#include "tcenterlinevectP.h"
 
//==========================================================================
 
//************************
//*    Polygonization    *
//************************
 
//--------------------------------------------------------------------------
 
//===============================
//    Raw Borders Extraction
//===============================
 
//Raw contour class definition
 
class RawBorderPoint
{
 
	TPoint m_position;
	int m_ambiguousTurn; //used to remember cases of multiple turning directions
						 //in a RawBorder extraction.
 
public:
	RawBorderPoint() : m_ambiguousTurn(0) {}
	RawBorderPoint(int i, int j) : m_position(i, j), m_ambiguousTurn(0) {}
 
	inline TPoint pos() const { return m_position; }
	inline int x() const { return m_position.x; }
	inline int y() const { return m_position.y; }
 
	enum { left = 1,
		   right = 2 }; //Direction taken at ambiguous turning point
	inline int getAmbiguous() const { return m_ambiguousTurn; }
	inline void setAmbiguous(int direction) { m_ambiguousTurn = direction; }
};
 
//--------------------------------------------------------------------------
 
class RawBorder : public std::vector<RawBorderPoint>
{
	int m_xExternal; //x coordinate of a specific vertex in the outer
					 //RawBorder which contains this inner one.
	TPointD *m_coordinateSums;
	TPointD *m_coordinateSquareSums;
	double *m_coordinateMixedSums;
 
public:
	RawBorder() {}
	~RawBorder() {}
 
	void setXExternalPixel(int a) { m_xExternal = a; }
	int xExternalPixel() { return m_xExternal; }
	TPointD *&sums() { return m_coordinateSums; }
	TPointD *&sums2() { return m_coordinateSquareSums; }
	double *&sumsMix() { return m_coordinateMixedSums; }
};
 
//--------------------------------------------------------------------------
 
//Of course we don't want RawBorders to be entirely copied whenever STL
//requires to resize a BorderFamily...
typedef std::vector<RawBorder *> BorderFamily;
typedef std::vector<BorderFamily> BorderList;
 
//--------------------------------------------------------------------------
 
//==========================================================================
 
//============================
//    Polygonizer Locals
//============================
 
namespace
{
//Const names
enum { white = 0,
	   black = 1 };
enum { inner = 0,
	   outer = 1,
	   none = 2,
	   invalid = 3 };
}
 
//=======================================================================================
 
//-------------------------------
//    Raster Data Functions
//-------------------------------
 
//NOTA: Il tono di un TPixelCM32 rappresenta la transizione tra colore ink e colore paint.
//      di solito, se il tono e' basso abbiamo un colore ink - che puo' anche essere bianco,
//      in teoria...
//      Sarebbe opportuno che il vettorizzatore riconoscesse - per colormap - il colore
//      delle strokes.
//      Approcci: a)  la Signaturemap diventa *piu'* di una bitmap e si seguono le outline
//                    dei singoli colori.
//                 => Sconnessioni tra i colori adiacenti. Bisogna introdurre la distanza tra
//                    colori per seguire l'outline (ossia, i pixel tenuti a dx della outline
//                    devono essere simili).
//
//                b)  Una volta vettorizzato tutto, si sceglie il colore della stroke.
//                    E' possibile controllare il colore sui vertici delle sequenze semplificate
//                    e fare una media.
 
//NOTE: Transparency makes colors fade to white. Full transparent black pixels are considered white.
 
//--------------------------------------------------------------------------
 
template <typename T>
class PixelEvaluator
{
	TRasterPT<T> m_ras;
	int m_threshold;
 
public:
	PixelEvaluator(const TRasterPT<T> &ras, int threshold)
		: m_ras(ras), m_threshold(threshold) {}
 
	inline unsigned char getBlackOrWhite(int x, int y);
};
 
//--------------------------------------------------------------------------
 
template <>
inline unsigned char PixelEvaluator<TPixel32>::getBlackOrWhite(int x, int y)
{
	//return ras->pixels(y)[x].r + 2 * ras->pixels(y)[x].g + ras->pixels(y)[x].b <
	//   threshold * (ras->pixels(y)[x].m / 255.0);
	//NOTE: Green is considered twice brighter than red or blue channel.
 
