replace alpha1 by phi2_1 and alpha_1 by phi12 in 2D Algorithms

Apps/Examples/Tests/test_compact.cpp

@@ -103,7 +103,7 @@ void test_compact_map(const std::string& name)
 			do						// mark all edges incident to vertex;
 			{
 				dm.markOrbit( EDGE, e);
-				e = myMap.alpha1(e);
+				e = myMap.phi2_1(e);
 			}while (e!=d);
 		}
 		i++;

include/Algo/BooleanOperator/mergeVertices.hpp

@@ -38,17 +38,17 @@ void mergeVertex(typename PFP::MAP& map, const typename PFP::TVEC3& positions, D
 	Dart dd;
 	do
 	{
-		dd = map.alpha1(d);
+		dd = map.phi2_1(d);
 		map.removeEdgeFromVertex(dd);
 		Dart ee = e;
 		do
 		{
 			if(Geom::testOrientation2D(positions[map.phi1(dd)],positions[ee],positions[map.phi1(ee)])!=Geom::RIGHT
-					&& Geom::testOrientation2D(positions[map.phi1(dd)],positions[ee],positions[map.phi1(map.alpha1(ee))])==Geom::RIGHT)
+					&& Geom::testOrientation2D(positions[map.phi1(dd)],positions[ee],positions[map.phi1(map.phi2_1(ee))])==Geom::RIGHT)
 			{
 				break;
 			}
-			ee = map.alpha1(ee);
+			ee = map.phi2_1(ee);
 		} while(ee != e);
 		map.insertEdgeInVertex(ee,dd);
 	} while(dd!=d);

include/Algo/Decimation/basic.h

@@ -56,18 +56,18 @@ bool edgeCanCollapse(typename PFP::MAP& map, Dart d, AttributeHandler<unsigned i
 	unsigned int vu1[32]; // pas de vector mais un tableau (find a la main, mais pas d'allocation par reserve)
 	val_vd -= 3; // evite le -3 dans la boucle
 	val_vdd -= 3;
-	Dart vit1 = map.alpha1(map.alpha1(d));
+	Dart vit1 = map.phi2_1(map.phi2_1(d));
 
 	for (unsigned int i = 0; i< val_vd; ++i)
 	{
 		unsigned int ve = map.getEmbedding(map.phi2(vit1),VERTEX);
 		vu1[i] = ve;
-		vit1 = map.alpha1(vit1);
+		vit1 = map.phi2_1(vit1);
 	}
 
 	val_vd--; // pour le parcours avec while >=0
 
-	Dart vit2 = map.alpha1(map.alpha1(dd));
+	Dart vit2 = map.phi2_1(map.phi2_1(dd));
 	for (unsigned int i = 0; i< val_vdd; ++i)
 	{
 		unsigned int ve = map.getEmbedding(map.phi2(vit2),VERTEX);
@@ -79,7 +79,7 @@ bool edgeCanCollapse(typename PFP::MAP& map, Dart d, AttributeHandler<unsigned i
 				return false;
 			--j;
 		}
-		vit2 = map.alpha1(vit2);
+		vit2 = map.phi2_1(vit2);
 	}
 
 	return true;
@@ -96,16 +96,16 @@ bool edgeCanCollapse(typename PFP::MAP& map, Dart d)
 
 	int val_vd = 0 ;
 	Dart tmp = d ;
-	do { ++val_vd ;	tmp = map.alpha1(tmp) ; } while(tmp != d) ;
+	do { ++val_vd ;	tmp = map.phi2_1(tmp) ; } while(tmp != d) ;
 	int val_vdd = 0 ;
 	tmp = dd ;
-	do { ++val_vdd ; tmp = map.alpha1(tmp) ; } while(tmp != dd) ;
+	do { ++val_vdd ; tmp = map.phi2_1(tmp) ; } while(tmp != dd) ;
 	int val_vdp = 0 ;
 	tmp = dp ;
-	do { ++val_vdp ; tmp = map.alpha1(tmp) ; } while(tmp != dp) ;
+	do { ++val_vdp ; tmp = map.phi2_1(tmp) ; } while(tmp != dp) ;
 	int val_vddp = 0 ;
 	tmp = ddp ;
-	do { ++val_vddp ; tmp = map.alpha1(tmp) ; } while(tmp != ddp) ;
+	do { ++val_vddp ; tmp = map.phi2_1(tmp) ; } while(tmp != ddp) ;
 
