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dwilliamson/ModifiedMarchingCubes.js

Created February 8, 2022 16:20
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Transvoxel's Modified Marching Cubes Lookup Tables
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ModifiedMarchingCubes.js
//
// Lookup Tables for Transvoxel's Modified Marching Cubes
//
// Unlike the original paper (Marching Cubes: A High Resolution 3D Surface Construction Algorithm), these tables guarantee
// a closed mesh "whose connected components are continuous and free of holes."
//
// Rotations are prioritised over inversions so that 3 of the 6 cases containing ambiguous faces are never added. 3 extra
// cases are added as a post-process, overriding inverses through custom-build rotations to eliminate the rest.
//
// Uses the exact same co-ordinate system as https://gist.github.com/dwilliamson/c041e3454a713e58baf6e4f8e5fffecd
//
// The co-ordinate system has the more convenient properties:
//
// i = cube index [0, 7]
// x = (i & 1) >> 0
// y = (i & 2) >> 1
// z = (i & 4) >> 2
//
// Axes are:
//
// y
// | z
// | /
// | /
// +----- x
//
// Vertex and edge layout:
//
// 6 7
// +-------------+ +-----6-------+
// / | / | / | /|
// / | / | 11 7 10 5
// 2 +-----+-------+ 3 | +-----+2------+ |
// | 4 +-------+-----+ 5 | +-----4-+-----+
// | / | / 3 8 1 9
// | / | / | / | /
// 0 +-------------+ 1 +------0------+
//
// Triangulation cases are generated prioritising rotations over inversions, which can introduce non-manifold geometry.
//
// Pair of vertex indices for each edge on the cube
const EdgeVertexIndices = [
[0, 1],
[1, 3],
[3, 2],
[2, 0],
[4, 5],
[5, 7],
[7, 6],
[6, 4],
[0, 4],
[1, 5],
[3, 7],
[2, 6],
];
// For each MC case, a mask of edge indices that need to be split
const EdgeMasks = [
0x0, 0x109, 0x203, 0x30a, 0x80c, 0x905, 0xa0f, 0xb06,
0x406, 0x50f, 0x605, 0x70c, 0xc0a, 0xd03, 0xe09, 0xf00,
0x190, 0x99, 0x393, 0x29a, 0x99c, 0x895, 0xb9f, 0xa96,
