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💿🐜 Antkeeper source code https://antkeeper.com
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source/src/game/terrain.cpp

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#include "terrain.hpp"
Terrain::Terrain()
{
surfaceOctree = nullptr;
}
Terrain::~Terrain()
{
delete surfaceOctree;
}
void Terrain::create(int columns, int rows, const Vector3& dimensions)
{
this->columns = columns;
this->rows = rows;
this->dimensions = dimensions;
createSurface();
createSubsurface();
}
void Terrain::createSurface()
{
surfaceVertexSize = 3 + 3 + 2;
surfaceVertexCount = (columns + 1) * (rows + 1);
surfaceTriangleCount = columns * rows * 2;
surfaceIndexCount = surfaceTriangleCount * 3;
surfaceVertexData = new float[surfaceVertexSize * surfaceVertexCount];
surfaceIndexData = new std::uint32_t[surfaceIndexCount];
surfaceVertices.resize(surfaceVertexCount);
surfaceIndices.resize(surfaceIndexCount);
// Calculate scale and offset
Vector2 scale(dimensions.x / (float)columns, dimensions.z / (float)rows);
Vector2 offset(dimensions.x * -0.5f, dimensions.z * -0.5f);
// Calculate vertex positions
for (int i = 0; i <= rows; ++i)
{
for (int j = 0; j <= columns; ++j)
{
std::size_t index = i * (columns + 1) + j;
Vector3* vertex = &surfaceVertices[index];
vertex->x = (float)j * scale.x + offset.x;
vertex->y = 0.0f;
vertex->z = (float)i * scale.y + offset.y;
float* data = &surfaceVertexData[index * surfaceVertexSize];
*(data++) = vertex->x;
*(data++) = vertex->y;
*(data++) = vertex->z;
*(data++) = 0.0f;
*(data++) = 1.0f;
*(data++) = 0.0f;
*(data++) = static_cast<float>(j) / static_cast<float>(columns) * 2.0f;
*(data++) = static_cast<float>(i) / static_cast<float>(rows) * 2.0f;
}
}
// Generate indices
for (int i = 0; i < rows; ++i)
{
for (int j = 0; j < columns; ++j)
{
unsigned int a = i * (columns + 1) + j;
unsigned int b = (i + 1) * (columns + 1) + j;
unsigned int c = i * (columns + 1) + j + 1;
unsigned int d = (i + 1) * (columns + 1) + j + 1;
std::size_t index = (i * columns + j) * 2 * 3;
surfaceIndices[index++] = a;
surfaceIndices[index++] = b;
surfaceIndices[index++] = c;
surfaceIndices[index++] = c;
surfaceIndices[index++] = b;
surfaceIndices[index] = d;
}
}
// Generate index data
for (std::size_t i = 0; i < surfaceIndexCount; ++i)
{
surfaceIndexData[i] = surfaceIndices[i];
}
// Generate navmesh
surfaceNavmesh.create(surfaceVertices, surfaceIndices);
// Calculate vertex normals
calculateSurfaceNormals();
// Create and load VAO, VBO, and IBO
glGenVertexArrays(1, &surfaceVAO);
glBindVertexArray(surfaceVAO);
glGenBuffers(1, &surfaceVBO);
glBindBuffer(GL_ARRAY_BUFFER, surfaceVBO);
glBufferData(GL_ARRAY_BUFFER, sizeof(float) * surfaceVertexSize * surfaceVertexCount, surfaceVertexData, GL_STATIC_DRAW);
glEnableVertexAttribArray(EMERGENT_VERTEX_POSITION);
glVertexAttribPointer(EMERGENT_VERTEX_POSITION, 3, GL_FLOAT, GL_FALSE, surfaceVertexSize * sizeof(float), (char*)0 + 0 * sizeof(float));
glEnableVertexAttribArray(EMERGENT_VERTEX_NORMAL);
glVertexAttribPointer(EMERGENT_VERTEX_NORMAL, 3, GL_FLOAT, GL_FALSE, surfaceVertexSize * sizeof(float), (char*)0 + 3 * sizeof(float));
glEnableVertexAttribArray(EMERGENT_VERTEX_TEXCOORD);
glVertexAttribPointer(EMERGENT_VERTEX_TEXCOORD, 2, GL_FLOAT, GL_FALSE, surfaceVertexSize * sizeof(float), (char*)0 + 6 * sizeof(float));
glGenBuffers(1, &surfaceIBO);
glBindBuffer(GL_ELEMENT_ARRAY_BUFFER, surfaceIBO);
glBufferData(GL_ELEMENT_ARRAY_BUFFER, sizeof(std::uint32_t) * surfaceIndexCount, surfaceIndexData, GL_STATIC_DRAW);
// Setup material
surfaceMaterial.flags = static_cast<unsigned int>(PhysicalMaterial::Flags::OBJECT);
// Setup buffers
surfaceModel.setVAO(surfaceVAO);
surfaceModel.setVBO(surfaceVBO);
surfaceModel.setIBO(surfaceIBO);
// Create model group
Model::Group* group = new Model::Group();
group->name = "default";
group->material = &surfaceMaterial;
group->indexOffset = 0;
group->triangleCount = surfaceTriangleCount;
// Add group to the model
surfaceModel.addGroup(group);
// Set model bounds
surfaceModel.setBounds(surfaceNavmesh.getBounds());
// Calculate octree
surfaceOctree = surfaceNavmesh.createOctree(5);
}
void Terrain::createSubsurface()
{
subsurfaceVertexSize = 3 + 3 + 2;
subsurfaceVertexCount = (columns + 1) * 4 + (rows + 1) * 4;
