MSD Version 0.02

svn path=/trunk/externals/nusmuk/; revision=2795

7 files changed, 718 insertions, 416 deletions

diff --git a/msd/help-msd.pd b/msd/help-msd.pd
index 80d792d..e77b750 100644
--- a/msd/help-msd.pd
+++ b/msd/help-msd.pd
@@ -1,76 +1,170 @@
-#N canvas 0 0 794 877 10;
+#N canvas 367 274 570 449 10;
+#N canvas 271 52 742 843 masses 1;
 #X obj 33 821 msd;
-#X obj 62 14 cnv 15 610 305 empty empty CREATION 20 12 0 14 -262131
+#X obj 62 154 cnv 15 610 180 empty empty CREATION 20 12 0 14 -262131
 -66577 0;
-#X msg 79 43 reset;
-#X text 249 74 Add a mass;
-#X text 335 75 \$1 : Id (symbol);
-#X text 334 95 \$2 : fixed or mobile (0/1);
-#X text 334 113 \$3 : mass;
-#X text 334 151 \$1 : Id (symbol);
-#X text 246 151 Add a link;
-#X text 333 171 \$2 : creation No of mass1;
-#X text 333 189 \$3 : creation No of mass2;
-#X text 332 207 \$4 : rigidity;
-#X text 251 44 Delete all masses and links;
-#X text 332 225 \$5 : viscosity;
-#X text 332 242 \$6 : damping;
-#X obj 62 324 cnv 15 610 60 empty empty COMPUTATION 20 12 0 14 -261689
+#X msg 79 183 reset;
+#X text 249 214 Add a mass;
+#X text 335 215 \$1 : Id (symbol);
+#X text 334 235 \$2 : fixed or mobile (0/1);
+#X text 334 253 \$3 : mass;
+#X text 251 184 Delete all masses and links;
+#X obj 62 338 cnv 15 610 60 empty empty COMPUTATION 20 12 0 14 -261689
 -66577 0;
-#X msg 82 353 bang;
-#X text 235 353 Compute new masses positions;
-#X obj 61 388 cnv 15 610 220 empty empty DYNAMIC_SETTING 20 12 0 14
+#X msg 82 367 bang;
+#X text 235 367 Compute new masses positions;
+#X obj 61 403 cnv 15 610 210 empty empty DYNAMIC_SETTING 20 12 0 14
 -262131 -66577 0;
-#X msg 169 410 setD \$1 \$2;
-#X text 354 428 \$1 : Id (symbol);
-#X text 354 446 \$2 : New value;
-#X msg 87 410 setK \$1 \$2;
-#X text 350 482 \$1 : Id (symbol);
-#X text 350 500 \$2 : New value;
-#X text 348 539 \$1 : Id (symbol);
-#X text 348 557 \$2 : New value;
-#X msg 87 462 posX \$1 \$2;
-#X text 350 464 Set position of mass(es);
-#X text 347 522 Add force on mass(es);
-#X msg 85 521 forceX \$1 \$2;
-#X msg 255 410 setD2 \$1 \$2;
-#X text 354 410 Set rigidity \, viscosity or damping of link(s);
-#X obj 60 617 cnv 15 610 198 empty empty GET_ATTRIBUTES 20 12 0 14
+#X text 350 449 \$1 : Id (symbol);
+#X text 350 467 \$2 : New value;
+#X text 348 503 \$1 : Id (symbol);
+#X text 348 521 \$2 : New value;
+#X msg 87 429 posX \$1 \$2;
+#X text 350 431 Set position of mass(es);
+#X text 347 486 Add force on mass(es);
+#X msg 85 485 forceX \$1 \$2;
+#X obj 61 617 cnv 15 610 198 empty empty GET_ATTRIBUTES 20 12 0 14
 -261689 -66577 0;
-#X msg 146 644 massePosL;
-#X msg 146 672 masseForcesL;
-#X text 247 644 output all masses positions in a list on outlet No
+#X msg 147 644 massePosL;
+#X msg 147 672 masseForcesL;
+#X text 248 644 output all masses positions in a list on outlet No
 1;
-#X text 246 673 output all masses forces in a list on outlet No 1;
-#X msg 145 710 get \$1 \$2;
-#X text 248 711 Get specific attribute;
-#X text 248 736 \$1 : Attribute type ( massesPos / massesSpeeds / massesForces
+#X text 247 673 output all masses forces in a list on outlet No 1;
+#X msg 146 710 get \$1 \$2;
+#X text 249 711 Get specific attribute;
+#X text 249 736 \$1 : Attribute type ( massesPos / massesSpeeds / massesForces
 / linksPos );
-#X text 248 773 \$2 : Id (symbol or creations numbers);
-#X text 334 131 \$4 : position;
-#X msg 79 74 mass \$1 \$2 \$3 \$4;
-#X msg 76 151 link \$1 \$2 \$3 \$4 \$5 \$6;
-#X msg 75 258 deleteMass \$1;
-#X text 240 260 Delete a mass and associated links;
-#X text 330 277 \$1 : Creation No of mass;
-#X msg 74 294 deleteLink \$1;
-#X text 239 296 Delete a link;
-#X text 340 296 \$1 : Creation No of link;
-#X msg 143 793 infosL;
-#X text 246 793 Get infos on all masses and links on outlet No 2;
-#X msg 84 573 Xmin \$1 \, Xmax \$1;
-#X text 347 576 Set minimimum and maximum X of masses;
-#X text 347 593 \$1 : Value;
+#X text 249 773 \$2 : Id (symbol or creations numbers);
+#X msg 79 214 mass \$1 \$2 \$3 \$4;
+#X msg 79 290 deleteMass \$1;
+#X text 248 292 Delete a mass and associated links;
+#X text 338 309 \$1 : Creation No of mass;
+#X msg 144 793 infosL;
+#X text 247 793 Get infos on all masses and links on outlet No 2;
+#X msg 84 535 Xmin \$1 \, Xmax \$1;
+#X text 347 538 Set minimimum and maximum X of masses;
+#X text 347 555 \$1 : Value;
+#X text 73 22 MASSES :;
+#X text 66 69 They got only one physical parameter \, the value of
+their;
+#X text 67 83 mass. They can be mobile or fixed \, in this case forces
+;
+#X text 67 54 The msd masses are the principals objects of the model.
+;
+#X text 66 97 applied on them automatically \, by links \, or manually
+\, by;
+#X text 67 112 messages \, don't do anything.;
+#X msg 81 574 setMobile \$1 \, setFixed \$1;
+#X text 345 578 Change mobile parameter;
+#X text 345 594 \$1 : Creation No of mass;
+#X text 334 271 \$4 : initial position;
 #X connect 2 0 0 0;
+#X connect 9 0 0 0;
 #X connect 16 0 0 0;
+#X connect 19 0 0 0;
+#X connect 21 0 0 0;
 #X connect 22 0 0 0;
-#X connect 27 0 0 0;
+#X connect 25 0 0 0;
+#X connect 29 0 0 0;
 #X connect 30 0 0 0;
-#X connect 34 0 0 0;
+#X connect 33 0 0 0;
 #X connect 35 0 0 0;
-#X connect 38 0 0 0;
-#X connect 43 0 0 0;
 #X connect 44 0 0 0;
-#X connect 45 0 0 0;
-#X connect 48 0 0 0;
-#X connect 51 0 0 0;
+#X restore 281 323 pd masses;
+#N canvas 222 83 808 841 links 0;
+#X obj 33 821 msd;
+#X obj 62 250 cnv 15 610 305 empty empty CREATION 20 12 0 14 -262131
+-66577 0;
+#X msg 79 279 reset;
+#X text 338 308 \$1 : Id (symbol);
+#X text 250 308 Add a link;
+#X text 337 328 \$2 : creation No of mass1;
+#X text 337 346 \$3 : creation No of mass2;
+#X text 336 364 \$4 : rigidity;
+#X text 251 280 Delete all masses and links;
+#X text 336 382 \$5 : viscosity;
+#X text 336 399 \$6 : damping;
+#X obj 61 561 cnv 15 610 82 empty empty DYNAMIC_SETTING 20 12 0 14
+-262131 -66577 0;
+#X msg 172 583 setD \$1 \$2;
+#X text 354 601 \$1 : Id (symbol);
+#X text 354 619 \$2 : New value;
+#X msg 87 583 setK \$1 \$2;
+#X msg 255 583 setD2 \$1 \$2;
+#X text 354 583 Set rigidity \, viscosity or damping of link(s);
+#X obj 60 650 cnv 15 610 140 empty empty GET_ATTRIBUTES 20 12 0 14
+-261689 -66577 0;
+#X msg 75 679 get \$1 \$2;
+#X text 237 680 Get specific attribute;
+#X text 237 705 \$1 : Attribute type ( massesPos / massesSpeeds / massesForces
+/ linksPos );
+#X text 237 742 \$2 : Id (symbol or creations numbers);
+#X msg 78 308 link \$1 \$2 \$3 \$4 \$5 \$6;
+#X msg 74 532 deleteLink \$1;
+#X text 239 534 Delete a link;
+#X text 340 534 \$1 : Creation No of link;
+#X msg 73 762 infosL;
+#X text 236 762 Get infos on all masses and links on outlet No 2;
+#X msg 73 423 iLink \$1 \$2 \$3 \$4 \$5 \$6;
+#X text 338 308 \$1 : Id (symbol);
+#X text 250 308 Add a link;
+#X text 337 328 \$2 : creation No of mass1;
+#X text 337 346 \$3 : creation No of mass2;
+#X text 336 364 \$4 : rigidity;
+#X text 336 382 \$5 : viscosity;
+#X text 336 399 \$6 : damping;
+#X text 410 422 \$1 : Id (symbol);
+#X text 409 478 \$4 : rigidity;
+#X text 409 496 \$5 : viscosity;
+#X text 409 513 \$6 : damping;
+#X text 410 422 \$1 : Id (symbol);
+#X text 409 478 \$4 : rigidity;
+#X text 409 496 \$5 : viscosity;
+#X text 409 513 \$6 : damping;
+#X text 248 423 Add an interactor link;
+#X text 94 52 LINKS :;
+#X text 71 91 parameters : length \, rigidity \, viscosity and damping.
+;
+#X text 72 78 Links connect masses two by two. They got 4 physicals
+;
+#X text 70 134 the two masses at the creation.;
+#X text 71 120 message. The lenght is initialised to the distance between
+;
+#X text 71 106 Rigidity \, viscosity and damping are defined by the
+creation;
+#X text 409 442 \$2 : Id (symbol) of masses type 1;
+#X text 409 460 \$3 : Id (symbol) of masses type 2;
+#X text 70 148 Interactor links are links between mutiples masses \,
+instead;
+#X text 70 161 of creation number \, the masses linked are defined
+with;
+#X text 69 175 their Id.;
+#X connect 2 0 0 0;
+#X connect 15 0 0 0;
+#X connect 19 0 0 0;
+#X connect 23 0 0 0;
+#X connect 24 0 0 0;
+#X connect 27 0 0 0;
+#X connect 29 0 0 0;
+#X restore 283 353 pd links;
+#X text 135 323 HELP on masses --->;
+#X text 134 354 HELP on links --->;
+#X text 154 34 MSD : mass - spring - damper model;
+#X text 75 79 MSD is the 1D object of the msd objects collection.;
+#X text 73 128 There are 4 types of messages for msd :;
+#X text 74 92 It is designed to implement particules physical model
+in PD.The model is based on two elements type : mass and link.;
+#X obj 73 143 cnv 15 420 30 empty empty empty 20 12 0 14 -262131 -66577
+0;
+#X obj 73 176 cnv 15 420 30 empty empty empty 20 12 0 14 -261689 -66577
+0;
+#X obj 73 209 cnv 15 420 30 empty empty empty 20 12 0 14 -262131 -66577
+0;
+#X obj 73 242 cnv 15 420 30 empty empty empty 20 12 0 14 -261689 -66577
+0;
+#X text 76 150 CREATION : To create the model masses and links.;
+#X text 76 215 DYNAMIC SETTING : To set the model parameters dynamically.
+;
+#X text 76 248 ATTRIBUTES : To get the model parameters.;
+#X text 76 177 COMPUTATION : To compute the new model state based on
+previous instant.;
diff --git a/msd/main.cpp b/msd/main.cpp
index b01bc5e..a9aad8a 100755
--- a/msd/main.cpp
+++ b/msd/main.cpp
@@ -101,7 +101,7 @@ public:
 protected:
 