 	if(val_vd + val_vdd < 8 || val_vd + val_vdd > 11 || val_vdp < 5 || val_vddp < 5)
 		return false;
@@ -115,18 +115,18 @@ bool edgeCanCollapse(typename PFP::MAP& map, Dart d)
 	unsigned int vu1[32]; // pas de vector mais un tableau (find a la main, mais pas d'allocation par reserve)
 	val_vd -= 3; // evite le -3 dans la boucle
 	val_vdd -= 3;
-	Dart vit1 = map.alpha1(map.alpha1(d));
+	Dart vit1 = map.phi2_1(map.phi2_1(d));
 
 	for (int i = 0; i < val_vd; ++i)
 	{
 		unsigned int ve = map.getEmbedding(map.phi2(vit1),VERTEX);
 		vu1[i] = ve;
-		vit1 = map.alpha1(vit1);
+		vit1 = map.phi2_1(vit1);
 	}
 
 	val_vd--; // pour le parcours avec while >=0
 
-	Dart vit2 = map.alpha1(map.alpha1(dd));
+	Dart vit2 = map.phi2_1(map.phi2_1(dd));
 	for (int i = 0; i < val_vdd; ++i)
 	{
 		unsigned int ve = map.getEmbedding(map.phi2(vit2),VERTEX);
@@ -138,7 +138,7 @@ bool edgeCanCollapse(typename PFP::MAP& map, Dart d)
 				return false;
 			--j;
 		}
-		vit2 = map.alpha1(vit2);
+		vit2 = map.phi2_1(vit2);
 	}
 
 	return true;

include/Algo/Decimation/edgeSelector.hpp

@@ -204,19 +204,19 @@ void EdgeSelector_Length<PFP>::updateAfterCollapse(Dart d2, Dart dd2)
 		{
 			initEdgeInfo(vit) ;							// various optimizations are applied here by
 														// treating differently :
-			Dart vit2 = m.alpha_1(m.phi1(vit)) ;		// - edges for which the criteria must be recomputed
+			Dart vit2 = m.phi12(m.phi1(vit)) ;		// - edges for which the criteria must be recomputed
 			Dart stop = m.phi2(vit) ;					// - edges that must be re-embedded
 			do											// - edges for which only the collapsibility must be re-tested
 			{
 				updateEdgeInfo(vit2, false) ;
 				updateEdgeInfo(m.phi1(vit2), false) ;
-				vit2 = m.alpha_1(vit2) ;
+				vit2 = m.phi12(vit2) ;
 			} while(vit2 != stop) ;
 		}
 		else
 			updateEdgeInfo(vit, true) ;
 
-		vit = m.alpha1(vit) ;
+		vit = m.phi2_1(vit) ;
 	} while(vit != d2) ;
 
 	cur = edges.begin() ; // set the current edge to the first one
@@ -399,19 +399,19 @@ void EdgeSelector_QEM<PFP>::updateAfterCollapse(Dart d2, Dart dd2)
 		{
 			initEdgeInfo(vit) ;							// various optimizations are applied here by
 														// treating differently :
-			Dart vit2 = m.alpha_1(m.phi1(vit)) ;		// - edges for which the criteria must be recomputed
+			Dart vit2 = m.phi12(m.phi1(vit)) ;		// - edges for which the criteria must be recomputed
 			Dart stop = m.phi2(vit) ;					// - edges that must be re-embedded
 			do											// - edges for which only the collapsibility must be re-tested
 			{
 				updateEdgeInfo(vit2, false) ;
 				updateEdgeInfo(m.phi1(vit2), false) ;
-				vit2 = m.alpha_1(vit2) ;
+				vit2 = m.phi12(vit2) ;
 			} while(vit2 != stop) ;
 		}
 		else
 			updateEdgeInfo(vit, true) ;
 
