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nh-rep/code/pre_processing/ParametricSample/Mathematics/AdaptiveSkeletonClimbing3.h

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// David Eberly, Geometric Tools, Redmond WA 98052
// Copyright (c) 1998-2021
// Distributed under the Boost Software License, Version 1.0.
// https://www.boost.org/LICENSE_1_0.txt
// https://www.geometrictools.com/License/Boost/LICENSE_1_0.txt
// Version: 4.0.2020.09.14
#pragma once
#include <Mathematics/Logger.h>
#include <Mathematics/Array2.h>
#include <Mathematics/Math.h>
#include <Mathematics/TriangleKey.h>
#include <map>
#include <memory>
#include <ostream>
// Extract level surfaces using an adaptive approach to reduce the triangle
// count. The implementation is for the algorithm described in the paper
// Multiresolution Isosurface Extraction with Adaptive Skeleton Climbing
// Tim Poston, Tien-Tsin Wong and Pheng-Ann Heng
// Computer Graphics forum, volume 17, issue 3, September 1998
// pages 137-147
// https://onlinelibrary.wiley.com/doi/abs/10.1111/1467-8659.00261
namespace gte
{
// The image type T must be one of the integer types: int8_t, int16_t,
// int32_t, uint8_t, uint16_t or uint32_t. Internal integer computations
// are performed using int64_t. The type Real is for extraction to
// floating-point vertices.
template <typename T, typename Real>
class AdaptiveSkeletonClimbing3
{
public:
// Construction and destruction. The input image is assumed to
// contain (2^N+1)-by-(2^N+1)-by-(2^N+1) elements where N >= 0.
// The organization is lexicographic order for (x,y,z). When
// 'fixBoundary' is set to 'true', image boundary voxels are not
// allowed to merge with any other voxels. This forces highest
// level of detail on the boundary. The idea is that an image too
// large to process by itself can be partitioned into smaller
// subimages and the adaptive skeleton climbing applied to each
// subimage. By forcing highest resolution on the boundary,
// adjacent subimages will not have any cracking problems.
AdaptiveSkeletonClimbing3(int N, T const* inputVoxels,
bool fixBoundary = false)
:
mTwoPowerN(1 << N),
mSize(mTwoPowerN + 1),
mSizeSqr(mSize * mSize),
mInputVoxels(inputVoxels),
mLevel((Real)0),
mFixBoundary(fixBoundary),
mXMerge(mSize, mSize),
mYMerge(mSize, mSize),
mZMerge(mSize, mSize)
{
static_assert(std::is_integral<T>::value && sizeof(T) <= 4,
"Type T must be int{8,16,32}_t or uint{8,16,32}_t.");
if (N <= 0 || mInputVoxels == nullptr)
{
LogError("Invalid input.");
}
for (int i = 0; i < mSize; ++i)
{
for (int j = 0; j < mSize; ++j)
{
mXMerge[i][j] = std::make_shared<LinearMergeTree>(N);
mYMerge[i][j] = std::make_shared<LinearMergeTree>(N);
mZMerge[i][j] = std::make_shared<LinearMergeTree>(N);
}
}
}
// TODO: Refactor this class to have base class SurfaceExtractor.
typedef std::array<Real, 3> Vertex;
typedef std::array<int, 2> Edge;
typedef TriangleKey<true> Triangle;
void Extract(Real level, int depth,
std::vector<Vertex>& vertices, std::vector<Triangle>& triangles)
{
std::vector<Vertex> localVertices;
std::vector<Triangle> localTriangles;
mBoxes.clear();
mLevel = level;
Merge(depth);
Tessellate(localVertices, localTriangles);
vertices = std::move(localVertices);
triangles = std::move(localTriangles);
}
void MakeUnique(std::vector<Vertex>& vertices,
std::vector<Triangle>& triangles)
{
size_t numVertices = vertices.size();
size_t numTriangles = triangles.size();
if (numVertices == 0 || numTriangles == 0)
{
return;
}
// Compute the map of unique vertices and assign to them new and
// unique indices.
std::map<Vertex, int> vmap;
int nextVertex = 0;
for (size_t v = 0; v < numVertices; ++v)
{
// Keep only unique vertices.
auto result = vmap.insert(std::make_pair(vertices[v], nextVertex));
if (result.second)
{
++nextVertex;
}
}
// Compute the map of unique triangles and assign to them new and
// unique indices.
std::map<Triangle, int> tmap;
int nextTriangle = 0;
for (size_t t = 0; t < numTriangles; ++t)
{
Triangle& triangle = triangles[t];
for (int i = 0; i < 3; ++i)
{
auto iter = vmap.find(vertices[triangle.V[i]]);
LogAssert(iter != vmap.end(), "Expecting the vertex to be in the vmap.");
triangle.V[i] = iter->second;
}
// Keep only unique triangles.
auto result = tmap.insert(std::make_pair(triangle, nextTriangle));
if (result.second)
{
++nextTriangle;
}
}
// Pack the vertices into an array.
vertices.resize(vmap.size());
for (auto const& element : vmap)
{
vertices[element.second] = element.first;
}
// Pack the triangles into an array.
triangles.resize(tmap.size());
for (auto const& element : tmap)
{
triangles[element.second] = element.first;
}
}
void OrientTriangles(std::vector<Vertex>& vertices,
std::vector<Triangle>& triangles, bool sameDir)
{
for (auto& triangle : triangles)
{
// Get the triangle vertices.
std::array<Real, 3> v0 = vertices[triangle.V[0]];
std::array<Real, 3> v1 = vertices[triangle.V[1]];
std::array<Real, 3> v2 = vertices[triangle.V[2]];
// Construct the triangle normal based on the current
// orientation.
std::array<Real, 3> edge1, edge2, normal;
for (int i = 0; i < 3; ++i)
{
edge1[i] = v1[i] - v0[i];
edge2[i] = v2[i] - v0[i];
}
normal[0] = edge1[1] * edge2[2] - edge1[2] * edge2[1];
normal[1] = edge1[2] * edge2[0] - edge1[0] * edge2[2];
normal[2] = edge1[0] * edge2[1] - edge1[1] * edge2[0];
// Get the image gradient at the vertices.
std::array<Real, 3> grad0 = GetGradient(v0);
std::array<Real, 3> grad1 = GetGradient(v1);
std::array<Real, 3> grad2 = GetGradient(v2);
// Compute the average gradient.
std::array<Real, 3> gradAvr;
for (int i = 0; i < 3; ++i)
{
gradAvr[i] = (grad0[i] + grad1[i] + grad2[i]) / (Real)3;
}
// Compute the dot product of normal and average gradient.
Real dot = gradAvr[0] * normal[0] + gradAvr[1] * normal[1] + gradAvr[2] * normal[2];
// Choose triangle orientation based on gradient direction.
if (sameDir)
{
if (dot < (Real)0)
{
// Wrong orientation, reorder it.
std::swap(triangle.V[1], triangle.V[2]);
}
}
else
{
if (dot > (Real)0)
{
// Wrong orientation, reorder it.
std::swap(triangle.V[1], triangle.V[2]);
}
}
}
}
void ComputeNormals(std::vector<Vertex> const& vertices,
std::vector<Triangle> const& triangles,
std::vector<std::array<Real, 3>>& normals)
{
// Compute a vertex normal to be area-weighted sums of the normals
// to the triangles that share that vertex.
std::array<Real, 3> const zero{ (Real)0, (Real)0, (Real)0 };
normals.resize(vertices.size());
std::fill(normals.begin(), normals.end(), zero);
for (auto const& triangle : triangles)
{
// Get the triangle vertices.
std::array<Real, 3> v0 = vertices[triangle.V[0]];
std::array<Real, 3> v1 = vertices[triangle.V[1]];
std::array<Real, 3> v2 = vertices[triangle.V[2]];
// Construct the triangle normal.
std::array<Real, 3> edge1, edge2, normal;
for (int i = 0; i < 3; ++i)
{
edge1[i] = v1[i] - v0[i];
edge2[i] = v2[i] - v0[i];
}
normal[0] = edge1[1] * edge2[2] - edge1[2] * edge2[1];
normal[1] = edge1[2] * edge2[0] - edge1[0] * edge2[2];
normal[2] = edge1[0] * edge2[1] - edge1[1] * edge2[0];
// Maintain the sum of normals at each vertex.
for (int i = 0; i < 3; ++i)
{
for (int j = 0; j < 3; ++j)
{
normals[triangle.V[i]][j] += normal[j];
}
}
}
// The normal vector storage was used to accumulate the sum of
// triangle normals. Now these vectors must be rescaled to be
// unit length.
for (auto& normal : normals)
{
Real sqrLength = normal[0] * normal[0] + normal[1] * normal[1] + normal[2] * normal[2];
Real length = std::sqrt(sqrLength);
if (length > (Real)0)
{
for (int i = 0; i < 3; ++i)
{
normal[i] /= length;
}
}
else
{
for (int i = 0; i < 3; ++i)
{
normal[i] = (Real)0;
}
}
}
}
// Support for debugging.
void PrintBoxes(std::ostream& output)
{
output << mBoxes.size() << std::endl;
for (size_t i = 0; i < mBoxes.size(); ++i)
{
OctBox const& box = mBoxes[i];
output << "box " << i << ": ";
output << "x0 = " << box.x0 << ", ";
output << "y0 = " << box.y0 << ", ";
output << "z0 = " << box.z0 << ", ";
output << "dx = " << box.dx << ", ";
output << "dy = " << box.dy << ", ";
output << "dz = " << box.dz << std::endl;
}
}
private:
// Helper classes for the skeleton climbing.
struct OctBox
{
OctBox(int inX0, int inY0, int inZ0, int inDX, int inDY, int inDZ,
int inLX, int inLY, int inLZ)
:
x0(inX0), y0(inY0), z0(inZ0),
x1(inX0 + inDX), y1(inY0 + inDY), z1(inZ0 + inDZ),
dx(inDX), dy(inDY), dz(inDZ),
LX(inLX), LY(inLY), LZ(inLZ)
{
}
int x0, y0, z0, x1, y1, z1, dx, dy, dz, LX, LY, LZ;
};
struct MergeBox
{
MergeBox(int stride)
:
xStride(stride), yStride(stride), zStride(stride),
valid(true)
{
}
int xStride, yStride, zStride;
bool valid;
};
class LinearMergeTree
{
public:
LinearMergeTree(int N)
:
mTwoPowerN(1 << N),
mNodes(2 * mTwoPowerN - 1),
mZeroBases(2 * mTwoPowerN - 1)
{
}
enum
{
CFG_NONE = 0,
CFG_INCR = 1,
CFG_DECR = 2,
CFG_MULT = 3,
CFG_ROOT_MASK = 3,
CFG_EDGE = 4,
CFG_ZERO_SUBEDGE = 8
};
bool IsNone(int i) const
{
return (mNodes[i] & CFG_ROOT_MASK) == CFG_NONE;
}
int GetRootType(int i) const
{
return mNodes[i] & CFG_ROOT_MASK;
}
int GetZeroBase(int i) const
{
return mZeroBases[i];
}
void SetEdge(int i)
{
mNodes[i] |= CFG_EDGE;
// Inform all predecessors whether they have a zero subedge.
if (mZeroBases[i] >= 0)
{
while (i > 0)
{
i = (i - 1) / 2;
mNodes[i] |= CFG_ZERO_SUBEDGE;
}
}
}
bool IsZeroEdge(int i) const
{
return mNodes[i] == (CFG_EDGE | CFG_INCR)
|| mNodes[i] == (CFG_EDGE | CFG_DECR);
}
bool HasZeroSubedge(int i) const
{
return (mNodes[i] & CFG_ZERO_SUBEDGE) != 0;
}
void SetLevel(Real level, T const* data, int offset, int stride)
{
// Assert: The 'level' is not an image value. Because T is
// an integer type, choose 'level' to be a Real-valued number
// that does not represent an integer.
