#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)
{
	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)
{
	// 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);
 
int intersect(const TQuadratic &c0,
			  const TQuadratic &c1,
			  std::vector<DoublePair> &intersections, bool checksegments)
{
	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;
 
	std::vector<double> t;
	std::vector<double> solutions;
 
	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)
{
	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 = std::max(dist1, dist2) / std::min(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 = std::max(dist3, dist4) / std::min(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;
  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,
			  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);
	}
 
	std::vector<TPointD> bez, pol;
	bez.push_back(q.getP0());
	bez.push_back(q.getP1());
	bez.push_back(q.getP2());
 
	bezier2poly(bez, pol);
 
	std::vector<double> poly_1(3, 0), sol;
 
	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 = sqrt(2 * 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 std::min({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
//-----------------------------------------------------------------------------