0x596, 0x49f, 0x795, 0x69c, 0xd9a, 0xc93, 0xf99, 0xe90,
0x230, 0x339, 0x33, 0x13a, 0xa3c, 0xb35, 0x83f, 0x936,
0x636, 0x73f, 0x435, 0x53c, 0xe3a, 0xf33, 0xc39, 0xd30,
0x3a0, 0x2a9, 0x1a3, 0xaa, 0xbac, 0xaa5, 0x9af, 0x8a6,
0x7a6, 0x6af, 0x5a5, 0x4ac, 0xfaa, 0xea3, 0xda9, 0xca0,
0x8c0, 0x9c9, 0xac3, 0xbca, 0xcc, 0x1c5, 0x2cf, 0x3c6,
0xcc6, 0xdcf, 0xec5, 0xfcc, 0x4ca, 0x5c3, 0x6c9, 0x7c0,
0x950, 0x859, 0xb53, 0xa5a, 0x15c, 0x55, 0x35f, 0x256,
0xd56, 0xc5f, 0xf55, 0xe5c, 0x55a, 0x453, 0x759, 0x650,
0xaf0, 0xbf9, 0x8f3, 0x9fa, 0x2fc, 0x3f5, 0xff, 0x1f6,
0xef6, 0xfff, 0xcf5, 0xdfc, 0x6fa, 0x7f3, 0x4f9, 0x5f0,
0xb60, 0xa69, 0x963, 0x86a, 0x36c, 0x265, 0x16f, 0x66,
0xf66, 0xe6f, 0xd65, 0xc6c, 0x76a, 0x663, 0x569, 0x460,
0x460, 0x569, 0x663, 0x76a, 0xc6c, 0xd65, 0xe6f, 0xf66,
0x66, 0x16f, 0x265, 0x36c, 0x86a, 0x963, 0xa69, 0xb60,
0x5f0, 0x4f9, 0x7f3, 0x6fa, 0xdfc, 0xcf5, 0xfff, 0xef6,
0x1f6, 0xff, 0x3f5, 0x2fc, 0x9fa, 0x8f3, 0xbf9, 0xaf0,
0x650, 0x759, 0x453, 0x55a, 0xe5c, 0xf55, 0xc5f, 0xd56,
0x256, 0x35f, 0x55, 0x15c, 0xa5a, 0xb53, 0x859, 0x950,
0x7c0, 0x6c9, 0x5c3, 0x4ca, 0xfcc, 0xec5, 0xdcf, 0xcc6,
0x3c6, 0x2cf, 0x1c5, 0xcc, 0xbca, 0xac3, 0x9c9, 0x8c0,
0xca0, 0xda9, 0xea3, 0xfaa, 0x4ac, 0x5a5, 0x6af, 0x7a6,
0x8a6, 0x9af, 0xaa5, 0xbac, 0xaa, 0x1a3, 0x2a9, 0x3a0,
0xd30, 0xc39, 0xf33, 0xe3a, 0x53c, 0x435, 0x73f, 0x636,
0x936, 0x83f, 0xb35, 0xa3c, 0x13a, 0x33, 0x339, 0x230,
0xe90, 0xf99, 0xc93, 0xd9a, 0x69c, 0x795, 0x49f, 0x596,
0xa96, 0xb9f, 0x895, 0x99c, 0x29a, 0x393, 0x99, 0x190,
0xf00, 0xe09, 0xd03, 0xc0a, 0x70c, 0x605, 0x50f, 0x406,
0xb06, 0xa0f, 0x905, 0x80c, 0x30a, 0x203, 0x109, 0x0,
];
// For each MC case, a list of triangles, specified as triples of edge indices, terminated by -1
const TriangleTable = [
[ -1 ],
[ 3, 8, 0, -1 ],
[ 1, 0, 9, -1 ],
[ 9, 1, 8, 8, 1, 3, -1 ],
[ 3, 2, 11, -1 ],
[ 2, 11, 0, 0, 11, 8, -1 ],
[ 1, 0, 9, 3, 2, 11, -1 ],
[ 11, 1, 2, 11, 9, 1, 11, 8, 9, -1 ],
