#ifndef TCG_POLYLINE_OPS_HPP
#define TCG_POLYLINE_OPS_HPP

// tcg includes
#include "../polyline_ops.h"
#include "../iterator_ops.h"
#include "../sequence_ops.h"
#include "../point_ops.h"

// STD includes
#include <assert.h>

namespace tcg
{
namespace polyline_ops
{

using tcg::point_ops::operator/;

//***********************************************************************************
//    Standard Deviation Evaluator
//***********************************************************************************

template <typename RanIt>
StandardDeviationEvaluator<RanIt>::StandardDeviationEvaluator(const RanIt &begin, const RanIt &end)
	: m_begin(begin), m_end(end)
{
	//Let m_sum[i] and m_sum2[i] be respectively the sums of vertex coordinates
	//(relative to begin is sufficient) from 0 to i, and the sums of their squares;
	//m_sumsMix contain sums of xy terms.

	diff_type i, n = m_end - m_begin;
	diff_type n2 = n * 2;

	m_sums_x.resize(n);
	m_sums_y.resize(n);
	m_sums2_x.resize(n);
	m_sums2_y.resize(n);
	m_sums_xy.resize(n);

	m_sums_x[0] = m_sums_y[0] = m_sums2_x[0] = m_sums2_y[0] = m_sums_xy[0] = 0.0;

	//Build sums following the path

	point_type posToBegin;
	i = 0;

	iterator_type a = m_begin;
	for (a = m_begin, ++a; a != m_end; ++a, ++i) {
		posToBegin = point_type(a->x - m_begin->x, a->y - m_begin->y);

		m_sums_x[i + 1] = m_sums_x[i] + posToBegin.x;
		m_sums_y[i + 1] = m_sums_y[i] + posToBegin.y;
		m_sums2_x[i + 1] = m_sums2_x[i] + sq(posToBegin.x);
		m_sums2_y[i + 1] = m_sums2_y[i] + sq(posToBegin.y);
		m_sums_xy[i + 1] = m_sums_xy[i] + posToBegin.x * posToBegin.y;
	}
}

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

template <typename RanIt>
typename StandardDeviationEvaluator<RanIt>::penalty_type
StandardDeviationEvaluator<RanIt>::penalty(const iterator_type &a, const iterator_type &b)
{
	diff_type aIdx = a - m_begin, bIdx = b - m_begin;
	point_type v(b->x - a->x, b->y - a->y), a_(a->x - m_begin->x, a->y - m_begin->y);

	double n = b - a; //Needs to be of higher precision than diff_type
	double sumX = m_sums_x[bIdx] - m_sums_x[aIdx];
	double sumY = m_sums_y[bIdx] - m_sums_y[aIdx];
	double sum2X = m_sums2_x[bIdx] - m_sums2_x[aIdx];
	double sum2Y = m_sums2_y[bIdx] - m_sums2_y[aIdx];
	double sumMix = m_sums_xy[bIdx] - m_sums_xy[aIdx];

	if (bIdx < aIdx) {
		int count = m_end - m_begin, count_1 = count - 1;

		n += count;
		sumX += m_sums_x[count_1];
		sumY += m_sums_y[count_1];
		sum2X += m_sums2_x[count_1];
		sum2Y += m_sums2_y[count_1];
		sumMix += m_sums_xy[count_1];
	}

	double A = sum2Y - 2.0 * sumY * a_.y + n * sq(a_.y);
	double B = sum2X - 2.0 * sumX * a_.x + n * sq(a_.x);
	double C = sumMix - sumX * a_.y - sumY * a_.x + n * a_.x * a_.y;

	return sqrt((v.x * v.x * A + v.y * v.y * B - 2 * v.x * v.y * C) / n);
}

//***********************************************************************************
//    Quadratics approximation Evaluator
//***********************************************************************************

template <typename Point>
class _QuadraticsEdgeEvaluator
{
public:
	typedef Point point_type;
	typedef typename tcg::point_traits<point_type>::value_type value_type;
	typedef typename std::vector<Point>::iterator cp_iterator;
	typedef typename tcg::step_iterator<cp_iterator> quad_iterator;
	typedef double penalty_type;

private:
	quad_iterator m_begin, m_end;
	penalty_type m_tol;

public:
	_QuadraticsEdgeEvaluator(const quad_iterator &begin, const quad_iterator &end,
							 penalty_type tol);

	quad_iterator furthestFrom(const quad_iterator &a);
	penalty_type penalty(const quad_iterator &a, const quad_iterator &b);
};