// Determine the sign changes between pairs of consecutive
// samples.
int firstLeaf = mTwoPowerN - 1;
for (int i = 0, leaf = firstLeaf; i < mTwoPowerN; ++i, ++leaf)
{
int base = offset + stride * i;
Real value0 = static_cast<Real>(data[base]);
Real value1 = static_cast<Real>(data[base + stride]);
if (value0 > level)
{
if (value1 > level)
{
mNodes[leaf] = CFG_NONE;
mZeroBases[leaf] = -1;
}
else
{
mNodes[leaf] = CFG_DECR;
mZeroBases[leaf] = i;
}
}
else // value0 < level
{
if (value1 > level)
{
mNodes[leaf] = CFG_INCR;
mZeroBases[leaf] = i;
}
else
{
mNodes[leaf] = CFG_NONE;
mZeroBases[leaf] = -1;
}
}
}
// Propagate the sign change information up the binary tree.
for (int i = firstLeaf - 1; i >= 0; --i)
{
int twoIp1 = 2 * i + 1, twoIp2 = twoIp1 + 1;
int value0 = mNodes[twoIp1];
int value1 = mNodes[twoIp2];
int combine = (value0 | value1);
mNodes[i] = combine;
if (combine == CFG_INCR)
{
if (value0 == CFG_INCR)
{
mZeroBases[i] = mZeroBases[twoIp1];
}
else
{
mZeroBases[i] = mZeroBases[twoIp2];
}
}
else if (combine == CFG_DECR)
{
if (value0 == CFG_DECR)
{
mZeroBases[i] = mZeroBases[twoIp1];
}
else
{
mZeroBases[i] = mZeroBases[twoIp2];
}
}
else
{
mZeroBases[i] = -1;
}
}
}
private:
int mTwoPowerN;
std::vector<int> mNodes;
std::vector<int> mZeroBases;
};
class VETable
{
public:
VETable()
:
mVertices(18)
{
}
bool IsValidVertex(int i) const
{
return mVertices[i].valid;
}
int GetNumVertices() const
{
return static_cast<int>(mVertices.size());
}
Vertex const& GetVertex(int i) const
{
return mVertices[i].position;
}
void Insert(int i, Real x, Real y, Real z)
{
TVertex& vertex = mVertices[i];
vertex.position = Vertex{ x, y, z };
vertex.valid = true;
}
void Insert(Vertex const& position)
{
mVertices.push_back(TVertex(position));
}
void InsertEdge(int v0, int v1)
{
TVertex& vertex0 = mVertices[v0];
TVertex& vertex1 = mVertices[v1];
vertex0.adjacent[vertex0.adjQuantity] = v1;
++vertex0.adjQuantity;
vertex1.adjacent[vertex1.adjQuantity] = v0;
++vertex1.adjQuantity;
}
void RemoveTrianglesEC(std::vector<Vertex>& positions,
std::vector<Triangle>& triangles)
{
// Ear-clip the wireframe to get the triangles.
Triangle triangle;
while (RemoveEC(triangle))
{
int v0 = static_cast<int>(positions.size());
int v1 = v0 + 1;
int v2 = v1 + 1;
// Bypassing the constructor to avoid a warning in the
// release build by gcc 7.5.0 on Ubuntu 18.04.5 LTS:
// "assuming signed overflow does not occur when assuming
// that (X + c) >= X is always true." The correct
// constructor case is used because v0 < v1 < v2.
Triangle tkey;
tkey.V[0] = v0;
tkey.V[1] = v1;
tkey.V[2] = v2;
triangles.push_back(tkey);
positions.push_back(mVertices[triangle.V[0]].position);
positions.push_back(mVertices[triangle.V[1]].position);
positions.push_back(mVertices[triangle.V[2]].position);
}
}
void RemoveTrianglesSE(std::vector<Vertex>& positions,
std::vector<Triangle>& triangles)
{
// Compute centroid of vertices.
Vertex centroid = { (Real)0, (Real)0, (Real)0 };
int const vmax = static_cast<int>(mVertices.size());
int i, j, quantity = 0;
for (i = 0; i < vmax; i++)
{
TVertex const& vertex = mVertices[i];
if (vertex.valid)
{
for (j = 0; j < 3; ++j)
{
centroid[j] += vertex.position[j];
}
++quantity;
}
}
for (j = 0; j < 3; ++j)
{
centroid[j] /= static_cast<Real>(quantity);
}
int v0 = static_cast<int>(positions.size());
positions.push_back(centroid);
int i1 = 18;
int v1 = v0 + 1;
positions.push_back(mVertices[i1].position);
int i2 = mVertices[i1].adjacent[1], v2;
for (i = 0; i < quantity - 1; ++i)
{
v2 = v1 + 1;
positions.push_back(mVertices[i2].position);
// Bypassing the constructor to avoid a warning in the
// release build by gcc 7.5.0 on Ubuntu 18.04.5 LTS:
// "assuming signed overflow does not occur when assuming
// that (X + c) >= X is always true." The correct
// constructor case is used because v0 < v1 < v2.
Triangle tkey;
tkey.V[0] = v0;
tkey.V[1] = v1;
tkey.V[2] = v2;
triangles.push_back(tkey);
if (mVertices[i2].adjacent[1] != i1)
{
i1 = i2;
i2 = mVertices[i2].adjacent[1];
}
else
{
i1 = i2;
i2 = mVertices[i2].adjacent[0];
}
v1 = v2;
}
v2 = v0 + 1;
// Unlike the previous two constructor calls, it is not
// guaranteed that v0 < v1.
triangles.push_back(Triangle(v0, v1, v2));
}
protected:
void RemoveVertex(int i)
{
TVertex& vertex0 = mVertices[i];
int a0 = vertex0.adjacent[0];
int a1 = vertex0.adjacent[1];
TVertex& adjVertex0 = mVertices[a0];
TVertex& adjVertex1 = mVertices[a1];
int j;
for (j = 0; j < adjVertex0.adjQuantity; j++)
{
if (adjVertex0.adjacent[j] == i)
{
adjVertex0.adjacent[j] = a1;
break;
}
}
for (j = 0; j < adjVertex1.adjQuantity; j++)
{
if (adjVertex1.adjacent[j] == i)
{
adjVertex1.adjacent[j] = a0;
break;
}
}
vertex0.valid = false;
if (adjVertex0.adjQuantity == 2)
{
if (adjVertex0.adjacent[0] == adjVertex0.adjacent[1])
{
adjVertex0.valid = false;
}
}
if (adjVertex1.adjQuantity == 2)
{
if (adjVertex1.adjacent[0] == adjVertex1.adjacent[1])
{
adjVertex1.valid = false;
}
}
}
// ear clipping
bool RemoveEC(Triangle& triangle)
{
int numVertices = static_cast<int>(mVertices.size());
for (int i = 0; i < numVertices; ++i)
{
TVertex const& vertex = mVertices[i];
if (vertex.valid && vertex.adjQuantity == 2)
{
triangle.V[0] = i;
triangle.V[1] = vertex.adjacent[0];
triangle.V[2] = vertex.adjacent[1];
RemoveVertex(i);
return true;
}
}
return false;
}
class TVertex
{
public:
TVertex()
:
adjQuantity(0),
valid(false)
{
}
TVertex(Vertex const& inPosition)
:
position(inPosition),
adjQuantity(0),
valid(true)
{
}
Vertex position;
int adjQuantity;
std::array<int, 4> adjacent;
bool valid;
};
std::vector<TVertex> mVertices;
};
private:
// Support for merging monoboxes.
