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transvoxel.cpp
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transvoxel.cpp
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//================================================================================
//
// The Transvoxel Algorithm look-up tables
//
// Copyright 2009 by Eric Lengyel
//
// The following data originates from Eric Lengyel's Transvoxel Algorithm.
// http://transvoxel.org/
//
// The data in this file may be freely used in implementations of the Transvoxel
// Algorithm. If you do use this data, or any transformation of it, in your own
// projects, commercial or otherwise, please give credit by indicating in your
// source code that the data is part of the author's implementation of the
// Transvoxel Algorithm and that it came from the web address given above.
// (Simply copying and pasting the two lines of the previous paragraph would be
// perfect.) If you distribute a commercial product with source code included,
// then the credit in the source code is required.
//
// If you distribute any kind of product that uses this data, a credit visible to
// the end-user would be appreciated, but it is not required. However, you may
// not claim that the entire implementation of the Transvoxel Algorithm is your
// own if you use the data in this file or any transformation of it.
//
// The format of the data in this file is described in the dissertation "Voxel-
// Based Terrain for Real-Time Virtual Simulations", available at the web page
// given above. References to sections and figures below pertain to that paper.
//
// The contents of this file are protected by copyright and may not be publicly
// reproduced without permission.
//
//================================================================================
// The RegularCellData structure holds information about the triangulation
// used for a single equivalence class in the modified Marching Cubes algorithm,
// described in Section 3.2.
struct RegularCellData
{
unsigned char geometryCounts; // High nibble is vertex count, low nibble is triangle count.
unsigned char vertexIndex[15]; // Groups of 3 indexes giving the triangulation.
long GetVertexCount(void) const
{
return (geometryCounts >> 4);
}
long GetTriangleCount(void) const
{
return (geometryCounts & 0x0F);
}
};
// The TransitionCellData structure holds information about the triangulation
// used for a single equivalence class in the Transvoxel Algorithm transition cell,
// described in Section 4.3.
struct TransitionCellData
{
long geometryCounts; // High nibble is vertex count, low nibble is triangle count.
unsigned char vertexIndex[36]; // Groups of 3 indexes giving the triangulation.
long GetVertexCount(void) const
{
return (geometryCounts >> 4);
}
long GetTriangleCount(void) const
{
return (geometryCounts & 0x0F);
}
};
// The regularCellClass table maps an 8-bit regular Marching Cubes case index to
// an equivalence class index. Even though there are 18 equivalence classes in our
// modified Marching Cubes algorithm, a couple of them use the same exact triangulations,
// just with different vertex locations. We combined those classes for this table so
// that the class index ranges from 0 to 15.
const unsigned char regularCellClass[256] =
{
0x00, 0x01, 0x01, 0x03, 0x01, 0x03, 0x02, 0x04, 0x01, 0x02, 0x03, 0x04, 0x03, 0x04, 0x04, 0x03,
0x01, 0x03, 0x02, 0x04, 0x02, 0x04, 0x06, 0x0C, 0x02, 0x05, 0x05, 0x0B, 0x05, 0x0A, 0x07, 0x04,
0x01, 0x02, 0x03, 0x04, 0x02, 0x05, 0x05, 0x0A, 0x02, 0x06, 0x04, 0x0C, 0x05, 0x07, 0x0B, 0x04,
0x03, 0x04, 0x04, 0x03, 0x05, 0x0B, 0x07, 0x04, 0x05, 0x07, 0x0A, 0x04, 0x08, 0x0E, 0x0E, 0x03,
0x01, 0x02, 0x02, 0x05, 0x03, 0x04, 0x05, 0x0B, 0x02, 0x06, 0x05, 0x07, 0x04, 0x0C, 0x0A, 0x04,
0x03, 0x04, 0x05, 0x0A, 0x04, 0x03, 0x07, 0x04, 0x05, 0x07, 0x08, 0x0E, 0x0B, 0x04, 0x0E, 0x03,
0x02, 0x06, 0x05, 0x07, 0x05, 0x07, 0x08, 0x0E, 0x06, 0x09, 0x07, 0x0F, 0x07, 0x0F, 0x0E, 0x0D,
0x04, 0x0C, 0x0B, 0x04, 0x0A, 0x04, 0x0E, 0x03, 0x07, 0x0F, 0x0E, 0x0D, 0x0E, 0x0D, 0x02, 0x01,
0x01, 0x02, 0x02, 0x05, 0x02, 0x05, 0x06, 0x07, 0x03, 0x05, 0x04, 0x0A, 0x04, 0x0B, 0x0C, 0x04,
0x02, 0x05, 0x06, 0x07, 0x06, 0x07, 0x09, 0x0F, 0x05, 0x08, 0x07, 0x0E, 0x07, 0x0E, 0x0F, 0x0D,
0x03, 0x05, 0x04, 0x0B, 0x05, 0x08, 0x07, 0x0E, 0x04, 0x07, 0x03, 0x04, 0x0A, 0x0E, 0x04, 0x03,
0x04, 0x0A, 0x0C, 0x04, 0x07, 0x0E, 0x0F, 0x0D, 0x0B, 0x0E, 0x04, 0x03, 0x0E, 0x02, 0x0D, 0x01,
0x03, 0x05, 0x05, 0x08, 0x04, 0x0A, 0x07, 0x0E, 0x04, 0x07, 0x0B, 0x0E, 0x03, 0x04, 0x04, 0x03,
0x04, 0x0B, 0x07, 0x0E, 0x0C, 0x04, 0x0F, 0x0D, 0x0A, 0x0E, 0x0E, 0x02, 0x04, 0x03, 0x0D, 0x01,
0x04, 0x07, 0x0A, 0x0E, 0x0B, 0x0E, 0x0E, 0x02, 0x0C, 0x0F, 0x04, 0x0D, 0x04, 0x0D, 0x03, 0x01,
0x03, 0x04, 0x04, 0x03, 0x04, 0x03, 0x0D, 0x01, 0x04, 0x0D, 0x03, 0x01, 0x03, 0x01, 0x01, 0x00
};
// The regularCellData table holds the triangulation data for all 16 distinct classes to
// which a case can be mapped by the regularCellClass table.
const RegularCellData regularCellData[16] =
{
{0x00, {}},
{0x31, {0, 1, 2}},
{0x62, {0, 1, 2, 3, 4, 5}},
{0x42, {0, 1, 2, 0, 2, 3}},
{0x53, {0, 1, 4, 1, 3, 4, 1, 2, 3}},
{0x73, {0, 1, 2, 0, 2, 3, 4, 5, 6}},
{0x93, {0, 1, 2, 3, 4, 5, 6, 7, 8}},
{0x84, {0, 1, 4, 1, 3, 4, 1, 2, 3, 5, 6, 7}},
{0x84, {0, 1, 2, 0, 2, 3, 4, 5, 6, 4, 6, 7}},
{0xC4, {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}},
{0x64, {0, 4, 5, 0, 1, 4, 1, 3, 4, 1, 2, 3}},
{0x64, {0, 5, 4, 0, 4, 1, 1, 4, 3, 1, 3, 2}},
{0x64, {0, 4, 5, 0, 3, 4, 0, 1, 3, 1, 2, 3}},
{0x64, {0, 1, 2, 0, 2, 3, 0, 3, 4, 0, 4, 5}},
{0x75, {0, 1, 2, 0, 2, 3, 0, 3, 4, 0, 4, 5, 0, 5, 6}},
{0x95, {0, 4, 5, 0, 3, 4, 0, 1, 3, 1, 2, 3, 6, 7, 8}}
};
// The regularVertexData table gives the vertex locations for every one of the 256 possible
// cases in the modified Marching Cubes algorithm. Each 16-bit value also provides information
// about whether a vertex can be reused from a neighboring cell. See Section 3.3 for details.