 // ---------------------------------------------------------------  RESET 
-
+// ----------------------------------------------------------------------
 	void m_reset() 
 	{ 
 		t_int i;
@@ -121,6 +121,7 @@ protected:
 	}
 
 // --------------------------------------------------------------  COMPUTE 
+// -----------------------------------------------------------------------
 
 	void m_bang()
 	{
@@ -130,37 +131,37 @@ protected:
 	
 		for (i=0; i<nb_link; i++)	{

 		// compute link forces
-			distance = link[i]->mass1->posX-link[i]->mass2->posX;
-			F  = link[i]->K1 * (distance - link[i]->longueur) ;	// F = k1(x1-x2)
-			F += link[i]->D1 * (distance - link[i]->distance_old) ;	// F = F + D1(v1-v2)
+			distance = link[i]->mass1->posX-link[i]->mass2->posX;		// L[n] = x1 - x2
+			F  = link[i]->K1 * (distance - link[i]->longueur) ;		// F[n] = k1 (L[n] - L[0])
+			F += link[i]->D1 * (distance - link[i]->distance_old) ;		// F[n] = F[n] + D1 (L[n] - L[n-1])
 			if (distance != 0) 	{
-				Fx = F * (link[i]->mass1->posX - link[i]->mass2->posX)/distance;
+				Fx = F * (link[i]->mass1->posX - link[i]->mass2->posX)/distance; // Fx = F * Lx[n]/L[n]
 			}

-			link[i]->mass1->forceX -= Fx;
-			link[i]->mass1->forceX -= link[i]->D2*link[i]->mass1->speedX;

-			link[i]->mass2->forceX += Fx;
-			link[i]->mass2->forceX -= link[i]->D2*link[i]->mass2->speedX;
-			link[i]->distance_old = distance;
+			link[i]->mass1->forceX -= Fx;					// Fx1[n] = -Fx
+			link[i]->mass1->forceX -= link[i]->D2*link[i]->mass1->speedX; 	// Fx1[n] = Fx1[n] - D2 * vx1[n-1]

+			link[i]->mass2->forceX += Fx;					// Fx2[n] = Fx
+			link[i]->mass2->forceX -= link[i]->D2*link[i]->mass2->speedX; 	// Fx2[n] = Fx2[n] - D2 * vx2[n-1]
+			link[i]->distance_old = distance;				// L[n-1] = L[n]
 		}
 

 		for (i=0; i<nb_mass; i++)

 		// compute new masses position only if mobile = 1

 			if (mass[i]->mobile == 1)  		{

-				X_new = mass[i]->forceX * mass[i]->invM + 2*mass[i]->posX - mass[i]->posX2;
-				mass[i]->posX2 = mass[i]->posX;
-				mass[i]->posX = max(min(X_new,Xmax),Xmin);			// x = x + v
-				mass[i]->speedX = mass[i]->posX - mass[i]->posX2;	// v = v + F/M
+				X_new = mass[i]->forceX * mass[i]->invM + 2*mass[i]->posX - mass[i]->posX2; // x[n] =Fx[n]/M+2x[n]-x[n-1] 
+				mass[i]->posX2 = mass[i]->posX;				// x[n-2] = x[n-1]
+				mass[i]->posX = max(min(X_new,Xmax),Xmin);		// x[n-1] = x[n]	
+				mass[i]->speedX = mass[i]->posX - mass[i]->posX2;	// vx[n] = x[n] - x[n-1]
 				}
 
 		for (i=0; i<nb_mass; i++)	{

 		// clear forces
 			mass[i]->out_forceX = mass[i]->forceX;

-			mass[i]->forceX = 0;
+			mass[i]->forceX = 0;						// Fx[n] = 0
 		}

 	}
 
 // --------------------------------------------------------------  MASSES
-
+// ----------------------------------------------------------------------
 	void m_mass(int argc,t_atom *argv) 

 	// add a mass

 	// Id, nbr, mobile, invM, speedX, posX, forceX

@@ -168,18 +169,18 @@ protected:
 		t_atom sortie[5], aux[2];
 		t_float M;
 
-		mass[nb_mass] = new t_mass;			// new pointer

-		mass[nb_mass]->Id = GetSymbol(argv[0]);	// ID
+		mass[nb_mass] = new t_mass;			// new mass

+		mass[nb_mass]->Id = GetSymbol(argv[0]);		// ID
 		mass[nb_mass]->mobile = GetInt(argv[1]);	// mobile
 		if (GetFloat(argv[2])==0)
 			M=1;
 		else M = GetFloat(argv[2]);			
-		mass[nb_mass]->invM = 1/(M);			// invM
-		mass[nb_mass]->speedX = 0;			// vx

-		mass[nb_mass]->posX = GetFloat(argv[3]);		// x
-		mass[nb_mass]->posX2 = GetFloat(argv[3]);		// x

-		mass[nb_mass]->forceX = 0;			// Fx
-		mass[nb_mass]->nbr = id_mass;			// id_nbr
+		mass[nb_mass]->invM = 1/(M);			// 1/M
+		mass[nb_mass]->speedX = 0;			// vx[n]

+		mass[nb_mass]->posX = GetFloat(argv[3]);	// x[n]
+		mass[nb_mass]->posX2 = GetFloat(argv[3]);	// x[n-1]

+		mass[nb_mass]->forceX = 0;			// Fx[n]
+		mass[nb_mass]->nbr = id_mass;			// id number
 		nb_mass++ ;
 		id_mass++;

 		nb_mass = min ( nb_max_mass -1, nb_mass );
@@ -252,6 +253,8 @@ protected:
 	t_int i,nb_link_delete=0;
 	t_atom sortie[5], aux[nb_link];
 	
+
+	// Delete all associated links 
 	for (i=0; i<nb_link;i++)	{
 		if (link[i]->mass1->nbr == GetAInt(argv[0]) || link[i]->mass2->nbr == GetAInt(argv[0]))	{
 			SetFloat((aux[nb_link_delete]),link[i]->nbr);
@@ -261,7 +264,8 @@ protected:
 
 	for (i=0; i<nb_link_delete;i++)
 		m_delete_link(1,&aux[i]);
-
+	
+	// Delete mass
 	for (i=0; i<nb_mass;i++)
 		if (mass[i]->nbr == GetAInt(argv[0]))	{
 			SetFloat((sortie[0]),mass[i]->nbr);
@@ -270,7 +274,7 @@ protected:
 			SetFloat((sortie[3]),1/mass[i]->invM);
 			SetFloat((sortie[4]),mass[i]->posX);
 			delete mass[i];
-			mass[i] = mass[nb_mass-1];
+			mass[i] = mass[nb_mass-1]; 	// copy last mass instead 
 			nb_mass--;
 			ToOutAnything(1,S_Mass_deleted,5,sortie);
 			break;
@@ -281,17 +285,18 @@ protected:
 
 	void m_Xmax(int argc,t_atom *argv) 
 	{

-	// set damping of link(s) named Id
+	// set X max
 	Xmax = GetFloat(argv[0]);
 	}
 
 	void m_Xmin(int argc,t_atom *argv) 
 	{

-	// set damping of link(s) named Id
+	// set X min
 	Xmin = GetFloat(argv[0]);
 	}
 
 // --------------------------------------------------------------  LINKS 
+// ---------------------------------------------------------------------
 
 	void m_link(int argc,t_atom *argv) 
 	// add a link

@@ -300,20 +305,20 @@ protected:
 		t_atom sortie[7], aux[2];
 		t_int i;
 
-		link[nb_link] = new t_link;
-		link[nb_link]->Id = GetSymbol(argv[0]);
+		link[nb_link] = new t_link;			// New pointer
+		link[nb_link]->Id = GetSymbol(argv[0]);		// ID
 		for (i=0; i<nb_mass;i++)
-			if (mass[i]->nbr==GetAInt(argv[1]))
+			if (mass[i]->nbr==GetAInt(argv[1]))	// pointer to mass1
 				link[nb_link]->mass1 = mass[i];
-			else if(mass[i]->nbr==GetAInt(argv[2]))
+			else if(mass[i]->nbr==GetAInt(argv[2]))	// pointer to mass2
 				link[nb_link]->mass2 = mass[i];
-		link[nb_link]->K1 = GetFloat(argv[3]);

-		link[nb_link]->D1 = GetFloat(argv[4]);
-		link[nb_link]->D2 = GetFloat(argv[5]);
-		link[nb_link]->longx = link[nb_link]->mass1->posX - link[nb_link]->mass2->posX;
-		link[nb_link]->longueur = link[nb_link]->longx ;
-		link[nb_link]->nbr = id_link;
-		link[nb_link]->distance_old = link[nb_link]->longueur;
+		link[nb_link]->K1 = GetFloat(argv[3]);		// K1