void Merge(int depth)
{
int x, y, z, offset, stride;
for (y = 0; y < mSize; ++y)
{
for (z = 0; z < mSize; ++z)
{
offset = mSize * (y + mSize * z);
stride = 1;
mXMerge[y][z]->SetLevel(mLevel, mInputVoxels, offset, stride);
}
}
for (x = 0; x < mSize; ++x)
{
for (z = 0; z < mSize; ++z)
{
offset = x + mSizeSqr * z;
stride = mSize;
mYMerge[x][z]->SetLevel(mLevel, mInputVoxels, offset, stride);
}
}
for (x = 0; x < mSize; ++x)
{
for (y = 0; y < mSize; ++y)
{
offset = x + mSize * y;
stride = mSizeSqr;
mZMerge[x][y]->SetLevel(mLevel, mInputVoxels, offset, stride);
}
}
Merge(0, 0, 0, 0, 0, 0, 0, mTwoPowerN, depth);
}
bool Merge(int v, int LX, int LY, int LZ, int x0, int y0, int z0, int stride, int depth)
{
if (stride > 1) // internal nodes
{
int hStride = stride / 2;
int vBase = 8 * v;
int v000 = vBase + 1;
int v100 = vBase + 2;
int v010 = vBase + 3;
int v110 = vBase + 4;
int v001 = vBase + 5;
int v101 = vBase + 6;
int v011 = vBase + 7;
int v111 = vBase + 8;
int LX0 = 2 * LX + 1, LX1 = LX0 + 1;
int LY0 = 2 * LY + 1, LY1 = LY0 + 1;
int LZ0 = 2 * LZ + 1, LZ1 = LZ0 + 1;
int x1 = x0 + hStride, y1 = y0 + hStride, z1 = z0 + hStride;
int dm1 = depth - 1;
bool m000 = Merge(v000, LX0, LY0, LZ0, x0, y0, z0, hStride, dm1);
bool m100 = Merge(v100, LX1, LY0, LZ0, x1, y0, z0, hStride, dm1);
bool m010 = Merge(v010, LX0, LY1, LZ0, x0, y1, z0, hStride, dm1);
bool m110 = Merge(v110, LX1, LY1, LZ0, x1, y1, z0, hStride, dm1);
bool m001 = Merge(v001, LX0, LY0, LZ1, x0, y0, z1, hStride, dm1);
bool m101 = Merge(v101, LX1, LY0, LZ1, x1, y0, z1, hStride, dm1);
bool m011 = Merge(v011, LX0, LY1, LZ1, x0, y1, z1, hStride, dm1);
bool m111 = Merge(v111, LX1, LY1, LZ1, x1, y1, z1, hStride, dm1);
MergeBox r000(hStride), r100(hStride), r010(hStride), r110(hStride);
MergeBox r001(hStride), r101(hStride), r011(hStride), r111(hStride);
if (depth <= 0)
{
if (m000 && m001)
{
DoZMerge(r000, r001, x0, y0, LZ);
}
if (m100 && m101)
{
DoZMerge(r100, r101, x1, y0, LZ);
}
if (m010 && m011)
{
DoZMerge(r010, r011, x0, y1, LZ);
}
if (m110 && m111)
{
DoZMerge(r110, r111, x1, y1, LZ);
}
if (m000 && m010)
{
DoYMerge(r000, r010, x0, LY, z0);
}
if (m100 && m110)
{
DoYMerge(r100, r110, x1, LY, z0);
}
if (m001 && m011)
{
DoYMerge(r001, r011, x0, LY, z1);
}
if (m101 && m111)
{
DoYMerge(r101, r111, x1, LY, z1);
}
if (m000 && m100)
{
DoXMerge(r000, r100, LX, y0, z0);
}
if (m010 && m110)
{
DoXMerge(r010, r110, LX, y1, z0);
}
if (m001 && m101)
{
DoXMerge(r001, r101, LX, y0, z1);
}
if (m011 && m111)
{
DoXMerge(r011, r111, LX, y1, z1);
}
}
if (depth <= 1)
{
if (r000.valid)
{
if (r000.xStride == stride)
{
if (r000.yStride == stride)
{
if (r000.zStride == stride)
{
return true;
}
else
{
AddBox(x0, y0, z0, stride, stride, hStride, LX, LY, LZ0);
}
}
else
{
if (r000.zStride == stride)
{
AddBox(x0, y0, z0, stride, hStride, stride, LX, LY0, LZ);
}
else
{
AddBox(x0, y0, z0, stride, hStride, hStride, LX, LY0, LZ0);
}
}
}
else
{
if (r000.yStride == stride)
{
if (r000.zStride == stride)
{
AddBox(x0, y0, z0, hStride, stride, stride, LX0, LY, LZ);
}
else
{
AddBox(x0, y0, z0, hStride, stride, hStride, LX0, LY, LZ0);
}
}
else
{
if (r000.zStride == stride)
{
AddBox(x0, y0, z0, hStride, hStride, stride, LX0, LY0, LZ);
}
else if (m000)
{
AddBox(x0, y0, z0, hStride, hStride, hStride, LX0, LY0, LZ0);
}
}
}
}
if (r100.valid)
{
if (r100.yStride == stride)
{
if (r100.zStride == stride)
{
AddBox(x1, y0, z0, hStride, stride, stride, LX1, LY, LZ);
}
else
{
AddBox(x1, y0, z0, hStride, stride, hStride, LX1, LY, LZ0);
}
}
else
{
if (r100.zStride == stride)
{
AddBox(x1, y0, z0, hStride, hStride, stride, LX1, LY0, LZ);
}
else if (m100)
{
AddBox(x1, y0, z0, hStride, hStride, hStride, LX1, LY0, LZ0);
}
}
}
if (r010.valid)
{
if (r010.xStride == stride)
{
if (r010.zStride == stride)
{
AddBox(x0, y1, z0, stride, hStride, stride, LX, LY1, LZ);
}
else
{
AddBox(x0, y1, z0, stride, hStride, hStride, LX, LY1, LZ0);
}
}
else
{
if (r010.zStride == stride)
{
AddBox(x0, y1, z0, hStride, hStride, stride, LX0, LY1, LZ);
}
else if (m010)
{
AddBox(x0, y1, z0, hStride, hStride, hStride, LX0, LY1, LZ0);
}
}
}
if (r001.valid)
{
if (r001.xStride == stride)
{
if (r001.yStride == stride)
{
AddBox(x0, y0, z1, stride, stride, hStride, LX, LY, LZ1);
}
else
{
AddBox(x0, y0, z1, stride, hStride, hStride, LX, LY0, LZ1);
}
}
else
{
if (r001.yStride == stride)
{
AddBox(x0, y0, z1, hStride, stride, hStride, LX0, LY, LZ1);
}
else if (m001)
{
AddBox(x0, y0, z1, hStride, hStride, hStride, LX0, LY0, LZ1);
}
}
}
if (r110.valid)
{
if (r110.zStride == stride)
{
AddBox(x1, y1, z0, hStride, hStride, stride, LX1, LY1, LZ);
}
else if (m110)
{
AddBox(x1, y1, z0, hStride, hStride, hStride, LX1, LY1, LZ0);
}
}
if (r101.valid)
{
if (r101.yStride == stride)
{
AddBox(x1, y0, z1, hStride, stride, hStride, LX1, LY, LZ1);
}
else if (m101)
{
AddBox(x1, y0, z1, hStride, hStride, hStride, LX1, LY0, LZ1);
}
}
if (r011.valid)
{
if (r011.xStride == stride)
{
AddBox(x0, y1, z1, stride, hStride, hStride, LX, LY1, LZ1);
}
else if (m011)
{
AddBox(x0, y1, z1, hStride, hStride, hStride, LX0, LY1, LZ1);
}
}
if (r111.valid && m111)
{
AddBox(x1, y1, z1, hStride, hStride, hStride, LX1, LY1, LZ1);
}
}
return false;
}
else // leaf nodes
{
if (mFixBoundary)
{
// Do not allow boundary voxels to merge with any other
// voxels.
AddBox(x0, y0, z0, 1, 1, 1, LX, LY, LZ);
return false;
}
// A leaf box is mergeable with neighbors as long as all its
// faces have 0 or 2 sign changes on the edges. That is, a
// face may not have sign changes on all four edges. If it
// does, the resulting box for tessellating is 1x1x1 and is
// handled separately from boxes of larger dimensions.
// xmin face
int z1 = z0 + 1;
int rt0 = mYMerge[x0][z0]->GetRootType(LY);
int rt1 = mYMerge[x0][z1]->GetRootType(LY);
if ((rt0 | rt1) == LinearMergeTree::CFG_MULT)
{
AddBox(x0, y0, z0, 1, 1, 1, LX, LY, LZ);
return false;
}
// xmax face
int x1 = x0 + 1;
rt0 = mYMerge[x1][z0]->GetRootType(LY);
rt1 = mYMerge[x1][z1]->GetRootType(LY);
if ((rt0 | rt1) == LinearMergeTree::CFG_MULT)
{
AddBox(x0, y0, z0, 1, 1, 1, LX, LY, LZ);
return false;
}
// ymin face
rt0 = mZMerge[x0][y0]->GetRootType(LZ);
rt1 = mZMerge[x1][y0]->GetRootType(LZ);
if ((rt0 | rt1) == LinearMergeTree::CFG_MULT)
{
AddBox(x0, y0, z0, 1, 1, 1, LX, LY, LZ);
return false;
}
// ymax face
int y1 = y0 + 1;
rt0 = mZMerge[x0][y1]->GetRootType(LZ);
rt1 = mZMerge[x1][y1]->GetRootType(LZ);
if ((rt0 | rt1) == LinearMergeTree::CFG_MULT)
{
AddBox(x0, y0, z0, 1, 1, 1, LX, LY, LZ);
return false;
}
// zmin face
rt0 = mXMerge[y0][z0]->GetRootType(LX);
rt1 = mXMerge[y1][z0]->GetRootType(LX);
if ((rt0 | rt1) == LinearMergeTree::CFG_MULT)
{
AddBox(x0, y0, z0, 1, 1, 1, LX, LY, LZ);
return false;
}
// zmax face
rt0 = mXMerge[y0][z1]->GetRootType(LX);
rt1 = mXMerge[y1][z1]->GetRootType(LX);
if ((rt0 | rt1) == LinearMergeTree::CFG_MULT)
{
AddBox(x0, y0, z0, 1, 1, 1, LX, LY, LZ);
return false;
}
return true;
}
}
bool DoXMerge(MergeBox& r0, MergeBox& r1, int LX, int y0, int z0)
{
if (!r0.valid || !r1.valid || r0.yStride != r1.yStride || r0.zStride != r1.zStride)
{
return false;
}
// Boxes are potentially x-mergeable.
int y1 = y0 + r0.yStride, z1 = z0 + r0.zStride;
int incr = 0, decr = 0;
for (int y = y0; y <= y1; ++y)
{
for (int z = z0; z <= z1; ++z)
{
switch (mXMerge[y][z]->GetRootType(LX))
{
case LinearMergeTree::CFG_MULT:
return false;
case LinearMergeTree::CFG_INCR:
++incr;
break;
case LinearMergeTree::CFG_DECR:
++decr;
break;
}
}
}
if (incr != 0 && decr != 0)
{
return false;
}
// Strongly mono, x-merge the boxes.
r0.xStride *= 2;
r1.valid = false;
return true;
}
bool DoYMerge(MergeBox& r0, MergeBox& r1, int x0, int LY, int z0)
{
if (!r0.valid || !r1.valid || r0.xStride != r1.xStride || r0.zStride != r1.zStride)
{
return false;
}
// Boxes are potentially y-mergeable.
int x1 = x0 + r0.xStride, z1 = z0 + r0.zStride;
int incr = 0, decr = 0;
for (int x = x0; x <= x1; ++x)
{
for (int z = z0; z <= z1; ++z)
{
switch (mYMerge[x][z]->GetRootType(LY))
{
case LinearMergeTree::CFG_MULT:
return false;
case LinearMergeTree::CFG_INCR:
++incr;
break;
case LinearMergeTree::CFG_DECR:
++decr;
break;
}
}
}
if (incr != 0 && decr != 0)
{
return false;
}
// Strongly mono, y-merge the boxes.
