// outlineApproximation.cpp: implementation of the outlineApproximation class.
//
//////////////////////////////////////////////////////////////////////
 
#include "tstrokeoutline.h"
#include "tstroke.h"
#include "tcurves.h"
#include "tmathutil.h"
#include "tgl.h"
 
//#include "tcolorfunctions.h"
 
typedef std::pair<TQuadratic *, TQuadratic *> outlineEdge;
typedef std::vector<outlineEdge> outlineBoundary;
 
const double infDouble = (std::numeric_limits<double>::max)();
 
/*
ONLY FOT TEST
 
TSegment  g_tangEnvelope_1;  
TSegment  g_tangEnvelope_2;
 
vector<TQuadratic>  g_testOutline;
*/
namespace Outline
{
 
class infinityCurvature
{
};
 
class notValidOutline
{
};
}
 
namespace
{
 
/*
  This formule is derived from Graphic Gems pag. 600
 
    e = h^2 |a|/8
  
      e = pixel size
      h = step
      a = acceleration of curve (for a quadratic is a costant value)
  */
double localComputeStep(const TQuadratic &quad, double pixelSize)
{
	double step = 2;
 
	TPointD A = quad.getP0() - 2.0 * quad.getP1() + quad.getP2(); // 2*A is the acceleration of the curve
 
	double A_len = norm(A);
	if (A_len > 0)
		step = sqrt(2 * pixelSize / A_len);
 
	return step;
}
//---------------------------------------------------------------------------
 
// selezionano lo spicchio da calcolare nella costruzione dei tappi
// (semicirconferenze iniziali e finali)
const int QUARTER_BEGIN = 1;
const int QUARTER_END = 0;
 
// selezionano il pezzo d'outline da calcolare (sopra/sotto)
const int OUTLINE_UP = 1;
const int OUTLINE_DOWN = 0;
 
// utili
const double ratio_1_3 = 1.0 / 3.0;
const double ratio_2_3 = 2.0 / 3.0;
 
//---------------------------------------------------------------------------
 
// torna la curvature per t=0
template <class T>
double curvature_t0(const T *curve)
{
	assert(curve);
	TPointD v1 = curve->getP1() - curve->getP0();
	TPointD v2 = curve->getP2() - curve->getP1();
 
	double v_cross = cross(v1, v2);
 
	if (isAlmostZero(v_cross))
		return infDouble;
 
	return ratio_2_3 * v_cross / pow(norm(v1), ratio_1_3);
}
 
//---------------------------------------------------------------------------
 
// torna la curvature per t=1
double curvature_t1(const TThickQuadratic *curve)
{
	assert(curve);
	TThickQuadratic tmp;
 
	tmp.setThickP0(curve->getThickP2());
	tmp.setThickP1(curve->getThickP1());
	tmp.setThickP2(curve->getThickP0());
 
	return curvature_t0(&tmp);
}
 
//---------------------------------------------------------------------------
 
// estrae il punto dell'outline per il parametro specificato
// N.B: e' sbagliata non tiene conto degli inviluppi
TPointD getPointInOutline(const TThickQuadratic *tq, double t, int upOrDown)
{
	assert(tq);
	const TThickPoint &p = tq->getThickPoint(t);
	TPointD n = tq->getSpeed(t);
	if (norm2(n)) {
		n = normalize(n);
		n = upOrDown ? rotate90(n) : rotate270(n);
	}
 
	return convert(p) + p.thick * n;
}
 
//---------------------------------------------------------------------------
 
bool checkPointInOutline(const TPointD &pointToTest,
						 const TThickQuadratic *tq,
						 double t,
						 double error)
{
	assert(tq);
	TThickPoint tpnt = tq->getThickPoint(t);
 
	if (fabs(sq(pointToTest.x - tpnt.x) +
			 sq(pointToTest.y - tpnt.y) -
			 sq(tpnt.thick)) < error)
		return true;
 
	return false;
}
 
//---------------------------------------------------------------------------
 
// costruisce un ramo di outline (sopra o sotto) per una quadratica cicciona
TQuadratic *makeOutlineForThickQuadratic(const TThickQuadratic *tq, int upOrDown)
{
	assert(tq);
	// if(!outline) return 0;
 