[ 10, 2, 1, -1 ],
[ 2, 1, 10, 0, 3, 8, -1 ],
[ 0, 9, 2, 2, 9, 10, -1 ],
[ 8, 2, 3, 8, 10, 2, 8, 9, 10, -1 ],
[ 1, 10, 3, 3, 10, 11, -1 ],
[ 10, 0, 1, 10, 8, 0, 10, 11, 8, -1 ],
[ 9, 3, 0, 9, 11, 3, 9, 10, 11, -1 ],
[ 9, 10, 8, 8, 10, 11, -1 ],
[ 7, 4, 8, -1 ],
[ 0, 3, 4, 4, 3, 7, -1 ],
[ 0, 9, 1, 4, 8, 7, -1 ],
[ 1, 4, 9, 1, 7, 4, 1, 3, 7, -1 ],
[ 11, 3, 2, 8, 7, 4, -1 ],
[ 4, 11, 7, 4, 2, 11, 4, 0, 2, -1 ],
[ 3, 2, 11, 0, 9, 1, 4, 8, 7, -1 ],
[ 9, 1, 4, 4, 1, 7, 7, 1, 2, 7, 2, 11, -1 ],
[ 7, 4, 8, 1, 10, 2, -1 ],
[ 7, 4, 3, 3, 4, 0, 10, 2, 1, -1 ],
[ 10, 2, 9, 9, 2, 0, 7, 4, 8, -1 ],
[ 7, 4, 9, 7, 9, 2, 9, 10, 2, 3, 7, 2, -1 ],
[ 1, 10, 3, 3, 10, 11, 4, 8, 7, -1 ],
[ 4, 0, 7, 0, 1, 10, 7, 0, 10, 7, 10, 11, -1 ],
[ 7, 4, 8, 9, 3, 0, 9, 11, 3, 9, 10, 11, -1 ],
[ 7, 4, 11, 4, 9, 11, 9, 10, 11, -1 ],
[ 5, 9, 4, -1 ],
[ 8, 0, 3, 9, 4, 5, -1 ],
[ 1, 0, 5, 5, 0, 4, -1 ],
[ 5, 8, 4, 5, 3, 8, 5, 1, 3, -1 ],
[ 3, 2, 11, 5, 9, 4, -1 ],
[ 2, 11, 0, 0, 11, 8, 5, 9, 4, -1 ],
[ 4, 5, 0, 0, 5, 1, 11, 3, 2, -1 ],
[ 11, 8, 2, 8, 4, 5, 2, 8, 5, 2, 5, 1, -1 ],
[ 5, 9, 4, 1, 10, 2, -1 ],
[ 0, 3, 8, 1, 10, 2, 5, 9, 4, -1 ],
[ 2, 5, 10, 2, 4, 5, 2, 0, 4, -1 ],
[ 4, 5, 8, 8, 5, 3, 3, 5, 10, 3, 10, 2, -1 ],
[ 11, 3, 10, 10, 3, 1, 4, 5, 9, -1 ],
[ 4, 5, 9, 10, 0, 1, 10, 8, 0, 10, 11, 8, -1 ],
[ 4, 5, 10, 4, 10, 3, 10, 11, 3, 0, 4, 3, -1 ],
[ 4, 5, 8, 5, 10, 8, 10, 11, 8, -1 ],
[ 5, 9, 7, 7, 9, 8, -1 ],
[ 3, 9, 0, 3, 5, 9, 3, 7, 5, -1 ],
[ 7, 0, 8, 7, 1, 0, 7, 5, 1, -1 ],
[ 3, 7, 1, 1, 7, 5, -1 ],
[ 5, 9, 7, 7, 9, 8, 2, 11, 3, -1 ],
[ 5, 9, 0, 5, 0, 11, 0, 2, 11, 7, 5, 11, -1 ],
[ 2, 11, 3, 7, 0, 8, 7, 1, 0, 7, 5, 1, -1 ],
[ 2, 11, 1, 11, 7, 1, 7, 5, 1, -1 ],
[ 8, 7, 9, 9, 7, 5, 2, 1, 10, -1 ],
[ 10, 2, 1, 3, 9, 0, 3, 5, 9, 3, 7, 5, -1 ],
[ 2, 0, 10, 0, 8, 7, 10, 0, 7, 10, 7, 5, -1 ],
[ 10, 2, 5, 2, 3, 5, 3, 7, 5, -1 ],
[ 5, 9, 8, 5, 8, 7, 1, 10, 3, 10, 11, 3, -1 ],
[ 1, 10, 0, 0, 10, 11, 0, 11, 7, 0, 7, 5, 0, 5, 9, -1 ],