+		link[nb_link]->D1 = GetFloat(argv[4]);		// D1
+		link[nb_link]->D2 = GetFloat(argv[5]);		// D2
+		link[nb_link]->longx = link[nb_link]->mass1->posX - link[nb_link]->mass2->posX;	// Lx[0]
+		link[nb_link]->longueur = link[nb_link]->longx ;// L[0]
+		link[nb_link]->nbr = id_link;			// id number
+		link[nb_link]->distance_old = link[nb_link]->longueur;	// L[n-1]
 		nb_link++;
 		id_link++;

 		nb_link = min ( nb_max_link -1, nb_link );
@@ -356,7 +361,7 @@ protected:
 					SetSymbol((arglist[0]),GetSymbol(argv[0]));
 					SetFloat((arglist[1]),mass[imass1[i]]->nbr);
 					SetFloat((arglist[2]),mass[imass2[j]]->nbr);
-					SetFloat((arglist[3]),GetInt(argv[3]));
+					SetFloat((arglist[3]),GetFloat(argv[3]));
 					SetFloat((arglist[4]),GetFloat(argv[4]));
 					SetFloat((arglist[5]),GetFloat(argv[5]));
 					m_link(6,arglist);
@@ -418,7 +423,7 @@ protected:
 			SetFloat((sortie[5]),link[i]->D1);
 			SetFloat((sortie[6]),link[i]->D2);
 			delete link[i];
-			link[i]=link[nb_link-1];
+			link[i]=link[nb_link-1];	// copy last link instead
 			nb_link--;
 			ToOutAnything(1,S_Link_deleted,7,sortie);
 			break;
@@ -427,6 +432,7 @@ protected:
 
 
 // --------------------------------------------------------------  GET 
+// -------------------------------------------------------------------
 
 	void m_get(int argc,t_atom *argv)
 	// get attributes
@@ -595,7 +601,7 @@ protected:
 	}
 
 	void m_force_dumpl()
-	// List of masses positions on first outlet
+	// List of masses forces on first outlet
 	{	
 		t_atom sortie[nb_mass];
 		t_int i;
@@ -607,7 +613,7 @@ protected:
 	}
 
 	void m_info_dumpl()
-	// List of masses positions on first outlet
+	// List of masses and links infos on first outlet
 	{	
 		t_atom sortie[7];
 		t_int i;
@@ -636,16 +642,19 @@ protected:
 
 
 // --------------------------------------------------------------  PROTECTED VARIABLES 
+// -----------------------------------------------------------------------------------
 
-	t_link * link[nb_max_link];

-	t_mass * mass[nb_max_mass];
-	t_float Xmin, Xmax, Ymin, Ymax;
+	t_link * link[nb_max_link];		// Pointer table on links

+	t_mass * mass[nb_max_mass];		// Pointer table on masses
+	t_float Xmin, Xmax;			// Limit values
 	int nb_link, nb_mass, id_mass, id_link;
 
 // --------------------------------------------------------------  SETUP
+// ---------------------------------------------------------------------
 
 private:
 
+	// Static symbols
 	const static t_symbol *S_Reset;
 	const static t_symbol *S_Mass;
 	const static t_symbol *S_Link;
@@ -721,7 +730,8 @@ private:
 	FLEXT_CALLBACK_V(m_delete_link)
 	FLEXT_CALLBACK_V(m_delete_mass)
 };
-
+// -------------------------------------------------------------- STATIC VARIABLES
+// -------------------------------------------------------------------------------
 
 	const t_symbol *msd::S_Reset = MakeSymbol("Reset");
 	const t_symbol *msd::S_Mass = MakeSymbol("Mass");
diff --git a/msd2D/help-msd2D.pd b/msd2D/help-msd2D.pd
index 9662c14..d2f051a 100644
--- a/msd2D/help-msd2D.pd
+++ b/msd2D/help-msd2D.pd
@@ -1,78 +1,173 @@
-#N canvas 0 0 823 885 10;
-#X obj 51 13 cnv 15 610 305 empty empty CREATION 20 12 0 14 -262131
+#N canvas 0 0 478 397 10;
+#N canvas 271 52 742 843 masses 1;
+#X obj 62 154 cnv 15 610 180 empty empty CREATION 20 12 0 14 -262131
 -66577 0;
-#X msg 68 42 reset;
-#X text 238 73 Add a mass;
-#X text 324 74 \$1 : Id (symbol);
-#X text 323 94 \$2 : fixed or mobile (0/1);
-#X text 323 112 \$3 : mass;
-#X text 323 150 \$1 : Id (symbol);
-#X text 235 150 Add a link;
-#X text 322 170 \$2 : creation No of mass1;
-#X text 322 188 \$3 : creation No of mass2;
-#X text 321 206 \$4 : rigidity;
-#X text 240 43 Delete all masses and links;
-#X text 321 224 \$5 : viscosity;
-#X text 321 241 \$6 : damping;
-#X obj 51 323 cnv 15 610 60 empty empty COMPUTATION 20 12 0 14 -261689
+#X msg 79 183 reset;
+#X text 249 214 Add a mass;
+#X text 335 215 \$1 : Id (symbol);
+#X text 334 235 \$2 : fixed or mobile (0/1);
+#X text 334 253 \$3 : mass;
+#X text 251 184 Delete all masses and links;
+#X obj 62 338 cnv 15 610 60 empty empty COMPUTATION 20 12 0 14 -261689
 -66577 0;
-#X msg 71 352 bang;
-#X text 224 352 Compute new masses positions;
-#X obj 50 387 cnv 15 610 220 empty empty DYNAMIC_SETTING 20 12 0 14
+#X msg 82 367 bang;
+#X text 235 367 Compute new masses positions;
+#X obj 61 403 cnv 15 610 210 empty empty DYNAMIC_SETTING 20 12 0 14
 -262131 -66577 0;
-#X msg 158 409 setD \$1 \$2;
-#X text 343 427 \$1 : Id (symbol);
-#X text 343 445 \$2 : New value;
-#X msg 76 409 setK \$1 \$2;
-#X text 339 481 \$1 : Id (symbol);
-#X text 339 499 \$2 : New value;
-#X text 337 538 \$1 : Id (symbol);
-#X text 337 556 \$2 : New value;
-#X msg 76 461 posX \$1 \$2;
-#X text 339 463 Set position of mass(es);
-#X text 336 521 Add force on mass(es);
-#X msg 74 520 forceX \$1 \$2;
-#X msg 244 409 setD2 \$1 \$2;
-#X text 343 409 Set rigidity \, viscosity or damping of link(s);
-#X obj 49 616 cnv 15 610 198 empty empty GET_ATTRIBUTES 20 12 0 14
+#X text 350 449 \$1 : Id (symbol);
+#X text 350 467 \$2 : New value;
+#X text 348 503 \$1 : Id (symbol);
+#X text 348 521 \$2 : New value;
+#X msg 87 429 posX \$1 \$2;
+#X text 350 431 Set position of mass(es);
+#X text 347 486 Add force on mass(es);
+#X msg 85 485 forceX \$1 \$2;
+#X obj 61 617 cnv 15 610 198 empty empty GET_ATTRIBUTES 20 12 0 14
 -261689 -66577 0;
-#X msg 135 643 massePosL;
-#X msg 135 671 masseForcesL;
-#X text 236 643 output all masses positions in a list on outlet No
+#X msg 147 644 massePosL;
+#X msg 147 672 masseForcesL;
+#X text 248 644 output all masses positions in a list on outlet No
 1;
-#X text 235 672 output all masses forces in a list on outlet No 1;
-#X msg 134 709 get \$1 \$2;
-#X text 237 710 Get specific attribute;
-#X text 237 735 \$1 : Attribute type ( massesPos / massesSpeeds / massesForces
+#X text 247 673 output all masses forces in a list on outlet No 1;
+#X msg 146 710 get \$1 \$2;
+#X text 249 711 Get specific attribute;
+#X text 249 736 \$1 : Attribute type ( massesPos / massesSpeeds / massesForces
 / linksPos );
-#X text 237 772 \$2 : Id (symbol or creations numbers);
-#X msg 65 150 link \$1 \$2 \$3 \$4 \$5 \$6;
-#X msg 64 257 deleteMass \$1;
-#X text 229 259 Delete a mass and associated links;
-#X text 319 276 \$1 : Creation No of mass;
-#X msg 63 293 deleteLink \$1;
-#X text 228 295 Delete a link;
-#X text 329 295 \$1 : Creation No of link;
-#X msg 132 792 infosL;
-#X text 235 792 Get infos on all masses and links on outlet No 2;
-#X text 336 592 \$1 : Value;
-#X obj 22 820 msd2D;
-#X msg 169 519 forceY \$1 \$2;
-#X msg 158 461 posY \$1 \$2;
-#X msg 68 73 mass \$1 \$2 \$3 \$4 \$5;
-#X text 323 130 \$4 \, \$5 : position;
-#X msg 73 572 Xmin \$1 \, Xmax \$1 \, Ymin \$1 \, Ymax \$1;
-#X text 336 575 Set minimimum and maximum of masses positions;
-#X connect 1 0 51 0;
-#X connect 15 0 51 0;
-#X connect 21 0 51 0;
-#X connect 26 0 51 0;
-#X connect 29 0 51 0;
-#X connect 33 0 51 0;
-#X connect 34 0 51 0;
-#X connect 37 0 51 0;
-#X connect 41 0 51 0;
-#X connect 42 0 51 0;
-#X connect 45 0 51 0;
-#X connect 48 0 51 0;
-#X connect 54 0 51 0;
+#X text 249 773 \$2 : Id (symbol or creations numbers);
+#X msg 79 290 deleteMass \$1;
+#X text 248 292 Delete a mass and associated links;
+#X text 338 309 \$1 : Creation No of mass;
+#X msg 144 793 infosL;
+#X text 247 793 Get infos on all masses and links on outlet No 2;
+#X text 347 555 \$1 : Value;
+#X text 73 22 MASSES :;
+#X text 66 69 They got only one physical parameter \, the value of
+their;
+#X text 67 83 mass. They can be mobile or fixed \, in this case forces
+;
+#X text 67 54 The msd masses are the principals objects of the model.
+;
+#X text 66 97 applied on them automatically \, by links \, or manually
+\, by;
+#X text 67 112 messages \, don't do anything.;
+#X msg 81 578 setMobile \$1 \, setFixed \$1;
+#X text 345 578 Change mobile parameter;
+#X text 345 594 \$1 : Creation No of mass;
+#X msg 79 214 mass \$1 \$2 \$3 \$4 \$5;
+#X msg 188 430 posY \$1 \$2;
+#X msg 186 486 forceY \$1 \$2;
+#X obj 33 821 msd2D;
+#X text 347 538 Set minimimum and maximum X \, Y of masses;
+#X msg 84 538 Xmin \$1 \, Xmax \$1 \, Ymin \$1 \, Ymax \$1;
+#X text 334 271 \$4 \, \$5 : initial position;
+#X connect 1 0 46 0;
+#X connect 8 0 46 0;
+#X connect 15 0 46 0;
+#X connect 18 0 46 0;
+#X connect 20 0 46 0;
+#X connect 21 0 46 0;
+#X connect 24 0 46 0;
+#X connect 28 0 46 0;
+#X connect 31 0 46 0;
+#X connect 40 0 46 0;
+#X connect 43 0 46 0;
+#X connect 48 0 46 0;
+#X restore 221 312 pd masses;
+#N canvas 222 83 808 841 links 0;
+#X obj 62 250 cnv 15 610 305 empty empty CREATION 20 12 0 14 -262131
+-66577 0;
+#X msg 79 279 reset;
+#X text 338 308 \$1 : Id (symbol);
+#X text 250 308 Add a link;
+#X text 337 328 \$2 : creation No of mass1;
+#X text 337 346 \$3 : creation No of mass2;
+#X text 336 364 \$4 : rigidity;
+#X text 251 280 Delete all masses and links;
+#X text 336 382 \$5 : viscosity;
+#X text 336 399 \$6 : damping;
+#X obj 61 561 cnv 15 610 82 empty empty DYNAMIC_SETTING 20 12 0 14
+-262131 -66577 0;
+#X msg 172 583 setD \$1 \$2;
+#X text 354 601 \$1 : Id (symbol);
+#X text 354 619 \$2 : New value;
+#X msg 87 583 setK \$1 \$2;
+#X msg 255 583 setD2 \$1 \$2;
+#X text 354 583 Set rigidity \, viscosity or damping of link(s);
+#X obj 60 650 cnv 15 610 140 empty empty GET_ATTRIBUTES 20 12 0 14
+-261689 -66577 0;
+#X msg 75 679 get \$1 \$2;
+#X text 237 680 Get specific attribute;
+#X text 237 705 \$1 : Attribute type ( massesPos / massesSpeeds / massesForces
+/ linksPos );
+#X text 237 742 \$2 : Id (symbol or creations numbers);
+#X msg 78 308 link \$1 \$2 \$3 \$4 \$5 \$6;
+#X msg 74 532 deleteLink \$1;
+#X text 239 534 Delete a link;
+#X text 340 534 \$1 : Creation No of link;
+#X msg 73 762 infosL;
+#X text 236 762 Get infos on all masses and links on outlet No 2;
+#X msg 73 423 iLink \$1 \$2 \$3 \$4 \$5 \$6;
+#X text 338 308 \$1 : Id (symbol);
+#X text 250 308 Add a link;
+#X text 337 328 \$2 : creation No of mass1;
+#X text 337 346 \$3 : creation No of mass2;
+#X text 336 364 \$4 : rigidity;
+#X text 336 382 \$5 : viscosity;
+#X text 336 399 \$6 : damping;
+#X text 410 422 \$1 : Id (symbol);
+#X text 409 478 \$4 : rigidity;
+#X text 409 496 \$5 : viscosity;
+#X text 409 513 \$6 : damping;
+#X text 410 422 \$1 : Id (symbol);
+#X text 409 478 \$4 : rigidity;
+#X text 409 496 \$5 : viscosity;
+#X text 409 513 \$6 : damping;
+#X text 248 423 Add an interactor link;
+#X text 94 52 LINKS :;
+#X text 71 91 parameters : length \, rigidity \, viscosity and damping.
+;
+#X text 72 78 Links connect masses two by two. They got 4 physicals
+;
+#X text 70 134 the two masses at the creation.;
+#X text 71 120 message. The lenght is initialised to the distance between
+;
+#X text 71 106 Rigidity \, viscosity and damping are defined by the
+creation;
+#X text 409 442 \$2 : Id (symbol) of masses type 1;
+#X text 409 460 \$3 : Id (symbol) of masses type 2;
+#X text 70 148 Interactor links are links between mutiples masses \,
+instead;
+#X text 70 161 of creation number \, the masses linked are defined
+with;
+#X text 69 175 their Id.;
+#X obj 33 821 msd2D;
+#X connect 1 0 56 0;
+#X connect 14 0 56 0;
+#X connect 18 0 56 0;
+#X connect 22 0 56 0;
+#X connect 23 0 56 0;
+#X connect 26 0 56 0;
+#X connect 28 0 56 0;
+#X restore 223 342 pd links;
+#X text 75 312 HELP on masses --->;
+#X text 74 343 HELP on links --->;
+#X text 13 117 There are 4 types of messages for msd :;
+#X text 14 81 It is designed to implement particules physical model
+in PD.The model is based on two elements type : mass and link.;
+#X obj 13 132 cnv 15 420 30 empty empty empty 20 12 0 14 -262131 -66577
+0;
+#X obj 13 165 cnv 15 420 30 empty empty empty 20 12 0 14 -261689 -66577
+0;
+#X obj 13 198 cnv 15 420 30 empty empty empty 20 12 0 14 -262131 -66577
+0;
+#X obj 13 231 cnv 15 420 30 empty empty empty 20 12 0 14 -261689 -66577
+0;
+#X text 16 139 CREATION : To create the model masses and links.;
+#X text 16 204 DYNAMIC SETTING : To set the model parameters dynamically.
+;
+#X text 16 237 ATTRIBUTES : To get the model parameters.;
+#X text 16 166 COMPUTATION : To compute the new model state based on
+previous instant.;
+#X text 94 23 MSD2D : mass - spring - damper model;
+#X text 15 68 MSD2D is the 2D object of the msd objects collection.
+;
diff --git a/msd2D/main.cpp b/msd2D/main.cpp
index 863513c..7872cbf 100755
--- a/msd2D/main.cpp
+++ b/msd2D/main.cpp
@@ -101,6 +101,7 @@ public:
 protected:
 
