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Spherical Cow

A high volume fraction sphere packing library Travis-ci Codecov FOSSA Status

Based on the advancing fronts algorithm outlined in Valera et al., Computational Particle Mechanics 2, 161 (2015).

Milk production at a dairy farm was low, so the farmer wrote to the local university, asking for help from academia. A multidisciplinary team of professors was assembled, headed by a theoretical physicist, and two weeks of intensive on-site investigation took place. The scholars then returned to the university, notebooks crammed with data, where the task of writing the report was left to the team leader. Shortly thereafter the physicist returned to the farm, saying to the farmer, "I have the solution, but it works only in the case of spherical cows in a vacuum".


Complete documentation can be found at

A simple example to get you packing spheres of radii (0.1..0.2) into a container sphere of radius 2.

use spherical_cow::shapes::Sphere;
use rand::distributions::Uniform;
use nalgebra::Point3;

fn main() {
    let boundary = Sphere::new(Point3::origin(), 2.0).unwrap();
    let mut sizes = Uniform::new(0.1, 0.2);

    let spheres = spherical_cow::pack_spheres(boundary, &mut sizes).unwrap();

    println!("Number of spheres: {}", spheres.len());

More elaborate examples can be found in the examples directory.


True to its name, it is indeed possible to build a spherical cow:

spherical cow in vacuum

You can run this example yourself from show_in_cow.

Example use cases

The paper which this algorithm comes from gives two examples of real world use cases:

  1. Sphere packing a skull model to study fractures due to shocks and penetrating objects.
  2. Sphere packing a cutting tool to identify the failure / breaking points when the tool is placed under load.

The reason this library was initially written was to optimise the layout of inflatable space habitats which may one day be constructed on the Moon and Mars.


Licensed under the Apache License, Version 2.0 or the MIT license, at your option. These files may not be copied, modified, or distributed except according to those terms.

FOSSA Status

Deeply linked dependencies

A large number of example files within this repository (but NOT distributed as part of this library) have GPL licensing obligations. Below is one example:

The wayland-protocols library (released under an MIT license) is used by kiss3d (used for visualisation previews in the examples). Content therein: the file misc/server-decoration.xml, is Copyright (C) 2015 Martin Gräßlin and licensed under the GNU Lesser General Public Library, version 2.1. You can find a copy of this license at

For a complete list of these obligations, please refer to the license information from the associated crates. The Fossa links above can also assist.


A high volume fraction sphere packing library




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