[ 8, 7, 0, 0, 7, 5, 0, 5, 10, 0, 10, 11, 0, 11, 3, -1 ],
[ 5, 11, 7, 10, 11, 5, -1 ],
[ 11, 6, 7, -1 ],
[ 3, 8, 0, 7, 11, 6, -1 ],
[ 1, 0, 9, 7, 11, 6, -1 ],
[ 9, 1, 8, 8, 1, 3, 6, 7, 11, -1 ],
[ 6, 7, 2, 2, 7, 3, -1 ],
[ 0, 7, 8, 0, 6, 7, 0, 2, 6, -1 ],
[ 6, 7, 2, 2, 7, 3, 9, 1, 0, -1 ],
[ 9, 1, 2, 9, 2, 7, 2, 6, 7, 8, 9, 7, -1 ],
[ 10, 2, 1, 11, 6, 7, -1 ],
[ 2, 1, 10, 3, 8, 0, 7, 11, 6, -1 ],
[ 0, 9, 2, 2, 9, 10, 7, 11, 6, -1 ],
[ 6, 7, 11, 8, 2, 3, 8, 10, 2, 8, 9, 10, -1 ],
[ 7, 10, 6, 7, 1, 10, 7, 3, 1, -1 ],
[ 1, 10, 0, 0, 10, 8, 8, 10, 6, 8, 6, 7, -1 ],
[ 9, 10, 0, 10, 6, 7, 0, 10, 7, 0, 7, 3, -1 ],
[ 6, 7, 10, 7, 8, 10, 8, 9, 10, -1 ],
[ 4, 8, 6, 6, 8, 11, -1 ],
[ 6, 3, 11, 6, 0, 3, 6, 4, 0, -1 ],
[ 11, 6, 8, 8, 6, 4, 1, 0, 9, -1 ],
[ 6, 4, 11, 4, 9, 1, 11, 4, 1, 11, 1, 3, -1 ],
[ 2, 8, 3, 2, 4, 8, 2, 6, 4, -1 ],
[ 0, 2, 4, 4, 2, 6, -1 ],
[ 9, 1, 0, 2, 8, 3, 2, 4, 8, 2, 6, 4, -1 ],
[ 9, 1, 4, 1, 2, 4, 2, 6, 4, -1 ],
[ 4, 8, 6, 6, 8, 11, 1, 10, 2, -1 ],
[ 1, 10, 2, 6, 3, 11, 6, 0, 3, 6, 4, 0, -1 ],
[ 0, 9, 10, 0, 10, 2, 4, 8, 6, 8, 11, 6, -1 ],
[ 11, 6, 3, 3, 6, 4, 3, 4, 9, 3, 9, 10, 3, 10, 2, -1 ],
[ 1, 10, 6, 1, 6, 8, 6, 4, 8, 3, 1, 8, -1 ],
[ 1, 10, 0, 10, 6, 0, 6, 4, 0, -1 ],
[ 0, 9, 3, 3, 9, 10, 3, 10, 6, 3, 6, 4, 3, 4, 8, -1 ],
[ 4, 10, 6, 9, 10, 4, -1 ],
[ 4, 5, 9, 6, 7, 11, -1 ],
[ 7, 11, 6, 8, 0, 3, 9, 4, 5, -1 ],
[ 1, 0, 5, 5, 0, 4, 11, 6, 7, -1 ],
[ 11, 6, 7, 5, 8, 4, 5, 3, 8, 5, 1, 3, -1 ],
[ 3, 2, 7, 7, 2, 6, 9, 4, 5, -1 ],
[ 5, 9, 4, 0, 7, 8, 0, 6, 7, 0, 2, 6, -1 ],
[ 1, 0, 4, 1, 4, 5, 3, 2, 7, 2, 6, 7, -1 ],
[ 4, 5, 8, 8, 5, 1, 8, 1, 2, 8, 2, 6, 8, 6, 7, -1 ],
[ 6, 7, 11, 5, 9, 4, 1, 10, 2, -1 ],
[ 5, 9, 4, 7, 11, 6, 0, 3, 8, 2, 1, 10, -1 ],
[ 7, 11, 6, 2, 5, 10, 2, 4, 5, 2, 0, 4, -1 ],
[ 6, 7, 11, 3, 8, 4, 3, 4, 5, 3, 5, 2, 2, 5, 10, -1 ],
[ 9, 4, 5, 7, 10, 6, 7, 1, 10, 7, 3, 1, -1 ],
[ 5, 9, 4, 8, 0, 1, 8, 1, 10, 8, 10, 7, 7, 10, 6, -1 ],
[ 6, 7, 10, 10, 7, 3, 10, 3, 0, 10, 0, 4, 10, 4, 5, -1 ],
