// David Eberly, Geometric Tools, Redmond WA 98052
// Copyright (c) 1998-2020
// 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: 4.0.2019.08.13
#pragma once
#include <Mathematics/CurveExtractor.h>
// The level set extraction algorithm implemented here is described
// in Section 3 of the document
// https://www.geometrictools.com/Documentation/ExtractLevelCurves.pdf
namespace WwiseGTE
{
// 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 CurveExtractorSquares : public CurveExtractor<T, Real>
{
public:
// Convenience type definitions.
typedef typename CurveExtractor<T, Real>::Vertex Vertex;
typedef typename CurveExtractor<T, Real>::Edge Edge;
// The input is a 2D image with lexicographically ordered pixels (x,y)
// stored in a linear array. Pixel (x,y) is stored in the array at
// location index = x + xBound * y. The inputs xBound and yBound must
// each be 2 or larger so that there is at least one image square to
// process. The inputPixels must be nonnull and point to contiguous
// storage that contains at least xBound * yBound elements.
CurveExtractorSquares(int xBound, int yBound, T const* inputPixels)
:
CurveExtractor<T, Real>(xBound, yBound, inputPixels)
{
}
// Extract level curves and return rational vertices. Use the
// base-class Extract if you want real-valued vertices.
virtual void Extract(T level, std::vector<Vertex>& vertices,
std::vector<Edge>& edges) override
{
// Adjust the image so that the level set is F(x,y) = 0.
int64_t levelI64 = static_cast<int64_t>(level);
for (size_t i = 0; i < this->mPixels.size(); ++i)
{
int64_t inputI64 = static_cast<int64_t>(this->mInputPixels[i]);
this->mPixels[i] = inputI64 - levelI64;
}
vertices.clear();
edges.clear();
for (int y = 0, yp = 1; yp < this->mYBound; ++y, ++yp)
{
for (int x = 0, xp = 1; xp < this->mXBound; ++x, ++xp)
{
// Get the image values at the corners of the square.
int i00 = x + this->mXBound * y;
int i10 = i00 + 1;
int i01 = i00 + this->mXBound;
int i11 = i10 + this->mXBound;
int64_t f00 = this->mPixels[i00];
int64_t f10 = this->mPixels[i10];
int64_t f01 = this->mPixels[i01];
int64_t f11 = this->mPixels[i11];
// Construct the vertices and edges of the level curve in
// the square. The x, xp, y and yp values are implicitly
// converted from int to int64_t (which is guaranteed to
// be correct).
ProcessSquare(vertices, edges, x, xp, y, yp, f00, f10, f11, f01);
}
}
}
protected:
void ProcessSquare(std::vector<Vertex>& vertices, std::vector<Edge>& edges,
int64_t x, int64_t xp, int64_t y, int64_t yp,
int64_t f00, int64_t f10, int64_t f11, int64_t f01)
{
int64_t xn0, yn0, xn1, yn1, d0, d1, d2, d3, det;
if (f00 != 0)
{
// convert to case "+***"
if (f00 < 0)
{
f00 = -f00;
f10 = -f10;
f11 = -f11;
f01 = -f01;
}
if (f10 > 0)
{
if (f11 > 0)
{
if (f01 > 0)
{
// ++++
return;
}
else if (f01 < 0)
{
// +++-
d0 = f11 - f01;
xn0 = f11 * x - f01 * xp;
d1 = f00 - f01;
yn1 = f00 * yp - f01 * y;
this->AddEdge(vertices, edges, xn0, d0, yp, 1, x, 1, yn1, d1);
}
else
{
// +++0
this->AddVertex(vertices, x, 1, yp, 1);
}
}
else if (f11 < 0)
{
d0 = f10 - f11;