-		vit = m.alpha1(vit) ;
+		vit = m.phi2_1(vit) ;
 	} while(vit != d2) ;
 
 	cur = edges.begin() ; // set the current edge to the first one
@@ -604,7 +604,7 @@ void EdgeSelector_QEMml<PFP>::recomputeQuadric(const Dart d, const bool recomput
    	do {
    		// Make step
    		dBack = this->m_map.phi2(dFront) ;
-       	dFront = this->m_map.alpha1(dFront) ;
+       	dFront = this->m_map.phi2_1(dFront) ;
 
        	if (dBack != dFront) { // if dFront is no border
            	quadric[d] += Quadric<REAL>(this->m_position[d],this->m_position[this->m_map.phi2(dFront)],this->m_position[dBack]) ;
@@ -633,16 +633,16 @@ void EdgeSelector_QEMml<PFP>::updateAfterCollapse(Dart d2, Dart dd2)
 		else										// treating differently :
 			updateEdgeInfo(vit, true) ;
 
-		Dart vit2 = m.alpha_1(m.phi1(vit)) ;		// - edges for which the criteria must be recomputed
+		Dart vit2 = m.phi12(m.phi1(vit)) ;		// - edges for which the criteria must be recomputed
 		Dart stop = m.phi2(vit) ;					// - edges that must be re-embedded
 		do											// - edges for which only the collapsibility must be re-tested
 		{
 			updateEdgeInfo(vit2, true) ;
 			updateEdgeInfo(m.phi1(vit2), false) ;
-			vit2 = m.alpha_1(vit2) ;
+			vit2 = m.phi12(vit2) ;
 		} while(vit2 != stop) ;
 
-		vit = m.alpha1(vit) ;
+		vit = m.phi2_1(vit) ;
 	} while(vit != d2) ;
 
 	cur = edges.begin() ; // set the current edge to the first one
@@ -809,19 +809,19 @@ void EdgeSelector_Curvature<PFP>::updateAfterCollapse(Dart d2, Dart dd2)
 		{
 			initEdgeInfo(vit) ;							// various optimizations are applied here by
 														// treating differently :
-			Dart vit2 = m.alpha_1(m.phi1(vit)) ;		// - edges for which the criteria must be recomputed
+			Dart vit2 = m.phi12(m.phi1(vit)) ;		// - edges for which the criteria must be recomputed
 			Dart stop = m.phi2(vit) ;					// - edges that must be re-embedded
 			do											// - edges for which only the collapsibility must be re-tested
 			{
 				updateEdgeInfo(vit2, false) ;
 				updateEdgeInfo(m.phi1(vit2), false) ;
-				vit2 = m.alpha_1(vit2) ;
+				vit2 = m.phi12(vit2) ;
 			} while(vit2 != stop) ;
 		}
 		else
 			updateEdgeInfo(vit, true) ;
 
