/* Copyright (c) 2012 Patrick Ruoff
 *
 * Permission to use, copy, modify, and/or distribute this software for any
 * purpose with or without fee is hereby granted, provided that the above
 * copyright notice and this permission notice appear in all copies.
 */

#include "point_tracker.h"

#include <vector>
#include <algorithm>
#include <cmath>

#include <QDebug>

using namespace cv;
using namespace boost;
using namespace std;

const float PI = 3.14159265358979323846f;

// ----------------------------------------------------------------------------
static void get_row(const Matx33f& m, int i, Vec3f& v)
{
	v[0] = m(i,0);
	v[1] = m(i,1);
	v[2] = m(i,2);
}

static void set_row(Matx33f& m, int i, const Vec3f& v)
{
	m(i,0) = v[0];
	m(i,1) = v[1];
	m(i,2) = v[2];
}

// ----------------------------------------------------------------------------
PointModel::PointModel(Vec3f M01, Vec3f M02)
	: M01(M01), M02(M02)
{	
	// calculate u
	u = M01.cross(M02);
	u /= norm(u);

	// calculate projection matrix on M01,M02 plane
	float s11 = M01.dot(M01);
	float s12 = M01.dot(M02);
	float s22 = M02.dot(M02);
	P = 1.0/(s11*s22-s12*s12) * Matx22f(s22, -s12, 
		                               -s12,  s11);

	// calculate d and d_order for simple freetrack-like point correspondence
	vector<Vec2f> points;
	points.push_back(Vec2f(0,0));
	points.push_back(Vec2f(M01[0], M01[1]));
	points.push_back(Vec2f(M02[0], M02[1]));
	// fit line to orthographically projected points
	// ERROR: yields wrong results with colinear points?!
	/*
	Vec4f line;
	fitLine(points, line, CV_DIST_L2, 0, 0.01, 0.01);
	d[0] = line[0]; d[1] = line[1];
	*/
	// TODO: fix this
	d = Vec2f(M01[0]-M02[0], M01[1]-M02[1]);

	// sort model points
	get_d_order(points, d_order);
}

void PointModel::get_d_order(const std::vector<cv::Vec2f>& points, int d_order[]) const
{
	// get sort indices with respect to d scalar product
	vector< pair<float,int> > d_vals;
	for (int i = 0; i<points.size(); ++i)
		d_vals.push_back(pair<float, int>(d.dot(points[i]), i));

	struct
	{
		bool operator()(const pair<float, int>& a, const pair<float, int>& b) { return a.first < b.first; }
	} comp;
	sort(d_vals.begin(), d_vals.end(), comp);

	for (int i = 0; i<points.size(); ++i)
		d_order[i] = d_vals[i].second;
}


// ----------------------------------------------------------------------------
PointTracker::PointTracker() : init_phase(true), dt_valid(0), dt_reset(1), v_t(0,0,0), v_r(0,0,0)
{
	X_CM.t[2] = 1000;	// default position: 1 m away from cam;
}

void PointTracker::reset()
{
	// enter init phase and reset velocities
	init_phase = true;
	dt_valid = 0;
	reset_velocities();
}

void PointTracker::reset_velocities()
{	
	v_t = Vec3f(0,0,0);
	v_r = Vec3f(0,0,0);
}


bool PointTracker::track(const vector<Vec2f>& points, float f, float dt)
{
	dt_valid += dt;
	// if there was no valid tracking result for too long, do a reset
	if (dt_valid > dt_reset) 
	{
		//qDebug()<<"dt_valid "<<dt_valid<<" > dt_reset "<<dt_reset;
		reset();
	}

	// if there is a pointtracking problem, reset the velocities
	if (!point_model || points.size() != PointModel::N_POINTS) 
	{
		//qDebug()<<"Wrong number of points!";
		reset_velocities();
		return false;
	}

	X_CM_old = X_CM;	// backup old transformation for velocity calculation

	if (!init_phase) 
		predict(dt_valid);

