// 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;</tquadratic>

typedef std::vector<outlineedge> outlineBoundary;</outlineedge>

const double infDouble = (std::numeric_limits<double>::max)();</double>

/*

ONLY FOT TEST

TSegment  g_tangEnvelope_1;  

TSegment  g_tangEnvelope_2;

vector<tquadratic>  g_testOutline;</tquadratic>

*/

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 = TConsts::sqrt2 * sqrt(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=""></class>

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<

		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)</tquadratic>

{

	// 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,</tquadratic>

		  const std::vector<tquadratic *=""> &arrayDown,</tquadratic>

		  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])<

		//cout<"left: "<< arrayUp[i].getP0()<<", "arrayUp[i].getP1()<<", "arrayUp[i].getP2()<< "right: "<< << arrayDown[i].getP0()<<", "arrayDown[i].getP1()<<", "arrayDown[i].getP2()<

		ob.push_back(outlineEdge(arrayUp[i], arrayDown[i]));

	}

	if (arrayUp.size() != arrayDown.size()) {

		const std::vector<tquadratic *=""> &vMaxSize = arrayUp.size() > arrayDown.size() ? arrayUp : arrayDown;</tquadratic>

		const std::vector<tquadratic *=""> &vMinSize = arrayUp.size() < arrayDown.size() ? arrayUp : arrayDown;</tquadratic>

		int delta = vMaxSize.size() - vMinSize.size();

		if (arrayUp.size() > arrayDown.size())

			while (i < minSize + delta) {

				//cout<<"left: "<< arrayUp[i]<< "right: "<< 0<

				ob.push_back(outlineEdge(arrayUp[i], (TQuadratic *)0));

				i++;

			}

		else

			while (i < minSize + delta) {

				//cout<<"left: "<< 0 << "right: "<< arrayDown[i]<

				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)</tquadratic>

{

	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>

	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:"<

		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# "<

		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:"<

		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)</tquadratic>

{

	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

//-----------------------------------------------------------------------------