-		vit = m.alpha1(vit) ;
+		vit = m.phi2_1(vit) ;
 	} while(vit != d2) ;
 
 	cur = edges.begin() ; // set the current edge to the first one
@@ -1013,19 +1013,19 @@ void EdgeSelector_MinDetail<PFP>::updateAfterCollapse(Dart d2, Dart dd2)
 		{
 			initEdgeInfo(vit) ;							// various optimizations are applied here by
 														// treating differently :
-			Dart vit2 = m.alpha_1(m.phi1(vit)) ;		// - edges for which the criteria must be recomputed
+			Dart vit2 = m.phi12(m.phi1(vit)) ;		// - edges for which the criteria must be recomputed
 			Dart stop = m.phi2(vit) ;					// - edges that must be re-embedded
 			do											// - edges for which only the collapsibility must be re-tested
 			{
 				updateEdgeInfo(vit2, false) ;
 				updateEdgeInfo(m.phi1(vit2), false) ;
-				vit2 = m.alpha_1(vit2) ;
+				vit2 = m.phi12(vit2) ;
 			} while(vit2 != stop) ;
 		}
 		else
 			updateEdgeInfo(vit, true) ;
 
-		vit = m.alpha1(vit) ;
+		vit = m.phi2_1(vit) ;
 	} while(vit != d2) ;
 
 	cur = edges.begin() ; // set the current edge to the first one

include/Algo/Decimation/geometryApproximator.hpp

@@ -64,7 +64,7 @@ void Approximator_QEM<PFP>::approximate(Dart d)
 		{
 			Quadric<REAL> q(this->m_attrV[it], this->m_attrV[m.phi1(it)], this->m_attrV[m.phi_1(it)]) ;
 			q1 += q ;
-			it = m.alpha1(it) ;
+			it = m.phi2_1(it) ;
 		} while(it != d) ;
 
 		// compute the error quadric associated to v2
@@ -73,7 +73,7 @@ void Approximator_QEM<PFP>::approximate(Dart d)
 		{
 			Quadric<REAL> q(this->m_attrV[it], this->m_attrV[m.phi1(it)], this->m_attrV[m.phi_1(it)]) ;
 			q2 += q ;
-			it = m.alpha1(it) ;
+			it = m.phi2_1(it) ;
 		} while(it != dd) ;
 	}
 	else // if the selector is QEM, use the error quadrics computed by the selector
@@ -138,7 +138,7 @@ void Approximator_QEMhalfEdge<PFP>::approximate(Dart d)
 		{
 			Quadric<REAL> q(this->m_attrV[it], this->m_attrV[m.phi1(it)], this->m_attrV[m.phi_1(it)]) ;
 			q1 += q ;
-			it = m.alpha1(it) ;
+			it = m.phi2_1(it) ;
 		} while(it != d) ;
 
 		// compute the error quadric associated to v2
@@ -147,7 +147,7 @@ void Approximator_QEMhalfEdge<PFP>::approximate(Dart d)
 		{
 			Quadric<REAL> q(this->m_attrV[it], this->m_attrV[m.phi1(it)], this->m_attrV[m.phi_1(it)]) ;
 			q2 += q ;
-			it = m.alpha1(it) ;
+			it = m.phi2_1(it) ;
 		} while(it != dd) ;
 	}
 	else // if the selector is QEM, use the error quadrics computed by the selector
@@ -312,14 +312,14 @@ void Approximator_CornerCutting<PFP>::approximate(Dart d)
 	do
 	{
 		++k1 ;
-		it = m.alpha1(it) ;
+		it = m.phi2_1(it) ;
 	} while(it != d) ;
 	REAL k2 = 0 ;
 	it = dd ;
 	do
 	{
 		++k2 ;
-		it = m.alpha1(it) ;
+		it = m.phi2_1(it) ;
 	} while(it != dd) ;
 	REAL alpha = (k1-1) * (k2-1) / (k1*k2-1) ;
 