	//Using Value of HSV color model
	return tmax(m_ras->pixels(y)[x].r, tmax(m_ras->pixels(y)[x].g, m_ras->pixels(y)[x].b)) <
		   m_threshold * (m_ras->pixels(y)[x].m / 255.0);
 
	//Using Lightness of HSV color model
	//return (max(ras->pixels(y)[x].r, max(ras->pixels(y)[x].g, ras->pixels(y)[x].b)) +
	//       min(ras->pixels(y)[x].r, min(ras->pixels(y)[x].g, ras->pixels(y)[x].b))) / 2.0 <
	//  threshold * (ras->pixels(y)[x].m / 255.0);
 
	//Using (relative) Luminance
	//return 0.2126 * ras->pixels(y)[x].r + 0.7152 * ras->pixels(y)[x].g + 0.0722 * ras->pixels(y)[x].b <
	//  threshold * (ras->pixels(y)[x].m / 255.0);
}
 
template <>
inline unsigned char PixelEvaluator<TPixelGR8>::getBlackOrWhite(int x, int y)
{
	return m_ras->pixels(y)[x].value < m_threshold;
}
 
template <>
inline unsigned char PixelEvaluator<TPixelCM32>::getBlackOrWhite(int x, int y)
{
	return m_ras->pixels(y)[x].getTone() < m_threshold;
}
 
//--------------------------------------------------------------------------
 
//Signaturemap format:
//  stores a map of bytes, whose first bit represents the color (black/white) of corresponding pixel, and
//  the rest its 'signature', used as an int to store information.
//NOTE: given a TRaster32, the corresponding Signaturemap constructed is intended 0(white)-padded
 
class Signaturemap
{
	unsigned char *m_array;
	int m_rowSize;
	int m_colSize;
 
public:
	Signaturemap(const TRasterP &ras, int threshold);
	~Signaturemap() { delete[] m_array; }
 
	template <typename T>
	void readRasterData(const TRasterPT<T> &ras, int threshold);
 
	inline int getRowSize() const { return m_rowSize; }
	inline int getColSize() const { return m_colSize; }
 
	unsigned char *pixelByte(int x, int y) { return &m_array[(y + 1) * m_rowSize + x + 1]; }
 
	bool getBitmapColor(int x, int y) const
	{
		return m_array[(y + 1) * m_rowSize + x + 1] & 1;
	}
 
	inline unsigned char getSignature(int x, int y) const
	{
		return m_array[(y + 1) * m_rowSize + x + 1] >> 1;
	}
 
	void setSignature(int x, int y, int val)
	{
		unsigned char *pixel = pixelByte(x, y);
		*pixel &= 1;
		*pixel |= (val << 1); //Si puo' fare meglio??
	}
};
 
//--------------------------------------------------------------------------
 
Signaturemap::Signaturemap(const TRasterP &ras, int threshold)
{
	//Extrapolate raster type
	TRaster32P rr = (TRaster32P)ras;
	TRasterGR8P rgr = (TRasterGR8P)ras;
	TRasterCM32P rt = (TRasterCM32P)ras;
	assert(rr || rgr || rt);
 
	//Read raster data
	if (rr) {
		rr->lock();
		readRasterData(rr, threshold);
		rr->unlock();
	} else if (rgr) {
		rgr->lock();
		readRasterData(rgr, threshold);
		rgr->unlock();
	} else {
		rt->lock();
		readRasterData(rt, threshold);
		rt->unlock();
	}
}
 
//--------------------------------------------------------------------------
 
template <typename T>
void Signaturemap::readRasterData(const TRasterPT<T> &ras, int threshold)
{
	unsigned char *currByte;
	int x, y;
 