	// if there is a point correspondence problem something has gone wrong, do a reset
	if (!find_correspondences(points, f))
	{
		//qDebug()<<"Error in finding point correspondences!";
		X_CM = X_CM_old;	// undo prediction
		reset();
		return false;
	}

	int n_iter = POSIT(f);
	//qDebug()<<"Number of POSIT iterations: "<<n_iter;

	if (!init_phase)
		update_velocities(dt_valid);

	// we have a valid tracking result, leave init phase and reset time since valid result
	init_phase = false;
	dt_valid = 0;
	return true;
}

void PointTracker::predict(float dt)
{
	// predict with constant velocity
	Matx33f R;
	Rodrigues(dt*v_r, R);
	X_CM.R = R*X_CM.R;
	X_CM.t += dt * v_t;
}

void PointTracker::update_velocities(float dt)
{
	// update velocities
	Rodrigues(X_CM.R*X_CM_old.R.t(), v_r);
	v_r /= dt;
	v_t = (X_CM.t - X_CM_old.t)/dt;
}

bool PointTracker::find_correspondences(const vector<Vec2f>& points, float f)
{
	if (init_phase) {
		// We do a simple freetrack-like sorting in the init phase...
		// sort points
		int point_d_order[PointModel::N_POINTS];
		point_model->get_d_order(points, point_d_order);

		// set correspondences
		for (int i=0; i<PointModel::N_POINTS; ++i)
		{
			p[point_model->d_order[i]] = points[point_d_order[i]];
		}
	}
	else {
		// ... otherwise we look at the distance to the projection of the expected model points 
		// project model points under current pose
		p_exp[0] = project(Vec3f(0,0,0), f);
		p_exp[1] = project(point_model->M01, f);
		p_exp[2] = project(point_model->M02, f);

		// set correspondences by minimum distance to projected model point
		bool point_taken[PointModel::N_POINTS];
		for (int i=0; i<PointModel::N_POINTS; ++i)
			point_taken[i] = false;

		float min_sdist = 0;
		int min_idx = 0;
		
		for (int i=0; i<PointModel::N_POINTS; ++i)
		{
			// find closest point to projected model point i
			for (int j=0; j<PointModel::N_POINTS; ++j)
			{
				Vec2f d = p_exp[i]-points[j];
				float sdist = d.dot(d);
				if (sdist < min_sdist || j==0) 
				{
					min_idx = j;
					min_sdist = sdist;
				}
			}
			// if one point is closest to more than one model point, abort
			if (point_taken[min_idx]) return false;
			point_taken[min_idx] = true;
			p[i] = points[min_idx];
		}
	}
	return true;
}



int PointTracker::POSIT(float f)
{
	// POSIT algorithm for coplanar points as presented in
	// [Denis Oberkampf, Daniel F. DeMenthon, Larry S. Davis: "Iterative Pose Estimation Using Coplanar Feature Points"]
	// we use the same notation as in the paper here

	// The expected rotation used for resolving the ambiguity in POSIT:
	// In every iteration step the rotation closer to R_expected is taken 
	Matx33f R_expected;	
	if (init_phase)
		R_expected = Matx33f::eye(); // in the init phase, we want to be close to the default pose = no rotation
	else 
		R_expected = X_CM.R; // later we want to be close to the last (predicted) rotation
	
	// initial pose = last (predicted) pose
	Vec3f k;
	get_row(X_CM.R, 2, k);
	float Z0 = X_CM.t[2];

	float old_epsilon_1 = 0;
	float old_epsilon_2 = 0;
	float epsilon_1 = 1;
	float epsilon_2 = 1;

	Vec3f I0, J0;
	Vec2f I0_coeff, J0_coeff;

