rotations-py

A pure-numpy Python library for 3D rotation representations. Convert freely between four representations, compose rotations, and apply them to vectors.

Representations

Installation

uv add rotations-py

Usage

import numpy as np
from rotations import SO3, Quaternion, AxisAngle, Screw

# construct
r = AxisAngle([0, 0, 1], np.pi/2)   # 90° around z

# convert between representations
r.to_so3()
r.to_quaternion()
r.to_screw()

# apply to a vector
r @ [1, 0, 0]           # → [0, 1, 0]

# compose two rotations
r1 = AxisAngle([0, 0, 1], np.pi/2)
r2 = AxisAngle([1, 0, 0], np.pi/2)
r3 = r1 @ r2            # result is same type as r1

# inverse
~r                       # AxisAngle for 90° around -z
r @ ~r                   # → identity

Conversion graph

SO3  ←→  Quaternion  ←→  AxisAngle  ←→  Screw

See description.md for the full math behind each conversion.

Development

To run tests

uv run pytest

To run the linter and formatter

uv run ruff check           # check lint
uv run ruff format --check  # check format
uv run ruff check --fix     # lint and auto-fix
uv run ruff format          # format and fix

To run the static type checker

uv run mypy rotations/