// The low byte contains the indexes for the two endpoints of the edge on which the vertex lies,
// as numbered in Figure 3.7. The high byte contains the vertex reuse data shown in Figure 3.8.
const unsigned short regularVertexData[256][12] =
{
{},
{0x6201, 0x5102, 0x3304},
{0x6201, 0x2315, 0x4113},
{0x5102, 0x3304, 0x2315, 0x4113},
{0x5102, 0x4223, 0x1326},
{0x3304, 0x6201, 0x4223, 0x1326},
{0x6201, 0x2315, 0x4113, 0x5102, 0x4223, 0x1326},
{0x4223, 0x1326, 0x3304, 0x2315, 0x4113},
{0x4113, 0x8337, 0x4223},
{0x6201, 0x5102, 0x3304, 0x4223, 0x4113, 0x8337},
{0x6201, 0x2315, 0x8337, 0x4223},
{0x5102, 0x3304, 0x2315, 0x8337, 0x4223},
{0x5102, 0x4113, 0x8337, 0x1326},
{0x4113, 0x8337, 0x1326, 0x3304, 0x6201},
{0x6201, 0x2315, 0x8337, 0x1326, 0x5102},
{0x3304, 0x2315, 0x8337, 0x1326},
{0x3304, 0x1146, 0x2245},
{0x6201, 0x5102, 0x1146, 0x2245},
{0x6201, 0x2315, 0x4113, 0x3304, 0x1146, 0x2245},
{0x2315, 0x4113, 0x5102, 0x1146, 0x2245},
{0x5102, 0x4223, 0x1326, 0x3304, 0x1146, 0x2245},
{0x1146, 0x2245, 0x6201, 0x4223, 0x1326},
{0x3304, 0x1146, 0x2245, 0x6201, 0x2315, 0x4113, 0x5102, 0x4223, 0x1326},
{0x4223, 0x1326, 0x1146, 0x2245, 0x2315, 0x4113},
{0x4223, 0x4113, 0x8337, 0x3304, 0x1146, 0x2245},
{0x6201, 0x5102, 0x1146, 0x2245, 0x4223, 0x4113, 0x8337},
{0x4223, 0x6201, 0x2315, 0x8337, 0x3304, 0x1146, 0x2245},
{0x4223, 0x8337, 0x2315, 0x2245, 0x1146, 0x5102},
{0x5102, 0x4113, 0x8337, 0x1326, 0x3304, 0x1146, 0x2245},
{0x4113, 0x8337, 0x1326, 0x1146, 0x2245, 0x6201},
{0x6201, 0x2315, 0x8337, 0x1326, 0x5102, 0x3304, 0x1146, 0x2245},
{0x2245, 0x2315, 0x8337, 0x1326, 0x1146},
{0x2315, 0x2245, 0x8157},
{0x6201, 0x5102, 0x3304, 0x2315, 0x2245, 0x8157},
{0x4113, 0x6201, 0x2245, 0x8157},
{0x2245, 0x8157, 0x4113, 0x5102, 0x3304},
{0x5102, 0x4223, 0x1326, 0x2315, 0x2245, 0x8157},
{0x6201, 0x4223, 0x1326, 0x3304, 0x2315, 0x2245, 0x8157},
{0x6201, 0x2245, 0x8157, 0x4113, 0x5102, 0x4223, 0x1326},
{0x4223, 0x1326, 0x3304, 0x2245, 0x8157, 0x4113},
{0x4223, 0x4113, 0x8337, 0x2315, 0x2245, 0x8157},
{0x6201, 0x5102, 0x3304, 0x4223, 0x4113, 0x8337, 0x2315, 0x2245, 0x8157},
{0x8337, 0x4223, 0x6201, 0x2245, 0x8157},
{0x5102, 0x3304, 0x2245, 0x8157, 0x8337, 0x4223},
{0x5102, 0x4113, 0x8337, 0x1326, 0x2315, 0x2245, 0x8157},
{0x4113, 0x8337, 0x1326, 0x3304, 0x6201, 0x2315, 0x2245, 0x8157},
{0x5102, 0x1326, 0x8337, 0x8157, 0x2245, 0x6201},
{0x8157, 0x8337, 0x1326, 0x3304, 0x2245},
{0x2315, 0x3304, 0x1146, 0x8157},
{0x6201, 0x5102, 0x1146, 0x8157, 0x2315},
{0x3304, 0x1146, 0x8157, 0x4113, 0x6201},
{0x4113, 0x5102, 0x1146, 0x8157},
{0x2315, 0x3304, 0x1146, 0x8157, 0x5102, 0x4223, 0x1326},
{0x1326, 0x4223, 0x6201, 0x2315, 0x8157, 0x1146},
{0x3304, 0x1146, 0x8157, 0x4113, 0x6201, 0x5102, 0x4223, 0x1326},
{0x1326, 0x1146, 0x8157, 0x4113, 0x4223},
{0x2315, 0x3304, 0x1146, 0x8157, 0x4223, 0x4113, 0x8337},
{0x6201, 0x5102, 0x1146, 0x8157, 0x2315, 0x4223, 0x4113, 0x8337},
{0x3304, 0x1146, 0x8157, 0x8337, 0x4223, 0x6201},
{0x4223, 0x5102, 0x1146, 0x8157, 0x8337},
{0x2315, 0x3304, 0x1146, 0x8157, 0x5102, 0x4113, 0x8337, 0x1326},
{0x6201, 0x4113, 0x8337, 0x1326, 0x1146, 0x8157, 0x2315},
{0x6201, 0x3304, 0x1146, 0x8157, 0x8337, 0x1326, 0x5102},
{0x1326, 0x1146, 0x8157, 0x8337},
{0x1326, 0x8267, 0x1146},
{0x6201, 0x5102, 0x3304, 0x1326, 0x8267, 0x1146},
{0x6201, 0x2315, 0x4113, 0x1326, 0x8267, 0x1146},
{0x5102, 0x3304, 0x2315, 0x4113, 0x1326, 0x8267, 0x1146},
{0x5102, 0x4223, 0x8267, 0x1146},
{0x3304, 0x6201, 0x4223, 0x8267, 0x1146},
{0x5102, 0x4223, 0x8267, 0x1146, 0x6201, 0x2315, 0x4113},
{0x1146, 0x8267, 0x4223, 0x4113, 0x2315, 0x3304},
{0x4113, 0x8337, 0x4223, 0x1326, 0x8267, 0x1146},
{0x6201, 0x5102, 0x3304, 0x4223, 0x4113, 0x8337, 0x1326, 0x8267, 0x1146},
{0x6201, 0x2315, 0x8337, 0x4223, 0x1326, 0x8267, 0x1146},
{0x5102, 0x3304, 0x2315, 0x8337, 0x4223, 0x1326, 0x8267, 0x1146},
{0x8267, 0x1146, 0x5102, 0x4113, 0x8337},
{0x6201, 0x4113, 0x8337, 0x8267, 0x1146, 0x3304},
{0x6201, 0x2315, 0x8337, 0x8267, 0x1146, 0x5102},
{0x1146, 0x3304, 0x2315, 0x8337, 0x8267},
{0x3304, 0x1326, 0x8267, 0x2245},
{0x1326, 0x8267, 0x2245, 0x6201, 0x5102},
{0x3304, 0x1326, 0x8267, 0x2245, 0x6201, 0x2315, 0x4113},
{0x1326, 0x8267, 0x2245, 0x2315, 0x4113, 0x5102},
{0x5102, 0x4223, 0x8267, 0x2245, 0x3304},
{0x6201, 0x4223, 0x8267, 0x2245},
{0x5102, 0x4223, 0x8267, 0x2245, 0x3304, 0x6201, 0x2315, 0x4113},
{0x4113, 0x4223, 0x8267, 0x2245, 0x2315},
{0x3304, 0x1326, 0x8267, 0x2245, 0x4223, 0x4113, 0x8337},