	TThickPoint
		p0 = tq->getThickP0(),
		//p1 = tq->getThickP0(),
		p2 = tq->getThickP2();
 
	TPointD t0 = tq->getP1() - tq->getP0();
	TPointD t1 = tq->getP2() - tq->getP1();
 
	if (t0 == t1)
		return 0;
 
	TPointD
		N0 = tq->getSpeed(0.0),
		N2 = tq->getSpeed(1.0);
 
	if (!norm2(N0) && !norm2(N2))
		throw Outline::notValidOutline();
 
	if (norm2(N0)) {
		N0 = normalize(N0);
		N0 = upOrDown ? rotate90(N0) : rotate270(N0);
	}
 
	if (norm2(N2)) {
		N2 = normalize(N2);
		N2 = upOrDown ? rotate90(N2) : rotate270(N2);
	}
 
	TPointD p0aux = (convert(p0) + p0.thick * N0);
	TPointD p2aux = (convert(p2) + p2.thick * N2);
 
	TQuadratic
		radius(TPointD(tq->getThickP0().thick, 0.0),
			   TPointD(tq->getThickP1().thick, 0.0),
			   TPointD(tq->getThickP2().thick, 0.0));
 
	TPointD r0 = radius.getSpeed(0.0);
	TPointD r1 = radius.getSpeed(1.0);
 
	TPointD
		v0,
		v2;
 
	double ct0 = curvature_t0(tq);
 
	if (ct0 != infDouble)
		v0 = (1 + p0.thick * ct0) * t0 + 0.5 * r0.x * N0;
	else
		v0 = r0.x * N0;
 
	double ct1 = curvature_t1(tq);
 
	if (ct1 != infDouble)
		v2 = (1 + p2.thick * ct1) * t1 + 0.5 * r1.x * N2;
	else
		v2 = r1.x * N2;
 
	/*
    try {
      v0 = (1 + p0.thick * curvature_t0( tq )) * t0 + 0.5 * r0.x * N0;
    }
    catch( Outline::infinityCurvature& ) {
    }
    
    try {
      v2 = (1 + p2.thick * curvature_t1( tq )) * t1 + 0.5 * r1.x * N2;
    }
    catch( Outline::infinityCurvature& ) {
    }
    */
	//    g_tangEnvelope_1.setP0( outline.getP0() );
	//    g_tangEnvelope_1.setP1( outline.getP0() + v0 );
 
	//    g_tangEnvelope_2.setP0( outline.getP2() );
	//    g_tangEnvelope_2.setP1( outline.getP2() + v2 );
 
	//  solve sistem  p1 = p0 + k * v1 = p2 + m * v2 to find
 
	double det = v0.x * v0.y - v2.x * v2.y;
	if (areAlmostEqual(det, 0.0))
		return 0;
	double xsol;
	try {
		xsol = ((p0aux.x - p2aux.x) * v2.y - (p0aux.y - p2aux.y) * v2.x) / det;
		//tsolveSistem( A, 2, b );
	} catch (TMathException &) {
		return new TQuadratic((upOrDown) ? p0aux : p2aux, (p0aux + p2aux) * 0.5, (upOrDown) ? p2aux : p0aux);
	} catch (std::exception &e) {
		std::string s(e.what());
		abort();
	} catch (...) {
		abort();
	}
 
	return new TQuadratic((upOrDown) ? p0aux : p2aux, p0aux + xsol * v0, (upOrDown) ? p2aux : p0aux);
}
 
//---------------------------------------------------------------------------
 
/*
    costruisce l'outline per una singola quadratica senza 
    inserire le semicirconferenze iniziali e finali
   */
void makeOutline(/*std::ofstream& cout,*/
				 outlineBoundary &outl,
				 const TThickQuadratic &t,
				 double error)
{
	outlineEdge edge;
	const TThickQuadratic *tq = &t;
	edge.first = edge.second = 0;
	try {
		edge.first = makeOutlineForThickQuadratic(tq, OUTLINE_UP);
		edge.second = makeOutlineForThickQuadratic(tq, OUTLINE_DOWN);
	} catch (Outline::notValidOutline &) {
		delete edge.first;
		delete edge.second;
		return;
	}
 
	const TQuadratic *q_up = edge.first;
	const TQuadratic *q_down = edge.second;
	const double parameterTest = 0.5;
 