subsurfaceTriangleCount = columns * 4 + rows * 4 + 2;
subsurfaceIndexCount = subsurfaceTriangleCount * 3;
subsurfaceVertexData = new float[subsurfaceVertexSize * subsurfaceVertexCount];
subsurfaceIndexData = new std::uint32_t[subsurfaceIndexCount];
subsurfaceVertices.resize(subsurfaceVertexCount);
subsurfaceIndices.resize(subsurfaceIndexCount);
float maxDimension = dimensions.y;
float textureScaleX = dimensions.x / maxDimension;
float textureScaleY = dimensions.y / maxDimension;
float textureScaleZ = dimensions.z / maxDimension;
// Calculate floor position
float subsurfaceFloor = -dimensions.y;
// Calculate vertex positions
Vector3* vertex = &subsurfaceVertices[0];
float* data = &subsurfaceVertexData[0];
// Top row
for (int j = 0; j <= columns; ++j)
{
int i = 0;
std::size_t surfaceIndex = i * (columns + 1) + j;
const Vector3& surfaceVertex = surfaceVertices[surfaceIndex];
float u = 1.0f - (static_cast<float>(j) / static_cast<float>(columns)) * textureScaleX;
*(vertex++) = surfaceVertex;
*(data++) = surfaceVertex.x;
*(data++) = surfaceVertex.y;
*(data++) = surfaceVertex.z;
*(data++) = 0.0f;
*(data++) = 0.0f;
*(data++) = 1.0f;
*(data++) = u;
*(data++) = 0.0f;
*(vertex++) = Vector3(surfaceVertex.x, subsurfaceFloor, surfaceVertex.z);
*(data++) = surfaceVertex.x;
*(data++) = subsurfaceFloor;
*(data++) = surfaceVertex.z;
*(data++) = 0.0f;
*(data++) = 0.0f;
*(data++) = 1.0f;
*(data++) = u;
*(data++) = textureScaleY;
}
// Bottom row
for (int j = 0; j <= columns; ++j)
{
int i = rows;
std::size_t surfaceIndex = i * (columns + 1) + j;
const Vector3& surfaceVertex = surfaceVertices[surfaceIndex];
float u = (static_cast<float>(j) / static_cast<float>(columns)) * textureScaleX;
*(vertex++) = surfaceVertex;
*(data++) = surfaceVertex.x;
*(data++) = surfaceVertex.y;
*(data++) = surfaceVertex.z;
*(data++) = 0.0f;
*(data++) = 0.0f;
*(data++) = 1.0f;
*(data++) = u;
*(data++) = 0.0f;
*(vertex++) = Vector3(surfaceVertex.x, subsurfaceFloor, surfaceVertex.z);
*(data++) = surfaceVertex.x;
*(data++) = subsurfaceFloor;
*(data++) = surfaceVertex.z;
*(data++) = 0.0f;
*(data++) = 0.0f;
*(data++) = 1.0f;
*(data++) = u;
*(data++) = textureScaleY;
}
// Left column
for (int i = 0; i <= rows; ++i)
{
int j = 0;
std::size_t surfaceIndex = i * (columns + 1) + j;
const Vector3& surfaceVertex = surfaceVertices[surfaceIndex];
float u = (static_cast<float>(i) / static_cast<float>(rows)) * textureScaleZ;
*(vertex++) = surfaceVertex;
*(data++) = surfaceVertex.x;
*(data++) = surfaceVertex.y;
*(data++) = surfaceVertex.z;
*(data++) = 0.0f;
*(data++) = 0.0f;
*(data++) = 1.0f;
*(data++) = u;
*(data++) = 0.0f;
*(vertex++) = Vector3(surfaceVertex.x, subsurfaceFloor, surfaceVertex.z);
*(data++) = surfaceVertex.x;
*(data++) = subsurfaceFloor;
*(data++) = surfaceVertex.z;
*(data++) = 0.0f;
*(data++) = 0.0f;
*(data++) = 1.0f;
*(data++) = u;
*(data++) = textureScaleY;
}
// Right column
for (int i = 0; i <= rows; ++i)
{
int j = columns;
std::size_t surfaceIndex = i * (columns + 1) + j;
const Vector3& surfaceVertex = surfaceVertices[surfaceIndex];
float u = 1.0f - (static_cast<float>(i) / static_cast<float>(rows)) * textureScaleZ;
*(vertex++) = surfaceVertex;
*(data++) = surfaceVertex.x;
*(data++) = surfaceVertex.y;
*(data++) = surfaceVertex.z;
*(data++) = 0.0f;
*(data++) = 0.0f;
*(data++) = 1.0f;
*(data++) = u;
*(data++) = 0.0f;
*(vertex++) = Vector3(surfaceVertex.x, subsurfaceFloor, surfaceVertex.z);
*(data++) = surfaceVertex.x;
*(data++) = subsurfaceFloor;
*(data++) = surfaceVertex.z;
*(data++) = 0.0f;
*(data++) = 0.0f;
*(data++) = 1.0f;
*(data++) = u;
*(data++) = textureScaleY;
}
// Generate indices
std::size_t* index = &subsurfaceIndices[0];
for (int i = 0; i < columns; ++i)
{
std::size_t a = i * 2;
std::size_t b = i * 2 + 1;
std::size_t c = (i + 1) * 2;
std::size_t d = (i + 1) * 2 + 1;
(*(index++)) = b;
(*(index++)) = a;
(*(index++)) = c;
(*(index++)) = b;
(*(index++)) = c;
(*(index++)) = d;
a += (columns + 1) * 2;
b += (columns + 1) * 2;
c += (columns + 1) * 2;
d += (columns + 1) * 2;
(*(index++)) = a;
(*(index++)) = b;
(*(index++)) = c;
(*(index++)) = c;
(*(index++)) = b;
(*(index++)) = d;
}
for (int i = 0; i < rows; ++i)
{
std::size_t a = (columns + 1) * 4 + i * 2;
std::size_t b = (columns + 1) * 4 + i * 2 + 1;
std::size_t c = (columns + 1) * 4 + (i + 1) * 2;