{0x1326, 0x8267, 0x2245, 0x6201, 0x5102, 0x4223, 0x4113, 0x8337},
{0x3304, 0x1326, 0x8267, 0x2245, 0x4223, 0x6201, 0x2315, 0x8337},
{0x5102, 0x1326, 0x8267, 0x2245, 0x2315, 0x8337, 0x4223},
{0x3304, 0x2245, 0x8267, 0x8337, 0x4113, 0x5102},
{0x8337, 0x8267, 0x2245, 0x6201, 0x4113},
{0x5102, 0x6201, 0x2315, 0x8337, 0x8267, 0x2245, 0x3304},
{0x2315, 0x8337, 0x8267, 0x2245},
{0x2315, 0x2245, 0x8157, 0x1326, 0x8267, 0x1146},
{0x6201, 0x5102, 0x3304, 0x2315, 0x2245, 0x8157, 0x1326, 0x8267, 0x1146},
{0x6201, 0x2245, 0x8157, 0x4113, 0x1326, 0x8267, 0x1146},
{0x2245, 0x8157, 0x4113, 0x5102, 0x3304, 0x1326, 0x8267, 0x1146},
{0x4223, 0x8267, 0x1146, 0x5102, 0x2315, 0x2245, 0x8157},
{0x3304, 0x6201, 0x4223, 0x8267, 0x1146, 0x2315, 0x2245, 0x8157},
{0x4223, 0x8267, 0x1146, 0x5102, 0x6201, 0x2245, 0x8157, 0x4113},
{0x3304, 0x2245, 0x8157, 0x4113, 0x4223, 0x8267, 0x1146},
{0x4223, 0x4113, 0x8337, 0x2315, 0x2245, 0x8157, 0x1326, 0x8267, 0x1146},
{0x6201, 0x5102, 0x3304, 0x4223, 0x4113, 0x8337, 0x2315, 0x2245, 0x8157, 0x1326, 0x8267, 0x1146},
{0x8337, 0x4223, 0x6201, 0x2245, 0x8157, 0x1326, 0x8267, 0x1146},
{0x4223, 0x5102, 0x3304, 0x2245, 0x8157, 0x8337, 0x1326, 0x8267, 0x1146},
{0x8267, 0x1146, 0x5102, 0x4113, 0x8337, 0x2315, 0x2245, 0x8157},
{0x6201, 0x4113, 0x8337, 0x8267, 0x1146, 0x3304, 0x2315, 0x2245, 0x8157},
{0x8337, 0x8267, 0x1146, 0x5102, 0x6201, 0x2245, 0x8157},
{0x3304, 0x2245, 0x8157, 0x8337, 0x8267, 0x1146},
{0x8157, 0x2315, 0x3304, 0x1326, 0x8267},
{0x8267, 0x8157, 0x2315, 0x6201, 0x5102, 0x1326},
{0x8267, 0x1326, 0x3304, 0x6201, 0x4113, 0x8157},
{0x8267, 0x8157, 0x4113, 0x5102, 0x1326},
{0x5102, 0x4223, 0x8267, 0x8157, 0x2315, 0x3304},
{0x2315, 0x6201, 0x4223, 0x8267, 0x8157},
{0x3304, 0x5102, 0x4223, 0x8267, 0x8157, 0x4113, 0x6201},
{0x4113, 0x4223, 0x8267, 0x8157},
{0x8157, 0x2315, 0x3304, 0x1326, 0x8267, 0x4223, 0x4113, 0x8337},
{0x8157, 0x2315, 0x6201, 0x5102, 0x1326, 0x8267, 0x4223, 0x4113, 0x8337},
{0x8157, 0x8337, 0x4223, 0x6201, 0x3304, 0x1326, 0x8267},
{0x5102, 0x1326, 0x8267, 0x8157, 0x8337, 0x4223},
{0x8267, 0x8157, 0x2315, 0x3304, 0x5102, 0x4113, 0x8337},
{0x6201, 0x4113, 0x8337, 0x8267, 0x8157, 0x2315},
{0x6201, 0x3304, 0x5102, 0x8337, 0x8267, 0x8157},
{0x8337, 0x8267, 0x8157},
{0x8337, 0x8157, 0x8267},
{0x6201, 0x5102, 0x3304, 0x8337, 0x8157, 0x8267},
{0x6201, 0x2315, 0x4113, 0x8337, 0x8157, 0x8267},
{0x5102, 0x3304, 0x2315, 0x4113, 0x8337, 0x8157, 0x8267},
{0x5102, 0x4223, 0x1326, 0x8337, 0x8157, 0x8267},
{0x6201, 0x4223, 0x1326, 0x3304, 0x8337, 0x8157, 0x8267},
{0x6201, 0x2315, 0x4113, 0x5102, 0x4223, 0x1326, 0x8337, 0x8157, 0x8267},
{0x4223, 0x1326, 0x3304, 0x2315, 0x4113, 0x8337, 0x8157, 0x8267},
{0x4113, 0x8157, 0x8267, 0x4223},
{0x4223, 0x4113, 0x8157, 0x8267, 0x6201, 0x5102, 0x3304},
{0x8157, 0x8267, 0x4223, 0x6201, 0x2315},
{0x3304, 0x2315, 0x8157, 0x8267, 0x4223, 0x5102},
{0x1326, 0x5102, 0x4113, 0x8157, 0x8267},
{0x8157, 0x4113, 0x6201, 0x3304, 0x1326, 0x8267},
{0x1326, 0x5102, 0x6201, 0x2315, 0x8157, 0x8267},
{0x8267, 0x1326, 0x3304, 0x2315, 0x8157},
{0x3304, 0x1146, 0x2245, 0x8337, 0x8157, 0x8267},
{0x6201, 0x5102, 0x1146, 0x2245, 0x8337, 0x8157, 0x8267},
{0x6201, 0x2315, 0x4113, 0x3304, 0x1146, 0x2245, 0x8337, 0x8157, 0x8267},
{0x2315, 0x4113, 0x5102, 0x1146, 0x2245, 0x8337, 0x8157, 0x8267},
{0x5102, 0x4223, 0x1326, 0x3304, 0x1146, 0x2245, 0x8337, 0x8157, 0x8267},
{0x1146, 0x2245, 0x6201, 0x4223, 0x1326, 0x8337, 0x8157, 0x8267},
{0x6201, 0x2315, 0x4113, 0x5102, 0x4223, 0x1326, 0x3304, 0x1146, 0x2245, 0x8337, 0x8157, 0x8267},
{0x4113, 0x4223, 0x1326, 0x1146, 0x2245, 0x2315, 0x8337, 0x8157, 0x8267},
{0x4223, 0x4113, 0x8157, 0x8267, 0x3304, 0x1146, 0x2245},
{0x6201, 0x5102, 0x1146, 0x2245, 0x4223, 0x4113, 0x8157, 0x8267},
{0x8157, 0x8267, 0x4223, 0x6201, 0x2315, 0x3304, 0x1146, 0x2245},
{0x2315, 0x8157, 0x8267, 0x4223, 0x5102, 0x1146, 0x2245},
{0x1326, 0x5102, 0x4113, 0x8157, 0x8267, 0x3304, 0x1146, 0x2245},
{0x1326, 0x1146, 0x2245, 0x6201, 0x4113, 0x8157, 0x8267},
{0x5102, 0x6201, 0x2315, 0x8157, 0x8267, 0x1326, 0x3304, 0x1146, 0x2245},
{0x1326, 0x1146, 0x2245, 0x2315, 0x8157, 0x8267},
{0x2315, 0x2245, 0x8267, 0x8337},
{0x2315, 0x2245, 0x8267, 0x8337, 0x6201, 0x5102, 0x3304},
{0x4113, 0x6201, 0x2245, 0x8267, 0x8337},
{0x5102, 0x4113, 0x8337, 0x8267, 0x2245, 0x3304},
{0x2315, 0x2245, 0x8267, 0x8337, 0x5102, 0x4223, 0x1326},
{0x6201, 0x4223, 0x1326, 0x3304, 0x8337, 0x2315, 0x2245, 0x8267},
{0x4113, 0x6201, 0x2245, 0x8267, 0x8337, 0x5102, 0x4223, 0x1326},
