QGP3D – Quantized Global Parametrization of Volumes

QGP3D is an implementation of Volume Parametrization Quantization for Hexahedral Meshing [Brückler et al. 2022] (SIGGRAPH 2022) distributed under GPLv3.

If you make use of QGP3D in your scientific work, please cite our paper. For your convenience, you can use the following bibtex snippet:

@article{QGP3D,
    author     = {Hendrik Br{\"{u}}ckler and
                 David Bommes and
                 Marcel Campen},
    title      = {Volume Parametrization Quantization for Hexahedral Meshing},
    journal    = {ACM Trans. Graph.},
    volume     = {41},
    number     = {4},
    year       = {2022},
}

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How does it work?

QGP3D makes use of the 3D Motorcycle Complex to partition a tetrahedral mesh, equipped with a suitable seamless map, into blocks. It then constructs a valid quantization of the non-conforming partition, that is an assignment of integer lengths to the partition's edges, and deduces optimal integer spacings between all crucial entities like singularities and boundaries from this. We guarantee that these spacings, when used as constraints in reparametrization, permit the construction of a globally valid integer-grid-map parametrization from which a hex mesh without defects can be extracted. Greedy rounding, the previous state-of-the-art approach for quantization, can not provide this guarantee and therefore often enforces defects in the output.

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Dependencies

• GMP (NOT included, must be installed on your system)
• GUROBI (NOT included, must be installed on your system)
• MC3D (Included as submodule, together with all subdependencies)

Building

In root directory

mkdir build
cd build
cmake -DGUROBI_BASE=<path/to/gurobi/> ..
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 the integer spacing constraints between critical vertices of the input mesh.

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

QGP3D_cli --help

Example input can be found in folder extern/MC3D/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 pipeline for both simple and advanced usage.