 // ---------------------------------------------------------------  RESET 
+// ----------------------------------------------------------------------
 
 	void m_reset() 
 	{ 
@@ -121,6 +122,7 @@ protected:
 	}
 
 // --------------------------------------------------------------  COMPUTE 
+// -----------------------------------------------------------------------
 
 	void m_bang()
 	{
@@ -131,57 +133,58 @@ protected:
 		for (i=0; i<nb_link; i++)	{

 		// compute link forces
 			distance = sqrt(pow(link[i]->mass1->posX-link[i]->mass2->posX,2) + 
-				pow(link[i]->mass1->posY-link[i]->mass2->posY,2));
-			F  = link[i]->K1 * (distance - link[i]->longueur) ;	// F = k1(x1-x2)
-			F += link[i]->D1 * (distance - link[i]->distance_old) ;	// F = F + D1(v1-v2)
+				pow(link[i]->mass1->posY-link[i]->mass2->posY,2));		// L[n] = sqrt( (x1-x2)² +(y1-y2)²)
+			F  = link[i]->K1 * (distance - link[i]->longueur) ;			// F[n] = k1 (L[n] - L[0])
+			F += link[i]->D1 * (distance - link[i]->distance_old) ;			// F[n] = F[n] + D1 (L[n] - L[n-1])
 			if (distance != 0) 	{
-				Fx = F * (link[i]->mass1->posX - link[i]->mass2->posX)/distance;
-				Fy = F * (link[i]->mass1->posY - link[i]->mass2->posY)/distance;
+				Fx = F * (link[i]->mass1->posX - link[i]->mass2->posX)/distance; // Fx = F * Lx[n]/L[n]
+				Fy = F * (link[i]->mass1->posY - link[i]->mass2->posY)/distance; // Fy = F * Ly[n]/L[n]
 			}

-			link[i]->mass1->forceX -= Fx;
-			link[i]->mass1->forceX -= link[i]->D2*link[i]->mass1->speedX;

-			link[i]->mass2->forceX += Fx;
-			link[i]->mass2->forceX -= link[i]->D2*link[i]->mass2->speedX;
-			link[i]->mass1->forceY -= Fy;
-			link[i]->mass1->forceY -= link[i]->D2*link[i]->mass1->speedY;

-			link[i]->mass2->forceY += Fy;
-			link[i]->mass2->forceY -= link[i]->D2*link[i]->mass2->speedY;
-			link[i]->distance_old = distance;
+			link[i]->mass1->forceX -= Fx;					// Fx1[n] = -Fx
+			link[i]->mass1->forceX -= link[i]->D2*link[i]->mass1->speedX;	// Fx1[n] = Fx1[n] - D2 * vx1[n-1]

+			link[i]->mass2->forceX += Fx;					// Fx2[n] = Fx
+			link[i]->mass2->forceX -= link[i]->D2*link[i]->mass2->speedX;	// Fx2[n] = Fx2[n] - D2 * vx2[n-1]
+			link[i]->mass1->forceY -= Fy;					// Fy1[n] = -Fy
+			link[i]->mass1->forceY -= link[i]->D2*link[i]->mass1->speedY;	// Fy1[n] = Fy1[n] - D2 * vy1[n-1]

+			link[i]->mass2->forceY += Fy;					// Fy2[n] = Fy
+			link[i]->mass2->forceY -= link[i]->D2*link[i]->mass2->speedY;	// Fy1[n] = Fy1[n] - D2 * vy1[n-1]
+			link[i]->distance_old = distance;				// L[n-1] = L[n]
 		}
 

 		for (i=0; i<nb_mass; i++)

 		// compute new masses position only if mobile = 1

 			if (mass[i]->mobile == 1)  		{

-				X_new = mass[i]->forceX * mass[i]->invM + 2*mass[i]->posX - mass[i]->posX2;
-				mass[i]->posX2 = mass[i]->posX;
-				mass[i]->posX = max(min(X_new,Xmax),Xmin);			// x = x + v
-				mass[i]->speedX = mass[i]->posX - mass[i]->posX2;	// v = v + F/M
-				Y_new = mass[i]->forceY * mass[i]->invM + 2*mass[i]->posY - mass[i]->posY2;
-				mass[i]->posY2 = mass[i]->posY;
-				mass[i]->posY = max(min(Y_new,Ymax),Ymin);			// x = x + v
-				mass[i]->speedY = mass[i]->posY - mass[i]->posY2;	// v = v + F/M
+				X_new = mass[i]->forceX * mass[i]->invM + 2*mass[i]->posX - mass[i]->posX2; // x[n] =Fx[n]/M+2x[n]-x[n-1] 
+				mass[i]->posX2 = mass[i]->posX;				// x[n-2] = x[n-1]
+				mass[i]->posX = max(min(X_new,Xmax),Xmin);		// x[n-1] = x[n]
+				mass[i]->speedX = mass[i]->posX - mass[i]->posX2;	// vx[n] = x[n] - x[n-1]
+				Y_new = mass[i]->forceY * mass[i]->invM + 2*mass[i]->posY - mass[i]->posY2; // x[n] =Fx[n]/M+2x[n]-x[n-1]
+				mass[i]->posY2 = mass[i]->posY;				// x[n-2] = x[n-1]
+				mass[i]->posY = max(min(Y_new,Ymax),Ymin);		// x[n-1] = x[n]
+				mass[i]->speedY = mass[i]->posY - mass[i]->posY2;	// vx[n] = x[n] - x[n-1]
 				}
 
 		for (i=0; i<nb_mass; i++)	{

 		// clear forces
 			mass[i]->out_forceX = mass[i]->forceX;

-			mass[i]->forceX = 0;
+			mass[i]->forceX = 0;						// Fx[n] = 0
 			mass[i]->out_forceY = mass[i]->forceY;

-			mass[i]->forceY = 0;
+			mass[i]->forceY = 0;						// Fy[n] = 0
 		}

 	}
 
 // --------------------------------------------------------------  MASSES
+// ----------------------------------------------------------------------
 
 	void m_mass(int argc,t_atom *argv) 