	PixelEvaluator<T> evaluator(ras, threshold);
 
	m_rowSize = ras->getLx() + 2;
	m_colSize = ras->getLy() + 2;
	m_array = new unsigned char[m_rowSize * m_colSize];
 
	memset(m_array, none << 1, m_rowSize);
 
	currByte = m_array + m_rowSize;
	for (y = 0; y < ras->getLy(); ++y) {
		*currByte = none << 1;
		currByte++;
 
		for (x = 0; x < ras->getLx(); ++x, ++currByte)
			*currByte = evaluator.getBlackOrWhite(x, y) | (none << 1);
 
		*currByte = none << 1;
		currByte++;
	}
 
	memset(currByte, none << 1, m_rowSize);
}
 
//--------------------------------------------------------------------------
 
//Minority check for amiguous turning directions
inline bool getMinorityCheck(const Signaturemap &ras, int x, int y)
{
	//Assumes (x,y) is ambiguous case: 2 immediate surrounding pixels are white and 2 black
	return (ras.getBitmapColor(x + 1, y) +
			ras.getBitmapColor(x + 1, y - 1) +
			ras.getBitmapColor(x - 2, y) +
			ras.getBitmapColor(x - 2, y - 1) +
			ras.getBitmapColor(x - 1, y + 1) +
			ras.getBitmapColor(x - 1, y - 2) +
			ras.getBitmapColor(x, y + 1) +
			ras.getBitmapColor(x, y - 2)) > 4;
}
 
//--------------------------------------------------------------------------
 
//Sets signature of a given border
inline void setSignature(Signaturemap &ras, const RawBorder &border, int val)
{
	unsigned int j;
	int yOld;
 
	//Set border's alpha channel
	yOld = border.back().y();
	for (j = 0; j < border.size(); ++j) {
		if (border[j].y() < yOld) {
			ras.setSignature(border[j].x(), border[j].y(), val);
		} else if (border[j].y() > yOld) {
			ras.setSignature(border[j].x(), yOld, val);
		}
		yOld = border[j].y();
	}
}
 
//==========================================================================
 
//-------------------------------
//    Raw Borders Extraction
//-------------------------------
 
//RawBorderPoints correspond to lower-left pixel corners.
//EXAMPLE: (0,0) is the lower-left *corner* of the image, whereas (0,0) also
// represents coordinates of the lower-left *pixel*.
//NOTE: 'Ambiguous turning' vertices are those of kind:
//
//    B|W           W|B
//    -x-    -or-   -x-
//    W|B           B|W
//
//Keeping B on the right of our path-seeking direction, we may either turn
//left or right at these points.
 
RawBorder *extractPath(Signaturemap &ras, int x0, int y0,
					   int pathType, int xOuterPixel, int despeckling)
{
	RawBorder *path = new RawBorder;
	int x, y;
	short dirX, dirY;
	long int area = 0;
	bool nextLeftPixel, nextRightPixel;
 
	if (pathType == outer) {
		dirX = 0;
		dirY = 1;
	} else {
		dirX = 1;
		dirY = 0;
		area += y0;
		path->setXExternalPixel(xOuterPixel);
	}
 
	path->push_back(RawBorderPoint(x0, y0));
 
	//Check here if (x0, y0) is an ambiguous-direction point
	nextLeftPixel = ras.getBitmapColor(x0 + (dirY - dirX - 1) / 2, y0 + (-dirY - dirX - 1) / 2);
	nextRightPixel = ras.getBitmapColor(x0 + (-dirX - dirY - 1) / 2, y0 + (dirX - dirY - 1) / 2);
	if ((nextRightPixel == black) && (nextLeftPixel == white))
		path->back().setAmbiguous(dirX ? RawBorderPoint::left : RawBorderPoint::right);
 
	//Begin path extraction
 
	for (x = x0 + dirX, y = y0 + dirY; !(x == x0 && y == y0); x += dirX, y += dirY) {
		path->push_back(RawBorderPoint(x, y));
 