r0.yStride *= 2;
r1.valid = false;
return true;
}
bool DoZMerge(MergeBox& r0, MergeBox& r1, int x0, int y0, int LZ)
{
if (!r0.valid || !r1.valid || r0.xStride != r1.xStride || r0.yStride != r1.yStride)
{
return false;
}
// Boxes are potentially z-mergeable.
int x1 = x0 + r0.xStride, y1 = y0 + r0.yStride;
int incr = 0, decr = 0;
for (int x = x0; x <= x1; ++x)
{
for (int y = y0; y <= y1; ++y)
{
switch (mZMerge[x][y]->GetRootType(LZ))
{
case LinearMergeTree::CFG_MULT:
return false;
case LinearMergeTree::CFG_INCR:
++incr;
break;
case LinearMergeTree::CFG_DECR:
++decr;
break;
}
}
}
if (incr != 0 && decr != 0)
{
return false;
}
// Strongly mono, z-merge the boxes.
r0.zStride *= 2;
r1.valid = false;
return true;
}
void AddBox(int x0, int y0, int z0, int dx, int dy, int dz, int LX, int LY, int LZ)
{
OctBox box(x0, y0, z0, dx, dy, dz, LX, LY, LZ);
mBoxes.push_back(box);
// Mark box edges in linear merge trees. This information will be
// used later for extraction.
mXMerge[box.y0][box.z0]->SetEdge(box.LX);
mXMerge[box.y0][box.z1]->SetEdge(box.LX);
mXMerge[box.y1][box.z0]->SetEdge(box.LX);
mXMerge[box.y1][box.z1]->SetEdge(box.LX);
mYMerge[box.x0][box.z0]->SetEdge(box.LY);
mYMerge[box.x0][box.z1]->SetEdge(box.LY);
mYMerge[box.x1][box.z0]->SetEdge(box.LY);
mYMerge[box.x1][box.z1]->SetEdge(box.LY);
mZMerge[box.x0][box.y0]->SetEdge(box.LZ);
mZMerge[box.x0][box.y1]->SetEdge(box.LZ);
mZMerge[box.x1][box.y0]->SetEdge(box.LZ);
mZMerge[box.x1][box.y1]->SetEdge(box.LZ);
}
// Support for tessellating monoboxes.
void Tessellate(std::vector<Vertex>& positions, std::vector<Triangle>& triangles)
{
for (size_t i = 0; i < mBoxes.size(); ++i)
{
OctBox const& box = mBoxes[i];
// Get vertices on edges of box.
VETable table;
unsigned int type;
GetVertices(box, type, table);
if (type == 0)
{
continue;
}
// Add wireframe edges to table, add face-vertices if
// necessary.
if (box.dx > 1 || box.dy > 1 || box.dz > 1)
{
// Box is larger than voxel, each face has at most one
// edge.
GetXMinEdgesM(box, type, table);
GetXMaxEdgesM(box, type, table);
GetYMinEdgesM(box, type, table);
GetYMaxEdgesM(box, type, table);
GetZMinEdgesM(box, type, table);
GetZMaxEdgesM(box, type, table);
if (table.GetNumVertices() > 18)
{
table.RemoveTrianglesSE(positions, triangles);
}
else
{
table.RemoveTrianglesEC(positions, triangles);
}
}
else
{
// The box is a 1x1x1 voxel. Do the full edge analysis
// but no splitting is required.
GetXMinEdgesS(box, type, table);
GetXMaxEdgesS(box, type, table);
GetYMinEdgesS(box, type, table);
GetYMaxEdgesS(box, type, table);
GetZMinEdgesS(box, type, table);
GetZMaxEdgesS(box, type, table);
table.RemoveTrianglesEC(positions, triangles);
}
}
}
Real GetXInterp(int x, int y, int z) const
{
int index = x + mSize * (y + mSize * z);
Real f0 = static_cast<Real>(mInputVoxels[index]);
++index;
Real f1 = static_cast<Real>(mInputVoxels[index]);
return static_cast<Real>(x) + (mLevel - f0) / (f1 - f0);
}
Real GetYInterp(int x, int y, int z) const
{
int index = x + mSize * (y + mSize * z);
Real f0 = static_cast<Real>(mInputVoxels[index]);
index += mSize;
Real f1 = static_cast<Real>(mInputVoxels[index]);
return static_cast<Real>(y) + (mLevel - f0) / (f1 - f0);
}
Real GetZInterp(int x, int y, int z) const
{
int index = x + mSize * (y + mSize * z);
Real f0 = static_cast<Real>(mInputVoxels[index]);
index += mSizeSqr;
Real f1 = static_cast<Real>(mInputVoxels[index]);
return static_cast<Real>(z) + (mLevel - f0) / (f1 - f0);
}
void GetVertices(OctBox const& box, unsigned int& type, VETable& table)
{
int root;
type = 0;
// xmin-ymin edge
root = mZMerge[box.x0][box.y0]->GetZeroBase(box.LZ);
if (root != -1)
{
type |= EB_XMIN_YMIN;
table.Insert(EI_XMIN_YMIN,
static_cast<float>(box.x0),
static_cast<float>(box.y0),
GetZInterp(box.x0, box.y0, root));
}
// xmin-ymax edge
root = mZMerge[box.x0][box.y1]->GetZeroBase(box.LZ);
if (root != -1)
{
type |= EB_XMIN_YMAX;
table.Insert(EI_XMIN_YMAX,
static_cast<float>(box.x0),
static_cast<float>(box.y1),
GetZInterp(box.x0, box.y1, root));
}
// xmax-ymin edge
root = mZMerge[box.x1][box.y0]->GetZeroBase(box.LZ);
if (root != -1)
{
type |= EB_XMAX_YMIN;
table.Insert(EI_XMAX_YMIN,
static_cast<float>(box.x1),
static_cast<float>(box.y0),
GetZInterp(box.x1, box.y0, root));
}
// xmax-ymax edge
root = mZMerge[box.x1][box.y1]->GetZeroBase(box.LZ);
if (root != -1)
{
type |= EB_XMAX_YMAX;
table.Insert(EI_XMAX_YMAX,
static_cast<float>(box.x1),
static_cast<float>(box.y1),
GetZInterp(box.x1, box.y1, root));
}
// xmin-zmin edge
root = mYMerge[box.x0][box.z0]->GetZeroBase(box.LY);
if (root != -1)
{
type |= EB_XMIN_ZMIN;
table.Insert(EI_XMIN_ZMIN,
static_cast<float>(box.x0),
GetYInterp(box.x0, root, box.z0),
static_cast<float>(box.z0));
}
// xmin-zmax edge
root = mYMerge[box.x0][box.z1]->GetZeroBase(box.LY);
if (root != -1)
{
type |= EB_XMIN_ZMAX;
table.Insert(EI_XMIN_ZMAX,
static_cast<float>(box.x0),
GetYInterp(box.x0, root, box.z1),
static_cast<float>(box.z1));
}
// xmax-zmin edge
root = mYMerge[box.x1][box.z0]->GetZeroBase(box.LY);
if (root != -1)
{
type |= EB_XMAX_ZMIN;
table.Insert(EI_XMAX_ZMIN,
static_cast<float>(box.x1),
GetYInterp(box.x1, root, box.z0),
static_cast<float>(box.z0));
}
// xmax-zmax edge
root = mYMerge[box.x1][box.z1]->GetZeroBase(box.LY);
if (root != -1)
{
type |= EB_XMAX_ZMAX;
table.Insert(EI_XMAX_ZMAX,
static_cast<float>(box.x1),
GetYInterp(box.x1, root, box.z1),
static_cast<float>(box.z1));
}
// ymin-zmin edge
root = mXMerge[box.y0][box.z0]->GetZeroBase(box.LX);
if (root != -1)
{
type |= EB_YMIN_ZMIN;
table.Insert(EI_YMIN_ZMIN,
GetXInterp(root, box.y0, box.z0),
static_cast<float>(box.y0),
static_cast<float>(box.z0));
}
// ymin-zmax edge
root = mXMerge[box.y0][box.z1]->GetZeroBase(box.LX);
if (root != -1)
{
type |= EB_YMIN_ZMAX;
table.Insert(EI_YMIN_ZMAX,
GetXInterp(root, box.y0, box.z1),
static_cast<float>(box.y0),
static_cast<float>(box.z1));
}
// ymax-zmin edge
root = mXMerge[box.y1][box.z0]->GetZeroBase(box.LX);
if (root != -1)
{
type |= EB_YMAX_ZMIN;
table.Insert(EI_YMAX_ZMIN,
GetXInterp(root, box.y1, box.z0),
static_cast<float>(box.y1),
static_cast<float>(box.z0));
}
// ymax-zmax edge
root = mXMerge[box.y1][box.z1]->GetZeroBase(box.LX);
if (root != -1)
{
type |= EB_YMAX_ZMAX;
table.Insert(EI_YMAX_ZMAX,
GetXInterp(root, box.y1, box.z1),
static_cast<float>(box.y1),
static_cast<float>(box.z1));
}
}
// Edge extraction for single boxes (1x1x1).
void GetXMinEdgesS(OctBox const& box, unsigned int type, VETable& table)
{
unsigned int faceType = 0;
if (type & EB_XMIN_YMIN)
{
faceType |= 0x01;
}
if (type & EB_XMIN_YMAX)
{
faceType |= 0x02;
}
if (type & EB_XMIN_ZMIN)
{
faceType |= 0x04;
}
if (type & EB_XMIN_ZMAX)
{
faceType |= 0x08;
}
switch (faceType)
{
case 0:
return;
case 3:
table.InsertEdge(EI_XMIN_YMIN, EI_XMIN_YMAX);
break;
case 5:
table.InsertEdge(EI_XMIN_YMIN, EI_XMIN_ZMIN);
break;
case 6:
table.InsertEdge(EI_XMIN_YMAX, EI_XMIN_ZMIN);
break;
case 9:
table.InsertEdge(EI_XMIN_YMIN, EI_XMIN_ZMAX);
break;
case 10:
table.InsertEdge(EI_XMIN_YMAX, EI_XMIN_ZMAX);
break;
case 12:
table.InsertEdge(EI_XMIN_ZMIN, EI_XMIN_ZMAX);
break;
case 15:
{
// Four vertices, one per edge, need to disambiguate.