{0x4113, 0x4223, 0x1326, 0x3304, 0x2245, 0x8267, 0x8337},
{0x2315, 0x2245, 0x8267, 0x4223, 0x4113},
{0x2315, 0x2245, 0x8267, 0x4223, 0x4113, 0x6201, 0x5102, 0x3304},
{0x6201, 0x2245, 0x8267, 0x4223},
{0x3304, 0x2245, 0x8267, 0x4223, 0x5102},
{0x5102, 0x4113, 0x2315, 0x2245, 0x8267, 0x1326},
{0x4113, 0x2315, 0x2245, 0x8267, 0x1326, 0x3304, 0x6201},
{0x5102, 0x6201, 0x2245, 0x8267, 0x1326},
{0x3304, 0x2245, 0x8267, 0x1326},
{0x8267, 0x8337, 0x2315, 0x3304, 0x1146},
{0x5102, 0x1146, 0x8267, 0x8337, 0x2315, 0x6201},
{0x3304, 0x1146, 0x8267, 0x8337, 0x4113, 0x6201},
{0x8337, 0x4113, 0x5102, 0x1146, 0x8267},
{0x8267, 0x8337, 0x2315, 0x3304, 0x1146, 0x5102, 0x4223, 0x1326},
{0x1146, 0x8267, 0x8337, 0x2315, 0x6201, 0x4223, 0x1326},
{0x8267, 0x8337, 0x4113, 0x6201, 0x3304, 0x1146, 0x5102, 0x4223, 0x1326},
{0x4113, 0x4223, 0x1326, 0x1146, 0x8267, 0x8337},
{0x3304, 0x2315, 0x4113, 0x4223, 0x8267, 0x1146},
{0x2315, 0x6201, 0x5102, 0x1146, 0x8267, 0x4223, 0x4113},
{0x1146, 0x8267, 0x4223, 0x6201, 0x3304},
{0x5102, 0x1146, 0x8267, 0x4223},
{0x8267, 0x1326, 0x5102, 0x4113, 0x2315, 0x3304, 0x1146},
{0x6201, 0x4113, 0x2315, 0x1326, 0x1146, 0x8267},
{0x6201, 0x3304, 0x1146, 0x8267, 0x1326, 0x5102},
{0x1326, 0x1146, 0x8267},
{0x1326, 0x8337, 0x8157, 0x1146},
{0x8337, 0x8157, 0x1146, 0x1326, 0x6201, 0x5102, 0x3304},
{0x8337, 0x8157, 0x1146, 0x1326, 0x6201, 0x2315, 0x4113},
{0x4113, 0x5102, 0x3304, 0x2315, 0x1326, 0x8337, 0x8157, 0x1146},
{0x8337, 0x8157, 0x1146, 0x5102, 0x4223},
{0x6201, 0x4223, 0x8337, 0x8157, 0x1146, 0x3304},
{0x8337, 0x8157, 0x1146, 0x5102, 0x4223, 0x6201, 0x2315, 0x4113},
{0x4223, 0x8337, 0x8157, 0x1146, 0x3304, 0x2315, 0x4113},
{0x4223, 0x4113, 0x8157, 0x1146, 0x1326},
{0x4223, 0x4113, 0x8157, 0x1146, 0x1326, 0x6201, 0x5102, 0x3304},
{0x1146, 0x8157, 0x2315, 0x6201, 0x4223, 0x1326},
{0x4223, 0x5102, 0x3304, 0x2315, 0x8157, 0x1146, 0x1326},
{0x4113, 0x8157, 0x1146, 0x5102},
{0x6201, 0x4113, 0x8157, 0x1146, 0x3304},
{0x2315, 0x8157, 0x1146, 0x5102, 0x6201},
{0x2315, 0x8157, 0x1146, 0x3304},
{0x2245, 0x3304, 0x1326, 0x8337, 0x8157},
{0x6201, 0x2245, 0x8157, 0x8337, 0x1326, 0x5102},
{0x2245, 0x3304, 0x1326, 0x8337, 0x8157, 0x6201, 0x2315, 0x4113},
{0x2245, 0x2315, 0x4113, 0x5102, 0x1326, 0x8337, 0x8157},
{0x4223, 0x8337, 0x8157, 0x2245, 0x3304, 0x5102},
{0x8157, 0x2245, 0x6201, 0x4223, 0x8337},
{0x2245, 0x3304, 0x5102, 0x4223, 0x8337, 0x8157, 0x4113, 0x6201, 0x2315},
{0x4223, 0x8337, 0x8157, 0x2245, 0x2315, 0x4113},
{0x4113, 0x8157, 0x2245, 0x3304, 0x1326, 0x4223},
{0x1326, 0x4223, 0x4113, 0x8157, 0x2245, 0x6201, 0x5102},
{0x8157, 0x2245, 0x3304, 0x1326, 0x4223, 0x6201, 0x2315},
{0x5102, 0x1326, 0x4223, 0x2315, 0x8157, 0x2245},
{0x3304, 0x5102, 0x4113, 0x8157, 0x2245},
{0x4113, 0x8157, 0x2245, 0x6201},
{0x5102, 0x6201, 0x2315, 0x8157, 0x2245, 0x3304},
{0x2315, 0x8157, 0x2245},
{0x1146, 0x1326, 0x8337, 0x2315, 0x2245},
{0x1146, 0x1326, 0x8337, 0x2315, 0x2245, 0x6201, 0x5102, 0x3304},
{0x6201, 0x2245, 0x1146, 0x1326, 0x8337, 0x4113},
{0x2245, 0x1146, 0x1326, 0x8337, 0x4113, 0x5102, 0x3304},
{0x5102, 0x1146, 0x2245, 0x2315, 0x8337, 0x4223},
{0x1146, 0x3304, 0x6201, 0x4223, 0x8337, 0x2315, 0x2245},
{0x8337, 0x4113, 0x6201, 0x2245, 0x1146, 0x5102, 0x4223},
{0x4223, 0x8337, 0x4113, 0x3304, 0x2245, 0x1146},
{0x4113, 0x2315, 0x2245, 0x1146, 0x1326, 0x4223},
{0x1146, 0x1326, 0x4223, 0x4113, 0x2315, 0x2245, 0x6201, 0x5102, 0x3304},
{0x1326, 0x4223, 0x6201, 0x2245, 0x1146},
{0x4223, 0x5102, 0x3304, 0x2245, 0x1146, 0x1326},
{0x2245, 0x1146, 0x5102, 0x4113, 0x2315},
{0x4113, 0x2315, 0x2245, 0x1146, 0x3304, 0x6201},
{0x6201, 0x2245, 0x1146, 0x5102},
{0x3304, 0x2245, 0x1146},
{0x3304, 0x1326, 0x8337, 0x2315},
{0x5102, 0x1326, 0x8337, 0x2315, 0x6201},
{0x6201, 0x3304, 0x1326, 0x8337, 0x4113},
{0x5102, 0x1326, 0x8337, 0x4113},
{0x4223, 0x8337, 0x2315, 0x3304, 0x5102},
{0x6201, 0x4223, 0x8337, 0x2315},
{0x3304, 0x5102, 0x4223, 0x8337, 0x4113, 0x6201},
{0x4113, 0x4223, 0x8337},
{0x4113, 0x2315, 0x3304, 0x1326, 0x4223},
{0x1326, 0x4223, 0x4113, 0x2315, 0x6201, 0x5102},
{0x3304, 0x1326, 0x4223, 0x6201},
{0x5102, 0x1326, 0x4223},
{0x5102, 0x4113, 0x2315, 0x3304},
{0x6201, 0x4113, 0x2315},
{0x6201, 0x3304, 0x5102},
{}
};
// The transitionCellClass table maps a 9-bit transition cell case index to an equivalence
// class index. Even though there are 73 equivalence classes in the Transvoxel Algorithm,
// several of them use the same exact triangulations, just with different vertex locations.
