/****************************************************************************
* VCGLib                                                            o o     *
* Visual and Computer Graphics Library                            o     o   *
*                                                                _   O  _   *
* Copyright(C) 2004-2016                                           \/)\/    *
* Visual Computing Lab                                            /\/|      *
* ISTI - Italian National Research Council                           |      *
*                                                                    \      *
* All rights reserved.                                                      *
*                                                                           *
* This program is free software; you can redistribute it and/or modify      *
* it under the terms of the GNU General Public License as published by      *
* the Free Software Foundation; either version 2 of the License, or         *
* (at your option) any later version.                                       *
*                                                                           *
* This program is distributed in the hope that it will be useful,           *
* but WITHOUT ANY WARRANTY; without even the implied warranty of            *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the             *
* GNU General Public License (http://www.gnu.org/licenses/gpl.txt)          *
* for more details.                                                         *
*                                                                           *
****************************************************************************/
#ifndef VCG_ALIGN_PAIR_H
#define VCG_ALIGN_PAIR_H

#include <ctime>
#include <stdio.h>
#include <vcg/math/histogram.h>
#include <vcg/math/matrix44.h>
#include <vcg/math/random_generator.h>
#include <vcg/math/gen_normal.h>

#include <vcg/space/point_matching.h>
#include <vcg/space/index/grid_static_ptr.h>

#include <vcg/simplex/face/component_ep.h>

#include <vcg/complex/complex.h>
#include <vcg/complex/algorithms/clean.h>
#include <vcg/complex/algorithms/closest.h>
#include <vcg/complex/algorithms/update/normal.h>
#include <vcg/complex/algorithms/update/bounding.h>
#include <vcg/complex/algorithms/update/component_ep.h>
#include <vcg/complex/algorithms/update/position.h>
#include <vcg/complex/algorithms/update/flag.h>
#include <vcg/complex/algorithms/update/normal.h>
#include <vcg/complex/algorithms/update/bounding.h>
#include <vcg/complex/algorithms/point_matching_scale.h>


namespace vcg {
/*************************************************************************
								 AlignPair

Classe per gestire un allineamento tra DUE sole mesh.

**************************************************************************/

class AlignPair {
public:

	AlignPair()
	{
		clear();
		myrnd.initialize(time(NULL));
	}

	enum ErrorCode {
		SUCCESS,
		NO_COMMON_BBOX,
		TOO_FEW_POINTS,
		LSQ_DIVERGE,
		TOO_MUCH_SHEAR,
		TOO_MUCH_SCALE,
		FORBIDDEN,
		INVALID,
		UNKNOWN_MODE };


	/*********************** Classi Accessorie ****************************/

	class A2Vertex;

	class A2Face;

	class A2UsedTypes:
			public vcg::UsedTypes < vcg::Use<A2Vertex>::AsVertexType,
			vcg::Use<A2Face  >::AsFaceType >{};

	class A2Vertex : public vcg::Vertex<A2UsedTypes,vcg::vertex::Coord3d,vcg::vertex::Normal3d,vcg::vertex::BitFlags> {};
	class A2Face   : public vcg::Face< A2UsedTypes,vcg::face::VertexRef, vcg::face::Normal3d,vcg::face::Mark,vcg::face::BitFlags> {};

	class A2Mesh   : public vcg::tri::TriMesh< std::vector<A2Vertex>, std::vector<A2Face> >
	{
	public:
		//bool Import(const char *filename) { Matrix44d Tr; Tr.SetIdentity(); return Import(filename,Tr);}
		//bool Import(const char *filename, Matrix44d &Tr);

		inline bool initVert(const Matrix44d &Tr) {
			Matrix44d Idn; Idn.SetIdentity();
			if (Tr != Idn)
				tri::UpdatePosition<A2Mesh>::Matrix(*this, Tr);
			tri::UpdateNormal<A2Mesh>::NormalizePerVertex(*this);
			tri::UpdateBounding<A2Mesh>::Box(*this);
			return true;
		}
		inline bool init(const Matrix44d &Tr) {
			Matrix44d Idn; Idn.SetIdentity();
			tri::Clean<A2Mesh>::RemoveUnreferencedVertex(*this);
			if (Tr != Idn)
				tri::UpdatePosition<A2Mesh>::Matrix(*this, Tr);
			tri::UpdateNormal<A2Mesh>::PerVertexNormalizedPerFaceNormalized(*this);
			tri::UpdateFlags<A2Mesh>::FaceBorderFromNone(*this);
			tri::UpdateBounding<A2Mesh>::Box(*this);