		//Calculate next direction
		nextLeftPixel = ras.getBitmapColor(x + (dirX - dirY - 1) / 2, y + (dirY + dirX - 1) / 2);
		nextRightPixel = ras.getBitmapColor(x + (dirX + dirY - 1) / 2, y + (dirY - dirX - 1) / 2);
 
		if ((nextRightPixel == black) && (nextLeftPixel == black)) {
			//Left Turn
			std::swap(dirY, dirX);
			dirX = -dirX;
		} else if ((nextRightPixel == white) && (nextLeftPixel == white)) {
			//Right Turn
			std::swap(dirY, dirX);
			dirY = -dirY;
		} else if ((nextRightPixel == white) && (nextLeftPixel == black)) {
 
			//path->back().setAmbiguous();
 
			//Do a surrounding check and connect minority color
			if (getMinorityCheck(ras, x, y) == black) {
				std::swap(dirY, dirX);
				dirY = -dirY;
				path->back().setAmbiguous(RawBorderPoint::right);
			} //right turn
			else {
				std::swap(dirY, dirX);
				dirX = -dirX;
				path->back().setAmbiguous(RawBorderPoint::left);
			} //left turn
		}
 
		//Also calculate border area
		area += y * dirX;
 
		//And sign treated pixel
		if (dirY != 0)
			ras.setSignature(x, y + (dirY - 1) / 2, pathType);
	}
 
	//If the inner region's overall area is under a given threshold,
	//then erase it (intended as image noise).
	if (abs(area) < despeckling) {
		setSignature(ras, *path, invalid);
		delete path;
		path = 0;
	}
 
	return path;
}
 
//--------------------------------------------------------------------------
 
BorderList *extractBorders(const TRasterP &ras, int threshold, int despeckling)
{
	Signaturemap byteImage(ras, threshold);
 
	BorderList *borderHierarchy = new BorderList;
	vector<RawBorder *> outerBorders;
	list<RawBorder *> innerBorders;
	RawBorder *foundPath;
 
	int x, y;
	bool Color, oldColor;
	int xOuterPixel = 0;
	bool enteredRegionType;
	unsigned char signature;
 
	//Traverse image to extract raw borders
	for (y = 0; y < ras->getLy(); ++y) {
		oldColor = white;
		enteredRegionType = outer;
		for (x = 0; x < ras->getLx(); ++x) {
			if (oldColor ^ (Color = byteImage.getBitmapColor(x, y))) {
				//Region type changes
				enteredRegionType = !enteredRegionType;
 
				if ((signature = byteImage.getSignature(x, y)) == none) {
					//We've found a border
					if (foundPath = extractPath(byteImage, x, y, !enteredRegionType, xOuterPixel, despeckling))
						if (enteredRegionType == outer)
							innerBorders.push_back(foundPath);
						else
							outerBorders.push_back(foundPath);
				}
 
				//If leaving a white region, remember it - in order to establish
				//border hierarchy in the future
				if (enteredRegionType == inner && signature != invalid)
					xOuterPixel = x;
 
				//Invalid pixels got signed by a cut-out path, due to insufficient area
				if (signature == invalid)
					byteImage.setSignature(x, y, none); //Restore them now
 
				oldColor = Color;
			}
		}
	}
 
	//Now, we have all borders found, but no hierarchy between them.
 
	unsigned int i;
	list<RawBorder *>::iterator l;
 
	//Build hierarchy
 
	innerBorders.push_front(0); //Just to keep a fixed list head
 
	for (i = 0; i < outerBorders.size(); ++i) {
 
		//Initialize a border family
		borderHierarchy->push_back(BorderFamily());
		borderHierarchy->back().push_back(outerBorders[i]);
 
		//Reset outerBorders[i]'s signature
		setSignature(byteImage, *outerBorders[i], none);
 