std::size_t d = (columns + 1) * 4 + (i + 1) * 2 + 1;
(*(index++)) = a;
(*(index++)) = b;
(*(index++)) = c;
(*(index++)) = c;
(*(index++)) = b;
(*(index++)) = d;
a += (rows + 1) * 2;
b += (rows + 1) * 2;
c += (rows + 1) * 2;
d += (rows + 1) * 2;
(*(index++)) = b;
(*(index++)) = a;
(*(index++)) = c;
(*(index++)) = b;
(*(index++)) = c;
(*(index++)) = d;
}
// Floor
std::size_t a = 1;
std::size_t b = 1 + (rows + 1) * 2;
std::size_t c = columns * 2 + 1;
std::size_t d = columns * 2 + 1 + (columns + 1) * 2;
(*(index++)) = a;
(*(index++)) = c;
(*(index++)) = b;
(*(index++)) = b;
(*(index++)) = c;
(*(index++)) = d;
// Generate index data
for (std::size_t i = 0; i < subsurfaceIndexCount; ++i)
{
subsurfaceIndexData[i] = subsurfaceIndices[i];
}
// Generate navmesh
subsurfaceNavmesh.create(subsurfaceVertices, subsurfaceIndices);
// Create and load VAO, VBO, and IBO
glGenVertexArrays(1, &subsurfaceVAO);
glBindVertexArray(subsurfaceVAO);
glGenBuffers(1, &subsurfaceVBO);
glBindBuffer(GL_ARRAY_BUFFER, subsurfaceVBO);
glBufferData(GL_ARRAY_BUFFER, sizeof(float) * subsurfaceVertexSize * subsurfaceVertexCount, subsurfaceVertexData, GL_STATIC_DRAW);
glEnableVertexAttribArray(EMERGENT_VERTEX_POSITION);
glVertexAttribPointer(EMERGENT_VERTEX_POSITION, 3, GL_FLOAT, GL_FALSE, subsurfaceVertexSize * sizeof(float), (char*)0 + 0 * sizeof(float));
glEnableVertexAttribArray(EMERGENT_VERTEX_NORMAL);
glVertexAttribPointer(EMERGENT_VERTEX_NORMAL, 3, GL_FLOAT, GL_FALSE, subsurfaceVertexSize * sizeof(float), (char*)0 + 3 * sizeof(float));
glEnableVertexAttribArray(EMERGENT_VERTEX_TEXCOORD);
glVertexAttribPointer(EMERGENT_VERTEX_TEXCOORD, 2, GL_FLOAT, GL_FALSE, subsurfaceVertexSize * sizeof(float), (char*)0 + 6 * sizeof(float));
glGenBuffers(1, &subsurfaceIBO);
glBindBuffer(GL_ELEMENT_ARRAY_BUFFER, subsurfaceIBO);
glBufferData(GL_ELEMENT_ARRAY_BUFFER, sizeof(std::uint32_t) * subsurfaceIndexCount, subsurfaceIndexData, GL_STATIC_DRAW);
// Setup material
subsurfaceMaterial.flags = static_cast<unsigned int>(PhysicalMaterial::Flags::SOIL);
// Setup buffers
subsurfaceModel.setVAO(subsurfaceVAO);
subsurfaceModel.setVBO(subsurfaceVBO);
subsurfaceModel.setIBO(subsurfaceIBO);
// Create model group
Model::Group* group = new Model::Group();
group->name = "default";
group->material = &subsurfaceMaterial;
group->indexOffset = 0;
group->triangleCount = subsurfaceTriangleCount;
// Add group to the model
subsurfaceModel.addGroup(group);
// Set model bounds
subsurfaceModel.setBounds(subsurfaceNavmesh.getBounds());
}
void Terrain::calculateSurfaceNormals()
{
for (std::size_t i = 0; i < surfaceVertexCount; ++i)
{
const Navmesh::Vertex* vertex = (*surfaceNavmesh.getVertices())[i];
Vector3 normal(0.0f);
const Navmesh::Edge* start = vertex->edge;
const Navmesh::Edge* e = start;
do
{
normal += e->triangle->normal;
e = e->previous->symmetric;
}
while (e != start && e != nullptr);
normal = glm::normalize(normal);
float* data = &surfaceVertexData[i * surfaceVertexSize];
data[3] = normal.x;
data[4] = normal.y;
data[5] = normal.z;
}
}
bool Terrain::load(const std::string& filename)
{
int width;
int height;
int channels;
stbi_set_flip_vertically_on_load(true);
// Load image data
unsigned char* pixels = stbi_load(filename.c_str(), &width, &height, &channels, 1);
if (width != columns + 1 || height != rows + 1)
{
// Free loaded image data
stbi_image_free(pixels);
return false;
}
// Set surface vertex heights
for (int i = 0; i <= rows; ++i)
{
for (int j = 0; j <= columns; ++j)
{
std::size_t index = i * (columns + 1) + j;
float elevation = (float)pixels[index] / 255.0f * 5.0f;
surfaceVertexData[index * surfaceVertexSize + 1] = elevation;
surfaceVertices[index].y = elevation;
(*surfaceNavmesh.getVertices())[index]->position.y = elevation;
}
}
// Free loaded image data
stbi_image_free(pixels);
// Set subsurface vertex heights
std::size_t subsurfaceIndex = 0;
// Top row
for (int j = 0; j <= columns; ++j)
{
int i = 0;
std::size_t surfaceIndex = i * (columns + 1) + j;
float elevation = surfaceVertices[surfaceIndex].y;
subsurfaceVertexData[subsurfaceIndex * subsurfaceVertexSize + 1] = elevation;
subsurfaceVertices[subsurfaceIndex].y = elevation;
(*subsurfaceNavmesh.getVertices())[subsurfaceIndex]->position.y = elevation;
subsurfaceIndex += 2;
}