			return true;
		}
	};

	typedef A2Mesh::FaceContainer FaceContainer;
	typedef A2Mesh::FaceType      FaceType;
	typedef GridStaticPtr<FaceType, double > A2Grid;
	typedef GridStaticPtr<A2Mesh::VertexType, double > A2GridVert;

	class Stat
	{
	public:

		class IterInfo
		{
		public:
			IterInfo()
			{
				memset ( (void *) this, 0, sizeof(IterInfo));
			}

			double MinDistAbs;
			int DistanceDiscarded;
			int AngleDiscarded;
			int BorderDiscarded;
			int SampleTested;  // quanti punti ho testato con la mindist
			int SampleUsed;    // quanti punti ho scelto per la computematrix
			double pcl50;
			double pclhi;
			double AVG;
			double RMS;
			double StdDev;
			int Time;  // quando e' finita questa iterazione

		};

		std::vector<IterInfo> I;

		double lastPcl50() const
		{
			return I.back().pcl50;
		}

		int lastSampleUsed() const {
			return I.back().SampleUsed;
		}

		int MovVertNum;
		int FixVertNum;
		int FixFaceNum;

		int totTime() {
			return I.back().Time-StartTime;
		}

		int iterTime(unsigned int i) const
		{
			const int clock_per_ms = std::max<int>(CLOCKS_PER_SEC / 1000,1);
			assert(i<I.size());
			if(i==0) return  (I[i].Time-StartTime )/clock_per_ms;
			else return (I[i].Time - I[i-1].Time)/clock_per_ms ;
		}
		int StartTime;

		inline void clear()
		{
			I.clear();
			StartTime = 0;
			MovVertNum = 0;
			FixVertNum = 0;
			FixFaceNum = 0;
		}

		inline void dump(FILE *fp)
		{
			if (I.size() == 0) {
				fprintf(fp, "Empty AlignPair::Stat\n");
				return;
			}
			fprintf(fp, "Final Err %8.5f In %i iterations Total Time %ims\n", lastPcl50(), (int)I.size(), totTime());
			fprintf(fp, "Mindist   Med   Hi    Avg  RMS   StdDev   Time Tested Used  Dist Bord Angl \n");
			for (unsigned int qi = 0; qi < I.size(); ++qi)
				fprintf(
							fp,
							"%5.2f (%6.3f:%6.3f) (%6.3f %6.3f %6.3f) %4ims %5i %5i %4i+%4i+%4i\n",
							I[qi].MinDistAbs,
							I[qi].pcl50, I[qi].pclhi,
							I[qi].AVG, I[qi].RMS, I[qi].StdDev,
							iterTime(qi),
							I[qi].SampleTested, I[qi].SampleUsed, I[qi].DistanceDiscarded, I[qi].BorderDiscarded, I[qi].AngleDiscarded);
		}

		// Scrive una tabella con tutti i valori
		inline void htmlDump(FILE *fp)
		{
			fprintf(fp, "Final Err %8.5f In %i iterations Total Time %ims\n", lastPcl50(), (int)I.size(), totTime());
			fprintf(fp, "<table border>\n");
			fprintf(fp, "<tr> <th>Mindist</th><th>    50ile </th><th>  Hi </th><th>   Avg  </th><th> RMS </th><th>  StdDev  </th><th> Time </th><th> Tested </th><th> Used </th><th> Dist </th><th> Bord </th><th> Angl \n");
			for (unsigned int qi = 0; qi < I.size(); ++qi)
				fprintf(
						fp, "<tr> <td> %8.5f </td><td align=\"right\"> %9.6f </td><td align=\"right\"> %8.5f </td><td align=\"right\"> %5.3f </td><td align=\"right\"> %8.5f </td><td align=\"right\"> %9.6f </td><td align=\"right\"> %4ims </td><td align=\"right\"> %5i </td><td align=\"right\"> %5i </td><td align=\"right\"> %4i </td><td align=\"right\"> %4i </td><td align=\"right\">%4i </td><td align=\"right\"></tr>\n",
							I[qi].MinDistAbs,
							I[qi].pcl50, I[qi].pclhi,
							I[qi].AVG, I[qi].RMS, I[qi].StdDev,
							iterTime(qi),
							I[qi].SampleTested, I[qi].SampleUsed, I[qi].DistanceDiscarded, I[qi].BorderDiscarded, I[qi].AngleDiscarded);
			fprintf(fp, "</table>\n");
		}

