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.)
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:
- libigl
v2.6.0(which in turn fetches CGAL and tetgen), - Eigen
3.4.0, - eltopo,
- collisiondetection,
- MeshFix,
- reference BLAS/LAPACK (built in isolation for eltopo), and
- nanobind
v2.7.0for the Python bindings.
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
1 maintainer
Metadata
1 maintainer
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