// We combined those classes for this table so that the class index ranges from 0 to 55.
// The high bit is set in the cases for which the inverse state of the voxel data maps to
// the equivalence class, meaning that the winding order of each triangle should be reversed.
const unsigned char transitionCellClass[512] =
{
0x00, 0x01, 0x02, 0x84, 0x01, 0x05, 0x04, 0x04, 0x02, 0x87, 0x09, 0x8C, 0x84, 0x0B, 0x05, 0x05,
0x01, 0x08, 0x07, 0x8D, 0x05, 0x0F, 0x8B, 0x0B, 0x04, 0x0D, 0x0C, 0x1C, 0x04, 0x8B, 0x85, 0x85,
0x02, 0x07, 0x09, 0x8C, 0x87, 0x10, 0x0C, 0x0C, 0x09, 0x12, 0x15, 0x9A, 0x8C, 0x19, 0x90, 0x10,
0x84, 0x8D, 0x8C, 0x9C, 0x0B, 0x9D, 0x0F, 0x0F, 0x05, 0x1B, 0x10, 0xAC, 0x05, 0x0F, 0x8B, 0x0B,
0x01, 0x05, 0x87, 0x0B, 0x08, 0x0F, 0x0D, 0x8B, 0x07, 0x10, 0x12, 0x19, 0x8D, 0x9D, 0x1B, 0x0F,
0x05, 0x0F, 0x10, 0x9D, 0x0F, 0x1E, 0x1D, 0xA1, 0x8B, 0x1D, 0x99, 0x32, 0x0B, 0xA1, 0x8F, 0x94,
0x04, 0x8B, 0x0C, 0x0F, 0x0D, 0x1D, 0x1C, 0x8F, 0x0C, 0x99, 0x1A, 0x31, 0x1C, 0x32, 0x2C, 0xA7,
0x04, 0x0B, 0x0C, 0x0F, 0x8B, 0xA1, 0x8F, 0x96, 0x85, 0x8F, 0x90, 0x27, 0x85, 0x94, 0x8B, 0x8A,
0x02, 0x04, 0x09, 0x05, 0x07, 0x8B, 0x0C, 0x85, 0x09, 0x0C, 0x15, 0x90, 0x8C, 0x0F, 0x10, 0x8B,
0x87, 0x0D, 0x12, 0x1B, 0x10, 0x1D, 0x99, 0x8F, 0x0C, 0x1C, 0x1A, 0x2C, 0x0C, 0x8F, 0x90, 0x8B,
0x09, 0x0C, 0x15, 0x10, 0x12, 0x99, 0x1A, 0x90, 0x15, 0x1A, 0x23, 0x30, 0x9A, 0x31, 0x30, 0x19,
0x8C, 0x1C, 0x9A, 0xAC, 0x19, 0x32, 0x31, 0x27, 0x90, 0x2C, 0x30, 0x29, 0x10, 0xA7, 0x19, 0x24,
0x84, 0x04, 0x8C, 0x05, 0x8D, 0x0B, 0x1C, 0x85, 0x8C, 0x0C, 0x9A, 0x10, 0x9C, 0x0F, 0xAC, 0x0B,
0x0B, 0x8B, 0x19, 0x0F, 0x9D, 0xA1, 0x32, 0x94, 0x0F, 0x8F, 0x31, 0xA7, 0x0F, 0x96, 0x27, 0x8A,
0x05, 0x85, 0x90, 0x8B, 0x1B, 0x8F, 0x2C, 0x8B, 0x10, 0x90, 0x30, 0x19, 0xAC, 0x27, 0x29, 0x24,
0x05, 0x85, 0x10, 0x0B, 0x0F, 0x94, 0xA7, 0x8A, 0x8B, 0x8B, 0x19, 0x24, 0x0B, 0x8A, 0x24, 0x83,
0x03, 0x06, 0x0A, 0x8B, 0x06, 0x0E, 0x0B, 0x0B, 0x0A, 0x91, 0x14, 0x8F, 0x8B, 0x17, 0x05, 0x85,
0x06, 0x13, 0x11, 0x98, 0x0E, 0x1F, 0x97, 0x2B, 0x0B, 0x18, 0x0F, 0x36, 0x0B, 0xAB, 0x05, 0x85,
0x0A, 0x11, 0x16, 0x8F, 0x91, 0x20, 0x0F, 0x8F, 0x14, 0x22, 0x21, 0x1D, 0x8F, 0x2D, 0x0B, 0x8B,
0x8B, 0x98, 0x8F, 0xB7, 0x17, 0xAE, 0x8C, 0x0C, 0x05, 0x2F, 0x8B, 0xB5, 0x85, 0xA6, 0x84, 0x04,
0x06, 0x0E, 0x91, 0x17, 0x13, 0x1F, 0x18, 0xAB, 0x11, 0x20, 0x22, 0x2D, 0x98, 0xAE, 0x2F, 0xA6,
0x0E, 0x1F, 0x20, 0xAE, 0x1F, 0x33, 0x2E, 0x2A, 0x97, 0x2E, 0xAD, 0x28, 0x2B, 0x2A, 0x26, 0x25,
0x0B, 0x97, 0x0F, 0x8C, 0x18, 0x2E, 0x37, 0x8C, 0x0F, 0xAD, 0x9D, 0x90, 0x36, 0x28, 0x35, 0x07,
0x0B, 0x2B, 0x8F, 0x0C, 0xAB, 0x2A, 0x8C, 0x89, 0x05, 0x26, 0x0B, 0x87, 0x85, 0x25, 0x84, 0x82,
0x0A, 0x0B, 0x14, 0x05, 0x11, 0x97, 0x0F, 0x05, 0x16, 0x0F, 0x21, 0x0B, 0x8F, 0x8C, 0x8B, 0x84,
0x91, 0x18, 0x22, 0x2F, 0x20, 0x2E, 0xAD, 0x26, 0x0F, 0x37, 0x9D, 0x35, 0x8F, 0x8C, 0x0B, 0x84,
0x14, 0x0F, 0x21, 0x8B, 0x22, 0xAD, 0x9D, 0x0B, 0x21, 0x9D, 0x9E, 0x8F, 0x1D, 0x90, 0x8F, 0x85,
0x8F, 0x36, 0x1D, 0xB5, 0x2D, 0x28, 0x90, 0x87, 0x0B, 0x35, 0x8F, 0x34, 0x8B, 0x07, 0x85, 0x81,
0x8B, 0x0B, 0x8F, 0x85, 0x98, 0x2B, 0x36, 0x85, 0x8F, 0x8F, 0x1D, 0x8B, 0xB7, 0x0C, 0xB5, 0x04,
0x17, 0xAB, 0x2D, 0xA6, 0xAE, 0x2A, 0x28, 0x25, 0x8C, 0x8C, 0x90, 0x07, 0x0C, 0x89, 0x87, 0x82,
0x05, 0x05, 0x0B, 0x84, 0x2F, 0x26, 0x35, 0x84, 0x8B, 0x0B, 0x8F, 0x85, 0xB5, 0x87, 0x34, 0x81,
0x85, 0x85, 0x8B, 0x04, 0xA6, 0x25, 0x07, 0x82, 0x84, 0x84, 0x85, 0x81, 0x04, 0x82, 0x81, 0x80
};
// The transitionCellData table holds the triangulation data for all 56 distinct classes to
// which a case can be mapped by the transitionCellClass table. The class index should be ANDed
// with 0x7F before using it to look up triangulation data in this table.