		// Restituisce true se nelle ultime <lastiter> iterazioni non e' diminuito
		// l'errore
		inline bool stable(int lastiter)
		{
			if (I.empty())
				return false;
			int parag = int(I.size()) - lastiter;

			if (parag < 0)
				parag = 0;
			if (I.back().pcl50 < I[parag].pcl50)
				return false; // se siamo diminuiti non e' stabile

			return true;
		}

	};


	class Param
	{
	public:
		enum MatchModeEnum  {MMSimilarity, MMRigid};
		enum SampleModeEnum {SMRandom, SMNormalEqualized};

		Param()
		{
			SampleNum    = 2000;
			MaxPointNum  = 100000;
			MinPointNum  = 30;

			MaxIterNum   = 75;
			TrgDistAbs   = 0.005f;

			MinDistAbs   = 10;
			MaxAngleRad  = math::ToRad(45.0);
			MaxShear     = 0.5;
			MaxScale     = 0.5; // significa che lo scale deve essere compreso tra 1-MaxScale e 1+MaxScale
			PassHiFilter = 0.75;
			ReduceFactorPerc = 0.80;
			MinMinDistPerc = 0.01;
			EndStepNum   = 5;
			MatchMode    = MMRigid;
			SampleMode   = SMNormalEqualized;
			UGExpansionFactor=10;
			MinFixVertNum=20000;
			MinFixVertNumPerc=.25;
			UseVertexOnly = false;
		}

		int SampleNum;			// numero di sample da prendere sulla mesh fix, utilizzando
		// il SampleMode scelto tra cui poi sceglierne al piu' <MaxPointNum>
		// e almeno <MinPointNum> da usare per l'allineamento.
		int MaxPointNum;		// numero di coppie di punti da usare quando si calcola la matrice
		// di allienamento e che poi si mettono da parte per il globale;
		// di solito non usato
		int MinPointNum;		// minimo numero di coppie di punti ammissibile perche' sia considerato
		// valido l'allineamento
		double MinDistAbs;	// distanza minima iniziale perche due punti vengano presi in
		// considerazione. NON e' piu espressa in percentuale sul bbox della mesh nella ug.
		// Ad ogni passo puo essere ridotta per
		// accellerare usando ReduceFactor
		double MaxAngleRad;	// massimo angolo in radianti tra due normali perche' i due
		// punti vengano presi in considerazione.

		int MaxIterNum;			// massimo numero di iterazioni da fare in align
		double TrgDistAbs;			// distanza obiettivo entro la quale devono stare almeno la meta'
		// dei campioni scelti; di solito non entra in gioco perche' ha un default molto basso

		int EndStepNum; // numero di iterazioni da considerare per decidere se icp ha converso.

		//double PassLoFilter; // Filtraggio utilizzato per decidere quali punti scegliere tra quello trovati abbastanza
		double PassHiFilter;   // vicini. Espresso in percentili. Di solito si scarta il quelli sopra il 75 e quelli sotto il 5
		double ReduceFactorPerc; // At each step we discard the points farther than a given threshold. The threshold is iterativeley reduced;
		// StartMinDist= min(StartMinDist, 5.0*H.Percentile(ap.ReduceFactorPerc))


		double MinMinDistPerc;	// Ratio between initial starting distance (MinDistAbs) and what can reach by the application of the ReduceFactor.

		int UGExpansionFactor; // Grandezza della UG per la mesh fix come rapporto del numero di facce della mesh fix

		// Nel caso si usi qualche struttura multiresolution
		int MinFixVertNum;			// Gli allineamenti si fanno mettendo nella ug come mesh fix una semplificata;
		float MinFixVertNumPerc;  // si usa il max tra MinFixVertNum e OrigMeshSize*MinFixVertNumPerc
		bool UseVertexOnly;       // if true all the Alignment pipeline ignores faces and works over point clouds.

		double MaxShear;
		double MaxScale;
		MatchModeEnum MatchMode;
		SampleModeEnum SampleMode;
		//void Dump(FILE *fp,double BoxDiag);

	};