	// forza l'uscita per valori troppo piccoli
	bool isAlmostAPoint =
		areAlmostEqual(tq->getThickP0(), tq->getThickP1(), 1e-2) &&
		areAlmostEqual(tq->getThickP1(), tq->getThickP2(), 1e-2) /*&&
      areAlmostEqual( tq.getThickP0(), tq.getThickP2(), 1e-2 )*/;
 
	if (isAlmostAPoint ||
		q_up && checkPointInOutline(q_up->getPoint(parameterTest), tq, parameterTest, error) &&
			q_down && checkPointInOutline(q_down->getPoint(parameterTest), tq, parameterTest, error)) {
		/*	if (edge.first)
		  cout << "left: "<< *(edge.first);
	 else
		  cout << "left: "<< 0;
		if (edge.second)
		  cout << "right: "<<*(edge.second);
	 else
		  cout << "right: "<< 0;
		
		cout<<std::endl;*/
 
		outl.push_back(edge);
		return;
	} else {
		delete edge.first;
		delete edge.second;
	}
 
	TThickQuadratic
		tq_left,
		tq_rigth;
 
	tq->split(0.5, tq_left, tq_rigth);
 
	makeOutline(/*out,*/ outl, tq_left, error);
	makeOutline(/*cout,*/ outl, tq_rigth, error);
}
 
//---------------------------------------------------------------------------
 
void splitCircularArcIntoQuadraticCurves(const TPointD &Center,
										 const TPointD &Pstart,
										 const TPointD &Pend,
										 std::vector<TQuadratic *> &quadArray)
{
	// It splits a circular anticlockwise arc into a sequence of quadratic bezier curves
	// Every quadratic curve can approximate an arc no TLonger than 45 degrees (or 60).
	// It supposes that Pstart and Pend are onto the circumference (so that their lengths
	// are equal to tha radius of the circumference), otherwise the resulting curves could
	// be unpredictable.
	// The last component in quadCurve[] is an ending void curve
 
	/* ---------------------------------------------------------------------------------- */
	// If you want to split the arc into arcs no TLonger than 45 degrees (so that the whole
	// curve will be splitted into 8 pieces) you have to set these constants as follows:
	// cos_ang     ==> cos_45   = 0.5 * sqrt(2);
	// sin_ang     ==> sin_45   = 0.5 * sqrt(2);
	// tan_semiang ==> tan_22p5 = 0.4142135623730950488016887242097;
	// N_QUAD                   = 8;
 
	// If you want to split the arc into arcs no TLonger than 60 degrees (so that the whole
	// curve will be splitted into 6 pieces) you have to set these constants as follows:
	// cos_ang     ==> cos_60 = 0.5;
	// sin_ang     ==> sin_60 = 0.5 * sqrt(3);
	// tan_semiang ==> tan_30 = 0.57735026918962576450914878050196;
	// N_QUAD                 = 6;
	/* ---------------------------------------------------------------------------------- */
 
	// Defines some useful constant to split the arc into arcs no TLonger than 'ang' degrees
	// (the whole circumference will be splitted into 360/ang quadratic curves).
	const double cos_ang = 0.5 * sqrt(2.0);
	const double sin_ang = 0.5 * sqrt(2.0);
	const double tan_semiang = 0.4142135623730950488016887242097;
	const int N_QUAD = 8; // it's 360/ang
 
	// First of all, it computes the vectors from the center to the circumference,
	// in Pstart and Pend, and their cross and dot products
	TPointD Rstart = Pstart - Center;		 // its length is R (radius of the circle)
	TPointD Rend = Pend - Center;			 // its length is R (radius of the circle)
	double cross_prod = cross(Rstart, Rend); // it's Rstart x Rend
	double dot_prod = Rstart * Rend;
	const double sqr_radius = Rstart * Rstart;
	TPointD aliasPstart = Pstart;
	TQuadratic *quad;
 
	while ((cross_prod <= 0) || (dot_prod <= cos_ang * sqr_radius)) // the circular arc is TLonger
																	// than a 'ang' degrees arc
	{
		if ((int)quadArray.size() == N_QUAD) // this is possible if Pstart or Pend is not onto the circumference
			return;
		TPointD Rstart_rot_ang(cos_ang * Rstart.x - sin_ang * Rstart.y,
							   sin_ang * Rstart.x + cos_ang * Rstart.y);
		TPointD Rstart_rot_90(-Rstart.y, Rstart.x);
		quad = new TQuadratic(aliasPstart,
							  aliasPstart + tan_semiang * Rstart_rot_90,
							  Center + Rstart_rot_ang);
		quadArray.push_back(quad);
 