 	// add a mass

-	// Id, nbr, mobile, invM, speedX, posX, forceX

+	// Id, nbr, mobile, invM, speedX Y, posX Y, forceX Y

 	{
 		t_atom sortie[6], aux[2];
 		t_float M;
 
-		mass[nb_mass] = new t_mass;			// new pointer

-		mass[nb_mass]->Id = GetSymbol(argv[0]);	// ID
+		mass[nb_mass] = new t_mass;			// new mass

+		mass[nb_mass]->Id = GetSymbol(argv[0]);		// ID
 		mass[nb_mass]->mobile = GetInt(argv[1]);	// mobile
 		if (GetFloat(argv[2])==0)
 			M=1;
@@ -195,7 +198,7 @@ protected:
 		mass[nb_mass]->posY = GetFloat(argv[4]);	// y[n]
 		mass[nb_mass]->posY2 = GetFloat(argv[4]);	// y[n-1]

 		mass[nb_mass]->forceY = 0;			// Fy[n]
-		mass[nb_mass]->nbr = id_mass;			// id_nbr
+		mass[nb_mass]->nbr = id_mass;			// id number
 		nb_mass++ ;
 		id_mass++;

 		nb_mass = min ( nb_max_mass -1, nb_mass );
@@ -297,6 +300,7 @@ protected:
 	t_int i,nb_link_delete=0;
 	t_atom sortie[6], aux[nb_link];
 	
+	// Delete associated links
 	for (i=0; i<nb_link;i++)	{
 		if (link[i]->mass1->nbr == GetInt(argv[0]) || link[i]->mass2->nbr == GetInt(argv[0]))	{
 			SetFloat((aux[nb_link_delete]),link[i]->nbr);
@@ -307,7 +311,7 @@ protected:
 	for (i=0; i<nb_link_delete;i++)
 		m_delete_link(1,&aux[i]);
 
-
+	// delete mass
 	for (i=0; i<nb_mass;i++)
 		if (mass[i]->nbr == GetAInt(argv[0]))	{
 			SetFloat((sortie[0]),mass[i]->nbr);
@@ -327,29 +331,30 @@ protected:
 
 	void m_Xmax(int argc,t_atom *argv) 
 	{

-	// set damping of link(s) named Id
+	// set X max
 	Xmax = GetFloat(argv[0]);
 	}
 
 	void m_Ymax(int argc,t_atom *argv) 
 	{

-	// set damping of link(s) named Id
+	// set Y max
 	Ymax = GetFloat(argv[0]);
 	}
 
 	void m_Xmin(int argc,t_atom *argv) 
 	{

-	// set damping of link(s) named Id
+	// set X min
 	Xmin = GetFloat(argv[0]);
 	}
 
 	void m_Ymin(int argc,t_atom *argv) 
 	{

-	// set damping of link(s) named Id
+	// set Y min
 	Ymin = GetFloat(argv[0]);
 	}
 
 // --------------------------------------------------------------  LINKS 
+// ---------------------------------------------------------------------
 
 	void m_link(int argc,t_atom *argv) 
 	// add a link

@@ -358,21 +363,21 @@ protected:
 		t_atom sortie[7], aux[2];
 		t_int i;
 
-		link[nb_link] = new t_link;
+		link[nb_link] = new t_link;			// new link
 		link[nb_link]->Id = GetSymbol(argv[0]);
 		for (i=0; i<nb_mass;i++)
-			if (mass[i]->nbr==GetAInt(argv[1]))
+			if (mass[i]->nbr==GetAInt(argv[1]))	// pointer on mass 1
 				link[nb_link]->mass1 = mass[i];
-			else if(mass[i]->nbr==GetAInt(argv[2]))
+			else if(mass[i]->nbr==GetAInt(argv[2]))	// pointer on mass 2
 				link[nb_link]->mass2 = mass[i];
-		link[nb_link]->K1 = GetFloat(argv[3]);

-		link[nb_link]->D1 = GetFloat(argv[4]);	
-		link[nb_link]->D2 = GetFloat(argv[5]);
-		link[nb_link]->longx = link[nb_link]->mass1->posX - link[nb_link]->mass2->posX;
-		link[nb_link]->longy = link[nb_link]->mass1->posY - link[nb_link]->mass2->posY;
-		link[nb_link]->longueur = sqrt( pow(link[nb_link]->longx,2) + pow(link[nb_link]->longy,2));
-		link[nb_link]->nbr = id_link;
-		link[nb_link]->distance_old = link[nb_link]->longueur;
+		link[nb_link]->K1 = GetFloat(argv[3]);		// K1

+		link[nb_link]->D1 = GetFloat(argv[4]);		// D1
+		link[nb_link]->D2 = GetFloat(argv[5]);		// D2
+		link[nb_link]->longx = link[nb_link]->mass1->posX - link[nb_link]->mass2->posX;		// Lx[0]
+		link[nb_link]->longy = link[nb_link]->mass1->posY - link[nb_link]->mass2->posY;		// Ly[0]
+		link[nb_link]->longueur = sqrt( pow(link[nb_link]->longx,2) + pow(link[nb_link]->longy,2)); // L[0] = sq( Lx[0]²+Ly[0]²)
+		link[nb_link]->nbr = id_link;			// id number
+		link[nb_link]->distance_old = link[nb_link]->longueur;// L[n-1]
 		nb_link++;
 		id_link++;

 		nb_link = min ( nb_max_link -1, nb_link );
@@ -415,7 +420,7 @@ protected:
 					SetSymbol((arglist[0]),GetSymbol(argv[0]));
 					SetFloat((arglist[1]),mass[imass1[i]]->nbr);
 					SetFloat((arglist[2]),mass[imass2[j]]->nbr);
-					SetFloat((arglist[3]),GetAInt(argv[3]));
+					SetFloat((arglist[3]),GetFloat(argv[3]));
 					SetFloat((arglist[4]),GetFloat(argv[4]));
 					SetFloat((arglist[5]),GetFloat(argv[5]));
 					m_link(6,arglist);
@@ -437,7 +442,7 @@ protected:
 
 	void m_setD(int argc,t_atom *argv) 
 	{

-	// set damping of link(s) named Id
+	// set viscosity of link(s) named Id
 		t_int i;
 		const t_symbol *sym = GetSymbol(argv[0]);
 
@@ -477,7 +482,7 @@ protected:
 			SetFloat((sortie[5]),link[i]->D1);
 			SetFloat((sortie[6]),link[i]->D2);
 			delete link[i];
-			link[i]=link[nb_link-1];
+			link[i]=link[nb_link-1];	// copy last link instead
 			nb_link--;
 			ToOutAnything(1,S_Link_deleted,7,sortie);
 			break;
@@ -486,7 +491,7 @@ protected:
 
 
 // --------------------------------------------------------------  GET 
-
+// -------------------------------------------------------------------
 	void m_get(int argc,t_atom *argv)
 	// get attributes
 	{
@@ -498,21 +503,21 @@ protected:
 
 		if (argc == 1)
 		{
-			if (auxtype == S_massesPos)// get all masses positions
+			if (auxtype == S_massesPos)		// get all masses positions
 				for (i=0; i<nb_mass; i++)
 				{
 					SetFloat(sortie[0],mass[i]->posX);
 					SetFloat(sortie[1],mass[i]->posY);
 					ToOutAnything(0,S_massesPos,2,sortie);
 				}
-			else if (auxtype == S_massesForces)// get all masses forces
+			else if (auxtype == S_massesForces)	// get all masses forces
 				for (i=0; i<nb_mass; i++)
 				{
 					SetFloat(sortie[0],mass[i]->out_forceX);
 					SetFloat(sortie[1],mass[i]->out_forceY);
 					ToOutAnything(0,S_massesForces,2,sortie);
 				}
-			else if (auxtype == S_linksPos)// get all links positions
+			else if (auxtype == S_linksPos)		// get all links positions
 				for (i=0; i<nb_link; i++)
 				{
 					SetFloat(sortie[0],link[i]->mass1->posX);
@@ -521,7 +526,7 @@ protected:
 					SetFloat(sortie[3],link[i]->mass2->posY);
 					ToOutAnything(0,S_linksPos,4,sortie);
 				}
-			else 		// get all masses speeds
+			else 					// get all masses speeds
 				for (i=0; i<nb_mass; i++)
 				{
 					SetFloat(sortie[0],mass[i]->speedX);
@@ -529,7 +534,7 @@ protected:
 					ToOutAnything(0,S_massesSpeeds,2,sortie);
 				}
 		}
-		else if (auxtype == S_massesPos) // get mass positions
+		else if (auxtype == S_massesPos) 		// get mass positions
 		{
 			if (auxarg == 0) // No
 			{
@@ -559,7 +564,7 @@ protected:
 				}
 			}
 		}
-		else if (auxtype == S_massesForces)			 // get mass forces
+		else if (auxtype == S_massesForces)		// get mass forces
 		{
 			if (auxarg == 0) // No
 			{
@@ -589,7 +594,7 @@ protected:
 				}
 			}
 		}
-		else if (auxtype == S_linksPos)			 // get links positions
+		else if (auxtype == S_linksPos)			// get links positions
 		{
 			if (auxarg == 0) // No
 			{
@@ -623,7 +628,7 @@ protected:
 				}
 			}
 		}
-		else 			 // get mass speeds
+		else 			 			// get mass speeds
 		{
 			if (auxarg == 0) // No
 			{
@@ -671,7 +676,7 @@ protected:
 	}
 
 	void m_force_dumpl()
-	// List of masses positions on first outlet
+	// List of masses forces on first outlet
 	{	
 		t_atom sortie[2*nb_mass];
 		t_int i;
@@ -684,7 +689,7 @@ protected:
 	}
 
 	void m_info_dumpl()
-	// List of masses positions on first outlet
+	// List of infos on masses and links on  first outlet
 	{	
 		t_atom sortie[7];
 		t_int i;
@@ -713,6 +718,7 @@ protected:
 	}
 
 // --------------------------------------------------------------  GLOBAL VARIABLES 
+// --------------------------------------------------------------------------------
 
 	t_link * link[nb_max_link];

 	t_mass * mass[nb_max_mass];
@@ -720,9 +726,11 @@ protected:
 	int nb_link, nb_mass, id_mass, id_link;
 
 // --------------------------------------------------------------  SETUP
+// ---------------------------------------------------------------------
 
 private:
 
