#include "tcurveutil.h"

#include "tcurves.h"

#include "tmathutil.h"

#include "tbezier.h"

//=============================================================================

/*

Questa funzione ritorna un vettore di

coppie di double (DoublePair) che individua i parametri 

dei punti d'intersezione.

  L'intero restituito indica il numero d'intersezioni che 

  sono state individuate (per due segmenti una).

    Se i segmenti sono paralleli il parametro viene posto a -1.

*/

int intersect(const TSegment &first,

			  const TSegment &second,

			  std::vector<doublepair> &intersections)</doublepair>

{

	return intersect(first.getP0(), first.getP1(), second.getP0(), second.getP1(), intersections);

}

int intersect(const TPointD &p1, const TPointD &p2, const TPointD &p3, const TPointD &p4,

			  std::vector<doublepair> &intersections)</doublepair>

{

	// This algorithm is presented in Graphics Geems III pag 199

	static double Ax, Bx, Ay, By, Cx, Cy, d, f, e;

	static double x1lo, x1hi, y1lo, y1hi;

	Ax = p2.x - p1.x;

	Bx = p3.x - p4.x;

	//test delle BBox

	if (Ax < 0.0) {

		x1lo = p2.x;

		x1hi = p1.x;

	} else {

		x1lo = p1.x;

		x1hi = p2.x;

	}

	if (Bx > 0.0) {

		if (x1hi < p4.x || x1lo > p3.x)

			return 0;

	} else if (x1hi < p3.x || x1lo > p4.x)

		return 0;

	Ay = p2.y - p1.y;

	By = p3.y - p4.y;

	if (Ay < 0) {

		y1lo = p2.y;

		y1hi = p1.y;

	} else {

		y1lo = p1.y;

		y1hi = p2.y;

	}

	if (By > 0) {

		if (y1hi < p4.y || y1lo > p3.y)

			return 0;

	} else if (y1hi < p3.y || y1lo > p4.y)

		return 0;

	Cx = p1.x - p3.x;

	Cy = p1.y - p3.y;

	d = By * Cx - Bx * Cy;

	f = Ay * Bx - Ax * By;

	e = Ax * Cy - Ay * Cx;

	if (f > 0) {

		if (d < 0)

			return 0;

		if (!areAlmostEqual(d, f))

			if (d > f)

				return 0;

		if (e < 0)

			return 0;

		if (!areAlmostEqual(e, f))

			if (e > f)

				return 0;

	} else if (f < 0) {

		if (d > 0)

			return 0;

		if (!areAlmostEqual(d, f))

			if (d < f)

				return 0;

		if (e > 0)

			return 0;

		if (!areAlmostEqual(e, f))

			if (e < f)

				return 0;

	} else {

		if (d < 0 || d > 1 || e < 0 || e > 1)

			return 0;

		if (p1 == p2 && p3 == p4) {

			intersections.push_back(DoublePair(0, 0));

			return 1;

		}

		// controllo che i segmenti non siano sulla stessa retta

		if (!cross(p2 - p1, p4 - p1)) {

			// calcolo delle combinazioni baricentriche

			double distp2p1 = norm2(p2 - p1);

			double distp3p4 = norm2(p3 - p4);

			double dist2_p3p1 = norm2(p3 - p1);

			double dist2_p4p1 = norm2(p4 - p1);

			double dist2_p3p2 = norm2(p3 - p2);

			double dist2_p4p2 = norm2(p4 - p2);

			int intersection = 0;

			// calcolo delle prime due soluzioni

			double vol1;

			if (distp3p4) {

				distp3p4 = sqrt(distp3p4);

				vol1 = (p1 - p3) * normalize(p4 - p3);

				if (vol1 >= 0 && vol1 <= distp3p4) // combinazione baricentrica valida

				{

					intersections.push_back(DoublePair(0.0, vol1 / distp3p4));

					++intersection;

				}

				vol1 = (p2 - p3) * normalize(p4 - p3);

				if (vol1 >= 0 && vol1 <= distp3p4) {

					intersections.push_back(DoublePair(1.0, vol1 / distp3p4));

					++intersection;