		// quad->computeMinStepAtNormalSize ();
 
		// And moves anticlockwise the starting point on the circumference by 'ang' degrees
		Rstart = Rstart_rot_ang;
		aliasPstart = quad->getP2();
		cross_prod = cross(Rstart, Rend); // it's Rstart x Rend
		dot_prod = Rstart * Rend;
 
		// after the rotation of 'ang' degrees, the remaining part of the arc could be a 0 degree
		// arc, so it must stop and exit from the function
		if ((cross_prod <= 0) && (dot_prod > 0.95 * sqr_radius))
			return;
	}
 
	if ((cross_prod > 0) && (dot_prod > 0)) // the last quadratic curve approximates an arc shorter than a 'ang' degrees arc
	{
		TPointD Rstart_rot_90(-Rstart.y, Rstart.x);
 
		double deg_index = (sqr_radius - dot_prod) / (sqr_radius + dot_prod);
 
		quad = new TQuadratic(aliasPstart,
							  (deg_index < 0) ? 0.5 * (aliasPstart + Pend) : aliasPstart + sqrt(deg_index) * Rstart_rot_90,
							  Pend);
		quadArray.push_back(quad);
 
	} else // the last curve, already computed, is as TLong as a 'ang' degrees arc
		quadArray.back()->setP2(Pend);
}
 
//---------------------------------------------------------------------------
 
// copia arrayUp e arrayDown nel vettore dell'outline
// se le dimensioni sono diverse il vettore con il numero
// minore di quadratiche viene riempito con quadratiche degeneri
// con i punti di controllo coincidenti nell'ultimo estremo valido
void copy(/*std::ofstream& cout,*/
		  const std::vector<TQuadratic *> &arrayUp,
		  const std::vector<TQuadratic *> &arrayDown,
		  outlineBoundary &ob)
{
	int minSize = std::min(arrayUp.size(), arrayDown.size());
 
	assert(minSize > 0);
 
	int i;
 
	for (i = 0; i < minSize; ++i) {
		//cout<<"left: "<< *(arrayUp[i])<< "right: "<<*(arrayDown[i])<<std::endl;
		//cout<"left: "<< arrayUp[i].getP0()<<", "arrayUp[i].getP1()<<", "arrayUp[i].getP2()<< "right: "<< << arrayDown[i].getP0()<<", "arrayDown[i].getP1()<<", "arrayDown[i].getP2()<<endl;
		ob.push_back(outlineEdge(arrayUp[i], arrayDown[i]));
	}
	if (arrayUp.size() != arrayDown.size()) {
		const std::vector<TQuadratic *> &vMaxSize = arrayUp.size() > arrayDown.size() ? arrayUp : arrayDown;
		const std::vector<TQuadratic *> &vMinSize = arrayUp.size() < arrayDown.size() ? arrayUp : arrayDown;
 
		int delta = vMaxSize.size() - vMinSize.size();
 
		if (arrayUp.size() > arrayDown.size())
			while (i < minSize + delta) {
				//cout<<"left: "<< arrayUp[i]<< "right: "<< 0<<std::endl;
				ob.push_back(outlineEdge(arrayUp[i], (TQuadratic *)0));
				i++;
			}
		else
			while (i < minSize + delta) {
				//cout<<"left: "<< 0 << "right: "<< arrayDown[i]<<std::endl;
				ob.push_back(outlineEdge((TQuadratic *)0, arrayDown[i]));
				i++;
			}
	}
}
 
//---------------------------------------------------------------------------
 
inline void changeQuadraticDirection(TQuadratic *q)
{
	TPointD p = q->getP2();
	q->setP2(q->getP0());
	q->setP0(p);
}
 
