/*
 * icp6Dlumquat implementation
 *
 * Copyright (C) Andreas Nuechter, Alexandru-Eugen Ichim
 *
 * Released under the GPL version 3.
 *
 */


/** @file 
 *  @brief Implementation of the ICP error function minimization via
 *  via linearization with quaternions
 *
 *  @author Andreas Nuechter. Jacobs University Bremen gGmbH, Germany
 *  @author Alexandru-Eugen Ichim. Jacobs University Bremen gGmbH, Germany
 *
 */

#include "slam6d/icp6Dlumquat.h"

#include "slam6d/globals.icc"
#include <iomanip>
using std::ios;
using std::resetiosflags;
using std::setiosflags;

#include "newmat/newmat.h"
#include "newmat/newmatap.h"
using namespace NEWMAT;
/**
 * computes the rotation matrix consisting
 * of a rotation and translation that
 * minimizes the root-mean-square error of the
 * point pairs using linearization with quarernions
 * @param pairs Vector of point pairs (pairs of corresponding points)
 * @param *alignfx The resulting transformation matrix
 * @return Error estimation of the matching (rms)
 */
double icp6D_LUMQUAT::Point_Point_Align(const vector<PtPair>& pairs, double *alignfx,
		const double centroid_m[3], const double centroid_d[3])
{
	// alignfx is filled with the current pose, t is the translation, quat is the quaternion
	double t[3], quat[4];
	Matrix4ToQuat(alignfx, quat, t);


	double error = 0;
	double sum = 0.0;
	for(unsigned int i = 0; i <  pairs.size(); i++){
		sum += sqr(pairs[i].p1.x - pairs[i].p2.x)
			 + sqr(pairs[i].p1.y - pairs[i].p2.y)
			 + sqr(pairs[i].p1.z - pairs[i].p2.z) ;

	}

	error = sqrt(sum / (double)pairs.size());

	if (!quiet) {
		cout.setf(ios::basefield);
		cout << "LUMQUAT RMS point-to-point error = "
				<< resetiosflags(ios::adjustfield) << setiosflags(ios::internal)
				<< resetiosflags(ios::floatfield) << setiosflags(ios::fixed)
				<< std::setw(10) << std::setprecision(7)
		<< error
		<< "  using " << std::setw(6) << (int)pairs.size() << " points" << endl;
	}



/////////////////////////////////////////////////////////
/////////////////////////////////////////////////////////

	/// MZ = M^T * Z
	ColumnVector MZ(7); MZ = 0.0;
	/// MM = M^T * M
	Matrix MM(7, 7); MM = 0.0; 
	double x = 0.0, y = 0.0, z = 0.0, dx = 0.0, dy = 0.0, dz = 0.0, sx = 0.0, sy = 0.0, sz = 0.0, xpy = 0.0, xpz = 0.0, ypz = 0.0, xpypz = 0.0, xy = 0.0, yz = 0.0, xz = 0.0;

	for(unsigned int i = 0; i < pairs.size(); ++i) {
		/// temporary values that we shall use multiple times in the subsequent computations

		x = (pairs[i].p1.x + pairs[i].p1.x) / 2.0;
		y = (pairs[i].p1.y + pairs[i].p2.y) / 2.0;
		z = (pairs[i].p1.z + pairs[i].p2.z) / 2.0;
		dx = pairs[i].p1.x - pairs[i].p2.x;
		dy = pairs[i].p1.y - pairs[i].p2.y;
		dz = pairs[i].p1.z - pairs[i].p2.z;

		/// sums of each coordinate
		sx += x;
		sy += y;
		sz += z;

		/// sums of squares of coordinates
		xpy += x*x + y*y;
		xpz += x*x + z*z;
		ypz += y*y + z*z;
		xpypz += x*x + y*y + z*z;

		/// sums of products of pairs of coordinates
		xy += x*y;
		xz += x*z;
		yz += y*z;

		/// incrementally construct matrix M^T * Z
		MZ(1) += dx;
		MZ(2) += dy;
		MZ(3) += dz;
		MZ(4) += x*dx + y*dy + z*dz;
		MZ(5) += z*dy - y*dz;
		MZ(6) += x*dz - z*dx;
		MZ(7) += y*dx - x*dy;
	}