	// Classe per memorizzare il risultato di un allineamento tra due mesh
	// i punti si intendono nel sistema di riferimento iniziale delle due mesh.
	//
	// se le mesh hanno una trasformazione di base in ingresso,
	// questa appare solo durante la A2Mesh::Import e poi e' per sempre dimenticata.
	// Questi punti sono quindi nei sistemi di riferimento costruiti durante la Import
	// la matrice Tr quella che
	//
	// Tr*Pmov[i]== Pfix


	class Result
	{
	public:
		int MovName;
		int FixName;

		Matrix44d Tr;
		std::vector<Point3d> Pfix;		// vertici corrispondenti su fix (rossi)
		std::vector<Point3d> Nfix; 		// normali corrispondenti su fix (rossi)
		std::vector<Point3d> Pmov;		// vertici scelti su mov (verdi) prima della trasformazione in ingresso (Original Point Target)
		std::vector<Point3d> Nmov; 		// normali scelti su mov (verdi)
		Histogramf H;
		Stat as;
		Param ap;
		ErrorCode status;
		bool isValid()
		{
			return status==SUCCESS;
		}
		double err;
		float area; // the overlapping area, a percentage as computed in Occupancy Grid.

		bool operator <  (const Result & rr) const {return (err< rr.err);}
		bool operator <= (const Result & rr) const {return (err<=rr.err);}
		bool operator >  (const Result & rr) const {return (err> rr.err);}
		bool operator >= (const Result & rr) const {return (err>=rr.err);}
		bool operator == (const Result & rr) const {return (err==rr.err);}
		bool operator != (const Result & rr) const {return (err!=rr.err);}

		std::pair<double,double> computeAvgErr() const
		{
			double sum_before=0;
			double sum_after=0;
			for(unsigned int ii=0;ii<Pfix.size();++ii) {
				sum_before+=Distance(Pfix[ii],   Pmov[ii]);
				sum_after+=Distance(Pfix[ii], Tr*Pmov[ii]);
			}
			return std::make_pair(sum_before/double(Pfix.size()),sum_after/double(Pfix.size()) ) ;
		}

	};

	/******************* Fine Classi Accessorie ************************/

	static inline const char* errorMsg(ErrorCode code)
	{
		switch (code){
		case SUCCESS:
			return "Success";
		case NO_COMMON_BBOX:
			return "No Common BBox";
		case TOO_FEW_POINTS:
			return "Too few points";
		case LSQ_DIVERGE:
			return "LSQ not converge";
		case TOO_MUCH_SHEAR:
			return "Too much shear";
		case TOO_MUCH_SCALE:
			return "Too much scale";
		case UNKNOWN_MODE:
			return "Unknown mode ";
		default:
			assert(0);
			return "Catastrophic Error";
		}
		return 0;
	}

	void clear()
	{
		status=SUCCESS;
	}

	/******* Data Members *********/

	std::vector<A2Vertex> *mov;
	A2Mesh *fix;

	ErrorCode status;
	AlignPair::Param ap;

	math::SubtractiveRingRNG myrnd;

	/**** End Data Members *********/

	template < class MESH >
	void convertMesh(MESH &M1, A2Mesh &M2)
	{
		tri::Append<A2Mesh,MESH>::MeshCopy(M2,M1);
	}

	template < class VERTEX >
	void convertVertex(const std::vector<VERTEX> &vert1, std::vector<A2Vertex> &vert2, Box3d *Clip=0)
	{
		vert2.clear();
		typename std::vector<VERTEX>::const_iterator vi;
		A2Vertex tv;
		Box3<typename VERTEX::ScalarType> bb;
		if(Clip){
			bb.Import(*Clip);
			for(vi=vert1.begin();vi<vert1.end();++vi)
				if(!(*vi).IsD() && bb.IsIn((*vi).cP())){
					tv.P().Import((*vi).cP());
					tv.N().Import((*vi).cN());
					vert2.push_back(tv);
				}
		}
		else {
			for(vi=vert1.begin();vi<vert1.end();++vi) {
				if(!(*vi).IsD()){
					tv.P().Import((*vi).cP());
					tv.N().Import((*vi).cN());
					vert2.push_back(tv);
				}
			}
		}
	}

	inline bool sampleMovVert(
			std::vector<A2Vertex> &vert,
			int sampleNum,
			AlignPair::Param::SampleModeEnum sampleMode)
	{
		switch (sampleMode)
		{
		case AlignPair::Param::SMRandom:
			return SampleMovVertRandom(vert, sampleNum);
		case AlignPair::Param::SMNormalEqualized:
			return SampleMovVertNormalEqualized(vert, sampleNum);
		default:
			assert(0);
			return false;
		}
	}