//---------------------------------------------------------------------------
 
// cambia il verso del vettore di quadratiche (vedi changeDirection di tstroke.cpp)
void changeDirection(std::vector<TQuadratic *> &array, bool onlyQuads = false)
{
	UINT chunkCount = array.size();
	UINT to = tfloor(chunkCount * 0.5);
	UINT i;
 
	if (chunkCount & 1)
		changeQuadraticDirection(array[to]);
 
	--chunkCount;
 
	for (i = 0; i < to; ++i) {
		changeQuadraticDirection(array[i]);
		changeQuadraticDirection(array[chunkCount - i]);
 
		if (!onlyQuads)
			std::swap(array[i], array[chunkCount - i]);
	}
}
 
//---------------------------------------------------------------------------
 
// estrae i punti necessari a costruire la semicirconferenza
// iniziale e finale di una curva cicciona
TQuadratic getCircleQuarter(const TThickQuadratic *tq, int versus)
{
	TQuadratic out;
 
	TPointD v = versus ? -tq->getSpeed(0.0) : tq->getSpeed(1.0);
 
	if (norm2(v))
		v = normalize(v);
 
	TPointD center = versus ? tq->getP0() : tq->getP2();
	double radius = versus ? tq->getThickP0().thick : tq->getThickP2().thick;
 
	out.setP0(center + (versus ? rotate270(v) : rotate90(v)) * radius);
	out.setP1(center + v * radius);
	out.setP2(center + (versus ? rotate90(v) : rotate270(v)) * radius);
 
	return out;
}
 
//---------------------------------------------------------------------------
 
void drawQuadratic(const TQuadratic &quad, double pixelSize)
{
	double m_min_step_at_normal_size = localComputeStep(quad, pixelSize);
 
	// It draws the curve as a linear piecewise approximation
 
	double invSqrtScale = 1.0;
	// First of all, it computes the control circles of the curve in screen coordinates
	TPointD scP0 = quad.getP0();
	TPointD scP1 = quad.getP1();
	TPointD scP2 = quad.getP2();
 
	TPointD A = scP0 - 2 * scP1 + scP2;
	TPointD B = scP0 - scP1;
 
	double h;
	h = invSqrtScale * m_min_step_at_normal_size;
	double h2 = h * h;
 
	TPointD P = scP0, D2 = 2 * h2 * A, D1 = A * h2 - 2 * B * h;
 
	if (h < 0 || isAlmostZero(h))
		return;
	assert(h > 0);
 
	// It draws the whole curve, using forward differencing
	glBegin(GL_LINE_STRIP); // The curve starts from scP0
	glVertex2d(scP0.x, scP0.y);
 
	for (double t = h; t < 1; t = t + h) {
		P = P + D1;
		D1 = D1 + D2;
		glVertex2d(P.x, P.y);
	}
 
	glVertex2d(scP2.x, scP2.y); // The curve ends in scP2
	glEnd();
}
 
//---------------------------------------------------------------------------
 
} // end of unnamed namespace
 
//-----------------------------------------------------------------------------
 
void makeOutline(const TStroke *stroke, int startQuad, int endQuad,
				 outlineBoundary &ob, double error2)
{
	//std::ofstream cout("c:\\temp\\outline.txt");
 
	assert(stroke);
	assert(startQuad >= 0);
	assert(endQuad < stroke->getChunkCount());
	assert(startQuad <= endQuad);
	TThickQuadratic *tq;
	std::vector<TQuadratic *> arrayUp, arrayDown;
	TQuadratic arc;
 
	if (!stroke->getChunkCount())
		return;
	//if (startQuad==0)
	{
		const TThickQuadratic *tq = stroke->getChunk(startQuad);
 
		// trova i punti sul cerchio che corrispondono
		// a due fette di 90 gradi.
		// Ritorna una quadratica invece di tre singoli punti solo per compattezza.
		TQuadratic
			arc = getCircleQuarter(tq, QUARTER_BEGIN);
 