[ 4, 5, 8, 8, 5, 10, 8, 10, 6, 8, 6, 7, -1 ],
[ 9, 6, 5, 9, 11, 6, 9, 8, 11, -1 ],
[ 0, 3, 9, 9, 3, 5, 5, 3, 11, 5, 11, 6, -1 ],
[ 1, 0, 8, 1, 8, 6, 8, 11, 6, 5, 1, 6, -1 ],
[ 11, 6, 3, 6, 5, 3, 5, 1, 3, -1 ],
[ 2, 6, 3, 6, 5, 9, 3, 6, 9, 3, 9, 8, -1 ],
[ 5, 9, 6, 9, 0, 6, 0, 2, 6, -1 ],
[ 3, 2, 8, 8, 2, 6, 8, 6, 5, 8, 5, 1, 8, 1, 0, -1 ],
[ 1, 6, 5, 2, 6, 1, -1 ],
[ 2, 1, 10, 9, 6, 5, 9, 11, 6, 9, 8, 11, -1 ],
[ 2, 1, 10, 5, 9, 0, 5, 0, 3, 5, 3, 6, 6, 3, 11, -1 ],
[ 10, 2, 5, 5, 2, 0, 5, 0, 8, 5, 8, 11, 5, 11, 6, -1 ],
[ 10, 2, 5, 5, 2, 3, 5, 3, 11, 5, 11, 6, -1 ],
[ 5, 9, 6, 6, 9, 8, 6, 8, 3, 6, 3, 1, 6, 1, 10, -1 ],
[ 5, 9, 6, 6, 9, 0, 6, 0, 1, 6, 1, 10, -1 ],
[ 8, 3, 0, 5, 10, 6, -1 ],
[ 6, 5, 10, -1 ],
[ 6, 10, 5, -1 ],
[ 3, 8, 0, 5, 6, 10, -1 ],
[ 9, 1, 0, 10, 5, 6, -1 ],
[ 3, 8, 1, 1, 8, 9, 6, 10, 5, -1 ],
[ 6, 10, 5, 2, 11, 3, -1 ],
[ 8, 0, 11, 11, 0, 2, 5, 6, 10, -1 ],
[ 10, 5, 6, 1, 0, 9, 3, 2, 11, -1 ],
[ 5, 6, 10, 11, 1, 2, 11, 9, 1, 11, 8, 9, -1 ],
[ 2, 1, 6, 6, 1, 5, -1 ],
[ 5, 6, 1, 1, 6, 2, 8, 0, 3, -1 ],
[ 6, 9, 5, 6, 0, 9, 6, 2, 0, -1 ],
[ 8, 9, 3, 9, 5, 6, 3, 9, 6, 3, 6, 2, -1 ],
[ 3, 6, 11, 3, 5, 6, 3, 1, 5, -1 ],
[ 5, 6, 11, 5, 11, 0, 11, 8, 0, 1, 5, 0, -1 ],
[ 0, 9, 3, 3, 9, 11, 11, 9, 5, 11, 5, 6, -1 ],
[ 5, 6, 9, 6, 11, 9, 11, 8, 9, -1 ],
[ 7, 4, 8, 5, 6, 10, -1 ],
[ 0, 3, 4, 4, 3, 7, 10, 5, 6, -1 ],
[ 4, 8, 7, 9, 1, 0, 10, 5, 6, -1 ],
[ 6, 10, 5, 1, 4, 9, 1, 7, 4, 1, 3, 7, -1 ],
[ 11, 3, 2, 7, 4, 8, 5, 6, 10, -1 ],
[ 10, 5, 6, 4, 11, 7, 4, 2, 11, 4, 0, 2, -1 ],
[ 7, 4, 8, 3, 2, 11, 9, 1, 0, 10, 5, 6, -1 ],
[ 10, 5, 6, 7, 4, 9, 7, 9, 1, 7, 1, 11, 11, 1, 2, -1 ],
[ 2, 1, 6, 6, 1, 5, 8, 7, 4, -1 ],
[ 7, 4, 0, 7, 0, 3, 5, 6, 1, 6, 2, 1, -1 ],
[ 8, 7, 4, 6, 9, 5, 6, 0, 9, 6, 2, 0, -1 ],
[ 5, 6, 9, 9, 6, 2, 9, 2, 3, 9, 3, 7, 9, 7, 4, -1 ],
[ 4, 8, 7, 3, 6, 11, 3, 5, 6, 3, 1, 5, -1 ],
[ 7, 4, 11, 11, 4, 0, 11, 0, 1, 11, 1, 5, 11, 5, 6, -1 ],
[ 4, 8, 7, 11, 3, 0, 11, 0, 9, 11, 9, 6, 6, 9, 5, -1 ],