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

template <typename Point>
_QuadraticsEdgeEvaluator<Point>::_QuadraticsEdgeEvaluator(
	const quad_iterator &begin, const quad_iterator &end, penalty_type tol)
	: m_begin(begin), m_end(end), m_tol(tol)
{
}

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

template <typename Point>
typename _QuadraticsEdgeEvaluator<Point>::quad_iterator
_QuadraticsEdgeEvaluator<Point>::furthestFrom(const quad_iterator &at)
{
	const point_type &A = *at;
	const point_type &A1 = *(at.it() + 1);

	//Build at (opposite) side
	int atSide_ = -tcg::numeric_ops::sign(cross(A - A1, *(at + 1) - A1));
	bool atSideNotZero = (atSide_ != 0);

	quad_iterator bt, last = this->m_end - 1; //Don't do the last (it's a dummy quad)
	for (bt = at + 1; bt != last; ++bt)		  //Always allow 1 step
	{
		//Trying to reach (bt + 1) from at
		const point_type &C = *(bt + 1);
		const point_type &C1 = *(bt.it() + 1);

		//Ensure that bt is not a corner
		if (abs(tcg::point_ops::cross(*(bt.it() - 1) - *bt, *(bt.it() + 1) - *bt)) > 1e-3)
			break;

		//Ensure there is no sign inversion
		int btSide = tcg::numeric_ops::sign(tcg::point_ops::cross(*bt - C1, C - C1));
		if (atSideNotZero && btSide != 0 && btSide == atSide_)
			break;

		//Build the approximating new quad if any
		value_type s, t;
		tcg::point_ops::intersectionSegCoords(A, A1, C, C1, s, t, 1e-4);
		if (s == tcg::numeric_ops::NaN<value_type>()) {
			//A-A1 and C1-C are parallel. There are 2 cases:
			if ((A1 - A) * (C - C1) >= 0)
				//Either we're still on a straight line
				continue;
			else
				//Or, we just can't build the new quad
				break;
		}

		point_type B(A + s * (A1 - A));

		point_type A_B(A - B);
		point_type AC_2B(A_B + C - B);

		//Now, for each quadratic between at and bt, build the 'distance' from our new
		//approximating quad (ABC)

		quad_iterator qt, end = bt + 1;
		for (qt = at; qt != end; ++qt) {
			const point_type &Q_A(*qt);
			const point_type &Q_B(*(qt.it() + 1));
			const point_type &Q_C(*(qt + 1));

			//Check the distance of Q_B from the ABC tangent whose direction
			//is the same as Q'_B - ie, Q_A -> Q_C.

			point_type dir(Q_C - Q_A);
			value_type dirNorm = tcg::point_ops::norm(dir);
			if (dirNorm < 1e-4)
				break;

			dir = dir / dirNorm;

			value_type den = tcg::point_ops::cross(AC_2B, dir);
			if (den < 1e-4 && den > -1e-4)
				break;

			value_type t = tcg::point_ops::cross(A_B, dir) / den;
			if (t < 0.0 || t > 1.0)
				break;

			value_type t1 = 1.0 - t;
			point_type P(sq(t1) * A + 2.0 * t * t1 * B + sq(t) * C);
			point_type Q(0.25 * Q_A + 0.5 * Q_B + 0.25 * Q_C);

			if (tcg::point_ops::lineDist(Q, P, dir) > m_tol)
				break;

			value_type pos = ((P - Q_A) * dir);
			if (pos < 0.0 || pos > dirNorm)
				break;
			/*if(pos < -m_tol || pos > dirNorm + m_tol)     //Should this be relaxed too?
        break;*/

			if (qt == bt)
				continue;