	Vec3f I_1, J_1, I_2, J_2;
	Matx33f R_1, R_2;
	Matx33f* R_current;

	const int MAX_ITER = 100;
	const float EPS_THRESHOLD = 1e-4;

	int i=1;
	for (; i<MAX_ITER; ++i)
	{
		epsilon_1 = k.dot(point_model->M01)/Z0;
		epsilon_2 = k.dot(point_model->M02)/Z0;

		// vector of scalar products <I0, M0i> and <J0, M0i>
		Vec2f I0_M0i(p[1][0]*(1.0 + epsilon_1) - p[0][0], 
			         p[2][0]*(1.0 + epsilon_2) - p[0][0]);
		Vec2f J0_M0i(p[1][1]*(1.0 + epsilon_1) - p[0][1],
			         p[2][1]*(1.0 + epsilon_2) - p[0][1]);

		// construct projection of I, J onto M0i plane: I0 and J0
		I0_coeff = point_model->P * I0_M0i;
		J0_coeff = point_model->P * J0_M0i;
		I0 = I0_coeff[0]*point_model->M01 + I0_coeff[1]*point_model->M02;
		J0 = J0_coeff[0]*point_model->M01 + J0_coeff[1]*point_model->M02;

		// calculate u component of I, J		
		float II0 = I0.dot(I0);
		float IJ0 = I0.dot(J0);
		float JJ0 = J0.dot(J0);
		float rho, theta;
		if (JJ0 == II0) {
			rho = sqrt(abs(2*IJ0));
			theta = -PI/4;
			if (IJ0<0) theta *= -1;
		}
		else {
			rho = sqrt(sqrt( (JJ0-II0)*(JJ0-II0) + 4*IJ0*IJ0 ));
			theta = atan( -2*IJ0 / (JJ0-II0) );
			if (JJ0 - II0 < 0) theta += PI;
			theta /= 2;
		}

		// construct the two solutions
		I_1 = I0 + rho*cos(theta)*point_model->u;	
		I_2 = I0 - rho*cos(theta)*point_model->u;

		J_1 = J0 + rho*sin(theta)*point_model->u;
		J_2 = J0 - rho*sin(theta)*point_model->u;

		float norm_const = 1.0/norm(I_1); // all have the same norm
		
		// create rotation matrices
		I_1 *= norm_const; J_1 *= norm_const;
		I_2 *= norm_const; J_2 *= norm_const;

		set_row(R_1, 0, I_1);
		set_row(R_1, 1, J_1);
		set_row(R_1, 2, I_1.cross(J_1));
		
		set_row(R_2, 0, I_2);
		set_row(R_2, 1, J_2);
		set_row(R_2, 2, I_2.cross(J_2));

		// the single translation solution
		Z0 = norm_const * f;

		// pick the rotation solution closer to the expected one
		// in simple metric d(A,B) = || I - A * B^T ||
		float R_1_deviation = norm(Matx33f::eye() - R_expected * R_1.t());
		float R_2_deviation = norm(Matx33f::eye() - R_expected * R_2.t());

		if (R_1_deviation < R_2_deviation)
			R_current = &R_1;
		else
			R_current = &R_2;

		get_row(*R_current, 2, k);

		// check for convergence condition
		if (abs(epsilon_1 - old_epsilon_1) +  abs(epsilon_2 - old_epsilon_2) < EPS_THRESHOLD)
			break;
		old_epsilon_1 = epsilon_1;
		old_epsilon_2 = epsilon_2;
	}	

	// apply results
	X_CM.R = *R_current;
	X_CM.t[0] = p[0][0] * Z0/f;
	X_CM.t[1] = p[0][1] * Z0/f;
	X_CM.t[2] = Z0;

	return i;

	//Rodrigues(X_CM.R, r);
	//qDebug()<<"iter: "<<i;
	//qDebug()<<"t: "<<X_CM.t[0]<<' '<<X_CM.t[1]<<' '<<X_CM.t[2];
	//Vec3f r;
	//
	//qDebug()<<"r: "<<r[0]<<' '<<r[1]<<' '<<r[2]<<'\n';
}