				}

			}

			if (distp2p1) {

				distp2p1 = sqrt(distp2p1);

				vol1 = (p3 - p1) * normalize(p2 - p1);

				if (dist2_p3p2 && dist2_p3p1)

					if (vol1 >= 0 && vol1 <= distp2p1) {

						intersections.push_back(DoublePair(vol1 / distp2p1, 0.0));

						++intersection;

					}

				vol1 = (p4 - p1) * normalize(p2 - p1);

				if (dist2_p4p2 && dist2_p4p1)

					if (vol1 >= 0 && vol1 <= distp2p1) {

						intersections.push_back(DoublePair(vol1 / distp2p1, 1.0));

						++intersection;

					}

			}

			return intersection;

		}

		return -1;

	}

	double par_s = d / f;

	double par_t = e / f;

	intersections.push_back(DoublePair(par_s, par_t));

	return 1;

}

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

int intersectCloseControlPoints(const TQuadratic &c0,

								const TQuadratic &c1,

								std::vector<doublepair> &intersections);</doublepair>

int intersect(const TQuadratic &c0,

			  const TQuadratic &c1,

			  std::vector<doublepair> &intersections, bool checksegments)</doublepair>

{

	int ret;

	// funziona male, a volte toppa le intersezioni...

	if (checksegments) {

		ret = intersectCloseControlPoints(c0, c1, intersections);

		if (ret != -2)

			return ret;

	}

	double a = c0.getP0().x - 2 * c0.getP1().x + c0.getP2().x;

	double b = 2 * (c0.getP1().x - c0.getP0().x);

	double d = c0.getP0().y - 2 * c0.getP1().y + c0.getP2().y;

	double e = 2 * (c0.getP1().y - c0.getP0().y);

	double coeff = b * d - a * e;

	int i = 0;

	if (areAlmostEqual(coeff, 0.0)) //c0 is a Segment, or a single point!!!

	{

		TSegment s = TSegment(c0.getP0(), c0.getP2());

		ret = intersect(s, c1, intersections);

		if (a == 0 && d == 0) //values of t in s coincide with values of t in c0

			return ret;

		for (i = intersections.size() - ret; i < (int)intersections.size(); i++) {

			intersections[i].first = c0.getT(s.getPoint(intersections[i].first));

		}

		return ret;

	}

	double c = c0.getP0().x;

	double f = c0.getP0().y;

	double g = c1.getP0().x - 2 * c1.getP1().x + c1.getP2().x;

	double h = 2 * (c1.getP1().x - c1.getP0().x);

	double k = c1.getP0().x;

	double m = c1.getP0().y - 2 * c1.getP1().y + c1.getP2().y;

	double p = 2 * (c1.getP1().y - c1.getP0().y);

	double q = c1.getP0().y;

	if (areAlmostEqual(h * m - g * p, 0.0)) //c1 is a Segment, or a single point!!!

	{

		TSegment s = TSegment(c1.getP0(), c1.getP2());

		ret = intersect(c0, s, intersections);

		if (g == 0 && m == 0) //values of t in s coincide with values of t in c0

			return ret;

		for (i = intersections.size() - ret; i < (int)intersections.size(); i++) {

			intersections[i].second = c1.getT(s.getPoint(intersections[i].second));

		}

		return ret;

	}

	double a2 = (g * d - a * m);

	double b2 = (h * d - a * p);

	double c2 = ((k - c) * d + (f - q) * a);

	coeff = 1.0 / coeff;

	double A = (a * a + d * d) * coeff * coeff;

	double aux = A * c2 + (a * b + d * e) * coeff;

	vector<double> t;</double>

	vector<double> solutions;</double>

	t.push_back(aux * c2 + a * c + d * f - k * a - d * q);

	aux += A * c2;

	t.push_back(aux * b2 - h * a - d * p);

	t.push_back(aux * a2 + A * b2 * b2 - g * a - d * m);

	t.push_back(2 * A * a2 * b2);

	t.push_back(A * a2 * a2);

	rootFinding(t, solutions);

	//  solutions.push_back(0.0); //per convenzione; un valore vale l'altro....

	for (i = 0; i < (int)solutions.size(); i++) {

		if (solutions[i] < 0) {

			if (areAlmostEqual(solutions[i], 0, 1e-6))

				solutions[i] = 0;

			else

				continue;

