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Nested Cages

This C++ project implements:

[Nested Cages] (http://www.cs.columbia.edu/cg/nested-cages/)
ACM Transactions on Graphics, vol. 34, no. 6 (SIGGRAPH Asia 2015).
Leonardo Sacht, Etienne Vouga and Alec Jacobson

Get started with:

git clone https://github.com/alecjacobson/nested_cages.git

(No --recursive needed — all dependencies are fetched by CMake.)

Bunny teaser from "Nested Cages"

Compilation

This code has been tested on Linux and Mac OS X. In theory this should also work on Windows.

To compile the command-line tool:

cmake -S . -B build -DCMAKE_BUILD_TYPE=Release
cmake --build build -j

This will fetch and build all dependencies and produce the nested_cages executable in build/.

Dependencies

All third-party libraries are fetched automatically by CMake (via FetchContent/ExternalProject) — there are no git submodules to initialize:

The only system prerequisites are a C++17 compiler, a Fortran compiler (for BLAS/LAPACK), CMake ≥ 3.16, and the Boost headers (used by CGAL). On Debian/Ubuntu:

sudo apt-get install build-essential gfortran cmake libboost-dev

(GMP/MPFR are not required: libigl v2.6.0 builds CGAL in its GMP-free CGAL_DISABLE_GMP configuration.)

By default the build fetches and compiles reference BLAS/LAPACK. To instead use a system BLAS/LAPACK (e.g. OpenBLAS) for speed, configure with -DNESTED_CAGES_FETCH_BLAS=OFF.

Python bindings

The pipeline is also exposed as a Python module built with nanobind, mirroring the layout of the libigl Python bindings. Installing with pip compiles the C++ code (and fetches all dependencies) via scikit-build-core, so it needs the same system prerequisites listed above (C++17 + Fortran compilers, CMake, Boost headers).

Install directly from GitHub — no need to clone first:

# latest on the default branch
pip install "git+https://github.com/alecjacobson/nested_cages.git"

# or pin a branch / tag / commit with the usual `@ref` suffix
pip install "git+https://github.com/alecjacobson/nested_cages.git@modernize-deps-and-python-bindings"

Or, from a local checkout of this repository:

pip install .            # regular install
pip install -e .         # editable/development install

The first build fetches and compiles all dependencies, so it can take several minutes.

Then, from Python:

import numpy as np
import nested_cages

# V: (#V,3) float64 vertices, F: (#F,3) int faces of the fine mesh
cages = nested_cages.nested_cages(
    V, F,
    num_faces=[1000, 500],      # one target face count per cage level
    quad_order=2,
    energy_expansion="None",
    energy_final="Volume",
    regular=[True, True],        # regular (vs adaptive) decimation per level
)
# cages is a list of (V_i, F_i) numpy arrays, one nested cage per level.

See tests/regression.py for a check that the Python bindings and the CLI produce identical cages.

Wheels / publishing to PyPI

.github/workflows/wheels.yml builds redistributable wheels with cibuildwheel for Linux (x86_64, aarch64) and macOS (x86_64, arm64), CPython 3.8–3.13, plus an sdist. It runs the full matrix on tags/releases/manual dispatch and a single-version smoke build on pushes and PRs. Each macOS arch is built natively (macos-15-intel for x86_64, macos-14 for arm64), because eltopo's Fortran BLAS/LAPACK cannot be cross-compiled (Homebrew's gfortran only targets the host arch).

Note: Apple has retired the Intel architecture, and GitHub will drop macOS x86_64 runners after macos-15-intel is retired (~Fall 2027); at that point Intel-Mac users would install from the sdist.

Windows is not built (eltopo links a Fortran BLAS/LAPACK, for which there is no turn-key CI toolchain); Windows users install from the sdist.

Publishing to PyPI happens automatically when a GitHub Release is published, via trusted publishing (OIDC, no API token). To enable it once: on PyPI, add a trusted publisher for this project pointing at alecjacobson/nested_cages, workflow wheels.yml, environment pypi.

Example usages

Help information

./nested_cages

Obtain 2 volume minimizing nested cages for ../gargo.off: one regular with 1000 faces and the other regular with 500 faces. Output resulting cages to ../test_1.off and ../test_2.off

./nested_cages ../gargo.off 2 1000r 500r None Volume ../test

The same as above, but outputs adaptive decimations (instead of regular)

./nested_cages ../gargo.off 2 1000 500 None Volume ../test

Obtain 2 nested cages for ../gargo.off that minimize surface ARAP energy, using as input decimations ../gargo_1000.off and gargo_500.off

./nested_cages ../gargo.off 2 ../gargo_1000.off ../gargo_500.off SurfARAP None ../test

Contact

If you have any comments or questions, please contact Leonardo Sacht by e-mail: leo@mtm.ufsc.br

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