Indirect hex-dominant meshing relies on the detection of adjacent tetrahedra that may be combined to form hexahedra. In this paper we introduce an algorithm that performs this identification and builds the largest set of potential hexahedra from an input tetrahedral mesh . The new method does not rely on a predefined set of patterns of tetrahedral decompositions of hexahedra but allows to look for all combinations of eight vertices whose connectivity matches the connectivity of a hexahedron. The method relies on a backtracking algorithm where connectivity checks and minimum bound quality checks are used to discard invalid hexahedra. The subset of tetrahedra of triangulating each potential hexahedron is determined once its eight vertices are computed. The new algorithm computes around 3 millions potential hexahedra in 10 seconds and ensures that each potential hexahedron is computed only once.  We finally demonstrate that the set of potential hexes built by our algorithm is significantly larger than those built by pattern based methods .
Indirect hex-dominant meshing methods rely on the detection of adjacent tetrahedra that may be combined to form hexahedra. In this paper we introduce an algorithm that performs this identification and builds the set of all possible combinations of tetrahedral elements of an input mesh into hexahedra. All identified hexahedral elements are valid for engineering analysis. The new method first computes all combinations of eight vertices whose connectivity matches the connectivity of a hexahedron. The subset of tetrahedra triangulating each potential hexahedron is then determined. Quality checks allow to early discard poor quality hexahedra and to dramatically improve the efficiency of the method. Each potential hexahedron is computed only once. Around 3 millions potential hexahedra are computed in 10 seconds on a laptop. We finally demonstrate that the set of potential hexes built by our algorithm is significantly larger than those built using predefined patterns of subdivision of a hexahedron in tetrahedral elements .
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Around 3 millions potential hexahedra are computed in 10 seconds on a laptop.
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by pattern based methods
using predefined patterns of subdivision of a hexahedron in tetrahedral elements