		//Now check inner borders for insideness - check if the outerPixel
		//remembered in path extraction has been cleared
		for (l = innerBorders.begin(), ++l; l != innerBorders.end(); ++l) {
			if (byteImage.getSignature((*l)->xExternalPixel(), (**l)[0].y()) == none) {
				borderHierarchy->back().push_back(*l);
				setSignature(byteImage, **l, none);
				l = innerBorders.erase(l);
				--l;
			}
		}
	}
 
	return borderHierarchy;
}
 
//--------------------------------------------------------------------------
 
//==================================
//    Calculate optimal polygons
//==================================
 
//The optimal polygon for a given original border is found like:
 
// 1) Find couples (i,k(i)), so that k(i) be the largest k:
//        d(j,ik) <= 1;  for *all* i<j<k.  (d is infinite-norm distance)
//    It can be shown that such a condition is equivalent to:
//      exists line l : d(l,j)<=1/2, for all i<=j<=k(i).
// 2) Clean the above couples - find couples (i,l(i)):
//        l(i)=min{k(j)},  j=i..n.
// 3) Calculate clipped couples (i',l'); where i'=i+1, l'=l(i)-1.
// 4) Calculate sums for path penalties.
// 5) Apply optimality algorithm.
 
//NOTE: Weak simpleness reads like: a set of polygons is weak-simple if no edge
//      *crosses* another edge. Superposition and collision of edges with vertices
//      are still admitted.
//        =>  It can be shown that due to 1) and special conditions on ambiguous
//            turnings applied in both 1) and 3), weak simpleness is insured in
//            our polygonization.
 
//--------------------------------------------------------------------------
 
//Helper functions/classes: circular-indexed vectors
 
//returns 1 whenever the triple (a,b,c) is 'circular' mod n.
//NOTE: We'll find useful taking (i,i,j) as 1 and (i,j,j) as 0.
inline bool isCircular(int a, int b, int c)
{
	return a <= c ? a <= b && b < c : c > b || b >= a;
}
 
//--------------------------------------------------------------------------
 
//Extracts a 'next corner' array - helps improving overall speed
inline int *findNextCorners(RawBorder &path)
{
	int i, currentCorner;
	int *corners = new int[path.size()];
 
	//NOTE: 0 is a corner, due to the path extraction procedure.
	currentCorner = 0;
	for (i = path.size() - 1; i >= 0; --i) {
		if (path[currentCorner].x() != path[i].x() &&
			path[currentCorner].y() != path[i].y())
			currentCorner = i + 1;
		corners[i] = currentCorner;
	}
 
	return corners;
}
 
//--------------------------------------------------------------------------
 
//Calculate furthest k satisfying 1) for all fixed i.
inline int *furthestKs(RawBorder &path, int *&nextCorners)
{
 
	int n = path.size();
	int *kVector = new int[n];
 
	enum { left,
		   up,
		   right,
		   down };
	int directionsOccurred[4];
 
	nextCorners = findNextCorners(path);
 
	int i, j, k;
	TPoint shift;
	TPoint leftConstraint, rightConstraint, violatedConstraint;
	TPoint newLeftConstraint, newRightConstraint;
	TPoint jPoint, jNextPoint, iPoint, direction;
 
	int directionSignature;
 
	for (i = 0; i < n; ++i) {
		//Initialize search
		leftConstraint = rightConstraint = TPoint();
		directionsOccurred[0] = directionsOccurred[1] = directionsOccurred[2] =
			directionsOccurred[3] = 0;
		j = i;
		jNextPoint = iPoint = path[i].pos();
 
		//Search for k(i)
		while (1) {
 
			//NOTE: Here using TPoint::operator= is less effective than setting
			//its x and y components directly...
 
			jPoint = jNextPoint;
			jNextPoint = path[nextCorners[j]].pos();
 
			//Update directions count
			directionSignature = jNextPoint.x > jPoint.x ? right : jNextPoint.x < jPoint.x ? left
																						   : jNextPoint.y > jPoint.y ? up : down;
			directionsOccurred[directionSignature] = 1;
 