	inline bool SampleMovVertRandom(std::vector<A2Vertex> &vert, int sampleNum)
	{
		if (int(vert.size()) <= sampleNum)
			return true;
		for (int i = 0; i < sampleNum; ++i) {
			int pos = myrnd.generate(vert.size());
			assert(pos >= 0 && pos < int(vert.size()));
			std::swap(vert[i], vert[pos]);
		}
		vert.resize(sampleNum);
		return true;
	}

	bool SampleMovVertNormalEqualized(std::vector<A2Vertex> &vert, int sampleNum)
	{
		std::vector<Point3d> NV;
		if (NV.size() == 0) {
			GenNormal<double>::Fibonacci(30, NV);
			printf("Generated %i normals\n", int(NV.size()));
		}
		// Bucket vector dove, per ogni normale metto gli indici
		// dei vertici ad essa corrispondenti
		std::vector<std::vector <int> > BKT(NV.size());
		for (size_t i = 0; i < vert.size(); ++i) {
			int ind = GenNormal<double>::BestMatchingNormal(vert[i].N(), NV);
			BKT[ind].push_back(int(i));
		}

		// vettore di contatori per sapere quanti punti ho gia' preso per ogni bucket
		std::vector <int> BKTpos(BKT.size(), 0);

		if (sampleNum >= int(vert.size()))
			sampleNum = vert.size() - 1;

		for (int i = 0; i < sampleNum;) {
			int ind = myrnd.generate(BKT.size()); // Scelgo un Bucket
			int &CURpos = BKTpos[ind];
			std::vector<int> &CUR = BKT[ind];

			if (CURpos<int(CUR.size())) {
				std::swap(CUR[CURpos], CUR[CURpos + myrnd.generate(BKT[ind].size() - CURpos)]);
				std::swap(vert[i], vert[CUR[CURpos]]);
				++BKTpos[ind];
				++i;
			}
		}
		vert.resize(sampleNum);

		return true;
	}

	/*
	This function is used to choose remove outliers after each ICP iteration.
	All the points with a distance over the given Percentile are discarded.
	It uses two parameters
	MaxPointNum an (unused) hard limit on the number of points that are chosen
	MinPointNum the minimum number of points that have to be chosen to be usable
	*/
	inline bool choosePoints(
		std::vector<Point3d> &ps, // vertici corrispondenti su fix (rossi)
		std::vector<Point3d> &ns, // normali corrispondenti su fix (rossi)
		std::vector<Point3d> &pt, // vertici scelti su mov (verdi)
		std::vector<Point3d> &opt,		// vertici scelti su mov (verdi)
		//vector<Point3d> &Nt, 		// normali scelti su mov (verdi)
		double passHi,
		Histogramf &h)
	{
		const int N = ap.MaxPointNum;
		double newmaxd = h.Percentile(float(passHi));
		int sz = int(ps.size());
		int fnd = 0;
		int lastgood = sz - 1;
		math::SubtractiveRingRNG myrnd;
		while (fnd < N && fnd < lastgood) {
			int index = fnd + myrnd.generate(lastgood - fnd);
			double dd = Distance(ps[index], pt[index]);
			if (dd <= newmaxd){
				std::swap(ps[index], ps[fnd]);
				std::swap(ns[index], ns[fnd]);
				std::swap(pt[index], pt[fnd]);
				std::swap(opt[index], opt[fnd]);
				++fnd;
			}
			else {
				std::swap(ps[index], ps[lastgood]);
				std::swap(ns[index], ns[lastgood]);
				std::swap(pt[index], pt[lastgood]);
				std::swap(opt[index], opt[lastgood]);
				lastgood--;
			}
		}
		ps.resize(fnd);
		ns.resize(fnd);
		pt.resize(fnd);
		opt.resize(fnd);

		if ((int)ps.size() < ap.MinPointNum){
			printf("Troppi pochi punti!\n");
			ps.clear();
			ns.clear();
			pt.clear();
			opt.clear();
			return false;
		}
		return true;
	}

/*
Minimo esempio di codice per l'uso della funzione di allineamento.

AlignPair::A2Mesh Mov,Fix;										// le due mesh da allineare
vector<AlignPair::A2Vertex> MovVert;					// i punti sulla mov da usare per l'allineamento
Matrix44d In;	In.SetIdentity();               // la trasformazione iniziale che applicata a mov la porterebbe su fix.