int i = box.x0 + mSize * (box.y0 + mSize * box.z0);
// F(x,y,z)
int64_t f00 = static_cast<int64_t>(mInputVoxels[i]);
i += mSize;
// F(x,y+1,z)
int64_t f10 = static_cast<int64_t>(mInputVoxels[i]);
i += mSizeSqr;
// F(x,y+1,z+1)
int64_t f11 = static_cast<int64_t>(mInputVoxels[i]);
i -= mSize;
// F(x,y,z+1)
int64_t f01 = static_cast<int64_t>(mInputVoxels[i]);
int64_t det = f00 * f11 - f01 * f10;
if (det > 0)
{
// Disjoint hyperbolic segments, pair <P0,P2>, <P1,P3>.
table.InsertEdge(EI_XMIN_YMIN, EI_XMIN_ZMIN);
table.InsertEdge(EI_XMIN_YMAX, EI_XMIN_ZMAX);
}
else if (det < 0)
{
// Disjoint hyperbolic segments, pair <P0,P3>, <P1,P2>.
table.InsertEdge(EI_XMIN_YMIN, EI_XMIN_ZMAX);
table.InsertEdge(EI_XMIN_YMAX, EI_XMIN_ZMIN);
}
else
{
// Plus-sign configuration, add branch point to
// tessellation.
table.Insert(FI_XMIN,
table.GetVertex(EI_XMIN_ZMIN)[0],
table.GetVertex(EI_XMIN_ZMIN)[1],
table.GetVertex(EI_XMIN_YMIN)[2]);
// Add edges sharing the branch point.
table.InsertEdge(EI_XMIN_YMIN, FI_XMIN);
table.InsertEdge(EI_XMIN_YMAX, FI_XMIN);
table.InsertEdge(EI_XMIN_ZMIN, FI_XMIN);
table.InsertEdge(EI_XMIN_ZMAX, FI_XMIN);
}
break;
}
default:
LogError("The level value cannot be an exact integer.");
}
}
void GetXMaxEdgesS(OctBox const& box, unsigned int type, VETable& table)
{
unsigned int faceType = 0;
if (type & EB_XMAX_YMIN)
{
faceType |= 0x01;
}
if (type & EB_XMAX_YMAX)
{
faceType |= 0x02;
}
if (type & EB_XMAX_ZMIN)
{
faceType |= 0x04;
}
if (type & EB_XMAX_ZMAX)
{
faceType |= 0x08;
}
switch (faceType)
{
case 0:
return;
case 3:
table.InsertEdge(EI_XMAX_YMIN, EI_XMAX_YMAX);
break;
case 5:
table.InsertEdge(EI_XMAX_YMIN, EI_XMAX_ZMIN);
break;
case 6:
table.InsertEdge(EI_XMAX_YMAX, EI_XMAX_ZMIN);
break;
case 9:
table.InsertEdge(EI_XMAX_YMIN, EI_XMAX_ZMAX);
break;
case 10:
table.InsertEdge(EI_XMAX_YMAX, EI_XMAX_ZMAX);
break;
case 12:
table.InsertEdge(EI_XMAX_ZMIN, EI_XMAX_ZMAX);
break;
case 15:
{
// Four vertices, one per edge, need to disambiguate.
int i = box.x1 + mSize * (box.y0 + mSize * box.z0);
// F(x,y,z)
int64_t f00 = static_cast<int64_t>(mInputVoxels[i]);
i += mSize;
// F(x,y+1,z)
int64_t f10 = static_cast<int64_t>(mInputVoxels[i]);
i += mSizeSqr;
// F(x,y+1,z+1)
int64_t f11 = static_cast<int64_t>(mInputVoxels[i]);
i -= mSize;
// F(x,y,z+1)
int64_t f01 = static_cast<int64_t>(mInputVoxels[i]);
int64_t det = f00 * f11 - f01 * f10;
if (det > 0)
{
// Disjoint hyperbolic segments, pair <P0,P2>, <P1,P3>.
table.InsertEdge(EI_XMAX_YMIN, EI_XMAX_ZMIN);
table.InsertEdge(EI_XMAX_YMAX, EI_XMAX_ZMAX);
}
else if (det < 0)
{
// Disjoint hyperbolic segments, pair <P0,P3>, <P1,P2>.
table.InsertEdge(EI_XMAX_YMIN, EI_XMAX_ZMAX);
table.InsertEdge(EI_XMAX_YMAX, EI_XMAX_ZMIN);
}
else
{
// Plus-sign configuration, add branch point to
// tessellation.
table.Insert(FI_XMAX,
table.GetVertex(EI_XMAX_ZMIN)[0],
table.GetVertex(EI_XMAX_ZMIN)[1],
table.GetVertex(EI_XMAX_YMIN)[2]);
// Add edges sharing the branch point.
table.InsertEdge(EI_XMAX_YMIN, FI_XMAX);
table.InsertEdge(EI_XMAX_YMAX, FI_XMAX);
table.InsertEdge(EI_XMAX_ZMIN, FI_XMAX);
table.InsertEdge(EI_XMAX_ZMAX, FI_XMAX);
}
break;
}
default:
LogError("The level value cannot be an exact integer.");
}
}
void GetYMinEdgesS(OctBox const& box, unsigned int type, VETable& table)
{
unsigned int faceType = 0;
if (type & EB_XMIN_YMIN)
{
faceType |= 0x01;
}
if (type & EB_XMAX_YMIN)
{
faceType |= 0x02;
}
if (type & EB_YMIN_ZMIN)
{
faceType |= 0x04;
}
if (type & EB_YMIN_ZMAX)
{
faceType |= 0x08;
}
switch (faceType)
{
case 0:
return;
case 3:
table.InsertEdge(EI_XMIN_YMIN, EI_XMAX_YMIN);
break;
case 5:
table.InsertEdge(EI_XMIN_YMIN, EI_YMIN_ZMIN);
break;
case 6:
table.InsertEdge(EI_XMAX_YMIN, EI_YMIN_ZMIN);
break;
case 9:
table.InsertEdge(EI_XMIN_YMIN, EI_YMIN_ZMAX);
break;
case 10:
table.InsertEdge(EI_XMAX_YMIN, EI_YMIN_ZMAX);
break;
case 12:
table.InsertEdge(EI_YMIN_ZMIN, EI_YMIN_ZMAX);
break;
case 15:
{
// Four vertices, one per edge, need to disambiguate.
int i = box.x0 + mSize * (box.y0 + mSize * box.z0);
// F(x,y,z)
int64_t f00 = static_cast<int64_t>(mInputVoxels[i]);
++i;
// F(x+1,y,z)
int64_t f10 = static_cast<int64_t>(mInputVoxels[i]);
i += mSizeSqr;
// F(x+1,y,z+1)
int64_t f11 = static_cast<int64_t>(mInputVoxels[i]);
--i;
// F(x,y,z+1)
int64_t f01 = static_cast<int64_t>(mInputVoxels[i]);
int64_t det = f00 * f11 - f01 * f10;
if (det > 0)
{
// Disjoint hyperbolic segments, pair <P0,P2>, <P1,P3>.
table.InsertEdge(EI_XMIN_YMIN, EI_YMIN_ZMIN);
table.InsertEdge(EI_XMAX_YMIN, EI_YMIN_ZMAX);
}
else if (det < 0)
{
// Disjoint hyperbolic segments, pair <P0,P3>, <P1,P2>.
table.InsertEdge(EI_XMIN_YMIN, EI_YMIN_ZMAX);
table.InsertEdge(EI_XMAX_YMIN, EI_YMIN_ZMIN);
}
else
{
// Plus-sign configuration, add branch point to
// tessellation.
table.Insert(FI_YMIN,
table.GetVertex(EI_YMIN_ZMIN)[0],
table.GetVertex(EI_XMIN_YMIN)[1],
table.GetVertex(EI_XMIN_YMIN)[2]);
// Add edges sharing the branch point.
table.InsertEdge(EI_XMIN_YMIN, FI_YMIN);
table.InsertEdge(EI_XMAX_YMIN, FI_YMIN);
table.InsertEdge(EI_YMIN_ZMIN, FI_YMIN);
table.InsertEdge(EI_YMIN_ZMAX, FI_YMIN);
}
break;
}
default:
LogError("The level value cannot be an exact integer.");
}
}
void GetYMaxEdgesS(OctBox const& box, unsigned int type, VETable& table)
{
unsigned int faceType = 0;
if (type & EB_XMIN_YMAX)
{
faceType |= 0x01;
}
if (type & EB_XMAX_YMAX)
{
faceType |= 0x02;
}
if (type & EB_YMAX_ZMIN)
{
faceType |= 0x04;
}
if (type & EB_YMAX_ZMAX)
{
faceType |= 0x08;
}
switch (faceType)
{
case 0:
return;
case 3:
table.InsertEdge(EI_XMIN_YMAX, EI_XMAX_YMAX);
break;
case 5:
table.InsertEdge(EI_XMIN_YMAX, EI_YMAX_ZMIN);
break;
case 6:
table.InsertEdge(EI_XMAX_YMAX, EI_YMAX_ZMIN);
break;
case 9:
table.InsertEdge(EI_XMIN_YMAX, EI_YMAX_ZMAX);
break;
case 10:
table.InsertEdge(EI_XMAX_YMAX, EI_YMAX_ZMAX);
break;
case 12:
table.InsertEdge(EI_YMAX_ZMIN, EI_YMAX_ZMAX);
break;
case 15:
{
// Four vertices, one per edge, need to disambiguate.
int i = box.x0 + mSize * (box.y1 + mSize * box.z0);
// F(x,y,z)
int64_t f00 = static_cast<int64_t>(mInputVoxels[i]);
++i;
// F(x+1,y,z)
int64_t f10 = static_cast<int64_t>(mInputVoxels[i]);
i += mSizeSqr;
// F(x+1,y,z+1)
int64_t f11 = static_cast<int64_t>(mInputVoxels[i]);
--i;
// F(x,y,z+1)
int64_t f01 = static_cast<int64_t>(mInputVoxels[i]);
int64_t det = f00 * f11 - f01 * f10;
if (det > 0)
{
// Disjoint hyperbolic segments, pair <P0,P2>, <P1,P3>.
table.InsertEdge(EI_XMIN_YMAX, EI_YMAX_ZMIN);
table.InsertEdge(EI_XMAX_YMAX, EI_YMAX_ZMAX);
}
else if (det < 0)
{
// Disjoint hyperbolic segments, pair <P0,P3>, <P1,P2>.