+	// static symbols
 	const static t_symbol *S_Reset;
 	const static t_symbol *S_Mass;
 	const static t_symbol *S_Link;
diff --git a/msd3D/filet.pd b/msd3D/filet.pd
index 3a4575b..ccc5fc5 100644
--- a/msd3D/filet.pd
+++ b/msd3D/filet.pd
@@ -20,9 +20,7 @@
 #X obj 330 218 + 1;
 #X obj 381 153 - 1;
 #X obj 387 340 moses;
-#X obj 46 257 * \$3;
 #X obj 46 280 + \$1;
-#X obj 176 256 * \$4;
 #X obj 176 278 + \$2;
 #X obj 46 234 mod \$6;
 #X obj 176 234 div \$6;
@@ -43,11 +41,13 @@
 #X obj 441 390 f;
 #X obj 473 395 + \$6;
 #X obj 521 313 - 1;
-#X msg 54 359 mass filet 1 80 \$1 \$2 50;
+#X msg 54 359 mass filet 1 80 \$1 \$2 0;
+#X obj 46 257 * \$3;
+#X obj 176 256 * \$4;
 #X connect 1 0 5 0;
-#X connect 1 0 43 0;
+#X connect 1 0 41 0;
 #X connect 2 0 5 1;
-#X connect 2 0 28 0;
+#X connect 2 0 26 0;
 #X connect 3 0 6 0;
 #X connect 4 0 7 0;
 #X connect 5 0 4 1;
@@ -60,47 +60,47 @@
 #X connect 8 0 10 0;
 #X connect 9 0 7 1;
 #X connect 9 0 17 1;
-#X connect 10 0 25 0;
-#X connect 10 1 26 0;
-#X connect 11 0 44 0;
+#X connect 10 0 23 0;
+#X connect 10 1 24 0;
+#X connect 11 0 42 0;
 #X connect 12 0 15 0;
 #X connect 13 0 9 0;
-#X connect 13 0 33 0;
+#X connect 13 0 31 0;
 #X connect 14 0 13 0;
 #X connect 15 0 16 0;
 #X connect 15 1 4 0;
 #X connect 16 0 17 0;
 #X connect 17 0 18 0;
 #X connect 18 0 17 1;
-#X connect 18 0 37 0;
+#X connect 18 0 35 0;
 #X connect 19 0 16 1;
-#X connect 20 0 34 0;
-#X connect 21 0 22 0;
-#X connect 22 0 11 0;
-#X connect 23 0 24 0;
-#X connect 24 0 11 1;
-#X connect 25 0 21 0;
-#X connect 26 0 23 0;
-#X connect 28 0 20 1;
-#X connect 29 0 20 0;
-#X connect 30 0 38 0;
-#X connect 31 0 32 1;
-#X connect 32 0 36 0;
-#X connect 33 0 1 0;
-#X connect 33 1 2 0;
-#X connect 34 0 35 0;
-#X connect 35 0 32 0;
-#X connect 36 0 0 0;
-#X connect 37 0 29 0;
-#X connect 37 1 31 0;
-#X connect 37 1 35 1;
-#X connect 37 2 30 0;
-#X connect 37 3 42 0;
-#X connect 37 3 41 1;
-#X connect 38 0 40 0;
-#X connect 39 0 36 0;
-#X connect 40 0 41 0;
-#X connect 41 0 39 0;
-#X connect 42 0 39 1;
-#X connect 43 0 38 1;
-#X connect 44 0 0 0;
+#X connect 20 0 32 0;
+#X connect 21 0 11 0;
+#X connect 22 0 11 1;
+#X connect 23 0 43 0;
+#X connect 24 0 44 0;
+#X connect 26 0 20 1;
+#X connect 27 0 20 0;
+#X connect 28 0 36 0;
+#X connect 29 0 30 1;
+#X connect 30 0 34 0;
+#X connect 31 0 1 0;
+#X connect 31 1 2 0;
+#X connect 32 0 33 0;
+#X connect 33 0 30 0;
+#X connect 34 0 0 0;
+#X connect 35 0 27 0;
+#X connect 35 1 29 0;
+#X connect 35 1 33 1;
+#X connect 35 2 28 0;
+#X connect 35 3 40 0;
+#X connect 35 3 39 1;
+#X connect 36 0 38 0;
+#X connect 37 0 34 0;
+#X connect 38 0 39 0;
+#X connect 39 0 37 0;
+#X connect 40 0 37 1;
+#X connect 41 0 36 1;
+#X connect 42 0 0 0;
+#X connect 43 0 21 0;
+#X connect 44 0 22 0;
diff --git a/msd3D/help-msd3D.pd b/msd3D/help-msd3D.pd
index aa1d899..14fd769 100644
--- a/msd3D/help-msd3D.pd
+++ b/msd3D/help-msd3D.pd
@@ -1,83 +1,176 @@
-#N canvas 0 0 743 844 10;
-#X obj 17 9 cnv 15 610 305 empty empty CREATION 20 12 0 14 -262131
+#N canvas 0 0 467 396 10;
+#N canvas 271 52 742 843 masses 0;
+#X obj 62 154 cnv 15 610 180 empty empty CREATION 20 12 0 14 -262131
 -66577 0;
-#X msg 34 38 reset;
-#X text 204 69 Add a mass;
-#X text 290 70 \$1 : Id (symbol);
-#X text 289 90 \$2 : fixed or mobile (0/1);
-#X text 289 108 \$3 : mass;
-#X text 289 146 \$1 : Id (symbol);
-#X text 201 146 Add a link;
-#X text 288 166 \$2 : creation No of mass1;
-#X text 288 184 \$3 : creation No of mass2;
-#X text 287 202 \$4 : rigidity;
-#X text 206 39 Delete all masses and links;
-#X text 287 220 \$5 : viscosity;
-#X text 287 237 \$6 : damping;
-#X obj 17 319 cnv 15 610 60 empty empty COMPUTATION 20 12 0 14 -261689
+#X msg 79 183 reset;
+#X text 249 214 Add a mass;
+#X text 335 215 \$1 : Id (symbol);
+#X text 334 235 \$2 : fixed or mobile (0/1);
+#X text 334 253 \$3 : mass;
+#X text 251 184 Delete all masses and links;
+#X obj 62 338 cnv 15 610 60 empty empty COMPUTATION 20 12 0 14 -261689
 -66577 0;
-#X msg 37 348 bang;
-#X text 190 348 Compute new masses positions;
-#X obj 16 383 cnv 15 610 220 empty empty DYNAMIC_SETTING 20 12 0 14
+#X msg 82 367 bang;
+#X text 235 367 Compute new masses positions;
+#X obj 61 403 cnv 15 610 210 empty empty DYNAMIC_SETTING 20 12 0 14
 -262131 -66577 0;
-#X msg 124 405 setD \$1 \$2;
-#X text 309 423 \$1 : Id (symbol);
-#X text 309 441 \$2 : New value;
-#X msg 42 405 setK \$1 \$2;
-#X text 305 477 \$1 : Id (symbol);
-#X text 305 495 \$2 : New value;
-#X text 353 532 \$1 : Id (symbol);
-#X text 353 550 \$2 : New value;
-#X msg 42 457 posX \$1 \$2;
-#X text 305 459 Set position of mass(es);
-#X text 352 515 Add force on mass(es);
-#X msg 40 516 forceX \$1 \$2;
-#X msg 210 405 setD2 \$1 \$2;
-#X text 309 405 Set rigidity \, viscosity or damping of link(s);
-#X obj 15 612 cnv 15 610 198 empty empty GET_ATTRIBUTES 20 12 0 14
+#X text 350 449 \$1 : Id (symbol);
+#X text 350 467 \$2 : New value;
+#X text 348 503 \$1 : Id (symbol);
+#X text 348 521 \$2 : New value;
+#X msg 87 429 posX \$1 \$2;
+#X text 350 431 Set position of mass(es);
+#X text 347 486 Add force on mass(es);
+#X msg 82 480 forceX \$1 \$2;
+#X obj 61 617 cnv 15 610 198 empty empty GET_ATTRIBUTES 20 12 0 14
 -261689 -66577 0;
-#X msg 101 639 massePosL;
-#X msg 101 667 masseForcesL;
-#X text 202 639 output all masses positions in a list on outlet No
+#X msg 147 644 massePosL;
+#X msg 147 672 masseForcesL;
+#X text 248 644 output all masses positions in a list on outlet No
 1;
-#X text 201 668 output all masses forces in a list on outlet No 1;
-#X msg 100 705 get \$1 \$2;
-#X text 203 706 Get specific attribute;
-#X text 203 731 \$1 : Attribute type ( massesPos / massesSpeeds / massesForces
+#X text 247 673 output all masses forces in a list on outlet No 1;
+#X msg 146 710 get \$1 \$2;
+#X text 249 711 Get specific attribute;
+#X text 249 736 \$1 : Attribute type ( massesPos / massesSpeeds / massesForces
 / linksPos );
-#X text 203 768 \$2 : Id (symbol or creations numbers);
-#X msg 31 146 link \$1 \$2 \$3 \$4 \$5 \$6;
-#X msg 30 253 deleteMass \$1;
-#X text 195 255 Delete a mass and associated links;
-#X text 285 272 \$1 : Creation No of mass;
-#X msg 29 289 deleteLink \$1;
-#X text 194 291 Delete a link;
-#X text 295 291 \$1 : Creation No of link;
-#X msg 98 788 infosL;
-#X text 201 788 Get infos on all masses and links on outlet No 2;
-#X text 302 588 \$1 : Value;
-#X msg 135 515 forceY \$1 \$2;
-#X msg 123 457 posY \$1 \$2;
-#X msg 39 568 Xmin \$1 \, Xmax \$1 \, Ymin \$1 \, Ymax \$1;
-#X text 302 571 Set minimimum and maximum of masses positions;
-#X msg 34 69 mass \$1 \$2 \$3 \$4 \$5 \$6;
-#X text 289 126 \$4 \, \$5 \, \$6 : position;
-#X msg 123 457 posY \$1 \$2;
-#X msg 204 457 posZ \$1 \$2;
-#X msg 229 515 forceZ \$1 \$2;
-#X obj -12 816 msd3D;
-#X msg 39 586 Zmin \$1 \, Zmax \$1;
-#X connect 1 0 60 0;
-#X connect 15 0 60 0;
-#X connect 21 0 60 0;
-#X connect 26 0 60 0;
-#X connect 29 0 60 0;
-#X connect 33 0 60 0;
-#X connect 34 0 60 0;
-#X connect 37 0 60 0;
-#X connect 41 0 60 0;
-#X connect 42 0 60 0;
-#X connect 45 0 60 0;
-#X connect 48 0 60 0;
-#X connect 53 0 60 0;
-#X connect 55 0 60 0;
+#X text 249 773 \$2 : Id (symbol or creations numbers);
+#X msg 79 290 deleteMass \$1;
+#X text 248 292 Delete a mass and associated links;
+#X text 338 309 \$1 : Creation No of mass;
+#X msg 144 793 infosL;
+#X text 247 793 Get infos on all masses and links on outlet No 2;
+#X text 347 555 \$1 : Value;
+#X text 73 22 MASSES :;
+#X text 66 69 They got only one physical parameter \, the value of
+their;
+#X text 67 83 mass. They can be mobile or fixed \, in this case forces
+;
+#X text 67 54 The msd masses are the principals objects of the model.
+;
+#X text 66 97 applied on them automatically \, by links \, or manually
+\, by;
+#X text 67 112 messages \, don't do anything.;
+#X msg 81 578 setMobile \$1 \, setFixed \$1;
+#X text 345 578 Change mobile parameter;
+#X text 345 594 \$1 : Creation No of mass;
+#X msg 166 429 posY \$1 \$2;
+#X msg 174 480 forceY \$1 \$2;
+#X text 347 538 Set minimimum and maximum X \, Y of masses;
+#X msg 83 525 Xmin \$1 \, Xmax \$1 \, Ymin \$1 \, Ymax \$1;
+#X msg 79 214 mass \$1 \$2 \$3 \$4 \$5 \$6;
+#X text 334 271 \$4 \, \$5 \, \$6 : initial position;
+#X msg 246 429 posZ \$1 \$2;
+#X msg 83 503 forceZ \$1 \$2;
+#X msg 83 548 Zmin \$1 \, Zmax \$1;
+#X obj 33 821 msd3D;
+#X connect 1 0 52 0;
+#X connect 8 0 52 0;
+#X connect 15 0 52 0;
+#X connect 18 0 52 0;
+#X connect 20 0 52 0;
+#X connect 21 0 52 0;
+#X connect 24 0 52 0;
+#X connect 28 0 52 0;
+#X connect 31 0 52 0;
+#X connect 40 0 52 0;
+#X connect 46 0 52 0;
+#X connect 47 0 52 0;
+#X restore 158 305 pd masses;
+#N canvas 222 83 808 841 links 0;
+#X obj 62 250 cnv 15 610 305 empty empty CREATION 20 12 0 14 -262131
+-66577 0;
+#X msg 79 279 reset;
+#X text 338 308 \$1 : Id (symbol);
+#X text 250 308 Add a link;
+#X text 337 328 \$2 : creation No of mass1;
+#X text 337 346 \$3 : creation No of mass2;
+#X text 336 364 \$4 : rigidity;
+#X text 251 280 Delete all masses and links;
+#X text 336 382 \$5 : viscosity;
+#X text 336 399 \$6 : damping;
+#X obj 61 561 cnv 15 610 82 empty empty DYNAMIC_SETTING 20 12 0 14
+-262131 -66577 0;
+#X msg 172 583 setD \$1 \$2;
+#X text 354 601 \$1 : Id (symbol);
+#X text 354 619 \$2 : New value;
+#X msg 87 583 setK \$1 \$2;
+#X msg 255 583 setD2 \$1 \$2;
+#X text 354 583 Set rigidity \, viscosity or damping of link(s);
+#X obj 60 650 cnv 15 610 140 empty empty GET_ATTRIBUTES 20 12 0 14
+-261689 -66577 0;
+#X msg 75 679 get \$1 \$2;
+#X text 237 680 Get specific attribute;
+#X text 237 705 \$1 : Attribute type ( massesPos / massesSpeeds / massesForces
+/ linksPos );
+#X text 237 742 \$2 : Id (symbol or creations numbers);
+#X msg 78 308 link \$1 \$2 \$3 \$4 \$5 \$6;
+#X msg 74 532 deleteLink \$1;
+#X text 239 534 Delete a link;
+#X text 340 534 \$1 : Creation No of link;
+#X msg 73 762 infosL;
+#X text 236 762 Get infos on all masses and links on outlet No 2;
+#X msg 73 423 iLink \$1 \$2 \$3 \$4 \$5 \$6;
+#X text 338 308 \$1 : Id (symbol);
+#X text 250 308 Add a link;
+#X text 337 328 \$2 : creation No of mass1;
+#X text 337 346 \$3 : creation No of mass2;
+#X text 336 364 \$4 : rigidity;
+#X text 336 382 \$5 : viscosity;
+#X text 336 399 \$6 : damping;
+#X text 410 422 \$1 : Id (symbol);
+#X text 409 478 \$4 : rigidity;
+#X text 409 496 \$5 : viscosity;
+#X text 409 513 \$6 : damping;
+#X text 410 422 \$1 : Id (symbol);
+#X text 409 478 \$4 : rigidity;
+#X text 409 496 \$5 : viscosity;
+#X text 409 513 \$6 : damping;
+#X text 248 423 Add an interactor link;
+#X text 94 52 LINKS :;
+#X text 71 91 parameters : length \, rigidity \, viscosity and damping.
+;
+#X text 72 78 Links connect masses two by two. They got 4 physicals
+;
+#X text 70 134 the two masses at the creation.;
+#X text 71 120 message. The lenght is initialised to the distance between
+;
+#X text 71 106 Rigidity \, viscosity and damping are defined by the
+creation;
+#X text 409 442 \$2 : Id (symbol) of masses type 1;
+#X text 409 460 \$3 : Id (symbol) of masses type 2;
+#X text 70 148 Interactor links are links between mutiples masses \,
+instead;
+#X text 70 161 of creation number \, the masses linked are defined
+with;
+#X text 69 175 their Id.;
+#X obj 33 821 msd3D;
+#X connect 1 0 56 0;
+#X connect 14 0 56 0;
+#X connect 18 0 56 0;
+#X connect 22 0 56 0;
+#X connect 23 0 56 0;
+#X connect 26 0 56 0;
+#X connect 28 0 56 0;
+#X restore 160 335 pd links;
+#X text 12 305 HELP on masses --->;
+#X text 11 336 HELP on links --->;
+#X text -50 110 There are 4 types of messages for msd :;
+#X text -49 74 It is designed to implement particules physical model
+in PD.The model is based on two elements type : mass and link.;
+#X obj -50 125 cnv 15 420 30 empty empty empty 20 12 0 14 -262131 -66577
+0;
+#X obj -50 158 cnv 15 420 30 empty empty empty 20 12 0 14 -261689 -66577
+0;
+#X obj -50 191 cnv 15 420 30 empty empty empty 20 12 0 14 -262131 -66577
+0;
+#X obj -50 224 cnv 15 420 30 empty empty empty 20 12 0 14 -261689 -66577
+0;
+#X text -47 132 CREATION : To create the model masses and links.;
+#X text -47 197 DYNAMIC SETTING : To set the model parameters dynamically.
+;
+#X text -47 230 ATTRIBUTES : To get the model parameters.;
+#X text -47 159 COMPUTATION : To compute the new model state based
+on previous instant.;
+#X text 32 16 MSD3D : mass - spring - damper model;
+#X text -48 61 MSD3D is the 3D object of the msd objects collection.
+;
diff --git a/msd3D/main.cpp b/msd3D/main.cpp
index a8cc727..428a86b 100755
--- a/msd3D/main.cpp
+++ b/msd3D/main.cpp
@@ -106,7 +106,7 @@ public:
 protected:
 