@@ -330,7 +330,7 @@ void Approximator_CornerCutting<PFP>::approximate(Dart d)
 	do
 	{
 		m1 += this->m_attrV[m.phi1(it)] ;
-		it = m.alpha1(it) ;
+		it = m.phi2_1(it) ;
 		++count ;
 	} while (it != d) ;
 	m1 /= REAL(count) ;
@@ -342,7 +342,7 @@ void Approximator_CornerCutting<PFP>::approximate(Dart d)
 	do
 	{
 		m2 += this->m_attrV[m.phi1(it)] ;
-		it = m.alpha1(it) ;
+		it = m.phi2_1(it) ;
 		++count ;
 	} while (it != dd) ;
 	m2 /= REAL(count) ;

include/Algo/Decimation/geometryPredictor.hpp

@@ -51,7 +51,7 @@ void Predictor_HalfCollapse<PFP>::predict(Dart d2, Dart dd2)
 	Dart it = dd2 ;
 	do {
 		s2_1 += this->m_attrV[m.phi1(it)] ;
-		it = m.alpha1(it) ;
+		it = m.phi2_1(it) ;
 		++k2 ;
 	} while (m.phi2(it) != m.phi_1(d2)) ;
 
@@ -84,12 +84,12 @@ typename PFP::REAL Predictor_CornerCutting<PFP>::autoAlpha(Dart d2, Dart dd2)
 	do
 	{
 		++k1 ;
-		it = m.alpha1(it) ;
+		it = m.phi2_1(it) ;
 	} while(it != dd2) ;
 	do
 	{
 		++k2 ;
-		it = m.alpha1(it) ;
+		it = m.phi2_1(it) ;
 	} while(it != d2) ;
 	return (k1-1) * (k2-1) / (k1*k2-1) ;
 }
@@ -116,7 +116,7 @@ void Predictor_CornerCutting<PFP>::predict(Dart d2, Dart dd2)
 	Dart it = d2 ;
 	do {
 		m1 += this->m_attrV[m.phi1(it)] ;
-		it = m.alpha1(it) ;
+		it = m.phi2_1(it) ;
 		++count ;
 	} while (m.phi2(it) != m.phi_1(dd2)) ;
 	m1 /= REAL(count) ;
@@ -130,7 +130,7 @@ void Predictor_CornerCutting<PFP>::predict(Dart d2, Dart dd2)
 	it = dd2 ;
 	do {
 		m2 += this->m_attrV[m.phi1(it)] ;
-		it = m.alpha1(it) ;
+		it = m.phi2_1(it) ;
 		++count ;
 	} while (m.phi2(it) != m.phi_1(d2)) ;
 	m2 /= REAL(count) ;
@@ -155,7 +155,7 @@ void Predictor_TangentPredict1<PFP>::predictedTangent(Dart d2, Dart dd2, VEC3& d
 	Dart it = d2 ;
 	do {
 		s1_1 += this->m_attrV[m.phi1(it)] ;
-		it = m.alpha1(it) ;
+		it = m.phi2_1(it) ;
 		++k1 ;
 	} while (m.phi2(it) != m.phi_1(dd2)) ;
 
@@ -163,7 +163,7 @@ void Predictor_TangentPredict1<PFP>::predictedTangent(Dart d2, Dart dd2, VEC3& d
 	it = dd2 ;
 	do {
 		s2_1 += this->m_attrV[m.phi1(it)] ;
-		it = m.alpha1(it) ;
+		it = m.phi2_1(it) ;
 		++k2 ;
 	} while (m.phi2(it) != m.phi_1(d2)) ;
 
@@ -210,7 +210,7 @@ void Predictor_TangentPredict2<PFP>::predictedTangent(Dart d2, Dart dd2, VEC3& d
 	Dart it = d2 ;
 	do {
 		s1_1 += this->m_attrV[m.phi1(it)] ;
-		it = m.alpha1(it) ;
+		it = m.phi2_1(it) ;
 		++k1 ;
 	} while (m.phi2(it) != m.phi_1(dd2)) ;
 
