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// Algorithm details and publications: http://www.golems.org/node/1570

#include "dart/planning/Path.hpp"

#include <iostream>
#include <vector>
#include <algorithm>
#include <cmath>
#include <Eigen/Geometry>
#include "dart/math/Constants.hpp"

using namespace std;
using namespace Eigen;

namespace dart {
namespace planning {

class LinearPathSegment : public PathSegment
{
public:
	LinearPathSegment(const Eigen::VectorXd &start, const Eigen::VectorXd &end) :
    PathSegment((end-start).norm()),
		start(start),
    end(end)
	{
	}

	Eigen::VectorXd getConfig(double s) const {
		s /= length;
		s = std::max(0.0, std::min(1.0, s));
		return (1.0 - s) * start + s * end;
	}

	Eigen::VectorXd getTangent(double /* s */) const {
		return (end - start) / length;
	}

	Eigen::VectorXd getCurvature(double /* s */) const {
		return Eigen::VectorXd::Zero(start.size());
	}

	list<double> getSwitchingPoints() const {
		return list<double>();
	}

	LinearPathSegment* clone() const {
		return new LinearPathSegment(*this);
	}

private:
	Eigen::VectorXd start;
	Eigen::VectorXd end;
};


class CircularPathSegment : public PathSegment
{
public:
	CircularPathSegment(const Eigen::VectorXd &start, const Eigen::VectorXd &intersection, const Eigen::VectorXd &end, double maxDeviation) {
		if((intersection - start).norm() < 0.000001 || (end - intersection).norm() < 0.000001) {
			length = 0.0;
			radius = 1.0;
			center = intersection;
			x = Eigen::VectorXd::Zero(start.size());
			y = Eigen::VectorXd::Zero(start.size());
			return;
		}

		const Eigen::VectorXd startDirection = (intersection - start).normalized();
		const Eigen::VectorXd endDirection = (end - intersection).normalized();

		if((startDirection - endDirection).norm() < 0.000001) {
			length = 0.0;
			radius = 1.0;
			center = intersection;
			x = Eigen::VectorXd::Zero(start.size());
			y = Eigen::VectorXd::Zero(start.size());
			return;
		}

    // const double startDistance = (start - intersection).norm();
    // const double endDistance = (end - intersection).norm();

		double distance = std::min((start - intersection).norm(), (end - intersection).norm());
		const double angle = acos(startDirection.dot(endDirection));

		distance = std::min(distance, maxDeviation * sin(0.5 * angle) / (1.0 - cos(0.5 * angle)));  // enforce max deviation

		radius = distance / tan(0.5 * angle);
		length = angle * radius;

		center = intersection + (endDirection - startDirection).normalized() * radius / cos(0.5 * angle);
		x = (intersection - distance * startDirection - center).normalized();
		y = startDirection;

		//debug
		double dotStart = startDirection.dot((intersection - getConfig(0.0)).normalized());
		double dotEnd = endDirection.dot((getConfig(length) - intersection).normalized());
    if(std::abs(dotStart - 1.0) > 0.0001 || std::abs(dotEnd - 1.0) > 0.0001) {
			std::cout << "Error\n";
		}
	}

	Eigen::VectorXd getConfig(double s) const {
		const double angle = s / radius;
		return center + radius * (x * cos(angle) + y * sin(angle));
	}

	Eigen::VectorXd getTangent(double s) const {
		const double angle = s / radius;
		return - x * sin(angle) + y * cos(angle);
	}

	Eigen::VectorXd getCurvature(double s) const {
		const double angle = s / radius;
		return - 1.0 / radius * (x * cos(angle) + y * sin(angle));
	}

	list<double> getSwitchingPoints() const {
        const double pi = math::constantsd::pi();
		list<double> switchingPoints;
		const double dim = x.size();
		for(unsigned int i = 0; i < dim; i++) {
			double switchingAngle = atan2(y[i], x[i]);
			if(switchingAngle < 0.0) {
				switchingAngle += pi;
			}
			const double switchingPoint = switchingAngle * radius;
			if(switchingPoint < length) {
				switchingPoints.push_back(switchingPoint);
			}
		}
		switchingPoints.sort();
		return switchingPoints;
	}

	CircularPathSegment* clone() const {
		return new CircularPathSegment(*this);
	}

private:
	double radius;
	Eigen::VectorXd center;
	Eigen::VectorXd x;
	Eigen::VectorXd y;
};