yn0 = f10 * yp - f11 * y;
if (f01 > 0)
{
// ++-+
d1 = f01 - f11;
xn1 = f01 * xp - f11 * x;
this->AddEdge(vertices, edges, xp, 1, yn0, d0, xn1, d1, yp, 1);
}
else if (f01 < 0)
{
// ++--
d1 = f01 - f00;
yn1 = f01 * y - f00 * yp;
this->AddEdge(vertices, edges, x, 1, yn1, d1, xp, 1, yn0, d0);
}
else
{
// ++-0
this->AddEdge(vertices, edges, x, 1, yp, 1, xp, 1, yn0, d0);
}
}
else
{
if (f01 > 0)
{
// ++0+
this->AddVertex(vertices, xp, 1, yp, 1);
}
else if (f01 < 0)
{
// ++0-
d0 = f01 - f00;
yn0 = f01 * y - f00 * yp;
this->AddEdge(vertices, edges, xp, 1, yp, 1, x, 1, yn0, d0);
}
else
{
// ++00
this->AddEdge(vertices, edges, xp, 1, yp, 1, x, 1, yp, 1);
}
}
}
else if (f10 < 0)
{
d0 = f00 - f10;
xn0 = f00 * xp - f10 * x;
if (f11 > 0)
{
d1 = f11 - f10;
yn1 = f11 * y - f10 * yp;
if (f01 > 0)
{
// +-++
this->AddEdge(vertices, edges, xn0, d0, y, 1, xp, 1, yn1, d1);
}
else if (f01 < 0)
{
// +-+-
d3 = f11 - f01;
xn1 = f11 * x - f01 * xp;
d2 = f01 - f00;
yn0 = f01 * y - f00 * yp;
if (d0*d3 > 0)
{
det = xn1 * d0 - xn0 * d3;
}
else
{
det = xn0 * d3 - xn1 * d0;
}
if (det > 0)
{
this->AddEdge(vertices, edges, xn1, d3, yp, 1, xp, 1, yn1, d1);
this->AddEdge(vertices, edges, xn0, d0, y, 1, x, 1, yn0, d2);
}
else if (det < 0)
{
this->AddEdge(vertices, edges, xn1, d3, yp, 1, x, 1, yn0, d2);
this->AddEdge(vertices, edges, xn0, d0, y, 1, xp, 1, yn1, d1);
}
else
{
this->AddEdge(vertices, edges, xn0, d0, yn0, d2, xn0, d0, y, 1);
this->AddEdge(vertices, edges, xn0, d0, yn0, d2, xn0, d0, yp, 1);
this->AddEdge(vertices, edges, xn0, d0, yn0, d2, x, 1, yn0, d2);
this->AddEdge(vertices, edges, xn0, d0, yn0, d2, xp, 1, yn0, d2);
}
}
else
{
// +-+0
this->AddEdge(vertices, edges, xn0, d0, y, 1, xp, 1, yn1, d1);
this->AddVertex(vertices, x, 1, yp, 1);
}
}
else if (f11 < 0)
{
if (f01 > 0)
{
// +--+
d1 = f11 - f01;
xn1 = f11 * x - f01 * xp;
this->AddEdge(vertices, edges, xn0, d0, y, 1, xn1, d1, yp, 1);
}
else if (f01 < 0)
{
// +---
d1 = f01 - f00;
yn1 = f01 * y - f00 * yp;
this->AddEdge(vertices, edges, x, 1, yn1, d1, xn0, d0, y, 1);
}
else
{
// +--0
this->AddEdge(vertices, edges, x, 1, yp, 1, xn0, d0, y, 1);
}
}
else
{
if (f01 > 0)
{
// +-0+
this->AddEdge(vertices, edges, xp, 1, yp, 1, xn0, d0, y, 1);
}
else if (f01 < 0)
{
// +-0-
d1 = f01 - f00;
yn1 = f01 * y - f00 * yp;
this->AddEdge(vertices, edges, x, 1, yn1, d1, xn0, d0, y, 1);
this->AddVertex(vertices, xp, 1, yp, 1);
}
else
{
// +-00
this->AddEdge(vertices, edges, xp, 1, yp, 1, xn0, d0, yp, 1);
this->AddEdge(vertices, edges, xn0, d0, yp, 1, x, 1, yp, 1);
this->AddEdge(vertices, edges, xn0, d0, yp, 1, xn0, d0, y, 1);
}
}
}
else
{
if (f11 > 0)
{
if (f01 > 0)
{
// +0++
this->AddVertex(vertices, xp, 1, y, 1);
}
else if (f01 < 0)
{
// +0+-
d0 = f11 - f01;
xn0 = f11 * x - f01 * xp;
d1 = f00 - f01;
yn1 = f00 * yp - f01 * y;
this->AddEdge(vertices, edges, xn0, d0, yp, 1, x, 1, yn1, d1);
this->AddVertex(vertices, xp, 1, y, 1);
}
else
{
// +0+0
this->AddVertex(vertices, xp, 1, y, 1);
this->AddVertex(vertices, x, 1, yp, 1);
}
}
else if (f11 < 0)
{
if (f01 > 0)
{
// +0-+
d0 = f11 - f01;
xn0 = f11 * x - f01 * xp;
