# QGP3D

A C++ implementation of quantized global parametrization for volumes, turning a tetrahedral mesh with a compatible input map into a valid integer-grid parametrization from which a defect-free hexahedral mesh can be extracted.

QGP3D partitions a tetrahedral mesh, equipped with a suitable compatible map, into blocks using the 3D Motorcycle Complex, then constructs a valid quantization of the resulting non-conforming partition: an assignment of integer lengths to the partition's edges and optimal integer spacings between its key entities. These spacings guarantee that reparametrization with them as constraints produces a globally valid integer-grid map, from which a hex mesh without defects can be extracted.

A newer integer-sheet-pump quantization method, integrated more recently, replaces the previous dependency on integer quadratic programming solvers with a greedy, near-optimal approach that needs only a continuous linear-programming solver, typically one to two orders of magnitude faster.

A further extension, Flexible Singularities, adaptively simplifies the initial singularity graph at the quantization stage, and requires a companion project, C4HexMeshing, to extract the simplified structure or a hex mesh. The project implements methods from papers presented at SIGGRAPH 2022, SGP 2024 and an upcoming Eurographics 2026 paper.

Website: https://github.com/HendrikBrueckler/QGP3D