			//If all 4 axis directions occurred, quit
			if (directionsOccurred[left] && directionsOccurred[right] &&
				directionsOccurred[up] && directionsOccurred[down]) {
				k = j;
				goto foundK;
			}
 
			//Update displacement from i
			shift = jNextPoint - iPoint;
 
			//Test j against constraints
			//if(cross(shift, leftConstraint)<0 || cross(shift, rightConstraint)>0)
			if (cross(shift, leftConstraint) < 0) {
				violatedConstraint = leftConstraint;
				break;
			}
			if (cross(shift, rightConstraint) > 0) {
				violatedConstraint = rightConstraint;
				break;
			}
 
			//Update constraints
			if (abs(shift.x) > 1 || abs(shift.y) > 1) {
 
				newLeftConstraint.x = shift.x +
									  (shift.y < 0 || (shift.y == 0 && shift.x < 0) ? 1 : -1);
				newLeftConstraint.y = shift.y +
									  (shift.x > 0 || (shift.x == 0 && shift.y < 0) ? 1 : -1);
 
				if (cross(newLeftConstraint, leftConstraint) >= 0)
					leftConstraint = newLeftConstraint;
 
				newRightConstraint.x = shift.x +
									   (shift.y > 0 || (shift.y == 0 && shift.x < 0) ? 1 : -1);
 
				newRightConstraint.y = shift.y +
									   (shift.x < 0 || (shift.x == 0 && shift.y < 0) ? 1 : -1);
 
				if (cross(newRightConstraint, rightConstraint) <= 0)
					rightConstraint = newRightConstraint;
			}
 
			//Imposing strict constraint for ambiguous turnings, to ensure polygons' weak simpleness.
			//Has to be defined *outside* abs checks.
			if (path[nextCorners[j]].getAmbiguous()) {
				if (path[nextCorners[j]].getAmbiguous() == RawBorderPoint::left)
					rightConstraint = shift;
				else
					leftConstraint = shift;
			}
 
			j = nextCorners[j];
		}
 
		//At this point, constraints are violated by the next corner.
		//Then, search for the last k between j and corners[j] not violating them.
 
		direction = convert(normalize(convert(jNextPoint - jPoint)));
		k = (j + cross(jPoint - iPoint, violatedConstraint) / cross(violatedConstraint, direction)) % n;
 
	foundK:
 
		kVector[i] = k;
	}
 
	return kVector;
}
 
//--------------------------------------------------------------------------
 
// Now find the effective intervals inside which we can define possible
// arcs approximating the given raw border:
//    for every a in [i,res[i]], the arc connecting border[i] and
//    border[a] will be a possible one.
inline int *calculateForwardArcs(RawBorder &border, bool ambiguitiesCheck)
{
	int i, j, n = (int)border.size();
 
	int *nextCorners;
	int *k = furthestKs(border, nextCorners);
	int *K = new int[n];
	int *res = new int[n];
 
	//find K[i]= min {k[j]}, j=i..n-1.
	for (i = 0; i < n; ++i) {
		for (j = i, K[i] = k[i]; isCircular(i, j, K[i]); j = (j + 1) % n)
			if (isCircular(j, k[j], K[i]))
				K[i] = k[j];
	}
 
	//Finally, we perform the following clean-up operations:
	//  first, extremities of [i,K[i]] are clipped away, to obtain a
	//    smoother optimal polygon (and deal with cases like the unitary
	//    square);
	//  second, arcs of the kind [i,j] with j<i, become [i,n].
 
	for (i = n - 1, j = 0; j < n; i = j, ++j) {
		res[j] = K[i] < j ? (K[i] == 0 ? n - 1 : n) : K[i] - 1;
	}
 
	//Amibiguities check for vertex and edge superpositions. Prevent problems in the forecoming
	//straight-skeleton thinning process.
 