[ 5, 6, 9, 9, 6, 11, 9, 11, 7, 9, 7, 4, -1 ],
[ 9, 4, 10, 10, 4, 6, -1 ],
[ 6, 10, 4, 4, 10, 9, 3, 8, 0, -1 ],
[ 0, 10, 1, 0, 6, 10, 0, 4, 6, -1 ],
[ 3, 8, 4, 3, 4, 10, 4, 6, 10, 1, 3, 10, -1 ],
[ 9, 4, 10, 10, 4, 6, 3, 2, 11, -1 ],
[ 8, 0, 2, 8, 2, 11, 9, 4, 10, 4, 6, 10, -1 ],
[ 11, 3, 2, 0, 10, 1, 0, 6, 10, 0, 4, 6, -1 ],
[ 2, 11, 1, 1, 11, 8, 1, 8, 4, 1, 4, 6, 1, 6, 10, -1 ],
[ 4, 1, 9, 4, 2, 1, 4, 6, 2, -1 ],
[ 3, 8, 0, 4, 1, 9, 4, 2, 1, 4, 6, 2, -1 ],
[ 4, 6, 0, 0, 6, 2, -1 ],
[ 3, 8, 2, 8, 4, 2, 4, 6, 2, -1 ],
[ 3, 1, 11, 1, 9, 4, 11, 1, 4, 11, 4, 6, -1 ],
[ 9, 4, 1, 1, 4, 6, 1, 6, 11, 1, 11, 8, 1, 8, 0, -1 ],
[ 11, 3, 6, 3, 0, 6, 0, 4, 6, -1 ],
[ 8, 6, 11, 4, 6, 8, -1 ],
[ 10, 7, 6, 10, 8, 7, 10, 9, 8, -1 ],
[ 10, 9, 6, 9, 0, 3, 6, 9, 3, 6, 3, 7, -1 ],
[ 8, 7, 0, 0, 7, 1, 1, 7, 6, 1, 6, 10, -1 ],
[ 6, 10, 7, 10, 1, 7, 1, 3, 7, -1 ],
[ 3, 2, 11, 10, 7, 6, 10, 8, 7, 10, 9, 8, -1 ],
[ 6, 10, 7, 7, 10, 9, 7, 9, 0, 7, 0, 2, 7, 2, 11, -1 ],
[ 11, 3, 2, 1, 0, 8, 1, 8, 7, 1, 7, 10, 10, 7, 6, -1 ],
[ 6, 10, 7, 7, 10, 1, 7, 1, 2, 7, 2, 11, -1 ],
[ 8, 7, 6, 8, 6, 1, 6, 2, 1, 9, 8, 1, -1 ],
[ 0, 3, 9, 9, 3, 7, 9, 7, 6, 9, 6, 2, 9, 2, 1, -1 ],
[ 8, 7, 0, 7, 6, 0, 6, 2, 0, -1 ],
[ 7, 2, 3, 6, 2, 7, -1 ],
[ 11, 3, 6, 6, 3, 1, 6, 1, 9, 6, 9, 8, 6, 8, 7, -1 ],
[ 11, 7, 6, 1, 9, 0, -1 ],
[ 11, 3, 6, 6, 3, 0, 6, 0, 8, 6, 8, 7, -1 ],
[ 11, 7, 6, -1 ],
[ 10, 5, 11, 11, 5, 7, -1 ],
[ 10, 5, 11, 11, 5, 7, 0, 3, 8, -1 ],
[ 7, 11, 5, 5, 11, 10, 0, 9, 1, -1 ],
[ 3, 8, 9, 3, 9, 1, 7, 11, 5, 11, 10, 5, -1 ],
[ 5, 2, 10, 5, 3, 2, 5, 7, 3, -1 ],
[ 0, 2, 8, 2, 10, 5, 8, 2, 5, 8, 5, 7, -1 ],
[ 0, 9, 1, 5, 2, 10, 5, 3, 2, 5, 7, 3, -1 ],
[ 10, 5, 2, 2, 5, 7, 2, 7, 8, 2, 8, 9, 2, 9, 1, -1 ],
[ 1, 11, 2, 1, 7, 11, 1, 5, 7, -1 ],
[ 8, 0, 3, 1, 11, 2, 1, 7, 11, 1, 5, 7, -1 ],
[ 0, 9, 5, 0, 5, 11, 5, 7, 11, 2, 0, 11, -1 ],
[ 3, 8, 2, 2, 8, 9, 2, 9, 5, 2, 5, 7, 2, 7, 11, -1 ],
[ 5, 7, 1, 1, 7, 3, -1 ],
[ 8, 0, 7, 0, 1, 7, 1, 5, 7, -1 ],
