation/rotation
    T1 = SE3()                 # Create identity transformation
    T2 = SE3(x, r)             # Lists, tuples, or ndarrays ok here
    callable(T1)               # True
    T2(x)                      # array([1., 1., 0.])
    T2.R @ x + T2.t            # same
    T2.inverse(T2(x))          # x
    T1.matrix                  # np.eye(4)
    T2.vec                     # array([1, 0, 0, 0, 0, 1.571])
    (T1 + T2.vec).vec          # same (in this case)
    T2 - T1                    # same (in this case)
    T1 + T2                    # ValueError! Cannot ⊞ two manifolds
    T1 + (T2 - T1) == T2       # always True
    (T1 + v) - T1 == v         # always True (v is any 6 DOF vector)

Conventions

Points, vectors, quaternions, and matrices are all represented as Numpy arrays that follow Numpy's row-major data layout. For example, five 3D points or vectors would be passed to the library functions as a 5x3 array.

Unit quaternions are always expressed in (w, x, y, z) order, where w is the real or scalar component. The Hamilton convention for quaternion muliplication (as opposed to JPL) is followed consistently.