 // ---------------------------------------------------------------  RESET 
-
+// ----------------------------------------------------------------------
 	void m_reset() 
 	{ 
 		t_int i;
@@ -126,7 +126,7 @@ protected:
 	}
 
 // --------------------------------------------------------------  COMPUTE 
-
+// -----------------------------------------------------------------------
 	void m_bang()
 	{
 		t_float F=0,Fx=0,Fy=0, Fz=0,distance,vitesse, X_new, Y_new, Z_new;

@@ -135,44 +135,44 @@ protected:
 	
 		for (i=0; i<nb_link; i++)	{

 		// compute link forces
-			distance = sqrt(pow(link[i]->mass1->posX-link[i]->mass2->posX,2) + 
-				pow(link[i]->mass1->posY-link[i]->mass2->posY,2) + pow(link[i]->mass1->posZ-link[i]->mass2->posZ,2));
-			F  = link[i]->K1 * (distance - link[i]->longueur) ;	// F = k1(x1-x2)
-			F += link[i]->D1 * (distance - link[i]->distance_old) ;	// F = F + D1(v1-v2)
+			distance = sqrt(pow(link[i]->mass1->posX-link[i]->mass2->posX,2) + pow(link[i]->mass1->posY
+				-link[i]->mass2->posY,2) + pow(link[i]->mass1->posZ-link[i]->mass2->posZ,2));	// L[n]
+			F  = link[i]->K1 * (distance - link[i]->longueur) ;			// F = K1(L[n] - L[0])
+			F += link[i]->D1 * (distance - link[i]->distance_old) ;			// F = F + D1(L[n] - L[n-1])
 			if (distance != 0) 	{
-				Fx = F * (link[i]->mass1->posX - link[i]->mass2->posX)/distance;
-				Fy = F * (link[i]->mass1->posY - link[i]->mass2->posY)/distance;
-				Fz = F * (link[i]->mass1->posZ - link[i]->mass2->posZ)/distance;
+				Fx = F * (link[i]->mass1->posX - link[i]->mass2->posX)/distance;	// Fx[n] = F * Lx[n]/L[n]
+				Fy = F * (link[i]->mass1->posY - link[i]->mass2->posY)/distance;	// Fy[n] = F * Ly[n]/L[n]
+				Fz = F * (link[i]->mass1->posZ - link[i]->mass2->posZ)/distance;	// Fy[n] = F * Lz[n]/L[n]
 			}

-			link[i]->mass1->forceX -= Fx;
-			link[i]->mass1->forceX -= link[i]->D2*link[i]->mass1->speedX;

-			link[i]->mass2->forceX += Fx;
-			link[i]->mass2->forceX -= link[i]->D2*link[i]->mass2->speedX;
-			link[i]->mass1->forceY -= Fy;
-			link[i]->mass1->forceY -= link[i]->D2*link[i]->mass1->speedY;

-			link[i]->mass2->forceY += Fy;
-			link[i]->mass2->forceY -= link[i]->D2*link[i]->mass2->speedY;
-			link[i]->mass1->forceZ -= Fz;
-			link[i]->mass1->forceZ -= link[i]->D2*link[i]->mass1->speedZ;

-			link[i]->mass2->forceZ += Fz;
-			link[i]->mass2->forceZ -= link[i]->D2*link[i]->mass2->speedZ;
-			link[i]->distance_old = distance;
+			link[i]->mass1->forceX -= Fx;					// Fx1[n] = -Fx
+			link[i]->mass1->forceX -= link[i]->D2*link[i]->mass1->speedX;	// Fx1[n] = Fx1[n] - D2 * vx1[n-1]

+			link[i]->mass2->forceX += Fx;					// Fx2[n] = Fx
+			link[i]->mass2->forceX -= link[i]->D2*link[i]->mass2->speedX;	// Fx2[n] = Fx2[n] - D2 * vx2[n-1]
+			link[i]->mass1->forceY -= Fy;					// Fy1[n] = -Fy
+			link[i]->mass1->forceY -= link[i]->D2*link[i]->mass1->speedY;	// Fy1[n] = Fy1[n] - D2 * vy1[n-1]

+			link[i]->mass2->forceY += Fy;					// Fy2[n] = Fy
+			link[i]->mass2->forceY -= link[i]->D2*link[i]->mass2->speedY;	// Fy2[n] = Fy2[n] - D2 * vy2[n-1]
+			link[i]->mass1->forceZ -= Fz;					// Fz1[n] = -Fz
+			link[i]->mass1->forceZ -= link[i]->D2*link[i]->mass1->speedZ;	// Fz1[n] = Fz1[n] - D2 * vz1[n-1]