// Bottom row
for (int j = 0; j <= columns; ++j)
{
int i = rows;
std::size_t surfaceIndex = i * (columns + 1) + j;
float elevation = surfaceVertices[surfaceIndex].y;
subsurfaceVertexData[subsurfaceIndex * subsurfaceVertexSize + 1] = elevation;
subsurfaceVertices[subsurfaceIndex].y = elevation;
(*subsurfaceNavmesh.getVertices())[subsurfaceIndex]->position.y = elevation;
subsurfaceIndex += 2;
}
// Left column
for (int i = 0; i <= rows; ++i)
{
int j = 0;
std::size_t surfaceIndex = i * (columns + 1) + j;
float elevation = surfaceVertices[surfaceIndex].y;
subsurfaceVertexData[subsurfaceIndex * subsurfaceVertexSize + 1] = elevation;
subsurfaceVertices[subsurfaceIndex].y = elevation;
(*subsurfaceNavmesh.getVertices())[subsurfaceIndex]->position.y = elevation;
subsurfaceIndex += 2;
}
// Right column
for (int i = 0; i <= rows; ++i)
{
int j = columns;
std::size_t surfaceIndex = i * (columns + 1) + j;
float elevation = surfaceVertices[surfaceIndex].y;
subsurfaceVertexData[subsurfaceIndex * subsurfaceVertexSize + 1] = elevation;
subsurfaceVertices[subsurfaceIndex].y = elevation;
(*subsurfaceNavmesh.getVertices())[subsurfaceIndex]->position.y = elevation;
subsurfaceIndex += 2;
}
// Calculate navmesh normals
surfaceNavmesh.calculateNormals();
subsurfaceNavmesh.calculateNormals();
// Calculate navmesh bounds
surfaceNavmesh.calculateBounds();
subsurfaceNavmesh.calculateBounds();
// Calculate vertex normals
calculateSurfaceNormals();
// Update VBOs
glBindBuffer(GL_ARRAY_BUFFER, surfaceVBO);
glBufferSubData(GL_ARRAY_BUFFER, 0, surfaceVertexCount * surfaceVertexSize * sizeof(float), surfaceVertexData);
glBindBuffer(GL_ARRAY_BUFFER, subsurfaceVBO);
glBufferSubData(GL_ARRAY_BUFFER, 0, subsurfaceVertexCount * subsurfaceVertexSize * sizeof(float), subsurfaceVertexData);
// Update bounds
surfaceModel.setBounds(surfaceNavmesh.getBounds());
subsurfaceModel.setBounds(subsurfaceNavmesh.getBounds());
// Calculate octree
delete surfaceOctree;
surfaceOctree = surfaceNavmesh.createOctree(5);
return true;
}
struct voxel
{
glm::vec3 vertices[8];
float values[8];
};
// LUT to map isosurface vertices to intersecting edges
static const int EDGE_TABLE[256] =
{
0x000, 0x109, 0x203, 0x30a, 0x406, 0x50f, 0x605, 0x70c,
0x80c, 0x905, 0xa0f, 0xb06, 0xc0a, 0xd03, 0xe09, 0xf00,
0x190, 0x099, 0x393, 0x29a, 0x596, 0x49f, 0x795, 0x69c,
0x99c, 0x895, 0xb9f, 0xa96, 0xd9a, 0xc93, 0xf99, 0xe90,
0x230, 0x339, 0x033, 0x13a, 0x636, 0x73f, 0x435, 0x53c,
0xa3c, 0xb35, 0x83f, 0x936, 0xe3a, 0xf33, 0xc39, 0xd30,
0x3a0, 0x2a9, 0x1a3, 0x0aa, 0x7a6, 0x6af, 0x5a5, 0x4ac,
0xbac, 0xaa5, 0x9af, 0x8a6, 0xfaa, 0xea3, 0xda9, 0xca0,
0x460, 0x569, 0x663, 0x76a, 0x066, 0x16f, 0x265, 0x36c,
0xc6c, 0xd65, 0xe6f, 0xf66, 0x86a, 0x963, 0xa69, 0xb60,
0x5f0, 0x4f9, 0x7f3, 0x6fa, 0x1f6, 0x0ff, 0x3f5, 0x2fc,
0xdfc, 0xcf5, 0xfff, 0xef6, 0x9fa, 0x8f3, 0xbf9, 0xaf0,
0x650, 0x759, 0x453, 0x55a, 0x256, 0x35f, 0x055, 0x15c,
0xe5c, 0xf55, 0xc5f, 0xd56, 0xa5a, 0xb53, 0x859, 0x950,
0x7c0, 0x6c9, 0x5c3, 0x4ca, 0x3c6, 0x2cf, 0x1c5, 0x0cc,
0xfcc, 0xec5, 0xdcf, 0xcc6, 0xbca, 0xac3, 0x9c9, 0x8c0,
0x8c0, 0x9c9, 0xac3, 0xbca, 0xcc6, 0xdcf, 0xec5, 0xfcc,
0x0cc, 0x1c5, 0x2cf, 0x3c6, 0x4ca, 0x5c3, 0x6c9, 0x7c0,
0x950, 0x859, 0xb53, 0xa5a, 0xd56, 0xc5f, 0xf55, 0xe5c,
0x15c, 0x055, 0x35f, 0x256, 0x55a, 0x453, 0x759, 0x650,
0xaf0, 0xbf9, 0x8f3, 0x9fa, 0xef6, 0xfff, 0xcf5, 0xdfc,
0x2fc, 0x3f5, 0x0ff, 0x1f6, 0x6fa, 0x7f3, 0x4f9, 0x5f0,
0xb60, 0xa69, 0x963, 0x86a, 0xf66, 0xe6f, 0xd65, 0xc6c,
0x36c, 0x265, 0x16f, 0x066, 0x76a, 0x663, 0x569, 0x460,
0xca0, 0xda9, 0xea3, 0xfaa, 0x8a6, 0x9af, 0xaa5, 0xbac,
0x4ac, 0x5a5, 0x6af, 0x7a6, 0x0aa, 0x1a3, 0x2a9, 0x3a0,
0xd30, 0xc39, 0xf33, 0xe3a, 0x936, 0x83f, 0xb35, 0xa3c,
0x53c, 0x435, 0x73f, 0x636, 0x13a, 0x033, 0x339, 0x230,
0xe90, 0xf99, 0xc93, 0xd9a, 0xa96, 0xb9f, 0x895, 0x99c,
0x69c, 0x795, 0x49f, 0x596, 0x29a, 0x393, 0x099, 0x190,
0xf00, 0xe09, 0xd03, 0xc0a, 0xb06, 0xa0f, 0x905, 0x80c,
0x70c, 0x605, 0x50f, 0x406, 0x30a, 0x203, 0x109, 0x000
};
static const int TRIANGLE_TABLE[256][16] =
{
{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{0, 8, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{0, 1, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{1, 8, 3, 9, 8, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{1, 2, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{0, 8, 3, 1, 2, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{9, 2, 10, 0, 2, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{2, 8, 3, 2, 10, 8, 10, 9, 8, -1, -1, -1, -1, -1, -1, -1},
