rigeo is a prototyping library for working with rigid bodies in Python: it combines three-dimensional geometry with the inertial properties of rigid bodies, with applications to robotic manipulation.

One of the main features of this library is a set of necessary conditions for density realizability on 3D shapes based on moment relaxations (see this paper for more information). A set of inertial parameters (i.e., mass, center of mass, inertia matrix) is called density realizable on a given shape if it can be physically realized by some rigid body contained in that shape. These conditions can be included as constraints in semidefinite programs for inertial parameter identification or for checking robustness to inertial parameter uncertainty.

• Build rigid bodies out of flexible shape primitives: convex polyhedra, ellipsoids, and cylinders.
• Obtain the intersection of two convex polyhedra (via cdd). This is particularly useful for obtaining contact patches between polyhedral objects for manipulation; e.g., when solving the waiter's problem
• Obtain the distance between primitive shapes using convex programming.
• Compute maximum-volume inscribed and minimum-volume bounding ellipsoids for sets of points.
• Compute convex hulls for degenerate sets of points (i.e., points that live in some lower-dimensional subspace than the ambient space).
• Uniform random sampling inside of and on the surface of ellipsoids.

The library requires Python >=3.8. It has been tested on Ubuntu 20.04 and 24.04. Optimization problems use cvxpy; MOSEK is installed by default and is used as the solver for the tests. Academic licenses for MOSEK can be obtained for free. If this is not an option for you, Clarabel is a reasonable open-source alternative.

From pip:

pip install rigeo

From source (using uv):

git clone https://github.com/utiasDSL/rigeo
cd rigeo
uv venv
uv sync

From source (using pip):

git clone https://github.com/utiasDSL/rigeo
cd rigeo
python -m pip install .

You can find a variety of scripts in the scripts directory:

• examples: numerical examples of approximating inertial parameters for particular bodies using random sampling (see this blog post);
• experiments: numerical experiments comparing density realizability constraints based on moment relaxations to custom constraints for boxes and cylinders (the custom ones yield the same results but result in much faster semidefinite programs);
• theory: symbolic derivations of some inertial parameter results.

Tests are run using pytest:

cd tests
python -m pytest .

To test against different Python versions, use:

# for example
uv run --isolated --python=3.9 pytest

MIT - see the LICENSE file.