this->AddEdge(vertices, edges, xp, 1, y, 1, xn0, d0, yp, 1);
}
else if (f01 < 0)
{
// +0--
d0 = f01 - f00;
yn0 = f01 * y - f00 * yp;
this->AddEdge(vertices, edges, xp, 1, y, 1, x, 1, yn0, d0);
}
else
{
// +0-0
this->AddEdge(vertices, edges, xp, 1, y, 1, x, 1, yp, 1);
}
}
else
{
if (f01 > 0)
{
// +00+
this->AddEdge(vertices, edges, xp, 1, y, 1, xp, 1, yp, 1);
}
else if (f01 < 0)
{
// +00-
d0 = f00 - f01;
yn0 = f00 * yp - f01 * y;
this->AddEdge(vertices, edges, xp, 1, y, 1, xp, 1, yn0, d0);
this->AddEdge(vertices, edges, xp, 1, yn0, d0, xp, 1, yp, 1);
this->AddEdge(vertices, edges, xp, 1, yn0, d0, x, 1, yn0, d0);
}
else
{
// +000
this->AddEdge(vertices, edges, x, 1, yp, 1, x, 1, y, 1);
this->AddEdge(vertices, edges, x, 1, y, 1, xp, 1, y, 1);
}
}
}
}
else if (f10 != 0)
{
// convert to case 0+**
if (f10 < 0)
{
f10 = -f10;
f11 = -f11;
f01 = -f01;
}
if (f11 > 0)
{
if (f01 > 0)
{
// 0+++
this->AddVertex(vertices, x, 1, y, 1);
}
else if (f01 < 0)
{
// 0++-
d0 = f11 - f01;
xn0 = f11 * x - f01 * xp;
this->AddEdge(vertices, edges, x, 1, y, 1, xn0, d0, yp, 1);
}
else
{
// 0++0
this->AddEdge(vertices, edges, x, 1, yp, 1, x, 1, y, 1);
}
}
else if (f11 < 0)
{
if (f01 > 0)
{
// 0+-+
d0 = f10 - f11;
yn0 = f10 * yp - f11 * y;
d1 = f01 - f11;
xn1 = f01 * xp - f11 * x;
this->AddEdge(vertices, edges, xp, 1, yn0, d0, xn1, d1, yp, 1);
this->AddVertex(vertices, x, 1, y, 1);
}
else if (f01 < 0)
{
// 0+--
d0 = f10 - f11;
yn0 = f10 * yp - f11 * y;
this->AddEdge(vertices, edges, x, 1, y, 1, xp, 1, yn0, d0);
}
else
{
// 0+-0
d0 = f10 - f11;
yn0 = f10 * yp - f11 * y;
this->AddEdge(vertices, edges, x, 1, y, 1, x, 1, yn0, d0);
this->AddEdge(vertices, edges, x, 1, yn0, d0, x, 1, yp, 1);
this->AddEdge(vertices, edges, x, 1, yn0, d0, xp, 1, yn0, d0);
}
}
else
{
if (f01 > 0)
{
// 0+0+
this->AddVertex(vertices, x, 1, y, 1);
this->AddVertex(vertices, xp, 1, yp, 1);
}
else if (f01 < 0)
{
// 0+0-
this->AddEdge(vertices, edges, x, 1, y, 1, xp, 1, yp, 1);
}
else
{
// 0+00
this->AddEdge(vertices, edges, xp, 1, yp, 1, x, 1, yp, 1);
this->AddEdge(vertices, edges, x, 1, yp, 1, x, 1, y, 1);
}
}
}
else if (f11 != 0)
{
// convert to case 00+*
if (f11 < 0)
{
f11 = -f11;
f01 = -f01;
}
if (f01 > 0)
{
// 00++
this->AddEdge(vertices, edges, x, 1, y, 1, xp, 1, y, 1);
}
else if (f01 < 0)
{
// 00+-
d0 = f01 - f11;
xn0 = f01 * xp - f11 * x;
this->AddEdge(vertices, edges, x, 1, y, 1, xn0, d0, y, 1);
this->AddEdge(vertices, edges, xn0, d0, y, 1, xp, 1, y, 1);
this->AddEdge(vertices, edges, xn0, d0, y, 1, xn0, d0, yp, 1);
}
else
{
// 00+0
this->AddEdge(vertices, edges, xp, 1, y, 1, xp, 1, yp, 1);
this->AddEdge(vertices, edges, xp, 1, yp, 1, x, 1, yp, 1);
}
}
else if (f01 != 0)
{
// cases 000+ or 000-
this->AddEdge(vertices, edges, x, 1, y, 1, xp, 1, y, 1);
this->AddEdge(vertices, edges, xp, 1, y, 1, xp, 1, yp, 1);
}
else
{
// case 0000
this->AddEdge(vertices, edges, x, 1, y, 1, xp, 1, y, 1);
this->AddEdge(vertices, edges, xp, 1, y, 1, xp, 1, yp, 1);
this->AddEdge(vertices, edges, xp, 1, yp, 1, x, 1, yp, 1);
this->AddEdge(vertices, edges, x, 1, yp, 1, x, 1, y, 1);
}
}
};
}