AlignPair aa;                                 // l'oggetto principale.
AlignPair::Param ap;
UGrid< AlignPair::A2Mesh::face_container > UG;

Fix.LoadPly("FixMesh.ply");										// Standard ply loading
Mov.LoadPly("MovMesh.ply");
Fix.Init( Ident, false);											// Inizializzazione necessaria (normali per vert,
Mov.Init( Ident, false);                      // info per distanza punto faccia ecc)

AlignPair::InitFix(&Fix, ap, UG);             // la mesh fix viene messa nella ug.

aa.ConvertVertex(Mov.vert,MovVert);           // si campiona la mesh Mov per trovare un po' di vertici.
aa.SampleMovVert(MovVert, ap.SampleNum, ap.SampleMode);

aa.mov=&MovVert;                              // si assegnano i membri principali dell'oggetto align pair
aa.fix=&Fix;
aa.ap = ap;

aa.Align(In,UG,res);                          // si spera :)
											  // il risultato sta nella matrice res.Tr;

res.as.Dump(stdout);
*/

	bool align(const Matrix44d &in, A2Grid &UG, A2GridVert &UGV, Result &res)
	{
		res.ap=ap;

		bool ret=align(UG, UGV, in, res.Tr, res.Pfix, res.Nfix, res.Pmov, res.Nmov, res.H, res.as);

		res.err=res.as.lastPcl50();
		res.status=status;
		return ret;
	}

	double abs2Perc(double val, Box3d bb) const
	{
		return val/bb.Diag();
	}

	double perc2Abs(double val, Box3d bb) const
	{
		return val*bb.Diag();
	}

/************************************************************************************
Versione Vera della Align a basso livello.

Si assume che la mesh fix sia gia' stata messa nella ug u con le debite trasformazioni.
in

************************************************************************************/

	/*
	The Main ICP alignment Function:
	It assumes that:
	we have two meshes:
	- Fix the mesh that does not move and stays in the spatial indexing structure.
	- Mov the mesh we 'move' e.g. the one for which we search the transforamtion.

	requires normalize normals for vertices AND faces
	Allinea due mesh;
	Assume che:
	la uniform grid sia gia' inizializzata con la mesh fix
	*/
	inline bool align(
			A2Grid &u,
			A2GridVert &uv,
			const Matrix44d &in,			// starting transformation that matches mov points to fix mesh
			Matrix44d &out,					// computed transformation
			std::vector<Point3d> &pfix,		// (red) corresponding vertices on src
			std::vector<Point3d> &nfix, 	// (red) corresponding normals on src
			std::vector<Point3d> &opmov,	// chosen vertices on trg (verdi) before the input transormation (Original Point Target)
			std::vector<Point3d> &onmov, 	// chosen normals on trg (verdi)
			Histogramf &h,
			Stat &as)
	{
		std::vector<char> beyondCntVec; // flag vector to set the movverts that we should not use
		// every time that a vertex is at a distance beyound max dist, its counter is incremented;
		// movverts that has been discarded more than MaxCntDist times will not be considered anymore
		const int maxBeyondCnt = 3;
		std::vector< Point3d > movvert;
		std::vector< Point3d > movnorm;
		std::vector<Point3d> pmov; // vertices chosen after the transformation
		status = SUCCESS;
		int tt0 = clock();

		out = in;

		int i;

		double cosAngleThr = cos(ap.MaxAngleRad);
		double startMinDist = ap.MinDistAbs;
		int tt1 = clock();
		int ttsearch = 0;
		int ttleast = 0;
		int nc = 0;
		as.clear();
		as.StartTime = clock();

		beyondCntVec.resize(mov->size(), 0);