Path::Path(const list<VectorXd> &path, double maxDeviation) :
	length(0.0)
{
	if(path.size() < 2)
		return;
	list<VectorXd>::const_iterator config1 = path.begin();
	list<VectorXd>::const_iterator config2 = config1;
  ++config2;
	list<VectorXd>::const_iterator config3;
	VectorXd startConfig = *config1;
	while(config2 != path.end()) {
		config3 = config2;
    ++config3;
		if(maxDeviation > 0.0 && config3 != path.end()) {
			CircularPathSegment* blendSegment = new CircularPathSegment(0.5 * (*config1 + *config2), *config2, 0.5 * (*config2 + *config3), maxDeviation);
			VectorXd endConfig = blendSegment->getConfig(0.0);
			if((endConfig - startConfig).norm() > 0.000001) {
				pathSegments.push_back(new LinearPathSegment(startConfig, endConfig));
			}
			pathSegments.push_back(blendSegment);
			
			startConfig = blendSegment->getConfig(blendSegment->getLength());

			//debug
			if(((endConfig - *config1).norm() > 0.000001 && (*config2 - endConfig).norm() > 0.000001
        && std::abs((endConfig - *config1).normalized().dot((*config2 - endConfig).normalized()) - 1.0) > 0.000001)
				|| ((startConfig - *config2).norm() > 0.000001 && (*config3 - startConfig).norm() > 0.000001
        && std::abs((startConfig - *config2).normalized().dot((*config3 - startConfig).normalized()) - 1.0) > 0.000001)) {
					cout << "error" << endl;
			}
		}
		else {
			pathSegments.push_back(new LinearPathSegment(startConfig, *config2));
			startConfig = *config2;
		}
		config1 = config2;
    ++config2;
	}

	// create list of switching point candidates, calculate total path length and absolute positions of path segments
  for(list<PathSegment*>::iterator segment = pathSegments.begin(); segment != pathSegments.end(); ++segment) {
		(*segment)->position = length;
		list<double> localSwitchingPoints = (*segment)->getSwitchingPoints();
    for(list<double>::const_iterator point = localSwitchingPoints.begin(); point != localSwitchingPoints.end(); ++point) {
			switchingPoints.push_back(make_pair(length + *point, false));
		}
		length += (*segment)->getLength();
		switchingPoints.push_back(make_pair(length, true));
	}
	switchingPoints.pop_back();
}

Path::Path(const Path &path) :
	length(path.length),
	switchingPoints(path.switchingPoints)
{
  for(list<PathSegment*>::const_iterator it = path.pathSegments.begin(); it != path.pathSegments.end(); ++it) {
		pathSegments.push_back((*it)->clone());
	}
}

Path::~Path() {
  for(list<PathSegment*>::iterator it = pathSegments.begin(); it != pathSegments.end(); ++it) {
		delete *it;
	}
}

double Path::getLength() const {
	return length;
}

PathSegment* Path::getPathSegment(double &s) const {
	list<PathSegment*>::const_iterator it = pathSegments.begin();
	list<PathSegment*>::const_iterator next = it;
  ++next;
	while(next != pathSegments.end() && s >= (*next)->position) {
		it = next;
    ++next;
	}
	s -= (*it)->position;
	return *it;
}

VectorXd Path::getConfig(double s) const {
	const PathSegment* pathSegment = getPathSegment(s);
	return pathSegment->getConfig(s);
}

VectorXd Path::getTangent(double s) const {
	const PathSegment* pathSegment = getPathSegment(s);
	return pathSegment->getTangent(s);
}

VectorXd Path::getCurvature(double s) const {
	const PathSegment* pathSegment = getPathSegment(s);
	return pathSegment->getCurvature(s);
}

double Path::getNextSwitchingPoint(double s, bool &discontinuity) const {
	list<pair<double, bool> >::const_iterator it = switchingPoints.begin();
	while(it != switchingPoints.end() && it->first <= s) {
    ++it;
	}
	if(it == switchingPoints.end()) {
		discontinuity = true;
		return length;
	}
	else {
		discontinuity = it->second;
		return it->first;
	}
}

list<pair<double, bool> > Path::getSwitchingPoints() const {
	return switchingPoints;
}

} // namespace planning
} // namespace dart