	if (ambiguitiesCheck) {
		for (i = 1; nextCorners[i] > 0; i = nextCorners[i]) {
			if (border[i].getAmbiguous() == RawBorderPoint::right) {
				//Check vertices from i (excluded) to res[res[i]]; if in it there exists vertex k so that pos(k)==pos(i)...
				//This prevents the existence of 0 degree angles in the optimal polygon.
 
				int rrPlus1 = (res[res[i] % n] + 1) % n;
 
				for (j = nextCorners[i];
					 isCircular(i, j, rrPlus1) && j != i; //remember that isCircular(a,a,b) == 1 ...
					 j = nextCorners[j]) {
					if (border[j].getAmbiguous() && (border[j].pos() == border[i].pos())) {
						res[res[i] % n] = j - 1;
						assert((res[i] % n) != j - 1);
 
						//Further, ensure res is increasing
						for (int k = res[i] % n; res[k] >= j - 1 && k >= 0; --k) {
							res[k] = j - 1;
							assert(k != j - 1);
						}
 
						break;
					}
				}
			}
		}
	}
 
	delete[] k;
	delete[] K;
	delete[] nextCorners;
 
	return res;
}
 
//--------------------------------------------------------------------------
 
//Let sum[i] and sum2[i] be respectively the sums of vertex coordinates
//from 0 to i, and the sums of their squares; sumsMix contain sums of
//xy terms.
inline void calculateSums(RawBorder &path)
{
	unsigned int i, n = path.size();
	TPointD currentRelativePos;
 
	path.sums() = new TPointD[n + 1];
	path.sums2() = new TPointD[n + 1];
	path.sumsMix() = new double[n + 1];
 
	path.sums()[0].x = path.sums()[0].y = path.sums2()[0].x = path.sums2()[0].y = 0;
	for (i = 1; i < path.size(); ++i) {
		currentRelativePos = convert(path[i].pos() - path[0].pos());
 
		path.sums()[i] = path.sums()[i - 1] + currentRelativePos;
 
		path.sums2()[i].x = path.sums2()[i - 1].x + currentRelativePos.x * currentRelativePos.x;
		path.sums2()[i].y = path.sums2()[i - 1].y + currentRelativePos.y * currentRelativePos.y;
 
		path.sumsMix()[i] = path.sumsMix()[i - 1] + currentRelativePos.x * currentRelativePos.y;
	}
 
	// path[n] is virtually intended as path[0], but we prefer to introduce
	// it in the optimality algorithm's count
	path.sums()[n].x = path.sums()[n].y = path.sums2()[n].x = path.sums2()[n].y = 0;
}
 
//--------------------------------------------------------------------------
 
//Let a,b the index-extremities of an arc of this path.
//Then return its penalty.
inline double penalty(RawBorder &path, int a, int b)
{
	int n = b - a + 1;
 
	TPointD v = convert(rotate90(path[b == path.size() ? 0 : b].pos() - path[a].pos()));
	TPointD sum = path.sums()[b] - path.sums()[a];
	TPointD sum2 = path.sums2()[b] - path.sums2()[a];
	double sumMix = path.sumsMix()[b] - path.sumsMix()[a];
 
	double F1 = sum2.x - 2 * sum.x * path[a].x() + n * path[a].x() * path[a].x();
	double F2 = sum2.y - 2 * sum.y * path[a].y() + n * path[a].y() * path[a].y();
	double F3 = sumMix - sum.x * path[a].y() - sum.y * path[a].x() + n * path[a].x() * path[a].y();
 
	return sqrt((v.y * v.y * F1 + v.x * v.x * F2 - 2 * v.x * v.y * F3) / n);
}
 
//--------------------------------------------------------------------------
 
//NOTA: Il seguente algoritmo di riduzione assicura la semplicita' (debole) dei poligoni prodotti.
//
 
inline void reduceBorder(RawBorder &border, Contour &res, bool ambiguitiesCheck)
{
	int i, j, k, a, *b, n = border.size(), m;
	double newPenalty;
	int minPenaltyNext;
	int *minPenaltyNextArray = new int[n];
 