table.InsertEdge(EI_XMIN_YMAX, EI_YMAX_ZMAX);
table.InsertEdge(EI_XMAX_YMAX, EI_YMAX_ZMIN);
}
else
{
// Plus-sign configuration, add branch point to
// tessellation.
table.Insert(FI_YMAX,
table.GetVertex(EI_YMAX_ZMIN)[0],
table.GetVertex(EI_XMIN_YMAX)[1],
table.GetVertex(EI_XMIN_YMAX)[2]);
// Add edges sharing the branch point.
table.InsertEdge(EI_XMIN_YMAX, FI_YMAX);
table.InsertEdge(EI_XMAX_YMAX, FI_YMAX);
table.InsertEdge(EI_YMAX_ZMIN, FI_YMAX);
table.InsertEdge(EI_YMAX_ZMAX, FI_YMAX);
}
break;
}
default:
LogError("The level value cannot be an exact integer.");
}
}
void GetZMinEdgesS(OctBox const& box, unsigned int type, VETable& table)
{
unsigned int faceType = 0;
if (type & EB_XMIN_ZMIN)
{
faceType |= 0x01;
}
if (type & EB_XMAX_ZMIN)
{
faceType |= 0x02;
}
if (type & EB_YMIN_ZMIN)
{
faceType |= 0x04;
}
if (type & EB_YMAX_ZMIN)
{
faceType |= 0x08;
}
switch (faceType)
{
case 0:
return;
case 3:
table.InsertEdge(EI_XMIN_ZMIN, EI_XMAX_ZMIN);
break;
case 5:
table.InsertEdge(EI_XMIN_ZMIN, EI_YMIN_ZMIN);
break;
case 6:
table.InsertEdge(EI_XMAX_ZMIN, EI_YMIN_ZMIN);
break;
case 9:
table.InsertEdge(EI_XMIN_ZMIN, EI_YMAX_ZMIN);
break;
case 10:
table.InsertEdge(EI_XMAX_ZMIN, EI_YMAX_ZMIN);
break;
case 12:
table.InsertEdge(EI_YMIN_ZMIN, EI_YMAX_ZMIN);
break;
case 15:
{
// Four vertices, one per edge, need to disambiguate.
int i = box.x0 + mSize * (box.y0 + mSize * box.z0);
// F(x,y,z)
int64_t f00 = static_cast<int64_t>(mInputVoxels[i]);
++i;
// F(x+1,y,z)
int64_t f10 = static_cast<int64_t>(mInputVoxels[i]);
i += mSize;
// F(x+1,y+1,z)
int64_t f11 = static_cast<int64_t>(mInputVoxels[i]);
--i;
// F(x,y+1,z)
int64_t f01 = static_cast<int64_t>(mInputVoxels[i]);
int64_t det = f00 * f11 - f01 * f10;
if (det > 0)
{
// Disjoint hyperbolic segments, pair <P0,P2>, <P1,P3>.
table.InsertEdge(EI_XMIN_ZMIN, EI_YMIN_ZMIN);
table.InsertEdge(EI_XMAX_ZMIN, EI_YMAX_ZMIN);
}
else if (det < 0)
{
// Disjoint hyperbolic segments, pair <P0,P3>, <P1,P2>.
table.InsertEdge(EI_XMIN_ZMIN, EI_YMAX_ZMIN);
table.InsertEdge(EI_XMAX_ZMIN, EI_YMIN_ZMIN);
}
else
{
// Plus-sign configuration, add branch point to
// tessellation.
table.Insert(FI_ZMIN,
table.GetVertex(EI_YMIN_ZMIN)[0],
table.GetVertex(EI_XMIN_ZMIN)[1],
table.GetVertex(EI_XMIN_ZMIN)[2]);
// Add edges sharing the branch point.
table.InsertEdge(EI_XMIN_ZMIN, FI_ZMIN);
table.InsertEdge(EI_XMAX_ZMIN, FI_ZMIN);
table.InsertEdge(EI_YMIN_ZMIN, FI_ZMIN);
table.InsertEdge(EI_YMAX_ZMIN, FI_ZMIN);
}
break;
}
default:
LogError("The level value cannot be an exact integer.");
}
}
void GetZMaxEdgesS(const OctBox& box, unsigned int type, VETable& table)
{
unsigned int faceType = 0;
if (type & EB_XMIN_ZMAX)
{
faceType |= 0x01;
}
if (type & EB_XMAX_ZMAX)
{
faceType |= 0x02;
}
if (type & EB_YMIN_ZMAX)
{
faceType |= 0x04;
}
if (type & EB_YMAX_ZMAX)
{
faceType |= 0x08;
}
switch (faceType)
{
case 0:
return;
case 3:
table.InsertEdge(EI_XMIN_ZMAX, EI_XMAX_ZMAX);
break;
case 5:
table.InsertEdge(EI_XMIN_ZMAX, EI_YMIN_ZMAX);
break;
case 6:
table.InsertEdge(EI_XMAX_ZMAX, EI_YMIN_ZMAX);
break;
case 9:
table.InsertEdge(EI_XMIN_ZMAX, EI_YMAX_ZMAX);
break;
case 10:
table.InsertEdge(EI_XMAX_ZMAX, EI_YMAX_ZMAX);
break;
case 12:
table.InsertEdge(EI_YMIN_ZMAX, EI_YMAX_ZMAX);
break;
case 15:
{
// Four vertices, one per edge, need to disambiguate.
int i = box.x0 + mSize * (box.y0 + mSize * box.z1);
// F(x,y,z)
int64_t f00 = static_cast<int64_t>(mInputVoxels[i]);
i++;
// F(x+1,y,z)
int64_t f10 = static_cast<int64_t>(mInputVoxels[i]);
i += mSize;
// F(x+1,y+1,z)
int64_t f11 = static_cast<int64_t>(mInputVoxels[i]);
i--;
// F(x,y+1,z)
int64_t f01 = static_cast<int64_t>(mInputVoxels[i]);
int64_t det = f00 * f11 - f01 * f10;
if (det > 0)
{
// Disjoint hyperbolic segments, pair <P0,P2>, <P1,P3>.
table.InsertEdge(EI_XMIN_ZMAX, EI_YMIN_ZMAX);
table.InsertEdge(EI_XMAX_ZMAX, EI_YMAX_ZMAX);
}
else if (det < 0)
{
// Disjoint hyperbolic segments, pair <P0,P3>, <P1,P2>.
table.InsertEdge(EI_XMIN_ZMAX, EI_YMAX_ZMAX);
table.InsertEdge(EI_XMAX_ZMAX, EI_YMIN_ZMAX);
}
else
{
// Plus-sign configuration, add branch point to
// tessellation.
table.Insert(FI_ZMAX,
table.GetVertex(EI_YMIN_ZMAX)[0],
table.GetVertex(EI_XMIN_ZMAX)[1],
table.GetVertex(EI_XMIN_ZMAX)[2]);
// Add edges sharing the branch point.
table.InsertEdge(EI_XMIN_ZMAX, FI_ZMAX);
table.InsertEdge(EI_XMAX_ZMAX, FI_ZMAX);
table.InsertEdge(EI_YMIN_ZMAX, FI_ZMAX);
table.InsertEdge(EI_YMAX_ZMAX, FI_ZMAX);
}
break;
}
default:
LogError("The level value cannot be an exact integer.");
}
}
// Edge extraction for merged boxes.
class Sort0
{
public:
bool operator()(Vertex const& arg0, Vertex const& arg1) const
{
if (arg0[0] < arg1[0])
{
return true;
}
if (arg0[0] > arg1[0])
{
return false;
}
if (arg0[1] < arg1[1])
{
return true;
}
if (arg0[1] > arg1[1])
{
return false;
}
return arg0[2] < arg1[2];
}
};
class Sort1
{
public:
bool operator()(Vertex const& arg0, Vertex const& arg1) const
{
if (arg0[2] < arg1[2])
{
return true;
}
if (arg0[2] > arg1[2])
{
return false;
}
if (arg0[0] < arg1[0])
{
return true;
}
if (arg0[0] > arg1[0])
{
return false;
}
return arg0[1] < arg1[1];
}
};
class Sort2
{
public:
bool operator()(Vertex const& arg0, Vertex const& arg1) const
{
if (arg0[1] < arg1[1])
{
return true;
}
if (arg0[1] > arg1[1])
{
return false;
}
if (arg0[2] < arg1[2])
{
return true;
}
if (arg0[2] > arg1[2])
{
return false;
}
return arg0[0] < arg1[0];
}
};
void GetZMinEdgesM(OctBox const& box, unsigned int type, VETable& table)
{
unsigned int faceType = 0;
if (type & EB_XMIN_ZMIN)
{
faceType |= 0x01;
}
if (type & EB_XMAX_ZMIN)
{
faceType |= 0x02;
}
if (type & EB_YMIN_ZMIN)
{
faceType |= 0x04;
}
if (type & EB_YMAX_ZMIN)
{
faceType |= 0x08;
}
int end0 = 0, end1 = 0;
switch (faceType)
{
case 0:
return;
case 3:
end0 = EI_XMIN_ZMIN;
end1 = EI_XMAX_ZMIN;
break;
case 5:
end0 = EI_XMIN_ZMIN;
end1 = EI_YMIN_ZMIN;
break;
case 6:
end0 = EI_YMIN_ZMIN;
end1 = EI_XMAX_ZMIN;
break;
case 9:
end0 = EI_XMIN_ZMIN;
end1 = EI_YMAX_ZMIN;
break;
case 10:
end0 = EI_YMAX_ZMIN;
end1 = EI_XMAX_ZMIN;
break;
case 12:
end0 = EI_YMIN_ZMIN;
end1 = EI_YMAX_ZMIN;
break;
default:
LogError("The level value cannot be an exact integer.");
}
std::set<Vertex, Sort0> vSet;
for (int x = box.x0 + 1; x < box.x1; ++x)
{
auto const& merge = mYMerge[x][box.z0];
if (merge->IsZeroEdge(box.LY) || merge->HasZeroSubedge(box.LY))
{
int root = merge->GetZeroBase(box.LY);
vSet.insert(Vertex{
static_cast<Real>(x),
GetYInterp(x, root, box.z0),
static_cast<Real>(box.z0) });
}
}
for (int y = box.y0 + 1; y < box.y1; ++y)
{
auto const& merge = mXMerge[y][box.z0];
if (merge->IsZeroEdge(box.LX) || merge->HasZeroSubedge(box.LX))
{
int root = merge->GetZeroBase(box.LX);
vSet.insert(Vertex{
GetXInterp(root, y, box.z0),
static_cast<Real>(y),
static_cast<Real>(box.z0) });
}
}
// Add subdivision.