[ 0, 9, 3, 9, 5, 3, 5, 7, 3, -1 ],
[ 9, 7, 8, 5, 7, 9, -1 ],
[ 8, 5, 4, 8, 10, 5, 8, 11, 10, -1 ],
[ 10, 5, 4, 10, 4, 3, 4, 0, 3, 11, 10, 3, -1 ],
[ 1, 0, 9, 8, 5, 4, 8, 10, 5, 8, 11, 10, -1 ],
[ 9, 1, 4, 4, 1, 3, 4, 3, 11, 4, 11, 10, 4, 10, 5, -1 ],
[ 10, 5, 2, 2, 5, 3, 3, 5, 4, 3, 4, 8, -1 ],
[ 10, 5, 2, 5, 4, 2, 4, 0, 2, -1 ],
[ 9, 1, 0, 3, 2, 10, 3, 10, 5, 3, 5, 8, 8, 5, 4, -1 ],
[ 10, 5, 2, 2, 5, 4, 2, 4, 9, 2, 9, 1, -1 ],
[ 1, 5, 2, 5, 4, 8, 2, 5, 8, 2, 8, 11, -1 ],
[ 2, 1, 11, 11, 1, 5, 11, 5, 4, 11, 4, 0, 11, 0, 3, -1 ],
[ 4, 8, 5, 5, 8, 11, 5, 11, 2, 5, 2, 0, 5, 0, 9, -1 ],
[ 5, 4, 9, 2, 3, 11, -1 ],
[ 4, 8, 5, 8, 3, 5, 3, 1, 5, -1 ],
[ 0, 5, 4, 1, 5, 0, -1 ],
[ 0, 9, 3, 3, 9, 5, 3, 5, 4, 3, 4, 8, -1 ],
[ 5, 4, 9, -1 ],
[ 11, 4, 7, 11, 9, 4, 11, 10, 9, -1 ],
[ 0, 3, 8, 11, 4, 7, 11, 9, 4, 11, 10, 9, -1 ],
[ 0, 4, 1, 4, 7, 11, 1, 4, 11, 1, 11, 10, -1 ],
[ 7, 11, 4, 4, 11, 10, 4, 10, 1, 4, 1, 3, 4, 3, 8, -1 ],
[ 9, 4, 7, 9, 7, 2, 7, 3, 2, 10, 9, 2, -1 ],
[ 8, 0, 7, 7, 0, 2, 7, 2, 10, 7, 10, 9, 7, 9, 4, -1 ],
[ 1, 0, 10, 10, 0, 4, 10, 4, 7, 10, 7, 3, 10, 3, 2, -1 ],
[ 7, 8, 4, 10, 1, 2, -1 ],
[ 9, 4, 1, 1, 4, 2, 2, 4, 7, 2, 7, 11, -1 ],
[ 8, 0, 3, 2, 1, 9, 2, 9, 4, 2, 4, 11, 11, 4, 7, -1 ],
[ 7, 11, 4, 11, 2, 4, 2, 0, 4, -1 ],
[ 3, 8, 2, 2, 8, 4, 2, 4, 7, 2, 7, 11, -1 ],
[ 9, 4, 1, 4, 7, 1, 7, 3, 1, -1 ],
[ 9, 4, 1, 1, 4, 7, 1, 7, 8, 1, 8, 0, -1 ],
[ 3, 4, 7, 0, 4, 3, -1 ],
[ 7, 8, 4, -1 ],
[ 8, 11, 9, 9, 11, 10, -1 ],
[ 0, 3, 9, 3, 11, 9, 11, 10, 9, -1 ],
[ 1, 0, 10, 0, 8, 10, 8, 11, 10, -1 ],
[ 10, 3, 11, 1, 3, 10, -1 ],
[ 3, 2, 8, 2, 10, 8, 10, 9, 8, -1 ],
[ 9, 2, 10, 0, 2, 9, -1 ],
[ 1, 0, 10, 10, 0, 8, 10, 8, 3, 10, 3, 2, -1 ],
[ 2, 10, 1, -1 ],
[ 2, 1, 11, 1, 9, 11, 9, 8, 11, -1 ],
[ 2, 1, 11, 11, 1, 9, 11, 9, 0, 11, 0, 3, -1 ],
[ 11, 0, 8, 2, 0, 11, -1 ],
[ 3, 11, 2, -1 ],
[ 1, 8, 3, 9, 8, 1, -1 ],
[ 1, 9, 0, -1 ],
[ 8, 3, 0, -1 ],
[ -1 ],
];
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