Kilian Verhetsel, Jeanne Pellerin,
Jean-FranÃ§ois
Remacle
UniversitÃ© catholique de Louvain
Two distinct cubes can share:
Boundary | Hex mesh | |
---|---|---|
V | H | V |
12 | 2 | 12 |
Boundary | Hex mesh | |
---|---|---|
V | H | V |
10 | > 20 | > 38 |
Boundary | Hex mesh | |
---|---|---|
V | H | V |
12 | > 17 | > 31 |
Boundary | Hex mesh | |
---|---|---|
V | H | V |
22 | 6 | 22 |
$\lbrack 0, 3, 7, 4, \mathbf{\color{red} 1}, \mathbf{\color{red}
2}, \mathbf{\color{red} 6}, \mathbf{\color{red} 5} \rbrack$
$\lbrack \mathbf{\color{red} 1}, \mathbf{\color{red} 5}, 11, 8,
\mathbf{\color{red} 2}, \mathbf{\color{red} 6}, 10, 9 \rbrack$
Start construction where we have as few options as possible
Best known solution: 88 hex [Yamakawa 2010]
Can we improve this mesh?
Yamakawa et al., 2010
H = 88, V = 105
Ours
H = 44, V = 62
Xiang et al., 2018
H = 36, V = 51
\[18 \le H_{\min} \le 36\] \[36 \le V_{\min} \le 51\]
H = 40, V = 52
\[21 \le H_{\min} \le 40\]
\[39 \le V_{\min} \le 52\]
Code and meshes available at
hextreme.eu
This research is supported by the European Research Council
(project HEXTREME, ERC-2015-AdG-694020)