		} else if (solutions[i] > 1) {

			if (areAlmostEqual(solutions[i], 1, 1e-6))

				solutions[i] = 1;

			else

				continue;

		}

		DoublePair tt;

		tt.second = solutions[i];

		tt.first = coeff * (tt.second * (a2 * tt.second + b2) + c2);

		if (tt.first < 0) {

			if (areAlmostEqual(tt.first, 0, 1e-6))

				tt.first = 0;

			else

				continue;

		} else if (tt.first > 1) {

			if (areAlmostEqual(tt.first, 1, 1e-6))

				tt.first = 1;

			else

				continue;

		}

		intersections.push_back(tt);

		assert(areAlmostEqual(c0.getPoint(tt.first), c1.getPoint(tt.second), 1e-1));

	}

	return intersections.size();

}

//=============================================================================

//questa funzione verifica se il punto di controllo p1 e' molto vicino a p0 o a p2:

//in tal caso, si approssima la quadratica al segmento p0-p2.

//se p1 e' vicino a p0, la relazione che lega il t del segmento al t della quadratica originaria e' tq = sqrt(ts),

//se p1 e' vicino a p2, invece e' tq = 1-sqrt(1-ts).

int intersectCloseControlPoints(const TQuadratic &c0,

								const TQuadratic &c1,

								std::vector<doublepair> &intersections)</doublepair>

{

	int ret = -2;

	double dist1 = tdistance2(c0.getP0(), c0.getP1());

	if (dist1 == 0)

		dist1 = 1e-20;

	double dist2 = tdistance2(c0.getP1(), c0.getP2());

	if (dist2 == 0)

		dist2 = 1e-20;

	double val0 = tmax(dist1, dist2) / tmin(dist1, dist2);

	double dist3 = tdistance2(c1.getP0(), c1.getP1());

	if (dist3 == 0)

		dist3 = 1e-20;

	double dist4 = tdistance2(c1.getP1(), c1.getP2());

	if (dist4 == 0)

		dist4 = 1e-20;

	double val1 = tmax(dist3, dist4) / tmin(dist3, dist4);

	if (val0 > 1000000 && val1 > 1000000) //entrambe c0 e c1  approssimate a segmenti

	{

		TSegment s0 = TSegment(c0.getP0(), c0.getP2());

		TSegment s1 = TSegment(c1.getP0(), c1.getP2());

		ret = intersect(s0, s1, intersections);

		for (UINT i = intersections.size() - ret; i < (int)intersections.size(); i++) {

			intersections[i].first = (dist1 < dist2) ? sqrt(intersections[i].first) : 1 - sqrt(1 - intersections[i].first);

			intersections[i].second = (dist3 < dist4) ? sqrt(intersections[i].second) : 1 - sqrt(1 - intersections[i].second);

		}

		//return ret;

	} else if (val0 > 1000000) //solo c0 approssimata  a segmento

	{

		TSegment s0 = TSegment(c0.getP0(), c0.getP2());

		ret = intersect(s0, c1, intersections);

		for (UINT i = intersections.size() - ret; i < (int)intersections.size(); i++)

			intersections[i].first = (dist1 < dist2) ? sqrt(intersections[i].first) : 1 - sqrt(1 - intersections[i].first);

		//return ret;

	} else if (val1 > 1000000) //solo c1 approssimata  a segmento

	{

		TSegment s1 = TSegment(c1.getP0(), c1.getP2());

		ret = intersect(c0, s1, intersections);

		for (UINT i = intersections.size() - ret; i < (int)intersections.size(); i++)

			intersections[i].second = (dist3 < dist4) ? sqrt(intersections[i].second) : 1 - sqrt(1 - intersections[i].second);

		//return ret;

	}

	/*

if (ret!=-2)

  {

  std::vector<doublepair> intersections1;</doublepair>

  int ret1 = intersect(c0, c1, intersections1, false);

  if (ret1>ret)

    {

    intersections = intersections1;

    return ret1;

    }

  }

*/

	return ret;

}

//=============================================================================

int intersect(const TQuadratic &q,

			  const TSegment &s,

			  std::vector<doublepair> &intersections,</doublepair>

			  bool firstIsQuad)

{

	int solutionNumber = 0;