const TransitionCellData transitionCellData[56] =
{
{0x00, {}},
{0x42, {0, 1, 3, 1, 2, 3}},
{0x31, {0, 1, 2}},
{0x42, {0, 1, 2, 0, 2, 3}},
{0x53, {0, 1, 4, 1, 3, 4, 1, 2, 3}},
{0x64, {0, 1, 5, 1, 2, 5, 2, 4, 5, 2, 3, 4}},
{0x84, {0, 1, 3, 1, 2, 3, 4, 5, 6, 4, 6, 7}},
{0x73, {0, 1, 3, 1, 2, 3, 4, 5, 6}},
{0x84, {0, 1, 3, 1, 2, 3, 4, 5, 7, 5, 6, 7}},
{0x62, {0, 1, 2, 3, 4, 5}},
{0x53, {0, 1, 3, 0, 3, 4, 1, 2, 3}},
{0x75, {0, 1, 6, 1, 2, 6, 2, 5, 6, 2, 3, 5, 3, 4, 5}},
{0x84, {0, 1, 4, 1, 3, 4, 1, 2, 3, 5, 6, 7}},
{0x95, {0, 1, 4, 1, 3, 4, 1, 2, 3, 5, 6, 8, 6, 7, 8}},
{0xA6, {0, 1, 5, 1, 2, 5, 2, 4, 5, 2, 3, 4, 6, 7, 8, 6, 8, 9}},
{0x86, {0, 1, 7, 1, 2, 7, 2, 3, 7, 3, 6, 7, 3, 4, 6, 4, 5, 6}},
{0x95, {0, 1, 5, 1, 2, 5, 2, 4, 5, 2, 3, 4, 6, 7, 8}},
{0x95, {0, 1, 3, 1, 2, 3, 4, 5, 7, 4, 7, 8, 5, 6, 7}},
{0xA4, {0, 1, 3, 1, 2, 3, 4, 5, 6, 7, 8, 9}},
{0xC6, {0, 1, 3, 1, 2, 3, 4, 5, 7, 5, 6, 7, 8, 9, 10, 8, 10, 11}},
{0x64, {0, 1, 3, 1, 2, 3, 0, 3, 4, 0, 4, 5}},
{0x93, {0, 1, 2, 3, 4, 5, 6, 7, 8}},
{0x64, {0, 1, 4, 0, 4, 5, 1, 3, 4, 1, 2, 3}},
{0x97, {0, 1, 8, 1, 7, 8, 1, 2, 7, 2, 3, 7, 3, 4, 7, 4, 5, 7, 5, 6, 7}},
{0xB7, {0, 1, 6, 1, 2, 6, 2, 5, 6, 2, 3, 5, 3, 4, 5, 7, 8, 10, 8, 9, 10}},
{0xA6, {0, 1, 6, 1, 2, 6, 2, 5, 6, 2, 3, 5, 3, 4, 5, 7, 8, 9}},
{0xB5, {0, 1, 4, 1, 3, 4, 1, 2, 3, 5, 6, 7, 8, 9, 10}},
{0xA6, {0, 1, 5, 1, 2, 5, 2, 4, 5, 2, 3, 4, 6, 7, 9, 7, 8, 9}},
{0xA6, {0, 1, 4, 1, 3, 4, 1, 2, 3, 5, 6, 9, 6, 8, 9, 6, 7, 8}},
{0x97, {0, 1, 8, 1, 2, 8, 2, 3, 8, 3, 7, 8, 3, 4, 7, 4, 5, 7, 5, 6, 7}},
{0x86, {0, 1, 7, 1, 6, 7, 1, 2, 6, 2, 5, 6, 2, 4, 5, 2, 3, 4}},
{0xC8, {0, 1, 7, 1, 2, 7, 2, 3, 7, 3, 6, 7, 3, 4, 6, 4, 5, 6, 8, 9, 10, 8, 10, 11}},
{0xB7, {0, 1, 5, 1, 2, 5, 2, 4, 5, 2, 3, 4, 6, 9, 10, 6, 7, 9, 7, 8, 9}},
{0x75, {0, 1, 6, 1, 3, 6, 1, 2, 3, 3, 4, 6, 4, 5, 6}},
{0xA6, {0, 1, 3, 1, 2, 3, 4, 5, 9, 5, 8, 9, 5, 6, 8, 6, 7, 8}},
{0xC4, {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}},
{0x86, {1, 2, 4, 2, 3, 4, 0, 1, 7, 1, 4, 7, 4, 6, 7, 4, 5, 6}},
{0x64, {0, 4, 5, 0, 1, 4, 1, 3, 4, 1, 2, 3}},
{0x86, {0, 1, 4, 1, 3, 4, 1, 2, 3, 0, 4, 7, 4, 6, 7, 4, 5, 6}},
{0x97, {1, 2, 3, 1, 3, 4, 1, 4, 5, 0, 1, 8, 1, 5, 8, 5, 7, 8, 5, 6, 7}},
{0xA6, {0, 1, 3, 1, 2, 3, 4, 5, 9, 5, 8, 9, 5, 6, 8, 6, 7, 8}},
{0xC8, {0, 1, 5, 1, 2, 5, 2, 4, 5, 2, 3, 4, 6, 7, 11, 7, 10, 11, 7, 8, 10, 8, 9, 10}},
{0x97, {0, 1, 8, 1, 2, 8, 2, 7, 8, 2, 3, 7, 3, 6, 7, 3, 4, 6, 4, 5, 6}},
{0x97, {0, 1, 4, 1, 3, 4, 1, 2, 3, 0, 4, 8, 4, 7, 8, 4, 5, 7, 5, 6, 7}},
{0xB7, {0, 1, 5, 1, 2, 5, 2, 4, 5, 2, 3, 4, 6, 7, 10, 7, 9, 10, 7, 8, 9}},
{0xA8, {0, 1, 9, 1, 2, 9, 2, 8, 9, 2, 3, 8, 3, 7, 8, 3, 4, 7, 4, 6, 7, 4, 5, 6}},
{0xB9, {0, 1, 7, 1, 6, 7, 1, 2, 6, 2, 5, 6, 2, 3, 5, 3, 4, 5, 0, 7, 10, 7, 9, 10, 7, 8, 9}},
{0xA6, {0, 1, 5, 1, 4, 5, 1, 2, 4, 2, 3, 4, 6, 7, 9, 7, 8, 9}},
{0xC6, {0, 1, 5, 1, 2, 5, 2, 4, 5, 2, 3, 4, 6, 7, 8, 9, 10, 11}},
{0xB7, {0, 1, 7, 1, 2, 7, 2, 3, 7, 3, 6, 7, 3, 4, 6, 4, 5, 6, 8, 9, 10}},
{0xA8, {1, 2, 3, 1, 3, 4, 1, 4, 6, 4, 5, 6, 0, 1, 9, 1, 6, 9, 6, 8, 9, 6, 7, 8}},
{0xCC, {0, 1, 9, 1, 8, 9, 1, 2, 8, 2, 11, 8, 2, 3, 11, 3, 4, 11, 4, 5, 11, 5, 10, 11, 5, 6, 10, 6, 9, 10, 6, 7, 9, 7, 0, 9}},
{0x86, {0, 1, 2, 0, 2, 3, 0, 6, 7, 0, 3, 6, 1, 4, 5, 1, 5, 2}},
{0x97, {0, 1, 4, 1, 3, 4, 1, 2, 3, 2, 5, 6, 2, 6, 3, 0, 7, 8, 0, 4, 7}},
{0xA8, {0, 1, 5, 1, 4, 5, 1, 2, 4, 2, 3, 4, 3, 6, 7, 3, 7, 4, 0, 8, 9, 0, 5, 8}},
{0xA8, {0, 1, 5, 1, 4, 5, 1, 2, 4, 2, 3, 4, 2, 6, 3, 3, 6, 7, 0, 8, 9, 0, 5, 8}}
};
// The transitionCornerData table contains the transition cell corner reuse data
// shown in Figure 4.18.