+			link[i]->mass2->forceZ += Fz;					// Fz2[n] = Fz
+			link[i]->mass2->forceZ -= link[i]->D2*link[i]->mass2->speedZ;	// Fz2[n] = Fz2[n] - D2 * vz2[n-1]
+			link[i]->distance_old = distance;				// L[n-1] = L[n]
 		}
 

 		for (i=0; i<nb_mass; i++)

 		// compute new masses position only if mobile = 1

 			if (mass[i]->mobile == 1)  		{

-				X_new = mass[i]->forceX * mass[i]->invM + 2*mass[i]->posX - mass[i]->posX2;
-				mass[i]->posX2 = mass[i]->posX;
-				mass[i]->posX = max(min(X_new,Xmax),Xmin);			
+				X_new = mass[i]->forceX * mass[i]->invM + 2*mass[i]->posX - mass[i]->posX2; // x[n] =Fx[n]/M+2x[n]-x[n-1]
+				mass[i]->posX2 = mass[i]->posX;				// x[n-2] = x[n-1]
+				mass[i]->posX = max(min(X_new,Xmax),Xmin);		// x[n-1] = x[n]	
 				mass[i]->speedX = mass[i]->posX - mass[i]->posX2;	// vx[n] = x[n] - x[n-1]
-				Y_new = mass[i]->forceY * mass[i]->invM + 2*mass[i]->posY - mass[i]->posY2;
-				mass[i]->posY2 = mass[i]->posY;
-				mass[i]->posY = max(min(Y_new,Ymax),Ymin);			
+				Y_new = mass[i]->forceY * mass[i]->invM + 2*mass[i]->posY - mass[i]->posY2; // y[n] =Fy[n]/M+2y[n]-y[n-1]
+				mass[i]->posY2 = mass[i]->posY;				// y[n-2] = y[n-1]
+				mass[i]->posY = max(min(Y_new,Ymax),Ymin);		// y[n-1] = y[n]	
 				mass[i]->speedY = mass[i]->posY - mass[i]->posY2;	// vy[n] = y[n] - y[n-1]
-				Z_new = mass[i]->forceZ * mass[i]->invM + 2*mass[i]->posZ - mass[i]->posZ2;
-				mass[i]->posZ2 = mass[i]->posZ;
-				mass[i]->posZ = max(min(Z_new,Zmax),Zmin);			
+				Z_new = mass[i]->forceZ * mass[i]->invM + 2*mass[i]->posZ - mass[i]->posZ2; // x[n] =Fx[n]/M+2x[n]-x[n-1]
+				mass[i]->posZ2 = mass[i]->posZ;				// z[n-2] = z[n-1]
+				mass[i]->posZ = max(min(Z_new,Zmax),Zmin);		// z[n-1] = z[n]	
 				mass[i]->speedZ = mass[i]->posZ - mass[i]->posZ2;	// vz[n] = z[n] - z[n-1]
 				}
 
@@ -188,7 +188,7 @@ protected:
 	}
 
 // --------------------------------------------------------------  MASSES
-
+// ----------------------------------------------------------------------
 	void m_mass(int argc,t_atom *argv) 

 	// add a mass

 	// Id, nbr, mobile, invM, speedX, posX, forceX

@@ -196,26 +196,26 @@ protected:
 		t_atom sortie[7], aux[2];
 		t_float M;
 
-		mass[nb_mass] = new t_mass;			// new pointer

-		mass[nb_mass]->Id = GetSymbol(argv[0]);	// Id
+		mass[nb_mass] = new t_mass;			// new mass

+		mass[nb_mass]->Id = GetSymbol(argv[0]);		// Id
 		mass[nb_mass]->mobile = GetInt(argv[1]);	// mobile
 		if (GetFloat(argv[2])==0)
 			M=1;
 		else M = GetFloat(argv[2]);			
-		mass[nb_mass]->invM = 1/(M);		// invM
+		mass[nb_mass]->invM = 1/(M);			// 1/M
 		mass[nb_mass]->speedX = 0;			// vx[n]

-		mass[nb_mass]->posX = GetFloat(argv[3]);		// x(n]
+		mass[nb_mass]->posX = GetFloat(argv[3]);	// x[n]
 		mass[nb_mass]->posX2 = GetFloat(argv[3]);	// x[n-1]

 		mass[nb_mass]->forceX = 0;			// Fx[n]
 		mass[nb_mass]->speedY = 0;			// vy[n]

-		mass[nb_mass]->posY = GetFloat(argv[4]);		// y[n]
+		mass[nb_mass]->posY = GetFloat(argv[4]);	// y[n]
 		mass[nb_mass]->posY2 = GetFloat(argv[4]);	// y[n-1]

 		mass[nb_mass]->forceY = 0;			// Fz[n]
 		mass[nb_mass]->speedZ = 0;			// vz[n]

-		mass[nb_mass]->posZ = GetFloat(argv[5]);		// z[n]
+		mass[nb_mass]->posZ = GetFloat(argv[5]);	// z[n]
 		mass[nb_mass]->posZ2 = GetFloat(argv[5]);	// z[n-1]

 		mass[nb_mass]->forceZ = 0;			// Fz[n]
-		mass[nb_mass]->nbr = id_mass;			// id_nbr
+		mass[nb_mass]->nbr = id_mass;			// id number
 		nb_mass++ ;
 		id_mass++;

 		nb_mass = min ( nb_max_mass -1, nb_mass );
@@ -346,6 +346,7 @@ protected:
 	t_int i,nb_link_delete=0;
 	t_atom sortie[7], aux[nb_link];
 	
+	// Delete associated links
 	for (i=0; i<nb_link;i++)	{
 		if (link[i]->mass1->nbr == GetInt(argv[0]) || link[i]->mass2->nbr == GetInt(argv[0]))	{
 			SetFloat((aux[nb_link_delete]),link[i]->nbr);
@@ -356,7 +357,7 @@ protected:
 	for (i=0; i<nb_link_delete;i++)
 		m_delete_link(1,&aux[i]);
 
-
+	// Delete mass
 	for (i=0; i<nb_mass;i++)
 		if (mass[i]->nbr == GetInt(argv[0]))	{
 			SetFloat((sortie[0]),mass[i]->nbr);
@@ -367,7 +368,7 @@ protected:
 			SetFloat((sortie[5]),mass[i]->posY);
 			SetFloat((sortie[6]),mass[i]->posZ);
 			delete mass[i];
-			mass[i] = mass[nb_mass-1];
+			mass[i] = mass[nb_mass-1];	// copy last mass indeed
 			nb_mass--;
 			ToOutAnything(1,S_Mass_deleted,7,sortie);
 			break;
@@ -410,8 +411,9 @@ protected:
 	// set minimum Z of all masses
 	Zmin = GetFloat(argv[0]);
 	}
-// --------------------------------------------------------------  LINKS 
 
+// --------------------------------------------------------------  LINKS 
+// ---------------------------------------------------------------------
 	void m_link(int argc,t_atom *argv) 
 	// add a link

 	// Id, nbr, *mass1, *mass2, K1, D1

@@ -419,21 +421,21 @@ protected:
 		t_atom sortie[7], aux[2];
 		t_int i;
 
-		link[nb_link] = new t_link;
-		link[nb_link]->Id = GetSymbol(argv[0]);
+		link[nb_link] = new t_link;			// new link
+		link[nb_link]->Id = GetSymbol(argv[0]);		// ID
 		for (i=0; i<nb_mass;i++)
-			if (mass[i]->nbr==GetInt(argv[1]))
+			if (mass[i]->nbr==GetInt(argv[1]))	// pointer on mass 1
 				link[nb_link]->mass1 = mass[i];
-			else if(mass[i]->nbr==GetInt(argv[2]))
+			else if(mass[i]->nbr==GetInt(argv[2]))	// pointer on mass 2
 				link[nb_link]->mass2 = mass[i];
-		link[nb_link]->K1 = GetFloat(argv[3]);

-		link[nb_link]->D1 = GetFloat(argv[4]);
-		link[nb_link]->D2 = GetFloat(argv[5]);
-		link[nb_link]->longx = link[nb_link]->mass1->posX - link[nb_link]->mass2->posX;
-		link[nb_link]->longy = link[nb_link]->mass1->posY - link[nb_link]->mass2->posY;
-		link[nb_link]->longz = link[nb_link]->mass1->posZ - link[nb_link]->mass2->posZ;
+		link[nb_link]->K1 = GetFloat(argv[3]);		// K1

+		link[nb_link]->D1 = GetFloat(argv[4]);		// D1
+		link[nb_link]->D2 = GetFloat(argv[5]);		// D2
+		link[nb_link]->longx = link[nb_link]->mass1->posX - link[nb_link]->mass2->posX;		// Lx[0]
+		link[nb_link]->longy = link[nb_link]->mass1->posY - link[nb_link]->mass2->posY;		// Ly[0]
+		link[nb_link]->longz = link[nb_link]->mass1->posZ - link[nb_link]->mass2->posZ;		// Lz[0]
 		link[nb_link]->longueur = sqrt( pow(link[nb_link]->longx,2) + pow(link[nb_link]->longy,2) + pow(link[nb_link]->longz,2));
-		link[nb_link]->nbr = id_link;
+		link[nb_link]->nbr = id_link;			// id number
 		link[nb_link]->distance_old = link[nb_link]->longueur;
 		nb_link++;
 		id_link++;

@@ -500,7 +502,7 @@ protected:
 
 	void m_setD(int argc,t_atom *argv) 
 	{

-	// set damping of link(s) named Id
+	// set viscosity of link(s) named Id
 		t_int i;
 		const t_symbol *sym = GetSymbol(argv[0]);
 
@@ -540,16 +542,15 @@ protected:
 			SetFloat((sortie[5]),link[i]->D1);
 			SetFloat((sortie[6]),link[i]->D2);
 			delete link[i];
-			link[i]=link[nb_link-1];
+			link[i]=link[nb_link-1];	// copy last link 
 			nb_link--;
 			ToOutAnything(1,S_Link_deleted,7,sortie);
 			break;
 		}
 	}
 
-
 // --------------------------------------------------------------  GET 
-
+// -------------------------------------------------------------------
 	void m_get(int argc,t_atom *argv)
 	// get attributes
 	{
@@ -794,16 +795,17 @@ protected:
 	}
 
 // --------------------------------------------------------------  GLOBAL VARIABLES 
-
+// --------------------------------------------------------------------------------
 	t_link * link[nb_max_link];

 	t_mass * mass[nb_max_mass];
 	t_float Xmin, Xmax, Ymin, Ymax, Zmin, Zmax;
 	int nb_link, nb_mass, id_mass, id_link;
 
 // --------------------------------------------------------------  SETUP
-
+// ---------------------------------------------------------------------
 private:
 
+	// static symbols
 	const static t_symbol *S_Reset;
 	const static t_symbol *S_Mass;
 	const static t_symbol *S_Link;