MC3D – An algorithm for Structured Volume Decomposition

MC3D is an implementation of The 3D Motorcycle Complex for Structured Volume Decomposition [Brückler et al. 2021] (Eurographics 2022) distributed under GPLv3.

If you make use of MC3D in your scientific work, please cite our paper. For your convenience, you can use the following bibtex snippet:

@article{DBLP:journals/corr/abs-2112-05793,
    author     = {Hendrik Br{\"{u}}ckler and
                 Ojaswi Gupta and
                 Manish Mandad and
                 Marcel Campen},
    title      = {The 3D Motorcycle Complex for Structured Volume Decomposition},
    journal    = {CoRR},
    volume     = {abs/2112.05793},
    year       = {2021},
    url        = {https://arxiv.org/abs/2112.05793},
    eprinttype = {arXiv},
    eprint     = {2112.05793},
}

What is the 3D Motorcycle Complex?

The 3D Motorcycle Complex partitions a tetrahedral mesh, equipped with a suitable seamless map, into blocks that are axis-aligned rectangular cuboids under the parametrization. The resulting partition is non-conforming (i.e. one where "T"-junctions exist) and therefore can be made much coarser than similar conforming partitions like the so called base complex (BC).

The construction algorithm is demonstrated in the following video:

https://user-images.githubusercontent.com/38473042/152365682-b0052ec2-df41-447a-bec4-c30865ea71b4.mp4

Dependencies

• GMP (NOT included, must be installed on your system)
• TrulySeamless3D (Included as submodule, together with subdependency libHexEx)
• OpenVolumeMesh (Included as submodule. A PATCHED version is required to fully support selfadjacent blocks! If you use CMake to build, it will automatically apply the patch in extern/patches/, otherwise you have to apply the patch yourself.)
• glog (Included as submodule)
• googletest (Included as submodule)
• CLI11 (Included as submodule)

Building

In root directory

mkdir build
cd build
cmake [-DMC3D_BUILD_CLI=Off] [-DMC3D_BUILD_TESTS=Off] [-DMC3D_ENABLE_LOGGING=Off] ..
make

Usage

An example command-line application is included that reads a tetrahedral mesh including a seamless parametrization from a file in .hexex-format, as used and documented in libHexEx. It outputs a file in the same format, containing a refined version of the input mesh, followed by the number and the list of wall triangles (three vertex indices, and a double indicating the wall triangle's distance from the brush fire's origin per line) at the end of the file.

After building the CLI app can be found in build/Build/bin/cli . For full information on its usage, execute

mc3d_cli --help

Example input can be found in folder tests/resources.

API

For details on the API of the library, check the headers in include, they are thoroughly documented. Apart from that, cli/main.cpp demonstrates usage of the entire MC3D-Pipeline for both simple and advanced usage.