		// estrae le quadratiche che corrispondono ad i due archi...
		splitCircularArcIntoQuadraticCurves(tq->getP0(), arc.getP0(), arc.getP1(), arrayUp);
		// e le ordina in modo che l'outline sia composta sempre da
		// una curva superiore ed una inferiore corrispondente
		changeDirection(arrayUp);
		splitCircularArcIntoQuadraticCurves(tq->getP0(), arc.getP1(), arc.getP2(), arrayDown);
		changeDirection(arrayDown, true);
		// copia le curve nell'outline; se gli array non hanno la stessa dimensione
		//  quello con meno curve viene riempito con curve improprie
		//  che hanno i punti di controllo coincidente con l'ultimo estremo valido
		//cout<<"quads del semicerchio left:"<<std::endl;
		copy(/*cout,  */ arrayUp, arrayDown, ob);
	}
 
	for (int i = startQuad; i <= endQuad; ++i) {
		tq = (TThickQuadratic *)stroke->getChunk(i);
		TThickPoint p0 = tq->getThickP0();
		TThickPoint p1 = tq->getThickP1();
		TThickPoint p2 = tq->getThickP2();
		if (p0.x == p1.x) {
			if (p1.x == p2.x && ((p1.y > p0.y && p1.y > p2.y) || (p1.y < p0.y && p1.y < p2.y)))
				tq = new TThickQuadratic(p0, 0.5 * (p0 + p1), p1);
		} else if (p0.y == p1.y) {
			if (p0.y == p2.y && ((p1.x > p0.x && p1.x > p2.x) || (p1.x < p0.x && p1.x < p2.x)))
				tq = new TThickQuadratic(p0, 0.5 * (p0 + p1), p1);
		} else {
			double fac1 = 1.0 / (p0.x - p1.x);
			double fac2 = 1.0 / (p0.y - p1.y);
 
			double aux1 = fac1 * (p2.x - p1.x);
			double aux2 = fac2 * (p2.y - p1.y);
			double aux3 = fac1 * (p0.x - p2.x);
			double aux4 = fac2 * (p0.y - p2.y);
 
			if ((areAlmostEqual(aux1, aux2) && aux1 >= 0) ||
				(areAlmostEqual(aux3, aux4) && aux3 >= 0 && aux3 <= 1))
				tq = new TThickQuadratic(p0, 0.5 * (p0 + p1), p1);
		}
 
		//cout<<"quad# "<<i<<":" <<*tq<<std::endl;
		makeOutline(/*cout, */ ob, *tq, error2);
		if (tq != stroke->getChunk(i))
			delete tq;
	}
 
	arrayUp.clear();
	arrayDown.clear();
 
	// come sopra ultimo pezzo di arco
	//	if (endQuad==stroke->getChunkCount()-1)
	{
		arc = getCircleQuarter(tq, QUARTER_END);
		splitCircularArcIntoQuadraticCurves(tq->getP2(), arc.getP1(), arc.getP0(), arrayUp);
		changeDirection(arrayUp);
		splitCircularArcIntoQuadraticCurves(tq->getP2(), arc.getP2(), arc.getP1(), arrayDown);
		changeDirection(arrayDown, true);
		//cout<<"quads del semicerchio right:"<<std::endl;
 
		copy(/*cout,*/ arrayUp, arrayDown, ob);
	}
}
 
//-----------------------------------------------------------------------------
 
void drawOutline(const outlineBoundary &ob, double pixelSize)
{
	for (UINT i = 0; i < ob.size(); ++i) {
		drawQuadratic(*ob[i].first, pixelSize);
		drawQuadratic(*ob[i].second, pixelSize);
	}
}
 
void computeOutlines(const TStroke *stroke, int startQuad, int endQuad,
					 std::vector<TQuadratic *> &quadArray, double error2)
{
	outlineBoundary ob;
	makeOutline(stroke, startQuad, endQuad, ob, error2);
 
	assert(quadArray.empty());
	quadArray.resize(ob.size() * 2);
 
	int i, count = 0;
	for (i = 0; i < (int)ob.size(); i++)
		if (ob[i].first)
			quadArray[count++] = ob[i].first;
 
	for (i = (int)ob.size() - 1; i >= 0; i--)
		if (ob[i].second)
			quadArray[count++] = ob[i].second;
 
	quadArray.resize(count);
	for (i = 0; i < (int)quadArray.size(); i++)
		quadArray[i]->reverse();
 
	std::reverse(quadArray.begin(), quadArray.end());
}
 
//-----------------------------------------------------------------------------
// End Of File
//-----------------------------------------------------------------------------