			//Check the distance of Q_C from the ABC tangent whose direction
			//is the same as Q'_C.

			dir = tcg::point_ops::direction(Q_B, Q_C);

			den = tcg::point_ops::cross(AC_2B, dir);
			if (den < 1e-4 && den > -1e-4)
				break;

			t = tcg::point_ops::cross(A_B, dir) / den;
			if (t < 0.0 || t > 1.0)
				break;

			t1 = 1.0 - t;
			P = sq(t1) * A + 2.0 * t * t1 * B + sq(t) * C;

			if (tcg::point_ops::lineDist(Q_C, P, dir) > m_tol)
				break;
		}

		if (qt != end)
			break; //Constraints were violated
	}

	return std::min(bt, this->m_end - 1);
}

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

template <typename Point>
typename _QuadraticsEdgeEvaluator<Point>::penalty_type
_QuadraticsEdgeEvaluator<Point>::penalty(const quad_iterator &at, const quad_iterator &bt)
{
	if (bt == at + 1)
		return 0.0;

	penalty_type penalty = 0.0;

	const point_type &A(*at);
	const point_type &A1(*(at.it() + 1));
	const point_type &C(*bt);
	const point_type &C1(*(bt.it() - 1));

	//Build B
	value_type s, t;
	tcg::point_ops::intersectionSegCoords(A, A1, C, C1, s, t, 1e-4);
	if (s == tcg::numeric_ops::NaN<value_type>())
		return 0.0;

	point_type B(A + s * (A1 - A));

	//Iterate and build penalties
	point_type A_B(A - B);
	point_type AC_2B(A_B + C - B);

	quad_iterator qt, bt_1 = bt - 1;
	for (qt = at; qt != bt; ++qt) {
		const point_type &Q_A(*qt);
		const point_type &Q_B(*(qt.it() + 1));
		const point_type &Q_C(*(qt + 1));

		//point_type dir(tcg::point_ops::direction(Q_A, Q_C));
		point_type dir(Q_C - Q_A);
		dir = dir / tcg::point_ops::norm(dir);

		value_type t = tcg::point_ops::cross(A_B, dir) / tcg::point_ops::cross(AC_2B, dir);
		assert(t >= 0.0 && t <= 1.0);

		value_type t1 = 1.0 - t;
		point_type P(sq(t1) * A + 2.0 * t * t1 * B + sq(t) * C);
		point_type Q(0.25 * Q_A + 0.5 * Q_B + 0.25 * Q_C);

		penalty += tcg::point_ops::lineDist(Q, P, dir);

		if (qt == bt_1)
			continue;

		dir = tcg::point_ops::direction(Q_B, Q_C);

		t = tcg::point_ops::cross(A_B, dir) / tcg::point_ops::cross(AC_2B, dir);
		assert(t >= 0.0 && t <= 1.0);

		t1 = 1.0 - t;
		P = sq(t1) * A + 2.0 * t * t1 * B + sq(t) * C;

		penalty += tcg::point_ops::lineDist(Q_C, P, dir);
	}

	return penalty;
}

//***********************************************************************************
//    Conversion to Quadratics functions
//***********************************************************************************

template <typename cps_reader>
class _QuadReader
{
public:
	typedef typename cps_reader::value_type point_type;
	typedef typename tcg::point_traits<point_type>::value_type value_type;
	typedef typename std::vector<point_type>::iterator cps_iterator;
	typedef typename tcg::step_iterator<cps_iterator> quad_iterator;

private:
	cps_reader &m_reader;
	quad_iterator m_it;

public:
	_QuadReader(cps_reader &reader) : m_reader(reader) {}

	void openContainer(const quad_iterator &it)
	{
		m_reader.openContainer(*it);
		m_it = it;
	}

	void addElement(const quad_iterator &it)
	{
		if (it == m_it + 1) {
			m_reader.addElement(*(it.it() - 1));
			m_reader.addElement(*it);
		} else {
			const point_type &A(*m_it);
			const point_type &A1(*(m_it.it() + 1));
			const point_type &C(*it);
			const point_type &C1(*(it.it() - 1));

