CutCells

CutCells is a lightweight C++20 geometry kernel with Python bindings to compute cut-cell decompositions of standard mesh elements by an implicit surface / level set φ(x).

Given one parent cell (or a whole mesh) and the level set values on its vertices, CutCells builds a local sub-mesh that describes:

• the inside region φ < 0,
• the outside region φ > 0,
• and/or the interface φ = 0 (as facets/segments embedded in the cell),

with explicit connectivity and element types.

It is designed as a building block for unfitted / immersed FEM workflows (e.g. CutFEM), where robust cut geometry and stable parent mappings are required for runtime quadrature.

Supported cell types

Current parent cell support:

• 1D: interval
• 2D: triangle, quadrilateral
• 3D: tetrahedron, hexahedron, prism, pyramid

Higher-order (currently pragmatic) support:

• P2 triangle (6 nodes) and P2 tetrahedron (10 nodes) via subdivision into linear sub-cells, cut, then merged back.

Performance and dependencies

• Few dependencies: the computational core is plain C++.
• Python bindings via nanobind: CutCells exposes arrays in NumPy-friendly form and is designed to avoid unnecessary overhead.
• Zero-copy where possible: large buffers (coords, connectivity/offsets, parent IDs, provenance tags) are exposed as views when layout permits, minimizing memory traffic between C++ and Python.

Applications

CutCells is intended as a reusable geometry backend for:

• CutFEM / unfitted FEM: robust sub-cell and interface extraction for integration on Ω∩K and Γ∩K
• runtime quadrature generation
• general embedded geometry workflows where remeshing is undesirable

Example gallery

Below is a gallery of example outputs generated by CutCells and the provided Python demos. See python/demo/ for scripts to reproduce these images.

<table> <tr> <td align="center"> <img src="./img/mesh2D.png" alt="2D mesh cut by circle" width="320"/><br/> _{2D mesh cut by a circular level set} </td> <td align="center"> <img src="./img/hybrid_flower.png" alt="Hybrid mesh flower cut" width="320"/><br/> _{Hybrid mesh (quads+tris) cut by flower level set} </td> <td align="center"> <img src="./img/quad_cases_with_disambiguation_panels_quads.png" alt="Quad cases with disambiguation" width="320"/><br/> _{Quad cases with disambiguation panels} </td> </tr> <tr> <td align="center"> <img src="./img/prism_n0_demo.png" alt="Cut prism demo" width="320"/><br/> _{Cut prism (wedge) demo} </td> <td align="center"> <img src="./img/pyramid_n0_demo.png" alt="Cut pyramid demo" width="320"/><br/> _{Cut pyramid demo} </td> <td align="center"> <img src="./img/cut_tetra_quad.png" alt="Cut pyramid demo" width="180"/> <img src="./img/cut_tetra_tri.png" alt="Cut pyramid demo" width="180"/><br/> _{Cut tetrahedron demo} </td> </tr> <tr> <td align="center"> <img src="./img/popcorn.png" alt="2D mesh cut by popcorn function" width="320"/><br/> _{Tetrahedral mesh cut by a popcorn level set} </td> <td align="center"> <img src="./img/popcorn_hex_mesh3D.png" alt="3D hex mesh cut by popcorn" width="320"/><br/> _{Hexahedral mesh cut by popcorn level set} </td> <td align="center"> <img src="./img/cut_hex_gyroid_grid.png" alt="Hexahedron gyroid grid" width="320"/><br/> _{Hexahedral mesh cut by gyroid level set} </td> </tr> </table>

Installation

To install the CutCells library, first install the C++ library and then build the python interface

C++ library

In the cpp/ directory:

cmake -DCMAKE_BUILD_TYPE=Release -B build-dir -S .
cmake --build build-dir
cmake --install build-dir

You may need to use sudo for the final install step. Using the CMake build type Release is recommended for performance.

Python interface

After installing the C++ library, install the Python interface by running in the directory python/:

cmake -DCMAKE_BUILD_TYPE=Release -B build-dir -S .
cmake --build build-dir
cmake --install build-dir

and then

python3 -m pip install .

Running demons

There are demons for both the C++ and the python interface. For the C++ interface the demos are located in cpp/demo. The C++ demos are built with

cmake -DCMAKE_BUILD_TYPE=Release -B build-dir -S .
cmake --build build-dir
cmake --install build-dir

in the corresponding demo folder, e.g. cpp/demo/cut_triangle

The python demos are located in python/demo.

Third-party notices

Some generated clip/cut case tables (hexahedron/prism/pyramid) are derived from VTK's vtkTableBasedClipCases.h. VTK's BSD-3-Clause license text is included in third_party/VTK-Copyright.txt.

Dependencies

CutCells requires a C++20 compiler and depends on the C++ standard template library. For the python interface, CutCells requires nanobind.

At runtime for the python examples, CutCells requires numpy and pyvista for visualizations.

The library contains python pytest tests in python/tests.