{3, 11, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{0, 11, 2, 8, 11, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{1, 9, 0, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{1, 11, 2, 1, 9, 11, 9, 8, 11, -1, -1, -1, -1, -1, -1, -1},
{3, 10, 1, 11, 10, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{0, 10, 1, 0, 8, 10, 8, 11, 10, -1, -1, -1, -1, -1, -1, -1},
{3, 9, 0, 3, 11, 9, 11, 10, 9, -1, -1, -1, -1, -1, -1, -1},
{9, 8, 10, 10, 8, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{4, 7, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{4, 3, 0, 7, 3, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{0, 1, 9, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{4, 1, 9, 4, 7, 1, 7, 3, 1, -1, -1, -1, -1, -1, -1, -1},
{1, 2, 10, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{3, 4, 7, 3, 0, 4, 1, 2, 10, -1, -1, -1, -1, -1, -1, -1},
{9, 2, 10, 9, 0, 2, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1},
{2, 10, 9, 2, 9, 7, 2, 7, 3, 7, 9, 4, -1, -1, -1, -1},
{8, 4, 7, 3, 11, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{11, 4, 7, 11, 2, 4, 2, 0, 4, -1, -1, -1, -1, -1, -1, -1},
{9, 0, 1, 8, 4, 7, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1},
{4, 7, 11, 9, 4, 11, 9, 11, 2, 9, 2, 1, -1, -1, -1, -1},
{3, 10, 1, 3, 11, 10, 7, 8, 4, -1, -1, -1, -1, -1, -1, -1},
{1, 11, 10, 1, 4, 11, 1, 0, 4, 7, 11, 4, -1, -1, -1, -1},
{4, 7, 8, 9, 0, 11, 9, 11, 10, 11, 0, 3, -1, -1, -1, -1},
{4, 7, 11, 4, 11, 9, 9, 11, 10, -1, -1, -1, -1, -1, -1, -1},
{9, 5, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{9, 5, 4, 0, 8, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{0, 5, 4, 1, 5, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{8, 5, 4, 8, 3, 5, 3, 1, 5, -1, -1, -1, -1, -1, -1, -1},
{1, 2, 10, 9, 5, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{3, 0, 8, 1, 2, 10, 4, 9, 5, -1, -1, -1, -1, -1, -1, -1},
{5, 2, 10, 5, 4, 2, 4, 0, 2, -1, -1, -1, -1, -1, -1, -1},
{2, 10, 5, 3, 2, 5, 3, 5, 4, 3, 4, 8, -1, -1, -1, -1},
{9, 5, 4, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{0, 11, 2, 0, 8, 11, 4, 9, 5, -1, -1, -1, -1, -1, -1, -1},
{0, 5, 4, 0, 1, 5, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1},
{2, 1, 5, 2, 5, 8, 2, 8, 11, 4, 8, 5, -1, -1, -1, -1},
{10, 3, 11, 10, 1, 3, 9, 5, 4, -1, -1, -1, -1, -1, -1, -1},
{4, 9, 5, 0, 8, 1, 8, 10, 1, 8, 11, 10, -1, -1, -1, -1},
{5, 4, 0, 5, 0, 11, 5, 11, 10, 11, 0, 3, -1, -1, -1, -1},
{5, 4, 8, 5, 8, 10, 10, 8, 11, -1, -1, -1, -1, -1, -1, -1},
{9, 7, 8, 5, 7, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{9, 3, 0, 9, 5, 3, 5, 7, 3, -1, -1, -1, -1, -1, -1, -1},
{0, 7, 8, 0, 1, 7, 1, 5, 7, -1, -1, -1, -1, -1, -1, -1},
{1, 5, 3, 3, 5, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{9, 7, 8, 9, 5, 7, 10, 1, 2, -1, -1, -1, -1, -1, -1, -1},
{10, 1, 2, 9, 5, 0, 5, 3, 0, 5, 7, 3, -1, -1, -1, -1},
{8, 0, 2, 8, 2, 5, 8, 5, 7, 10, 5, 2, -1, -1, -1, -1},
{2, 10, 5, 2, 5, 3, 3, 5, 7, -1, -1, -1, -1, -1, -1, -1},
{7, 9, 5, 7, 8, 9, 3, 11, 2, -1, -1, -1, -1, -1, -1, -1},
{9, 5, 7, 9, 7, 2, 9, 2, 0, 2, 7, 11, -1, -1, -1, -1},
{2, 3, 11, 0, 1, 8, 1, 7, 8, 1, 5, 7, -1, -1, -1, -1},
{11, 2, 1, 11, 1, 7, 7, 1, 5, -1, -1, -1, -1, -1, -1, -1},
{9, 5, 8, 8, 5, 7, 10, 1, 3, 10, 3, 11, -1, -1, -1, -1},
{5, 7, 0, 5, 0, 9, 7, 11, 0, 1, 0, 10, 11, 10, 0, -1},
{11, 10, 0, 11, 0, 3, 10, 5, 0, 8, 0, 7, 5, 7, 0, -1},
{11, 10, 5, 7, 11, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{10, 6, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{0, 8, 3, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{9, 0, 1, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{1, 8, 3, 1, 9, 8, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1},
{1, 6, 5, 2, 6, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{1, 6, 5, 1, 2, 6, 3, 0, 8, -1, -1, -1, -1, -1, -1, -1},
{9, 6, 5, 9, 0, 6, 0, 2, 6, -1, -1, -1, -1, -1, -1, -1},
{5, 9, 8, 5, 8, 2, 5, 2, 6, 3, 2, 8, -1, -1, -1, -1},
{2, 3, 11, 10, 6, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{11, 0, 8, 11, 2, 0, 10, 6, 5, -1, -1, -1, -1, -1, -1, -1},