			//Build B
			value_type s, t;
			tcg::point_ops::intersectionSegCoords(A, A1, C, C1, s, t, 1e-4);
			point_type B((s == tcg::numeric_ops::NaN<value_type>()) ? 0.5 * (A + C) : A + s * (A1 - A));

			m_reader.addElement(B);
			m_reader.addElement(C);
		}

		m_it = it;
	}

	void closeContainer() { m_reader.closeContainer(); }
};

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

template <typename iter_type, typename Reader, typename tripleToQuadsFunc>
void _naiveQuadraticConversion(const iter_type &begin, const iter_type &end,
							   Reader &reader, tripleToQuadsFunc &tripleToQuadsF)
{
	typedef typename std::iterator_traits<iter_type>::value_type point_type;

	point_type a, c;
	iter_type it, jt;
	iter_type last(end);
	--last;

	if (*begin != *last) {
		reader.openContainer();
		reader.addElement(*begin);

		++(it = begin);
		a = 0.5 * (*begin + *it);

		reader.addElement(0.5 * (*begin + a));
		reader.addElement(a);

		//Work out each quadratic
		for (++(jt = it); jt != end; it = jt, ++jt) {
			c = 0.5 * (*it + *jt);
			tripleToQuadsF(a, it, c, reader);
			a = c;
		}

		reader.addElement(0.5 * (a + *it));
		reader.addElement(*it);
	} else {
		++(it = begin);
		point_type first = a = 0.5 * (*begin + *it);

		reader.openContainer();
		reader.addElement(a);

		for (++(jt = it); jt != end; it = jt, ++jt) {
			c = 0.5 * (*it + *jt);
			tripleToQuadsF(a, it, c, reader);
			a = c;
		}

		tripleToQuadsF(a, last, first, reader);
	}

	reader.closeContainer();
}

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

template <typename iter_type, typename containers_reader, typename toQuadsFunc>
void toQuadratics(iter_type begin, iter_type end, containers_reader &output,
				  toQuadsFunc &toQuadsF, double reductionTol)
{
	typedef typename std::iterator_traits<iter_type>::difference_type diff_type;
	typedef typename std::iterator_traits<iter_type>::value_type point_type;
	typedef typename tcg::point_traits<point_type>::value_type value_type;

	if (begin == end)
		return;

	diff_type count = std::distance(begin, end);
	if (count < 2) {
		//Single point - add 2 points on top of it and quit.
		output.openContainer(*begin);
		output.addElement(*begin), output.addElement(*begin);
		output.closeContainer();
		return;
	}

	if (count == 2) {
		//Segment case
		iter_type it = begin;
		++it;

		output.openContainer(*begin);
		output.addElement(0.5 * (*begin + *it)), output.addElement(*it);
		output.closeContainer();
		return;
	}

	//Build an intermediate vector of points containing the naive quadratic
	//conversion.

	std::vector<point_type> cps;
	tcg::sequential_reader<std::vector<point_type>> cpsReader(&cps);

	_naiveQuadraticConversion(begin, end, cpsReader, toQuadsF);

	if (reductionTol <= 0) {
		output.openContainer(*cps.begin());

		//Directly output the naive conversion
		typename std::vector<point_type>::iterator it, end = cps.end();
		for (it = ++cps.begin(); it != end; ++it)
			output.addElement(*it);
		output.closeContainer();

		return;
	}

	//Resize the cps to cover a multiple of 2
	cps.resize(cps.size() + 2 - (cps.size() % 2));

	//Now, launch the quadratics reduction procedure
	tcg::step_iterator<typename std::vector<point_type>::iterator>
		bt(cps.begin(), 2), et(cps.end(), 2);

	_QuadraticsEdgeEvaluator<point_type> eval(bt, et, reductionTol);
	_QuadReader<containers_reader> quadReader(output);

	bool ret = tcg::sequence_ops::minimalPath(bt, et, eval, quadReader);
	assert(ret);
}
}
} // namespace tcg::polyline_ops

#endif // TCG_POLYLINE_OPS_HPP