	//Calculate preliminary infos
	int *longestArcFrom = calculateForwardArcs(border, ambiguitiesCheck);
	calculateSums(border);
 
	double *penaltyToEnd = new double[n + 1];
 
	//EXPLANATION:
	//The fastest way to extract the optimal reduced border is based on the
	//weakly monotonic property of longestArc[].
	//The minimal number of its vertices 'm' is easily found by
	//traversing the path with the longest step allowed. Let b[] be that
	//succession; then, given res[i], it has to be reached by a vertex in
	//the interval: {a[i-1], .. , b[i-1]}, where longestArc[a[i-1]]=a[i],
	//longestArc[a[i-1]-1]<a[i], and a[m]=n.
 
	//Calculate m
	for (i = 0, m = 0; i < n; i = longestArcFrom[i])
		++m;
 
	//Calculate b[]
	b = new int[m + 1];
	b[m] = n;
	for (i = 0, j = 0; j < m; i = longestArcFrom[i], ++j)
		b[j] = i;
 
	//NOTE: a[] need not be completely found - we just remember the
	//a=a[j+1] currently needed.
 
	//Now, build the optimal polygon
	for (j = m - 1, a = n; j >= 0; --j) {
		for (k = b[j]; k >= 0 && longestArcFrom[k] >= a; --k) {
			penaltyToEnd[k] = infinity;
			for (i = a; i <= longestArcFrom[k]; ++i) {
				newPenalty = penaltyToEnd[i] + penalty(border, k, i);
				if (newPenalty < penaltyToEnd[k])
					penaltyToEnd[k] = newPenalty;
				minPenaltyNext = i;
			}
			minPenaltyNextArray[k] = minPenaltyNext;
		}
		a = k + 1;
	}
 
	//Finally, read off the optimal polygon
 
	res.resize(m);
	for (i = j = 0; i < n; i = minPenaltyNextArray[i], ++j) {
		res[j] = ContourNode(border[i].x(), border[i].y());
 
		//Ambiguities are still remembered in the output polygon.
		if (border[i].getAmbiguous() == RawBorderPoint::left)
			res[j].setAttribute(ContourNode::AMBIGUOUS_LEFT);
		if (border[i].getAmbiguous() == RawBorderPoint::right)
			res[j].setAttribute(ContourNode::AMBIGUOUS_RIGHT);
	}
 
	delete[] longestArcFrom;
	delete[] minPenaltyNextArray;
	delete[] border.sums();
	delete[] border.sums2();
	delete[] border.sumsMix();
	delete[] penaltyToEnd;
	delete[] b;
}
 
//--------------------------------------------------------------------------
 
//Reduction caller and list copier.
inline void reduceBorders(BorderList &borders, Contours &result, bool ambiguitiesCheck)
{
	unsigned int i, j;
 
	//Initialize output container
	result.resize(borders.size());
 
	//Copy results
	for (i = 0; i < borders.size(); ++i) {
		result[i].resize(borders[i].size());
		for (j = 0; j < borders[i].size(); ++j) {
			reduceBorder(*borders[i][j], result[i][j], ambiguitiesCheck);
			delete borders[i][j];
		}
	}
}
 
//--------------------------------------------------------------------------
 
//===========================
//    Polygonization Main
//===========================
 
//Extracts a polygonal, minimal yet faithful representation of image contours
//Contours* polygonize(const TRasterP &ras){
void polygonize(const TRasterP &ras, Contours &polygons, VectorizerCoreGlobals &g)
{
	BorderList *borders;
 
	borders = extractBorders(ras, g.currConfig->m_threshold, g.currConfig->m_despeckling);
	reduceBorders(*borders, polygons, g.currConfig->m_maxThickness > 0.0);
}