{0, 1, 9, 2, 3, 11, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1},
{5, 10, 6, 1, 9, 2, 9, 11, 2, 9, 8, 11, -1, -1, -1, -1},
{6, 3, 11, 6, 5, 3, 5, 1, 3, -1, -1, -1, -1, -1, -1, -1},
{0, 8, 11, 0, 11, 5, 0, 5, 1, 5, 11, 6, -1, -1, -1, -1},
{3, 11, 6, 0, 3, 6, 0, 6, 5, 0, 5, 9, -1, -1, -1, -1},
{6, 5, 9, 6, 9, 11, 11, 9, 8, -1, -1, -1, -1, -1, -1, -1},
{5, 10, 6, 4, 7, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{4, 3, 0, 4, 7, 3, 6, 5, 10, -1, -1, -1, -1, -1, -1, -1},
{1, 9, 0, 5, 10, 6, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1},
{10, 6, 5, 1, 9, 7, 1, 7, 3, 7, 9, 4, -1, -1, -1, -1},
{6, 1, 2, 6, 5, 1, 4, 7, 8, -1, -1, -1, -1, -1, -1, -1},
{1, 2, 5, 5, 2, 6, 3, 0, 4, 3, 4, 7, -1, -1, -1, -1},
{8, 4, 7, 9, 0, 5, 0, 6, 5, 0, 2, 6, -1, -1, -1, -1},
{7, 3, 9, 7, 9, 4, 3, 2, 9, 5, 9, 6, 2, 6, 9, -1},
{3, 11, 2, 7, 8, 4, 10, 6, 5, -1, -1, -1, -1, -1, -1, -1},
{5, 10, 6, 4, 7, 2, 4, 2, 0, 2, 7, 11, -1, -1, -1, -1},
{0, 1, 9, 4, 7, 8, 2, 3, 11, 5, 10, 6, -1, -1, -1, -1},
{9, 2, 1, 9, 11, 2, 9, 4, 11, 7, 11, 4, 5, 10, 6, -1},
{8, 4, 7, 3, 11, 5, 3, 5, 1, 5, 11, 6, -1, -1, -1, -1},
{5, 1, 11, 5, 11, 6, 1, 0, 11, 7, 11, 4, 0, 4, 11, -1},
{0, 5, 9, 0, 6, 5, 0, 3, 6, 11, 6, 3, 8, 4, 7, -1},
{6, 5, 9, 6, 9, 11, 4, 7, 9, 7, 11, 9, -1, -1, -1, -1},
{10, 4, 9, 6, 4, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{4, 10, 6, 4, 9, 10, 0, 8, 3, -1, -1, -1, -1, -1, -1, -1},
{10, 0, 1, 10, 6, 0, 6, 4, 0, -1, -1, -1, -1, -1, -1, -1},
{8, 3, 1, 8, 1, 6, 8, 6, 4, 6, 1, 10, -1, -1, -1, -1},
{1, 4, 9, 1, 2, 4, 2, 6, 4, -1, -1, -1, -1, -1, -1, -1},
{3, 0, 8, 1, 2, 9, 2, 4, 9, 2, 6, 4, -1, -1, -1, -1},
{0, 2, 4, 4, 2, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{8, 3, 2, 8, 2, 4, 4, 2, 6, -1, -1, -1, -1, -1, -1, -1},
{10, 4, 9, 10, 6, 4, 11, 2, 3, -1, -1, -1, -1, -1, -1, -1},
{0, 8, 2, 2, 8, 11, 4, 9, 10, 4, 10, 6, -1, -1, -1, -1},
{3, 11, 2, 0, 1, 6, 0, 6, 4, 6, 1, 10, -1, -1, -1, -1},
{6, 4, 1, 6, 1, 10, 4, 8, 1, 2, 1, 11, 8, 11, 1, -1},
{9, 6, 4, 9, 3, 6, 9, 1, 3, 11, 6, 3, -1, -1, -1, -1},
{8, 11, 1, 8, 1, 0, 11, 6, 1, 9, 1, 4, 6, 4, 1, -1},
{3, 11, 6, 3, 6, 0, 0, 6, 4, -1, -1, -1, -1, -1, -1, -1},
{6, 4, 8, 11, 6, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{7, 10, 6, 7, 8, 10, 8, 9, 10, -1, -1, -1, -1, -1, -1, -1},
{0, 7, 3, 0, 10, 7, 0, 9, 10, 6, 7, 10, -1, -1, -1, -1},
{10, 6, 7, 1, 10, 7, 1, 7, 8, 1, 8, 0, -1, -1, -1, -1},
{10, 6, 7, 10, 7, 1, 1, 7, 3, -1, -1, -1, -1, -1, -1, -1},
{1, 2, 6, 1, 6, 8, 1, 8, 9, 8, 6, 7, -1, -1, -1, -1},
{2, 6, 9, 2, 9, 1, 6, 7, 9, 0, 9, 3, 7, 3, 9, -1},
{7, 8, 0, 7, 0, 6, 6, 0, 2, -1, -1, -1, -1, -1, -1, -1},
{7, 3, 2, 6, 7, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{2, 3, 11, 10, 6, 8, 10, 8, 9, 8, 6, 7, -1, -1, -1, -1},
{2, 0, 7, 2, 7, 11, 0, 9, 7, 6, 7, 10, 9, 10, 7, -1},
{1, 8, 0, 1, 7, 8, 1, 10, 7, 6, 7, 10, 2, 3, 11, -1},
{11, 2, 1, 11, 1, 7, 10, 6, 1, 6, 7, 1, -1, -1, -1, -1},
{8, 9, 6, 8, 6, 7, 9, 1, 6, 11, 6, 3, 1, 3, 6, -1},
{0, 9, 1, 11, 6, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{7, 8, 0, 7, 0, 6, 3, 11, 0, 11, 6, 0, -1, -1, -1, -1},
{7, 11, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{7, 6, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{3, 0, 8, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{0, 1, 9, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{8, 1, 9, 8, 3, 1, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1},
{10, 1, 2, 6, 11, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{1, 2, 10, 3, 0, 8, 6, 11, 7, -1, -1, -1, -1, -1, -1, -1},
{2, 9, 0, 2, 10, 9, 6, 11, 7, -1, -1, -1, -1, -1, -1, -1},
{6, 11, 7, 2, 10, 3, 10, 8, 3, 10, 9, 8, -1, -1, -1, -1},
{7, 2, 3, 6, 2, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{7, 0, 8, 7, 6, 0, 6, 2, 0, -1, -1, -1, -1, -1, -1, -1},
{2, 7, 6, 2, 3, 7, 0, 1, 9, -1, -1, -1, -1, -1, -1, -1},
{1, 6, 2, 1, 8, 6, 1, 9, 8, 8, 7, 6, -1, -1, -1, -1},
{10, 7, 6, 10, 1, 7, 1, 3, 7, -1, -1, -1, -1, -1, -1, -1},
{10, 7, 6, 1, 7, 10, 1, 8, 7, 1, 0, 8, -1, -1, -1, -1},
{0, 3, 7, 0, 7, 10, 0, 10, 9, 6, 10, 7, -1, -1, -1, -1},
{7, 6, 10, 7, 10, 8, 8, 10, 9, -1, -1, -1, -1, -1, -1, -1},
{6, 8, 4, 11, 8, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{3, 6, 11, 3, 0, 6, 0, 4, 6, -1, -1, -1, -1, -1, -1, -1},
{8, 6, 11, 8, 4, 6, 9, 0, 1, -1, -1, -1, -1, -1, -1, -1},