const unsigned char transitionCornerData[13] =
{
0x30, 0x21, 0x20, 0x12, 0x40, 0x82, 0x10, 0x81, 0x80, 0x37, 0x27, 0x17, 0x87
};
// The transitionVertexData table gives the vertex locations for every one of the 512 possible
// cases in the Tranvoxel Algorithm. Each 16-bit value also provides information about whether
// a vertex can be reused from a neighboring cell. See Section 4.5 for details. The low byte
// contains the indexes for the two endpoints of the edge on which the vertex lies, as numbered
// in Figure 4.16. The high byte contains the vertex reuse data shown in Figure 4.17.
const unsigned short transitionVertexData[512][12] =
{
{},
{0x2301, 0x1503, 0x199B, 0x289A},
{0x2301, 0x2412, 0x4514},
{0x1503, 0x4514, 0x2412, 0x289A, 0x199B},
{0x8525, 0x2412, 0x289A, 0x89AC},
{0x8525, 0x2412, 0x2301, 0x1503, 0x199B, 0x89AC},
{0x8525, 0x4514, 0x2301, 0x289A, 0x89AC},
{0x8525, 0x4514, 0x1503, 0x199B, 0x89AC},
{0x8525, 0x8658, 0x4445},
{0x1503, 0x2301, 0x289A, 0x199B, 0x8658, 0x8525, 0x4445},
{0x8525, 0x8658, 0x4445, 0x2301, 0x2412, 0x4514},
{0x1503, 0x4514, 0x2412, 0x289A, 0x199B, 0x8658, 0x8525, 0x4445},
{0x2412, 0x4445, 0x8658, 0x89AC, 0x289A},
{0x8658, 0x4445, 0x2412, 0x2301, 0x1503, 0x199B, 0x89AC},
{0x8658, 0x4445, 0x4514, 0x2301, 0x289A, 0x89AC},
{0x8658, 0x4445, 0x4514, 0x1503, 0x199B, 0x89AC},
{0x8478, 0x8658, 0x89AC, 0x88BC},
{0x2301, 0x1503, 0x199B, 0x289A, 0x8478, 0x8658, 0x89AC, 0x88BC},
{0x8478, 0x8658, 0x89AC, 0x88BC, 0x2301, 0x2412, 0x4514},
{0x1503, 0x4514, 0x2412, 0x289A, 0x199B, 0x8658, 0x8478, 0x88BC, 0x89AC},
{0x8478, 0x8658, 0x8525, 0x2412, 0x289A, 0x88BC},
{0x8478, 0x8658, 0x8525, 0x2412, 0x2301, 0x1503, 0x199B, 0x88BC},
{0x2301, 0x4514, 0x8525, 0x8658, 0x8478, 0x88BC, 0x289A},
{0x8478, 0x8658, 0x8525, 0x4514, 0x1503, 0x199B, 0x88BC},
{0x8478, 0x4445, 0x8525, 0x89AC, 0x88BC},
{0x8478, 0x4445, 0x8525, 0x89AC, 0x88BC, 0x2301, 0x1503, 0x199B, 0x289A},
{0x8478, 0x4445, 0x8525, 0x89AC, 0x88BC, 0x2301, 0x2412, 0x4514},
{0x8478, 0x4445, 0x8525, 0x89AC, 0x88BC, 0x2412, 0x4514, 0x1503, 0x199B, 0x289A},
{0x8478, 0x4445, 0x2412, 0x289A, 0x88BC},
{0x1503, 0x2301, 0x2412, 0x4445, 0x8478, 0x88BC, 0x199B},
{0x2301, 0x4514, 0x4445, 0x8478, 0x88BC, 0x289A},
{0x1503, 0x4514, 0x4445, 0x8478, 0x88BC, 0x199B},
{0x8478, 0x8367, 0x4647},
{0x2301, 0x1503, 0x199B, 0x289A, 0x8478, 0x8367, 0x4647},
{0x2301, 0x2412, 0x4514, 0x8478, 0x8367, 0x4647},
{0x1503, 0x4514, 0x2412, 0x289A, 0x199B, 0x8367, 0x8478, 0x4647},
{0x2412, 0x8525, 0x89AC, 0x289A, 0x8367, 0x8478, 0x4647},
{0x8525, 0x2412, 0x2301, 0x1503, 0x199B, 0x89AC, 0x8478, 0x8367, 0x4647},
{0x8525, 0x4514, 0x2301, 0x289A, 0x89AC, 0x8478, 0x8367, 0x4647},
{0x8525, 0x4514, 0x1503, 0x199B, 0x89AC, 0x8478, 0x8367, 0x4647},
{0x8478, 0x8367, 0x4647, 0x8525, 0x8658, 0x4445},
{0x2301, 0x1503, 0x199B, 0x289A, 0x8478, 0x8367, 0x4647, 0x8525, 0x8658, 0x4445},
{0x8478, 0x8367, 0x4647, 0x8525, 0x8658, 0x4445, 0x2301, 0x2412, 0x4514},
{0x1503, 0x4514, 0x2412, 0x289A, 0x199B, 0x8658, 0x8525, 0x4445, 0x8367, 0x8478, 0x4647},
{0x2412, 0x4445, 0x8658, 0x89AC, 0x289A, 0x8367, 0x8478, 0x4647},
{0x8658, 0x4445, 0x2412, 0x2301, 0x1503, 0x199B, 0x89AC, 0x8478, 0x8367, 0x4647},
{0x2301, 0x4514, 0x4445, 0x8658, 0x89AC, 0x289A, 0x8367, 0x8478, 0x4647},
{0x8658, 0x4445, 0x4514, 0x1503, 0x199B, 0x89AC, 0x8478, 0x8367, 0x4647},
{0x8658, 0x4647, 0x8367, 0x88BC, 0x89AC},
{0x8658, 0x4647, 0x8367, 0x88BC, 0x89AC, 0x1503, 0x2301, 0x289A, 0x199B},
{0x8658, 0x4647, 0x8367, 0x88BC, 0x89AC, 0x2412, 0x2301, 0x4514},
{0x1503, 0x4514, 0x2412, 0x289A, 0x199B, 0x8658, 0x4647, 0x8367, 0x88BC, 0x89AC},
{0x8367, 0x4647, 0x8658, 0x8525, 0x2412, 0x289A, 0x88BC},
{0x1503, 0x2301, 0x2412, 0x8525, 0x8658, 0x4647, 0x8367, 0x88BC, 0x199B},
{0x8367, 0x4647, 0x8658, 0x8525, 0x4514, 0x2301, 0x289A, 0x88BC},
{0x8367, 0x4647, 0x8658, 0x8525, 0x4514, 0x1503, 0x199B, 0x88BC},
{0x8367, 0x4647, 0x4445, 0x8525, 0x89AC, 0x88BC},
{0x8367, 0x4647, 0x4445, 0x8525, 0x89AC, 0x88BC, 0x2301, 0x1503, 0x199B, 0x289A},
{0x8367, 0x4647, 0x4445, 0x8525, 0x89AC, 0x88BC, 0x2301, 0x2412, 0x4514},
{0x8525, 0x4445, 0x4647, 0x8367, 0x88BC, 0x89AC, 0x1503, 0x4514, 0x2412, 0x289A, 0x199B},
{0x8367, 0x4647, 0x4445, 0x2412, 0x289A, 0x88BC},
{0x8367, 0x4647, 0x4445, 0x2412, 0x2301, 0x1503, 0x199B, 0x88BC},
