SE3kit documentation

Lightweight Python library for 3D rigid-body transformations and rotations.

Overview

SE3kit implements core SE(3) building blocks and a minimal robot FK example:

Homogeneous transforms follow the standard block form \(T = \begin{bmatrix} R & t \\ 0 & 1 \end{bmatrix}\) where \(R \in SO(3)\) and \(t \in \mathbb{R}^3\).
Rotations are stored as 3x3 matrices in se3kit.rotation.Rotation.
Translations are stored as 3-vectors in se3kit.translation.Translation.

Installation

Install using pip:

pip install se3kit

Quick usage examples

Create transforms and compose them:

import se3kit as se3

# Create a transformation: 1 meter up in Z, identity rotation
t1 = se3.Transformation(se3.Translation([0, 0, 1]), se3.Rotation())

# Compose transformations
t2 = se3.Transformation(
    se3.Translation([0.5, 0, 0]),
    se3.Rotation.from_rpy([0, 0, 1.57])  # Rotate 90° around Z
)

t_combined = t1 * t2

Transform a homogeneous point:

import se3kit as se3

p = se3.HPoint(0.1, 0.5, 0.0)
p_transformed = t_combined.transform_hpoint(p)

print(p_transformed.xyz)   # Access as standard 3D vector

Store and manipulate 3D points in either Cartesian or Full Homogeneous Form:

import se3kit as se3
import numpy as np

# Cartesian coordinates
p1 = se3.HPoint(0.2, 0.4, 0.1)

# From NumPy array
p2 = se3.HPoint(np.array([1.0, 2.0, 3.0]))

# From full homogeneous vector
p3 = se3.HPoint(np.array([0.5, 0.0, 1.0, 1.0]))

print(p1.xyz)          # [0.2, 0.4, 0.1]
print(p2.as_array())   # Full 4×1 homogeneous vector

Transform points attached to a robot’s tool through the end-effector pose:

import se3kit as se3

# A tool point on the robot’s end effector
tool_point = se3.HPoint(0.1, 0.0, 0.0)

# End-effector pose in world frame
T_world_ee = se3.Transformation(
    se3.Translation([0.5, 0.2, 1.0]),
    se3.Rotation.from_rpy([0, 0, 1.57])
)

p_world = T_world_ee.transform_hpoint(tool_point)
print(p_world.xyz)

Compose multiple transformations to represent an full kinematic chain.

import se3kit as se3

# Example arm links
T1 = se3.Transformation(se3.Translation([0, 0, 0.4]), se3.Rotation.from_rpy([0, 0, 0.5]))
T2 = se3.Transformation(se3.Translation([0, 0, 0.3]), se3.Rotation.from_rpy([0, 0.2, 0]))
T3 = se3.Transformation(se3.Translation([0.1, 0, 0]), se3.Rotation.from_rpy([0.1, 0, 0]))

T_end_effector = T1 * T2 * T3

print(T_end_effector.as_geometry_pose())

Seamlessly convert between millimeters and meters for transformations.

import se3kit as se3

T_mm = se3.Transformation.convert_m_to_mm(T_end_effector)
T_m  = se3.Transformation.convert_mm_to_m(T_mm)

print(T_mm.translation.xyz)

Contents:

SE3kit package