	// nota la retta a*x+b*y+c = 0 andiamo alla ricerca delle soluzioni

	//  di a*x(t)+b*y(t)+c=0 in [0,1]

	double

		a = s.getP0().y - s.getP1().y,

		b = s.getP1().x - s.getP0().x,

		c = -(a * s.getP0().x + b * s.getP0().y);

	// se il segmento e' un punto

	if (0.0 == a && 0.0 == b) {

		double outParForQuad = q.getT(s.getP0());

		if (areAlmostEqual(q.getPoint(outParForQuad), s.getP0())) {

			if (firstIsQuad)

				intersections.push_back(DoublePair(outParForQuad, 0));

			else

				intersections.push_back(DoublePair(0, outParForQuad));

			return 1;

		}

		return 0;

	}

	if (q.getP2() - q.getP1() == q.getP1() - q.getP0()) //pure il secondo e' unsegmento....

		if (firstIsQuad)

			return intersect(TSegment(q.getP0(), q.getP2()), s, intersections);

		else

			return intersect(s, TSegment(q.getP0(), q.getP2()), intersections);

	vector<tpointd> bez, pol;</tpointd>

	bez.push_back(q.getP0());

	bez.push_back(q.getP1());

	bez.push_back(q.getP2());

	bezier2poly(bez, pol);

	vector<double> poly_1(3, 0), sol;</double>

	poly_1[0] = a * pol[0].x + b * pol[0].y + c;

	poly_1[1] = a * pol[1].x + b * pol[1].y;

	poly_1[2] = a * pol[2].x + b * pol[2].y;

	if (!(rootFinding(poly_1, sol)))

		return 0;

	double

		segmentPar,

		solution;

	TPointD v10(s.getP1() - s.getP0());

	for (UINT i = 0; i < sol.size(); ++i) {

		solution = sol[i];

		if ((0.0 <= solution && solution <= 1.0) ||

			areAlmostEqual(solution, 0.0, 1e-6) ||

			areAlmostEqual(solution, 1.0, 1e-6)) {

			segmentPar = (q.getPoint(solution) - s.getP0()) * v10 / (v10 * v10);

			if ((0.0 <= segmentPar && segmentPar <= 1.0) ||

				areAlmostEqual(segmentPar, 0.0, 1e-6) ||

				areAlmostEqual(segmentPar, 1.0, 1e-6)) {

				TPointD p1 = q.getPoint(solution);

				TPointD p2 = s.getPoint(segmentPar);

				assert(areAlmostEqual(p1, p2, 1e-1));

				if (firstIsQuad)

					intersections.push_back(DoublePair(solution, segmentPar));

				else

					intersections.push_back(DoublePair(segmentPar, solution));

				solutionNumber++;

			}

		}

	}

	return solutionNumber;

}

//=============================================================================

bool isCloseToSegment(const TPointD &point, const TSegment &segment, double distance)

{

	TPointD a = segment.getP0();

	TPointD b = segment.getP1();

	double lenght2 = tdistance2(a, b);

	if (lenght2 < tdistance2(a, point) || lenght2 < tdistance2(point, b))

		return false;

	if (a.x == b.x)

		return fabs(point.x - a.x) <= distance;

	if (a.y == b.y)

		return fabs(point.y - a.y) <= distance;

	// y=mx+q

	double m = (a.y - b.y) / (a.x - b.x);

	double q = a.y - (m * a.x);

	double d2 = pow(fabs(point.y - (m * point.x) - q), 2) / (1 + (m * m));

	return d2 <= distance * distance;

}

//=============================================================================

double tdistance(const TSegment &segment, const TPointD &point)

{

	TPointD v1 = segment.getP1() - segment.getP0();

	TPointD v2 = point - segment.getP0();

	TPointD v3 = point - segment.getP1();

	if (v2 * v1 <= 0)

		return tdistance(point, segment.getP0());

	else if (v3 * v1 >= 0)

		return tdistance(point, segment.getP1());

	return fabs(v2 * rotate90(normalize(v1)));

}

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

/*

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 computeStep(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);

	/*

  A_len is equal to 2*norm(a)

  pixelSize will be 0.5*pixelSize

  now h is equal to sqrt( 8 * 0.5 * pixelSize / (2*norm(a)) ) = sqrt(2) * sqrt( pixelSize/A_len )

