Transforms

Python coordinate frame transform library

Library to ease work with 3D coordinate frame transformations, by two means:

• Easy-to-operate-with symbolic/numerical linear transformation classes
• LaTeX export and enhanced console printing of transformation matrices

API reference.

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1. Install

2. Usage and Syntax

3. To-do

1. Install

pip install linear_transforms

2. Usage and Syntax

To use the library, import it from Python with

from transforms import Tx, Ty, Tz

The code for the following examples can be found in demo/. Further examples can be found in tests/.

2.1 Creating a Linear Transformation

The three standard transformations, Tx, Ty and Tz, describe the original frame of reference of an object which undergoes a rotation from its body reference frame, for right-handed coordinate systems.

A transformation can be created in two ways:

• Using a SymPy symbol for the rotation angle, which greatly facilitates inspecting transform combination matrices (further discussion in Section 2.4 ):

    import sympy as sp
    a = sp.Symbol("alpha")
  
    Ta = Tx(a)
  

• Using a numerical variable for the rotation angle:

    import numpy as np
    a = np.pi/5
  
    Ta = Tx(a)
  

2.2 Lambdifying a symbolic linear transformation

Turning a symbolic linear transformation to a numerical one can be done by calling the transformation itself.

T_num = Ta(<VALUE>)

2.3 Operating with Linear Transformations

Transform concatenation is defined with the multiplication sign, as well as the addition sign. The multiplication notation is recommended.

Tt = Ta*Tb*Tc
TT = Ta+Tb+Tc

Tt == TT

Transform multiplication with NumPy or SymPy arrays is defined with the multiplication sign alone.

r = np.array([1, 1, 1])

r_tr = Tt*r

2.4 Inspecting matrices

LaTeX

Transformations, symbolic and numerical, can be outputed to LaTeX with the function call below. The latex equation will be visible in the terminal in light blue.

r_tr.to_latex()

Printing

Printing a transformation will output an ASCII representation in the terminal

print(r_tr)

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