if (vSet.size() == 0)
{
table.InsertEdge(end0, end1);
return;
}
Real v0x = std::floor((*vSet.begin())[0]);
Real v1x = std::floor((*vSet.rbegin())[0]);
Real e0x = std::floor(table.GetVertex(end0)[0]);
Real e1x = std::floor(table.GetVertex(end1)[0]);
if (e1x <= v0x && v1x <= e0x)
{
std::swap(end0, end1);
}
// Add vertices.
int v0 = table.GetNumVertices(), v1 = v0;
for (auto const& position : vSet)
{
table.Insert(position);
}
// Add edges.
table.InsertEdge(end0, v1);
++v1;
int const imax = static_cast<int>(vSet.size());
for (int i = 1; i < imax; ++i, ++v0, ++v1)
{
table.InsertEdge(v0, v1);
}
table.InsertEdge(v0, end1);
}
void GetZMaxEdgesM(OctBox const& box, unsigned int type, VETable& table)
{
unsigned int faceType = 0;
if (type & EB_XMIN_ZMAX)
{
faceType |= 0x01;
}
if (type & EB_XMAX_ZMAX)
{
faceType |= 0x02;
}
if (type & EB_YMIN_ZMAX)
{
faceType |= 0x04;
}
if (type & EB_YMAX_ZMAX)
{
faceType |= 0x08;
}
int end0 = 0, end1 = 0;
switch (faceType)
{
case 0:
return;
case 3:
end0 = EI_XMIN_ZMAX;
end1 = EI_XMAX_ZMAX;
break;
case 5:
end0 = EI_XMIN_ZMAX;
end1 = EI_YMIN_ZMAX;
break;
case 6:
end0 = EI_YMIN_ZMAX;
end1 = EI_XMAX_ZMAX;
break;
case 9:
end0 = EI_XMIN_ZMAX;
end1 = EI_YMAX_ZMAX;
break;
case 10:
end0 = EI_YMAX_ZMAX;
end1 = EI_XMAX_ZMAX;
break;
case 12:
end0 = EI_YMIN_ZMAX;
end1 = EI_YMAX_ZMAX;
break;
default:
LogError("The level value cannot be an exact integer.");
}
std::set<Vertex, Sort0> vSet;
for (int x = box.x0 + 1; x < box.x1; ++x)
{
auto const& merge = mYMerge[x][box.z1];
if (merge->IsZeroEdge(box.LY) || merge->HasZeroSubedge(box.LY))
{
int root = merge->GetZeroBase(box.LY);
vSet.insert(Vertex{
static_cast<Real>(x),
GetYInterp(x, root, box.z1),
static_cast<Real>(box.z1) });
}
}
for (int y = box.y0 + 1; y < box.y1; ++y)
{
auto const& merge = mXMerge[y][box.z1];
if (merge->IsZeroEdge(box.LX) || merge->HasZeroSubedge(box.LX))
{
int root = merge->GetZeroBase(box.LX);
vSet.insert(Vertex{
GetXInterp(root, y, box.z1),
static_cast<Real>(y),
static_cast<Real>(box.z1) });
}
}
// Add subdivision.
int v0 = table.GetNumVertices(), v1 = v0;
if (vSet.size() == 0)
{
table.InsertEdge(end0, end1);
return;
}
Real v0x = std::floor((*vSet.begin())[0]);
Real v1x = std::floor((*vSet.rbegin())[0]);
Real e0x = std::floor(table.GetVertex(end0)[0]);
Real e1x = std::floor(table.GetVertex(end1)[0]);
if (e1x <= v0x && v1x <= e0x)
{
std::swap(end0, end1);
}
// Add vertices.
for (auto const& position : vSet)
{
table.Insert(position);
}
// Add edges.
table.InsertEdge(end0, v1);
++v1;
int const imax = static_cast<int>(vSet.size());
for (int i = 1; i < imax; ++i, ++v0, ++v1)
{
table.InsertEdge(v0, v1);
}
table.InsertEdge(v0, end1);
}
void GetYMinEdgesM(OctBox const& box, unsigned int type, VETable& table)
{
unsigned int faceType = 0;
if (type & EB_XMIN_YMIN)
{
faceType |= 0x01;
}
if (type & EB_XMAX_YMIN)
{
faceType |= 0x02;
}
if (type & EB_YMIN_ZMIN)
{
faceType |= 0x04;
}
if (type & EB_YMIN_ZMAX)
{
faceType |= 0x08;
}
int end0 = 0, end1 = 0;
switch (faceType)
{
case 0:
return;
case 3:
end0 = EI_XMIN_YMIN;
end1 = EI_XMAX_YMIN;
break;
case 5:
end0 = EI_XMIN_YMIN;
end1 = EI_YMIN_ZMIN;
break;
case 6:
end0 = EI_YMIN_ZMIN;
end1 = EI_XMAX_YMIN;
break;
case 9:
end0 = EI_XMIN_YMIN;
end1 = EI_YMIN_ZMAX;
break;
case 10:
end0 = EI_YMIN_ZMAX;
end1 = EI_XMAX_YMIN;
break;
case 12:
end0 = EI_YMIN_ZMIN;
end1 = EI_YMIN_ZMAX;
break;
default:
LogError("The level value cannot be an exact integer.");
}
std::set<Vertex, Sort1> vSet;
for (int x = box.x0 + 1; x < box.x1; ++x)
{
auto const& merge = mZMerge[x][box.y0];
if (merge->IsZeroEdge(box.LZ) || merge->HasZeroSubedge(box.LZ))
{
int root = merge->GetZeroBase(box.LZ);
vSet.insert(Vertex{
static_cast<Real>(x),
static_cast<Real>(box.y0),
GetZInterp(x, box.y0, root) });
}
}
for (int z = box.z0 + 1; z < box.z1; ++z)
{
auto const& merge = mXMerge[box.y0][z];
if (merge->IsZeroEdge(box.LX) || merge->HasZeroSubedge(box.LX))
{
int root = merge->GetZeroBase(box.LX);
vSet.insert(Vertex{
GetXInterp(root, box.y0, z),
static_cast<Real>(box.y0),
static_cast<Real>(z) });
}
}
// Add subdivision.
int v0 = table.GetNumVertices(), v1 = v0;
if (vSet.size() == 0)
{
table.InsertEdge(end0, end1);
return;
}
Real v0z = std::floor((*vSet.begin())[2]);
Real v1z = std::floor((*vSet.rbegin())[2]);
Real e0z = std::floor(table.GetVertex(end0)[2]);
Real e1z = std::floor(table.GetVertex(end1)[2]);
if (e1z <= v0z && v1z <= e0z)
{
std::swap(end0, end1);
}
// Add vertices.
for (auto const& position : vSet)
{
table.Insert(position);
}
// Add edges.
table.InsertEdge(end0, v1);
++v1;
int const imax = static_cast<int>(vSet.size());
for (int i = 1; i < imax; ++i, ++v0, ++v1)
{
table.InsertEdge(v0, v1);
}
table.InsertEdge(v0, end1);
}
void GetYMaxEdgesM(OctBox const& box, unsigned int type, VETable& table)
{
unsigned int faceType = 0;
if (type & EB_XMIN_YMAX)
{
faceType |= 0x01;
}
if (type & EB_XMAX_YMAX)
{
faceType |= 0x02;
}
if (type & EB_YMAX_ZMIN)
{
faceType |= 0x04;
}
if (type & EB_YMAX_ZMAX)
{
faceType |= 0x08;
}
int end0 = 0, end1 = 0;
switch (faceType)
{
case 0:
return;
case 3:
end0 = EI_XMIN_YMAX;
end1 = EI_XMAX_YMAX;
break;
case 5:
end0 = EI_XMIN_YMAX;
end1 = EI_YMAX_ZMIN;
break;
case 6:
end0 = EI_YMAX_ZMIN;
end1 = EI_XMAX_YMAX;
break;
case 9:
end0 = EI_XMIN_YMAX;
end1 = EI_YMAX_ZMAX;
break;
case 10:
end0 = EI_YMAX_ZMAX;
end1 = EI_XMAX_YMAX;
break;
case 12:
end0 = EI_YMAX_ZMIN;
end1 = EI_YMAX_ZMAX;
break;
default:
LogError("The level value cannot be an exact integer.");
}
std::set<Vertex, Sort1> vSet;
for (int x = box.x0 + 1; x < box.x1; ++x)
{
auto const& merge = mZMerge[x][box.y1];
if (merge->IsZeroEdge(box.LZ) || merge->HasZeroSubedge(box.LZ))
{
int root = merge->GetZeroBase(box.LZ);
vSet.insert(Vertex{
static_cast<Real>(x),
static_cast<Real>(box.y1),
GetZInterp(x, box.y1, root) });
}
}
for (int z = box.z0 + 1; z < box.z1; ++z)
{
auto const& merge = mXMerge[box.y1][z];
if (merge->IsZeroEdge(box.LX) || merge->HasZeroSubedge(box.LX))
{
int root = merge->GetZeroBase(box.LX);
vSet.insert(Vertex{
GetXInterp(root, box.y1, z),
static_cast<Real>(box.y1),
static_cast<Real>(z) });
}
}
// Add subdivision.
if (vSet.size() == 0)
{
table.InsertEdge(end0, end1);
return;
}
Real v0z = std::floor((*vSet.begin())[2]);
Real v1z = std::floor((*vSet.rbegin())[2]);
Real e0z = std::floor(table.GetVertex(end0)[2]);
Real e1z = std::floor(table.GetVertex(end1)[2]);
if (e1z <= v0z && v1z <= e0z)
{
std::swap(end0, end1);
}
// Add vertices.
int v0 = table.GetNumVertices(), v1 = v0;
for (auto const& position : vSet)
{
table.Insert(position);
}
// Add edges.