{9, 4, 6, 9, 6, 3, 9, 3, 1, 11, 3, 6, -1, -1, -1, -1},
{6, 8, 4, 6, 11, 8, 2, 10, 1, -1, -1, -1, -1, -1, -1, -1},
{1, 2, 10, 3, 0, 11, 0, 6, 11, 0, 4, 6, -1, -1, -1, -1},
{4, 11, 8, 4, 6, 11, 0, 2, 9, 2, 10, 9, -1, -1, -1, -1},
{10, 9, 3, 10, 3, 2, 9, 4, 3, 11, 3, 6, 4, 6, 3, -1},
{8, 2, 3, 8, 4, 2, 4, 6, 2, -1, -1, -1, -1, -1, -1, -1},
{0, 4, 2, 4, 6, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{1, 9, 0, 2, 3, 4, 2, 4, 6, 4, 3, 8, -1, -1, -1, -1},
{1, 9, 4, 1, 4, 2, 2, 4, 6, -1, -1, -1, -1, -1, -1, -1},
{8, 1, 3, 8, 6, 1, 8, 4, 6, 6, 10, 1, -1, -1, -1, -1},
{10, 1, 0, 10, 0, 6, 6, 0, 4, -1, -1, -1, -1, -1, -1, -1},
{4, 6, 3, 4, 3, 8, 6, 10, 3, 0, 3, 9, 10, 9, 3, -1},
{10, 9, 4, 6, 10, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{4, 9, 5, 7, 6, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{0, 8, 3, 4, 9, 5, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1},
{5, 0, 1, 5, 4, 0, 7, 6, 11, -1, -1, -1, -1, -1, -1, -1},
{11, 7, 6, 8, 3, 4, 3, 5, 4, 3, 1, 5, -1, -1, -1, -1},
{9, 5, 4, 10, 1, 2, 7, 6, 11, -1, -1, -1, -1, -1, -1, -1},
{6, 11, 7, 1, 2, 10, 0, 8, 3, 4, 9, 5, -1, -1, -1, -1},
{7, 6, 11, 5, 4, 10, 4, 2, 10, 4, 0, 2, -1, -1, -1, -1},
{3, 4, 8, 3, 5, 4, 3, 2, 5, 10, 5, 2, 11, 7, 6, -1},
{7, 2, 3, 7, 6, 2, 5, 4, 9, -1, -1, -1, -1, -1, -1, -1},
{9, 5, 4, 0, 8, 6, 0, 6, 2, 6, 8, 7, -1, -1, -1, -1},
{3, 6, 2, 3, 7, 6, 1, 5, 0, 5, 4, 0, -1, -1, -1, -1},
{6, 2, 8, 6, 8, 7, 2, 1, 8, 4, 8, 5, 1, 5, 8, -1},
{9, 5, 4, 10, 1, 6, 1, 7, 6, 1, 3, 7, -1, -1, -1, -1},
{1, 6, 10, 1, 7, 6, 1, 0, 7, 8, 7, 0, 9, 5, 4, -1},
{4, 0, 10, 4, 10, 5, 0, 3, 10, 6, 10, 7, 3, 7, 10, -1},
{7, 6, 10, 7, 10, 8, 5, 4, 10, 4, 8, 10, -1, -1, -1, -1},
{6, 9, 5, 6, 11, 9, 11, 8, 9, -1, -1, -1, -1, -1, -1, -1},
{3, 6, 11, 0, 6, 3, 0, 5, 6, 0, 9, 5, -1, -1, -1, -1},
{0, 11, 8, 0, 5, 11, 0, 1, 5, 5, 6, 11, -1, -1, -1, -1},
{6, 11, 3, 6, 3, 5, 5, 3, 1, -1, -1, -1, -1, -1, -1, -1},
{1, 2, 10, 9, 5, 11, 9, 11, 8, 11, 5, 6, -1, -1, -1, -1},
{0, 11, 3, 0, 6, 11, 0, 9, 6, 5, 6, 9, 1, 2, 10, -1},
{11, 8, 5, 11, 5, 6, 8, 0, 5, 10, 5, 2, 0, 2, 5, -1},
{6, 11, 3, 6, 3, 5, 2, 10, 3, 10, 5, 3, -1, -1, -1, -1},
{5, 8, 9, 5, 2, 8, 5, 6, 2, 3, 8, 2, -1, -1, -1, -1},
{9, 5, 6, 9, 6, 0, 0, 6, 2, -1, -1, -1, -1, -1, -1, -1},
{1, 5, 8, 1, 8, 0, 5, 6, 8, 3, 8, 2, 6, 2, 8, -1},
{1, 5, 6, 2, 1, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{1, 3, 6, 1, 6, 10, 3, 8, 6, 5, 6, 9, 8, 9, 6, -1},
{10, 1, 0, 10, 0, 6, 9, 5, 0, 5, 6, 0, -1, -1, -1, -1},
{0, 3, 8, 5, 6, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{10, 5, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{11, 5, 10, 7, 5, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{11, 5, 10, 11, 7, 5, 8, 3, 0, -1, -1, -1, -1, -1, -1, -1},
{5, 11, 7, 5, 10, 11, 1, 9, 0, -1, -1, -1, -1, -1, -1, -1},
{10, 7, 5, 10, 11, 7, 9, 8, 1, 8, 3, 1, -1, -1, -1, -1},
{11, 1, 2, 11, 7, 1, 7, 5, 1, -1, -1, -1, -1, -1, -1, -1},
{0, 8, 3, 1, 2, 7, 1, 7, 5, 7, 2, 11, -1, -1, -1, -1},
{9, 7, 5, 9, 2, 7, 9, 0, 2, 2, 11, 7, -1, -1, -1, -1},
{7, 5, 2, 7, 2, 11, 5, 9, 2, 3, 2, 8, 9, 8, 2, -1},
{2, 5, 10, 2, 3, 5, 3, 7, 5, -1, -1, -1, -1, -1, -1, -1},
{8, 2, 0, 8, 5, 2, 8, 7, 5, 10, 2, 5, -1, -1, -1, -1},
{9, 0, 1, 5, 10, 3, 5, 3, 7, 3, 10, 2, -1, -1, -1, -1},
{9, 8, 2, 9, 2, 1, 8, 7, 2, 10, 2, 5, 7, 5, 2, -1},
{1, 3, 5, 3, 7, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{0, 8, 7, 0, 7, 1, 1, 7, 5, -1, -1, -1, -1, -1, -1, -1},
{9, 0, 3, 9, 3, 5, 5, 3, 7, -1, -1, -1, -1, -1, -1, -1},
{9, 8, 7, 5, 9, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{5, 8, 4, 5, 10, 8, 10, 11, 8, -1, -1, -1, -1, -1, -1, -1},
{5, 0, 4, 5, 11, 0, 5, 10, 11, 11, 3, 0, -1, -1, -1, -1},
{0, 1, 9, 8, 4, 10, 8, 10, 11, 10, 4, 5, -1, -1, -1, -1},
{10, 11, 4, 10, 4, 5, 11, 3, 4, 9, 4, 1, 3, 1, 4, -1},
{2, 5, 1, 2, 8, 5, 2, 11, 8, 4, 5, 8, -1, -1, -1, -1},
{0, 4, 11, 0, 11, 3, 4, 5, 11, 2, 11, 1, 5, 1, 11, -1},
{0, 2, 5, 0, 5, 9, 2, 11, 5, 4, 5, 8, 11, 8, 5, -1},
{9, 4, 5, 2, 11, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{2, 5, 10, 3, 5, 2, 3, 4, 5, 3, 8, 4, -1, -1, -1, -1},
{5, 10, 2, 5, 2, 4, 4, 2, 0, -1, -1, -1, -1, -1, -1, -1},
{3, 10, 2, 3, 5, 10, 3, 8, 5, 4, 5, 8, 0, 1, 9, -1},
{5, 10, 2, 5, 2, 4, 1, 9, 2, 9, 4, 2, -1, -1, -1, -1},
{8, 4, 5, 8, 5, 3, 3, 5, 1, -1, -1, -1, -1, -1, -1, -1},