		/**************** BEGIN ICP LOOP ****************/
		do {
			Stat::IterInfo ii;
			Box3d movbox;
			initMov(movvert, movnorm, movbox, out);
			h.SetRange(0.0f, float(startMinDist), 512, 2.5f);
			pfix.clear();
			nfix.clear();
			pmov.clear();
			opmov.clear();
			onmov.clear();
			int tts0 = clock();
			ii.MinDistAbs = startMinDist;
			int LocSampleNum = std::min(ap.SampleNum, int(movvert.size()));
			Box3d fixbox;
			if (u.Empty())
				fixbox = uv.bbox;
			else
				fixbox = u.bbox;
			for (i = 0; i < LocSampleNum; ++i) {
				if (beyondCntVec[i] < maxBeyondCnt) {
					if (fixbox.IsIn(movvert[i])) {
						double error = startMinDist;
						Point3d closestPoint, closestNormal;
						double maxd = startMinDist;
						ii.SampleTested++;
						if (u.Empty()) {// using the point cloud grid{
							A2Mesh::VertexPointer vp = tri::GetClosestVertex(*fix, uv, movvert[i], maxd, error);
							if (error >= startMinDist) {
								ii.DistanceDiscarded++; ++beyondCntVec[i]; continue;
							}
							if (movnorm[i].dot(vp->N()) < cosAngleThr) {
								ii.AngleDiscarded++; continue;
							}
							closestPoint = vp->P();
							closestNormal = vp->N();
						}
						else {// using the standard faces and grid
							A2Mesh::FacePointer f = vcg::tri::GetClosestFaceBase<vcg::AlignPair::A2Mesh, vcg::AlignPair::A2Grid >(*fix, u, movvert[i], maxd, error, closestPoint);
							if (error >= startMinDist) {
								ii.DistanceDiscarded++; ++beyondCntVec[i]; continue;
							}
							if (movnorm[i].dot(f->N()) < cosAngleThr) {
								ii.AngleDiscarded++; continue;
							}
							Point3d ip;
							InterpolationParameters<A2Face, double>(*f, f->N(), closestPoint, ip);
							const double IP_EPS = 0.00001;
							// If ip[i] == 0 it means that we are on the edge opposite to i
							if ((fabs(ip[0]) <= IP_EPS && f->IsB(1)) || (fabs(ip[1]) <= IP_EPS && f->IsB(2)) || (fabs(ip[2]) <= IP_EPS && f->IsB(0))){
								ii.BorderDiscarded++;  continue;
							}
							closestNormal = f->N();
						}
						// The sample was accepted. Store it.
						pmov.push_back(movvert[i]);
						opmov.push_back((*mov)[i].P());
						onmov.push_back((*mov)[i].N());
						nfix.push_back(closestNormal);
						pfix.push_back(closestPoint);
						h.Add(float(error));
						ii.SampleUsed++;
					}
					else {
						beyondCntVec[i] = maxBeyondCnt + 1;
					}
				}
			} // End for each pmov
			int tts1 = clock();
			printf("Found %d pairs\n",(int)pfix.size());
			if (!choosePoints(pfix, nfix, pmov, opmov, ap.PassHiFilter, h)) {
				if (int(pfix.size()) < ap.MinPointNum){
					status = TOO_FEW_POINTS;
					ii.Time = clock();
					as.I.push_back(ii);
					return false;
				}
			}
			Matrix44d newout;
			switch (ap.MatchMode){
			case AlignPair::Param::MMSimilarity:
				vcg::PointMatchingScale::computeRotoTranslationScalingMatchMatrix(newout, pfix, pmov);
				break;
			case AlignPair::Param::MMRigid:
				ComputeRigidMatchMatrix(pfix, pmov, newout);
				break;
			default:
				status = UNKNOWN_MODE;
				ii.Time = clock();
				as.I.push_back(ii);
				return false;
			}

			//double sum_before=0;
			//double sum_after=0;
			//for(unsigned int iii=0;iii<pfix.size();++iii){
			//	sum_before+=Distance(pfix[iii], out*OPmov[iii]);
			//	sum_after+=Distance(pfix[iii], newout*OPmov[iii]);
			//}
			//printf("Distance %f -> %f\n",sum_before/double(pfix.size()),sum_after/double(pfix.size()) ) ;

			// the following tuns will use as a initial transformation, the one that has been just found.
			// in the next loops the starting matrix will be this one.
			out = newout * out;

			assert(pfix.size() == pmov.size());
			int tts2 = clock();
			ttsearch += tts1 - tts0;
			ttleast += tts2 - tts1;
			ii.pcl50 = h.Percentile(.5);
			ii.pclhi = h.Percentile(float(ap.PassHiFilter));
			ii.AVG = h.Avg();
			ii.RMS = h.RMS();
			ii.StdDev = h.StandardDeviation();
			ii.Time = clock();
			as.I.push_back(ii);
			nc++;
			// The distance of the next points to be considered is lowered according to the <ReduceFactor> parameter.
			// We use 5 times the <ReduceFactor> percentile of the found points.
			if (ap.ReduceFactorPerc<1)
				startMinDist = std::max(ap.MinDistAbs*ap.MinMinDistPerc, std::min(startMinDist, 5.0*h.Percentile(float(ap.ReduceFactorPerc))));
			//as.dump(stderr);
		} while (
				nc <= ap.MaxIterNum &&
				h.Percentile(.5) > ap.TrgDistAbs &&
				(nc<ap.EndStepNum + 1 || !as.stable(ap.EndStepNum)) );