  */

	if (A_len > 0)

		step = TConsts::sqrt2 * sqrt(pixelSize / A_len);

	return step;

}

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

double computeStep(const TThickQuadratic &quad, double pixelSize)

{

	TThickPoint

		cp0 = quad.getThickP0(),

		cp1 = quad.getThickP1(),

		cp2 = quad.getThickP2();

	TQuadratic

		q1(TPointD(cp0.x, cp0.y), TPointD(cp1.x, cp1.y), TPointD(cp2.x, cp2.y)),

		q2(TPointD(cp0.y, cp0.thick), TPointD(cp1.y, cp1.thick), TPointD(cp2.y, cp2.thick)),

		q3(TPointD(cp0.x, cp0.thick), TPointD(cp1.x, cp1.thick), TPointD(cp2.x, cp2.thick));

	return tmin(computeStep(q1, pixelSize), computeStep(q2, pixelSize), computeStep(q3, pixelSize));

}

//=============================================================================

/*

  Explanation: The length of a Bezier quadratic can be calculated explicitly.

  Let Q be the quadratic. The tricks to explicitly integrate | Q'(t) | are:

    - The integrand can be reformulated as:  | Q'(t) | = sqrt(at^2 + bt + c);

    - Complete the square beneath the sqrt (add/subtract sq(b) / 4a)

      and perform a linear variable change. We reduce the integrand to: sqrt(kx^2 + k),

      where k can be taken outside => sqrt(x^2 + 1)

    - Use x = tan y. The integrand will yield sec^3 y.

    - Integrate by parts. In short, the resulting primitive of sqrt(x^2 + 1) is:

        F(x) = ( x * sqrt(x^2 + 1) + log(x + sqrt(x^2 + 1)) ) / 2;

*/

void TQuadraticLengthEvaluator::setQuad(const TQuadratic &quad)

{

	const TPointD &p0 = quad.getP0();

	const TPointD &p1 = quad.getP1();

	const TPointD &p2 = quad.getP2();

	TPointD speed0(2.0 * (p1 - p0));

	TPointD accel(2.0 * (p2 - p1) - speed0);

	double a = accel * accel;

	double b = 2.0 * accel * speed0;

	m_c = speed0 * speed0;

	m_constantSpeed = isAlmostZero(a); // => b isAlmostZero, too

	if (m_constantSpeed) {

		m_c = sqrt(m_c);

		return;

	}

	m_sqrt_a_div_2 = 0.5 * sqrt(a);

	m_noSpeed0 = isAlmostZero(m_c); // => b isAlmostZero, too

	if (m_noSpeed0)

		return;

	m_tRef = 0.5 * b / a;

	double d = m_c - 0.5 * b * m_tRef;

	m_squareIntegrand = (d < TConsts::epsilon);

	if (m_squareIntegrand) {

		m_f = (b > 0) ? -sq(m_tRef) : sq(m_tRef);

		return;

	}

	m_e = d / a;

	double sqrt_part = sqrt(sq(m_tRef) + m_e);

	double log_arg = m_tRef + sqrt_part;

	m_squareIntegrand = (log_arg < TConsts::epsilon);

	if (m_squareIntegrand) {

		m_f = (b > 0) ? -sq(m_tRef) : sq(m_tRef);

		return;

	}

	m_primitive_0 = m_sqrt_a_div_2 * (m_tRef * sqrt_part + m_e * log(log_arg));

}

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

double TQuadraticLengthEvaluator::getLengthAt(double t) const

{

	if (m_constantSpeed)

		return m_c * t;

	if (m_noSpeed0)

		return m_sqrt_a_div_2 * sq(t);

	if (m_squareIntegrand) {

		double t_plus_tRef = t + m_tRef;

		return m_sqrt_a_div_2 * (m_f + ((t_plus_tRef > 0) ? sq(t_plus_tRef) : -sq(t_plus_tRef)));

	}

	double y = t + m_tRef;

	double sqrt_part = sqrt(sq(y) + m_e);

	double log_arg = y + sqrt_part; //NOTE: log_arg >= log_arg0 >= TConsts::epsilon

	return m_sqrt_a_div_2 * (y * sqrt_part + m_e * log(log_arg)) - m_primitive_0;

}

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

//  End Of File

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