table.InsertEdge(end0, v1);
++v1;
int const imax = static_cast<int>(vSet.size());
for (int i = 1; i < imax; ++i, ++v0, ++v1)
{
table.InsertEdge(v0, v1);
}
table.InsertEdge(v0, end1);
}
void GetXMinEdgesM(OctBox const& box, unsigned int type, VETable& table)
{
unsigned int faceType = 0;
if (type & EB_XMIN_YMIN)
{
faceType |= 0x01;
}
if (type & EB_XMIN_YMAX)
{
faceType |= 0x02;
}
if (type & EB_XMIN_ZMIN)
{
faceType |= 0x04;
}
if (type & EB_XMIN_ZMAX)
{
faceType |= 0x08;
}
int end0 = 0, end1 = 0;
switch (faceType)
{
case 0:
return;
case 3:
end0 = EI_XMIN_YMIN;
end1 = EI_XMIN_YMAX;
break;
case 5:
end0 = EI_XMIN_YMIN;
end1 = EI_XMIN_ZMIN;
break;
case 6:
end0 = EI_XMIN_ZMIN;
end1 = EI_XMIN_YMAX;
break;
case 9:
end0 = EI_XMIN_YMIN;
end1 = EI_XMIN_ZMAX;
break;
case 10:
end0 = EI_XMIN_ZMAX;
end1 = EI_XMIN_YMAX;
break;
case 12:
end0 = EI_XMIN_ZMIN;
end1 = EI_XMIN_ZMAX;
break;
default:
LogError("The level value cannot be an exact integer.");
}
std::set<Vertex, Sort2> vSet;
for (int z = box.z0 + 1; z < box.z1; ++z)
{
auto const& merge = mYMerge[box.x0][z];
if (merge->IsZeroEdge(box.LY) || merge->HasZeroSubedge(box.LY))
{
int root = merge->GetZeroBase(box.LY);
vSet.insert(Vertex{
static_cast<Real>(box.x0),
GetYInterp(box.x0, root, z),
static_cast<Real>(z) });
}
}
for (int y = box.y0 + 1; y < box.y1; ++y)
{
auto const& merge = mZMerge[box.x0][y];
if (merge->IsZeroEdge(box.LZ) || merge->HasZeroSubedge(box.LZ))
{
int root = merge->GetZeroBase(box.LZ);
vSet.insert(Vertex{
static_cast<Real>(box.x0),
static_cast<Real>(y),
GetZInterp(box.x0, y, root) });
}
}
// Add subdivision.
int v0 = table.GetNumVertices(), v1 = v0;
if (vSet.size() == 0)
{
table.InsertEdge(end0, end1);
return;
}
Real v0y = std::floor((*vSet.begin())[1]);
Real v1y = std::floor((*vSet.rbegin())[1]);
Real e0y = std::floor(table.GetVertex(end0)[1]);
Real e1y = std::floor(table.GetVertex(end1)[1]);
if (e1y <= v0y && v1y <= e0y)
{
std::swap(end0, end1);
}
// Add vertices.
for (auto const& position : vSet)
{
table.Insert(position);
}
// Add edges.
table.InsertEdge(end0, v1);
++v1;
int const imax = static_cast<int>(vSet.size());
for (int i = 1; i < imax; ++i, ++v0, ++v1)
{
table.InsertEdge(v0, v1);
}
table.InsertEdge(v0, end1);
}
void GetXMaxEdgesM(OctBox const& box, unsigned int type, VETable& table)
{
unsigned int faceType = 0;
if (type & EB_XMAX_YMIN)
{
faceType |= 0x01;
}
if (type & EB_XMAX_YMAX)
{
faceType |= 0x02;
}
if (type & EB_XMAX_ZMIN)
{
faceType |= 0x04;
}
if (type & EB_XMAX_ZMAX)
{
faceType |= 0x08;
}
int end0 = 0, end1 = 0;
switch (faceType)
{
case 0:
return;
case 3:
end0 = EI_XMAX_YMIN;
end1 = EI_XMAX_YMAX;
break;
case 5:
end0 = EI_XMAX_YMIN;
end1 = EI_XMAX_ZMIN;
break;
case 6:
end0 = EI_XMAX_ZMIN;
end1 = EI_XMAX_YMAX;
break;
case 9:
end0 = EI_XMAX_YMIN;
end1 = EI_XMAX_ZMAX;
break;
case 10:
end0 = EI_XMAX_ZMAX;
end1 = EI_XMAX_YMAX;
break;
case 12:
end0 = EI_XMAX_ZMIN;
end1 = EI_XMAX_ZMAX;
break;
default:
LogError("The level value cannot be an exact integer.");
}
std::set<Vertex, Sort2> vSet;
for (int z = box.z0 + 1; z < box.z1; ++z)
{
auto const& merge = mYMerge[box.x1][z];
if (merge->IsZeroEdge(box.LY) || merge->HasZeroSubedge(box.LY))
{
int root = merge->GetZeroBase(box.LY);
vSet.insert(Vertex{
static_cast<Real>(box.x1),
GetYInterp(box.x1, root, z),
static_cast<Real>(z) });
}
}
for (int y = box.y0 + 1; y < box.y1; y++)
{
auto const& merge = mZMerge[box.x1][y];
if (merge->IsZeroEdge(box.LZ) || merge->HasZeroSubedge(box.LZ))
{
int root = merge->GetZeroBase(box.LZ);
vSet.insert(Vertex{
static_cast<Real>(box.x1),
static_cast<Real>(y),
GetZInterp(box.x1, y, root) });
}
}
// Add subdivision.
if (vSet.size() == 0)
{
table.InsertEdge(end0, end1);
return;
}
Real v0y = std::floor((*vSet.begin())[1]);
Real v1y = std::floor((*vSet.rbegin())[1]);
Real e0y = std::floor(table.GetVertex(end0)[1]);
Real e1y = std::floor(table.GetVertex(end1)[1]);
if (e1y <= v0y && v1y <= e0y)
{
std::swap(end0, end1);
}
// Add vertices.
int v0 = table.GetNumVertices(), v1 = v0;
for (auto const& position : vSet)
{
table.Insert(position);
}
// Add edges.
table.InsertEdge(end0, v1);
++v1;
int const imax = static_cast<int>(vSet.size());
for (int i = 1; i < imax; ++i, ++v0, ++v1)
{
table.InsertEdge(v0, v1);
}
table.InsertEdge(v0, end1);
}
// Support for normal vector calculations.
Vertex GetGradient(Vertex const& position) const
{
Vertex vzero = { (Real)0, (Real)0, (Real)0 };
int x = static_cast<int>(position[0]);
if (x < 0 || x >= mTwoPowerN)
{
return vzero;
}
int y = static_cast<int>(position[1]);
if (y < 0 || y >= mTwoPowerN)
{
return vzero;
}
int z = static_cast<int>(position[2]);
if (z < 0 || z >= mTwoPowerN)
{
return vzero;
}
int i000 = x + mSize * (y + mSize * z);
int i100 = i000 + 1;
int i010 = i000 + mSize;
int i110 = i100 + mSize;
int i001 = i000 + mSizeSqr;
int i101 = i100 + mSizeSqr;
int i011 = i010 + mSizeSqr;
int i111 = i110 + mSizeSqr;
Real f000 = static_cast<Real>(mInputVoxels[i000]);
Real f100 = static_cast<Real>(mInputVoxels[i100]);
Real f010 = static_cast<Real>(mInputVoxels[i010]);
Real f110 = static_cast<Real>(mInputVoxels[i110]);
Real f001 = static_cast<Real>(mInputVoxels[i001]);
Real f101 = static_cast<Real>(mInputVoxels[i101]);
Real f011 = static_cast<Real>(mInputVoxels[i011]);
Real f111 = static_cast<Real>(mInputVoxels[i111]);
Real fx = position[0] - static_cast<Real>(x);
Real fy = position[1] - static_cast<Real>(y);
Real fz = position[2] - static_cast<Real>(z);
Real oneMinusX = (Real)1 - fx;
Real oneMinusY = (Real)1 - fy;
Real oneMinusZ = (Real)1 - fz;
Real tmp0, tmp1;
Vertex gradient;
tmp0 = oneMinusY * (f100 - f000) + fy * (f110 - f010);
tmp1 = oneMinusY * (f101 - f001) + fy * (f111 - f011);
gradient[0] = oneMinusZ * tmp0 + fz * tmp1;
tmp0 = oneMinusX * (f010 - f000) + fx * (f110 - f100);
tmp1 = oneMinusX * (f011 - f001) + fx * (f111 - f101);
gradient[1] = oneMinusZ * tmp0 + fz * tmp1;
tmp0 = oneMinusX * (f001 - f000) + fx * (f101 - f100);
tmp1 = oneMinusX * (f011 - f010) + fx * (f111 - f110);
gradient[2] = oneMinusY * tmp0 + oneMinusY * tmp1;
return gradient;
}
enum
{
EI_XMIN_YMIN = 0,
EI_XMIN_YMAX = 1,
EI_XMAX_YMIN = 2,
EI_XMAX_YMAX = 3,
EI_XMIN_ZMIN = 4,
EI_XMIN_ZMAX = 5,
EI_XMAX_ZMIN = 6,
EI_XMAX_ZMAX = 7,
EI_YMIN_ZMIN = 8,
EI_YMIN_ZMAX = 9,
EI_YMAX_ZMIN = 10,
EI_YMAX_ZMAX = 11,
FI_XMIN = 12,
FI_XMAX = 13,
FI_YMIN = 14,
FI_YMAX = 15,
FI_ZMIN = 16,
FI_ZMAX = 17,
I_QUANTITY = 18,
EB_XMIN_YMIN = 1 << EI_XMIN_YMIN,
EB_XMIN_YMAX = 1 << EI_XMIN_YMAX,
EB_XMAX_YMIN = 1 << EI_XMAX_YMIN,
EB_XMAX_YMAX = 1 << EI_XMAX_YMAX,
EB_XMIN_ZMIN = 1 << EI_XMIN_ZMIN,
EB_XMIN_ZMAX = 1 << EI_XMIN_ZMAX,
EB_XMAX_ZMIN = 1 << EI_XMAX_ZMIN,
EB_XMAX_ZMAX = 1 << EI_XMAX_ZMAX,
EB_YMIN_ZMIN = 1 << EI_YMIN_ZMIN,
EB_YMIN_ZMAX = 1 << EI_YMIN_ZMAX,
EB_YMAX_ZMIN = 1 << EI_YMAX_ZMIN,
EB_YMAX_ZMAX = 1 << EI_YMAX_ZMAX,
FB_XMIN = 1 << FI_XMIN,
FB_XMAX = 1 << FI_XMAX,
FB_YMIN = 1 << FI_YMIN,
FB_YMAX = 1 << FI_YMAX,
FB_ZMIN = 1 << FI_ZMIN,
FB_ZMAX = 1 << FI_ZMAX
};
// image data
int mTwoPowerN, mSize, mSizeSqr;
T const* mInputVoxels;
Real mLevel;
bool mFixBoundary;
// Trees for linear merging.
Array2<std::shared_ptr<LinearMergeTree>> mXMerge, mYMerge, mZMerge;
// monoboxes
std::vector<OctBox> mBoxes;
};
}