{0, 4, 5, 1, 0, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{8, 4, 5, 8, 5, 3, 9, 0, 5, 0, 3, 5, -1, -1, -1, -1},
{9, 4, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{4, 11, 7, 4, 9, 11, 9, 10, 11, -1, -1, -1, -1, -1, -1, -1},
{0, 8, 3, 4, 9, 7, 9, 11, 7, 9, 10, 11, -1, -1, -1, -1},
{1, 10, 11, 1, 11, 4, 1, 4, 0, 7, 4, 11, -1, -1, -1, -1},
{3, 1, 4, 3, 4, 8, 1, 10, 4, 7, 4, 11, 10, 11, 4, -1},
{4, 11, 7, 9, 11, 4, 9, 2, 11, 9, 1, 2, -1, -1, -1, -1},
{9, 7, 4, 9, 11, 7, 9, 1, 11, 2, 11, 1, 0, 8, 3, -1},
{11, 7, 4, 11, 4, 2, 2, 4, 0, -1, -1, -1, -1, -1, -1, -1},
{11, 7, 4, 11, 4, 2, 8, 3, 4, 3, 2, 4, -1, -1, -1, -1},
{2, 9, 10, 2, 7, 9, 2, 3, 7, 7, 4, 9, -1, -1, -1, -1},
{9, 10, 7, 9, 7, 4, 10, 2, 7, 8, 7, 0, 2, 0, 7, -1},
{3, 7, 10, 3, 10, 2, 7, 4, 10, 1, 10, 0, 4, 0, 10, -1},
{1, 10, 2, 8, 7, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{4, 9, 1, 4, 1, 7, 7, 1, 3, -1, -1, -1, -1, -1, -1, -1},
{4, 9, 1, 4, 1, 7, 0, 8, 1, 8, 7, 1, -1, -1, -1, -1},
{4, 0, 3, 7, 4, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{4, 8, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{9, 10, 8, 10, 11, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{3, 0, 9, 3, 9, 11, 11, 9, 10, -1, -1, -1, -1, -1, -1, -1},
{0, 1, 10, 0, 10, 8, 8, 10, 11, -1, -1, -1, -1, -1, -1, -1},
{3, 1, 10, 11, 3, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{1, 2, 11, 1, 11, 9, 9, 11, 8, -1, -1, -1, -1, -1, -1, -1},
{3, 0, 9, 3, 9, 11, 1, 2, 9, 2, 11, 9, -1, -1, -1, -1},
{0, 2, 11, 8, 0, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{3, 2, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{2, 3, 8, 2, 8, 10, 10, 8, 9, -1, -1, -1, -1, -1, -1, -1},
{9, 10, 2, 0, 9, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{2, 3, 8, 2, 8, 10, 0, 1, 8, 1, 10, 8, -1, -1, -1, -1},
{1, 10, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{1, 3, 8, 9, 1, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{0, 9, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{0, 3, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}
};
// Lookup table which contains the indices of the vertices which define an edge.
static const int VERTEX_TABLE[12][2] =
{
{0, 1},
{1, 2},
{2, 3},
{3, 0},
{4, 5},
{5, 6},
{6, 7},
{7, 4},
{0, 4},
{1, 5},
{2, 6},
{3, 7}
};
/*
* The marching cubes algorithm can produce a maximum of 5 triangles per cell. Therefore the maximum triangle count of a grid is `w * h * d * 5`.
*/
struct triangle
{
glm::vec3 vertices[3];
};
bool less_than(const glm::vec3& a, const glm::vec3& b)
{
if (a.x < b.x)
return true;
else if (a.x > b.x)
return false;
if (a.y < b.y)
return true;
else if (a.y > b.y)
return false;
if (a.z < b.z)
return true;
return false;
}
glm::vec3 interpolate(float isolevel, glm::vec3 p0, glm::vec3 p1, float v0, float v1)
{
static const float epsilon = 0.00001f;
if (less_than(p1, p0))
{
glm::vec3 ptemp = p0;
p0 = p1;
p1 = ptemp;
float vtemp = v0;
v0 = v1;
v1 = vtemp;
}
if (std::fabs(v0 - v1) > epsilon)
{
return p0 + ((p1 - p0) / (v1 - v0) * (isolevel - v0));
}
return p0;
}
int polygonize(const voxel& vox, float isolevel, triangle* triangles)
{
// Set bitflags for each of the cube's 8 vertices, indicating whether or not they are inside the isosurface.
int edge_index = 0;
for (int i = 0; i < 8; ++i)
{
if (vox.values[i] < isolevel)
edge_index |= (1 << i);
}
// Get edge flags from lookup table
int edge_flags = EDGE_TABLE[edge_index];
if (edge_flags == 0)
{
// No intersections, cube is completely in or out of the isosurface.
return 0;
}
// Calculate vertex positions
glm::vec3 vertices[12];
// For each edge
for (int i = 0; i < 12; ++i)
{
// If this edge is intersected
if (edge_flags & (1 << i))
{
int a = VERTEX_TABLE[i][0];
int b = VERTEX_TABLE[i][1];
vertices[i] = interpolate(isolevel, vox.vertices[a], vox.vertices[b], vox.values[a], vox.values[b]);
}
}
// Form triangles
int triangle_count = 0;
for (int i = 0; TRIANGLE_TABLE[edge_index][i] != -1; i += 3)
{
int a = TRIANGLE_TABLE[edge_index][i];
int b = TRIANGLE_TABLE[edge_index][i + 1];
int c = TRIANGLE_TABLE[edge_index][i + 2];
triangles[triangle_count].vertices[0] = vertices[a];
triangles[triangle_count].vertices[1] = vertices[b];
triangles[triangle_count].vertices[2] = vertices[c];
++triangle_count;
}
return triangle_count;
}