		/**************** END ICP LOOP ****************/
		int tt2 = clock();
		out[3][0] = 0; out[3][1] = 0; out[3][2] = 0; out[3][3] = 1;
		Matrix44d ResCopy = out;
		Point3d scv, shv, rtv, trv;
		Decompose(ResCopy, scv, shv, rtv, trv);
		if ((ap.MatchMode == vcg::AlignPair::Param::MMRigid) && (math::Abs(1 - scv[0])>ap.MaxScale || math::Abs(1 - scv[1]) > ap.MaxScale || math::Abs(1 - scv[2]) > ap.MaxScale)) {
			status = TOO_MUCH_SCALE;
			return false;
		}
		if (shv[0] > ap.MaxShear || shv[1] > ap.MaxShear || shv[2] > ap.MaxShear) {
			status = TOO_MUCH_SHEAR;
			return false;
		}
		printf("Grid %i %i %i - fn %i\n", u.siz[0], u.siz[1], u.siz[2], fix->fn);
		printf("Init %8.3f Loop %8.3f Search %8.3f least sqrt %8.3f\n",
		float(tt1 - tt0) / CLOCKS_PER_SEC, float(tt2 - tt1) / CLOCKS_PER_SEC,
		float(ttsearch) / CLOCKS_PER_SEC, float(ttleast) / CLOCKS_PER_SEC);

		return true;
	}

	/*
	 * Function called by Align at every cycle.
	 * It fills the <MovVert> and <MovNorm> vectors with the coordinates and normals
	 * taken from the the vertex vector "mov" of the mesh to move according to the
	 * matrix <In>.
	 * It computes also the new bounding box of the transformed vertices
	*/
	inline bool initMov(
			std::vector< Point3d > &movvert,
			std::vector< Point3d > &movnorm,
			Box3d &movbox,
			const Matrix44d &in	)
	{
		Point3d pp, nn;

		movvert.clear();
		movnorm.clear();
		movbox.SetNull();

		A2Mesh::VertexIterator vi;
		for (vi = mov->begin(); vi != mov->end(); vi++) {
			pp = in*(*vi).P();
			nn = in*Point3d((*vi).P() + (*vi).N()) - pp;
			nn.Normalize();
			movvert.push_back(pp);
			movnorm.push_back(nn);
			movbox.Add(pp);
		}
		return true;
	}

	static inline bool InitFixVert(
			A2Mesh *fm,
			AlignPair::Param &pp,
			A2GridVert &u,
			int preferredGridSize=0)
	{
		Box3d bb2 = fm->bbox;
		double minDist = pp.MinDistAbs*1.1;
		//the bbox of the grid should be enflated of the mindist used in the ICP search
		bb2.Offset(Point3d(minDist, minDist, minDist));

		u.SetBBox(bb2);

		//Inserisco la src nella griglia
		if (preferredGridSize == 0)
			preferredGridSize = int(fm->vert.size())*pp.UGExpansionFactor;
		u.Set(fm->vert.begin(), fm->vert.end());//, PreferredGridSize);
		printf("UG %i %i %i\n", u.siz[0], u.siz[1], u.siz[2]);
		return true;
	}

	static inline bool initFix(
			A2Mesh *fm,
			AlignPair::Param &pp,
			A2Grid &u,
			int preferredGridSize=0)
	{
		tri::InitFaceIMark(*fm);

		Box3d bb2 = fm->bbox;
		//	double MinDist= fm->bbox.Diag()*pp.MinDistPerc;
		double minDist = pp.MinDistAbs*1.1;
		//gonfio della distanza utente il BBox della seconda mesh
		bb2.Offset(Point3d(minDist, minDist, minDist));

		u.SetBBox(bb2);

		//Inserisco la src nella griglia
		if (preferredGridSize == 0)
			preferredGridSize = int(fm->face.size())*pp.UGExpansionFactor;
		u.Set(fm->face.begin(), fm->face.end(), preferredGridSize);
		printf("UG %i %i %i\n", u.siz[0], u.siz[1], u.siz[2]);
		return true;
	}

}; // end class

} // end namespace vcg

#endif