	/// construct M^ * M
	MM(1,1) = MM(2,2) = MM(3,3) = pairs.size();
	MM(4,4) = xpypz;
	MM(5,5) = ypz;
	MM(6,6) = xpz;
	MM(7,7) = xpy;
	MM(1,4) = MM(4,1) = sx;
	MM(1,6) = MM(6,1) = -sz;
	MM(1,7) = MM(7,1) = sy;
	MM(2,4) = MM(4,2) = sy;
	MM(2,5) = MM(5,2) = sz;
	MM(2,7) = MM(7,2) = -sx;
	MM(3,4) = MM(4,3) = sz;
	MM(3,5) = MM(5,3) = -sy;
	MM(3,6) = MM(6,3) = sx;
	MM(5,6) = MM(6,5) = -xy;
	MM(5,7) = MM(7,5) = -xz;
	MM(6,7) = MM(7,6) = -yz;

	ColumnVector Ehat = MM.i() * MZ ;


	/// construct the auxiliary matrices U and T needed to build up H
	double p = quat[0], q = quat[1], r = quat[2], s = quat[3];
	x = t[0], y = t[1], z = t[2];
	Matrix U(4, 4); 
	U << p << q << r << s
			<< q <<-p << s <<-r
			<< r <<-s <<-p << q
			<< s << r <<-q <<-p;

	Matrix T(3, 4);
	T << p*x + s*y - r*z << q*x + r*y + s*z << r*x - q*y + p*z << s*x - p*y - q*z
			<<-s*x + p*y + q*z <<-r*x + q*y - p*z << q*x + r*y + s*z << p*x + s*y - r*z
			<< r*x - q*y + p*z <<-s*x + p*y + q*z <<-p*x - s*y + r*z << q*x + r*y - s*z;
	/// now actually compose matrix H
	Matrix H(7, 7); H = 0.0;
	H.SubMatrix(1, 3, 1, 3) = IdentityMatrix(3);
	H.SubMatrix(1, 3, 4, 7) = T *(-2);
	H.SubMatrix(4, 7, 4, 7) = U * 2;


	/// Xhat is the pose estimate for the second scan - use the pose of the first scan
	ColumnVector Xhat(7); Xhat << x << y << z << p << q << r << s;

	/// create a transformation matrix for the first scan with the given values
	Matrix T1(4, 4); T1 = 0.0;
	Matrix Cq(3, 3);
	ColumnVector qvec(3); qvec << q << r << s;
	Cq << 0 << -qvec(3) << qvec(2) << qvec(3) << 0 << -qvec(1) << -qvec(2) << qvec(1) << 0;
	ColumnVector qtq(1); qtq = qvec.t() *qvec * (-1);
	T1.SubMatrix(1, 3, 1, 3) = IdentityMatrix(3) * (p*p + qtq(1)) + qvec*qvec.t()*2 + Cq *2*p;
	T1(1, 4) = x;
	T1(2, 4) = y;
	T1(3, 4) = z;
	T1(4, 4) = 1;


	/// the translation and quaternion for the second scan are computed
	ColumnVector X = Xhat - H.i() * Ehat;


	/// create the transformation matrix for the second scan
	x = X(1), y = X(2), z = X(3);
	p = X(4); q = X(5); r = X(6); s = X(7);
	Matrix T2(4, 4); T2 = 0.0;
	qvec = 0.0; qvec << q << r << s;
	Cq = 0.0; Cq << 0 << -qvec(3) << qvec(2) << qvec(3) << 0 << -qvec(1) << -qvec(2) << qvec(1) << 0;
	qtq = qvec.t() *qvec * (-1);
	T2.SubMatrix(1, 3, 1, 3) = IdentityMatrix(3) * (p*p + qtq(1)) + qvec*qvec.t()*2 + Cq *2*p;
	T2(1, 4) = x;
	T2(2, 4) = y;
	T2(3, 4) = z;
	T2(4, 4) = 1;

	/// the incremental transform calculated from the absolute poses of the two scans
	Matrix T_inc = T1 * T2.i();

	/// convert our 4x4 transform to column-wise opengl form
	alignfx[0] = T_inc(1, 1);
	alignfx[1] = T_inc(2, 1);
	alignfx[2] = T_inc(3, 1);
	alignfx[3] = 0.0;
	alignfx[4] = T_inc(1, 2);
	alignfx[5] = T_inc(2, 2);
	alignfx[6] = T_inc(3, 2);
	alignfx[7] = 0.0;
	alignfx[8] = T_inc(1, 3);
	alignfx[9] = T_inc(2, 3);
	alignfx[10]= T_inc(3, 3);
	alignfx[11]= 0.0;
	alignfx[12]= T_inc(1, 4);
	alignfx[13]= T_inc(2, 4);
	alignfx[14]= T_inc(3, 4);
	alignfx[15]= 1.0;

	/////////////////////////////////////////////////////////
	/////////////////////////////////////////////////////////



	return error;
}