{0x2301, 0x4514, 0x4445, 0x4647, 0x8367, 0x88BC, 0x289A},
{0x8367, 0x4647, 0x4445, 0x4514, 0x1503, 0x199B, 0x88BC},
{0x1636, 0x8367, 0x88BC, 0x199B},
{0x2301, 0x1503, 0x1636, 0x8367, 0x88BC, 0x289A},
{0x8367, 0x1636, 0x199B, 0x88BC, 0x2412, 0x2301, 0x4514},
{0x2412, 0x4514, 0x1503, 0x1636, 0x8367, 0x88BC, 0x289A},
{0x8525, 0x2412, 0x289A, 0x89AC, 0x1636, 0x8367, 0x88BC, 0x199B},
{0x8525, 0x2412, 0x2301, 0x1503, 0x1636, 0x8367, 0x88BC, 0x89AC},
{0x8525, 0x4514, 0x2301, 0x289A, 0x89AC, 0x1636, 0x8367, 0x88BC, 0x199B},
{0x8367, 0x1636, 0x1503, 0x4514, 0x8525, 0x89AC, 0x88BC},
{0x1636, 0x8367, 0x88BC, 0x199B, 0x8525, 0x8658, 0x4445},
{0x2301, 0x1503, 0x1636, 0x8367, 0x88BC, 0x289A, 0x8525, 0x8658, 0x4445},
{0x1636, 0x8367, 0x88BC, 0x199B, 0x8525, 0x8658, 0x4445, 0x2301, 0x2412, 0x4514},
{0x2412, 0x4514, 0x1503, 0x1636, 0x8367, 0x88BC, 0x289A, 0x8525, 0x8658, 0x4445},
{0x2412, 0x4445, 0x8658, 0x89AC, 0x289A, 0x8367, 0x1636, 0x199B, 0x88BC},
{0x8367, 0x1636, 0x1503, 0x2301, 0x2412, 0x4445, 0x8658, 0x89AC, 0x88BC},
{0x8658, 0x4445, 0x4514, 0x2301, 0x289A, 0x89AC, 0x1636, 0x8367, 0x88BC, 0x199B},
{0x8658, 0x4445, 0x4514, 0x1503, 0x1636, 0x8367, 0x88BC, 0x89AC},
{0x1636, 0x8367, 0x8478, 0x8658, 0x89AC, 0x199B},
{0x2301, 0x1503, 0x1636, 0x8367, 0x8478, 0x8658, 0x89AC, 0x289A},
{0x1636, 0x8367, 0x8478, 0x8658, 0x89AC, 0x199B, 0x2301, 0x2412, 0x4514},
{0x8658, 0x8478, 0x8367, 0x1636, 0x1503, 0x4514, 0x2412, 0x289A, 0x89AC},
{0x1636, 0x8367, 0x8478, 0x8658, 0x8525, 0x2412, 0x289A, 0x199B},
{0x1636, 0x8367, 0x8478, 0x8658, 0x8525, 0x2412, 0x2301, 0x1503},
{0x1636, 0x8367, 0x8478, 0x8658, 0x8525, 0x4514, 0x2301, 0x289A, 0x199B},
{0x1503, 0x4514, 0x8525, 0x8658, 0x8478, 0x8367, 0x1636},
{0x8525, 0x4445, 0x8478, 0x8367, 0x1636, 0x199B, 0x89AC},
{0x2301, 0x1503, 0x1636, 0x8367, 0x8478, 0x4445, 0x8525, 0x89AC, 0x289A},
{0x8525, 0x4445, 0x8478, 0x8367, 0x1636, 0x199B, 0x89AC, 0x2412, 0x2301, 0x4514},
{0x2412, 0x4514, 0x1503, 0x1636, 0x8367, 0x8478, 0x4445, 0x8525, 0x89AC, 0x289A},
{0x1636, 0x8367, 0x8478, 0x4445, 0x2412, 0x289A, 0x199B},
{0x2412, 0x4445, 0x8478, 0x8367, 0x1636, 0x1503, 0x2301},
{0x2301, 0x4514, 0x4445, 0x8478, 0x8367, 0x1636, 0x199B, 0x289A},
{0x8367, 0x1636, 0x1503, 0x4514, 0x4445, 0x8478},
{0x1636, 0x4647, 0x8478, 0x88BC, 0x199B},
{0x8478, 0x4647, 0x1636, 0x1503, 0x2301, 0x289A, 0x88BC},
{0x1636, 0x4647, 0x8478, 0x88BC, 0x199B, 0x2301, 0x2412, 0x4514},
{0x2412, 0x4514, 0x1503, 0x1636, 0x4647, 0x8478, 0x88BC, 0x289A},
{0x1636, 0x4647, 0x8478, 0x88BC, 0x199B, 0x8525, 0x2412, 0x289A, 0x89AC},
{0x8525, 0x2412, 0x2301, 0x1503, 0x1636, 0x4647, 0x8478, 0x88BC, 0x89AC},
{0x8525, 0x4514, 0x2301, 0x289A, 0x89AC, 0x1636, 0x4647, 0x8478, 0x88BC, 0x199B},
{0x8478, 0x4647, 0x1636, 0x1503, 0x4514, 0x8525, 0x89AC, 0x88BC},
{0x1636, 0x4647, 0x8478, 0x88BC, 0x199B, 0x8525, 0x8658, 0x4445},
{0x8478, 0x4647, 0x1636, 0x1503, 0x2301, 0x289A, 0x88BC, 0x8658, 0x8525, 0x4445},
{0x1636, 0x4647, 0x8478, 0x88BC, 0x199B, 0x8525, 0x8658, 0x4445, 0x2301, 0x2412, 0x4514},
{0x2412, 0x4514, 0x1503, 0x1636, 0x4647, 0x8478, 0x88BC, 0x289A, 0x8525, 0x8658, 0x4445},
{0x1636, 0x4647, 0x8478, 0x88BC, 0x199B, 0x8658, 0x4445, 0x2412, 0x289A, 0x89AC},
{0x8658, 0x4445, 0x2412, 0x2301, 0x1503, 0x1636, 0x4647, 0x8478, 0x88BC, 0x89AC},
{0x8658, 0x4445, 0x4514, 0x2301, 0x289A, 0x89AC, 0x1636, 0x4647, 0x8478, 0x88BC, 0x199B},
{0x8478, 0x4647, 0x1636, 0x1503, 0x4514, 0x4445, 0x8658, 0x89AC, 0x88BC},
{0x1636, 0x4647, 0x8658, 0x89AC, 0x199B},
{0x2301, 0x1503, 0x1636, 0x4647, 0x8658, 0x89AC, 0x289A},
{0x1636, 0x4647, 0x8658, 0x89AC, 0x199B, 0x2301, 0x2412, 0x4514},
{0x2412, 0x4514, 0x1503, 0x1636, 0x4647, 0x8658, 0x89AC, 0x289A},
{0x2412, 0x8525, 0x8658, 0x4647, 0x1636, 0x199B, 0x289A},
{0x8658, 0x4647, 0x1636, 0x1503, 0x2301, 0x2412, 0x8525},
{0x2301, 0x4514, 0x8525, 0x8658, 0x4647, 0x1636, 0x199B, 0x289A},
{0x1503, 0x4514, 0x8525, 0x8658, 0x4647, 0x1636},
{0x8525, 0x4445, 0x4647, 0x1636, 0x199B, 0x89AC},
{0x8525, 0x4445, 0x4647, 0x1636, 0x1503, 0x2301, 0x289A, 0x89AC},
{0x8525, 0x4445, 0x4647, 0x1636, 0x199B, 0x89AC, 0x2412, 0x2301, 0x4514},
{0x2412, 0x4514, 0x1503, 0x1636, 0x4647, 0x4445, 0x8525, 0x89AC, 0x289A},
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