spatial math types

The module base/types.py defines a set of types for different arrays. These are all ndarray but giving them more meaningful types is helpful when writing code. The defined types are:

1D arrays for input to functions

• ArrayLikePure array like of arbitrary length, eg. `np.r_[1, 2, 3], [1], (1, 2, 3, 4)
• ArrayLike array like of arbitrary length including scalar, eg. 2, np.r_[2], [2], (2,)
• ArrayLike2 array like of length 2, eg. np.r_[1, 2], [1, 2], (1, 2)
• ArrayLike3 array like of length 3, eg. np.r_[1, 2, 3], [1, 2, 3], (1, 2, 3)
• ArrayLike4 array like of length 4, eg. np.r_[1, 2, 3, 4], [1, 2, 3, 4], (1, 2, 3, 4)
• ArrayLike6 array like of length 6

Real vectors

• R1 is a 1D ndarray $\sim \mathbb{R}^1$
• R2 is a 1D ndarray $\sim \mathbb{R}^2$
• R3 is a 1D ndarray $\sim \mathbb{R}^3$
• R4 is a 1D ndarray $\sim \mathbb{R}^4$
• R6 is a 1D ndarray $\sim \mathbb{R}^6$
• R8 is a 1D ndarray $\sim \mathbb{R}^8$

Real matrices

• R1x1 $\sim \mathbb{R}^{1\times 1}$
• R2x2 $\sim \mathbb{R}^{2\times 2}$
• R3x3 $\sim \mathbb{R}^{3\times 3}$
• R4x4 $\sim \mathbb{R}^{4\times 4}$
• R6x6 $\sim \mathbb{R}^{6\times 6}$
• R8x8 $\sim \mathbb{R}^{8\times 8}$
• R1x3 $\sim \mathbb{R}^{1\times 3}$
• R3x1 $\sim \mathbb{R}^{3\times 1}$
• R1x2 $\sim \mathbb{R}^{1\times 2}$
• R2x1 $\sim \mathbb{R}^{2\times 1}$

Points

• Points2 2D points, columnise, $\sim \mathbb{R}^{2\times N}$
• Points3 2D points, columnise, $\sim \mathbb{R}^{3\times N}$
• RNx3 $\sim \mathbb{R}^{N\times 3}$

Lie groups

• SO2Array 2D rotation matrix, element of $\mbox{SO(2)} \subset \mathbb{R}^{2\times 2}$
• SE2Array 2D rigid-body transformation matrix, element of $\mbox{SE(2)} \subset \mathbb{R}^{3\times 3}$
• SO3Array 3D rotation matrix, element of $\mbox{SO(3)} \subset \mathbb{R}^{3\times 3}$
• SE3Array 3D rigid-body transformation matrix, element of $\mbox{SE(32)} \subset \mathbb{R}^{4\times 4}$

Lie algebras, skew and augmented skew matrices

• so2Array Lie algebra of $\mbox{SO(2)} \subset \mathbb{R}^{2\times 2}$
• se2Array Lie algebra of $\mbox{SE(2)} \subset \mathbb{R}^{3\times 3}$
• so3Array Lie algebra of $\mbox{SO(3)} \subset \mathbb{R}^{3\times 3}$
• se3Array Lie algebra of $\mbox{SE(32)} \subset \mathbb{R}^{4\times 4}$

Quaternions

• QuaternionArray quaternion, element of $\mathbb{H} \sim \mathbb{R}^4$
• UnitQuaternionArray unit quaternion, element of ${\rm S}^3 \subset \mathbb{R}^4$

2D and 3D unions

• Rn = R2 | R3
• SOnArray = SO2Array | SO3Array
• SEnArray = SE2Array | SE3Array
• sonArray = so2Array | so3Array
• senArray = se2Array | se3Array