@@ -221,7 +221,7 @@ void Predictor_TangentPredict2<PFP>::predictedTangent(Dart d2, Dart dd2, VEC3& d
 		Dart p2 = m.phi2(p1) ;
 		if(p2 != p1)
 			s1_2 += this->m_attrV[m.phi_1(p2)] ;
-		it = m.alpha1(it) ;
+		it = m.phi2_1(it) ;
 	} while (it != dd2) ;
 	s1_2 += this->m_attrV[m.phi_1(d1)] ;
 	s1_2 += this->m_attrV[m.phi_1(dd2)] ;
@@ -230,7 +230,7 @@ void Predictor_TangentPredict2<PFP>::predictedTangent(Dart d2, Dart dd2, VEC3& d
 	it = dd2 ;
 	do {
 		s2_1 += this->m_attrV[m.phi2(it)] ;
-		it = m.alpha1(it) ;
+		it = m.phi2_1(it) ;
 		++k2 ;
 	} while (m.phi2(it) != m.phi_1(d2)) ;
 
@@ -241,7 +241,7 @@ void Predictor_TangentPredict2<PFP>::predictedTangent(Dart d2, Dart dd2, VEC3& d
 		Dart p2 = m.phi2(p1) ;
 		if(p2 != p1)
 			s2_2 += this->m_attrV[m.phi_1(p2)] ;
-		it = m.alpha1(it) ;
+		it = m.phi2_1(it) ;
 	} while (it != d2) ;
 	s2_2 += this->m_attrV[m.phi_1(dd1)] ;
 	s2_2 += this->m_attrV[m.phi_1(d2)] ;

include/Algo/Decimation/halfEdgeSelector.hpp

@@ -161,7 +161,7 @@ void HalfEdgeSelector_QEMml<PFP>::recomputeQuadric(const Dart d, const bool reco
    	do {
    		// Make step
    		dBack = this->m_map.phi1(dFront) ;
-       	dFront = this->m_map.alpha1(dFront) ;
+       	dFront = this->m_map.phi2_1(dFront) ;
 
        	if (this->m_map.phi2(dFront) != dFront) { // if dFront is no border
            	quadric[d] += Quadric<REAL>(this->m_position[d],this->m_position[dBack],this->m_position[this->m_map.phi1(dFront)]) ;
@@ -195,7 +195,7 @@ void HalfEdgeSelector_QEMml<PFP>::updateAfterCollapse(Dart d2, Dart dd2)
 
 		Dart stop = m.phi2(vit) ;
 		assert (stop != vit) ;
-		Dart vit2 = m.alpha_1(m.phi1(vit)) ;
+		Dart vit2 = m.phi12(m.phi1(vit)) ;
 		do {
 			updateHalfEdgeInfo(vit2, true) ;
 			d = m.phi2(vit2) ;
@@ -207,9 +207,9 @@ void HalfEdgeSelector_QEMml<PFP>::updateAfterCollapse(Dart d2, Dart dd2)
 			if (d != m.phi1(vit2)) ;
 				updateHalfEdgeInfo(d, false) ;
 
-			vit2 = m.alpha_1(vit2) ;
+			vit2 = m.phi12(vit2) ;
 		} while (stop != vit2) ;
-		vit = m.alpha1(vit) ;
+		vit = m.phi2_1(vit) ;
 	} while(vit != d2) ;
 
 	cur = halfEdges.begin() ; // set the current edge to the first one
@@ -418,7 +418,7 @@ void HalfEdgeSelector_Lightfield<PFP>::recomputeQuadric(const Dart d, const bool
    	do {
    		// Make step
    		dBack = this->m_map.phi1(dFront) ;
-       	dFront = this->m_map.alpha1(dFront) ;
+       	dFront = this->m_map.phi2_1(dFront) ;
 
        	if (dBack != dFront) { // if dFront is no border
            	quadric[d] += Quadric<REAL>(this->m_position[d],this->m_position[this->m_map.phi1(dFront)],this->m_position[dBack]) ;
@@ -451,7 +451,7 @@ void HalfEdgeSelector_Lightfield<PFP>::updateAfterCollapse(Dart d2, Dart dd2)
 
 		Dart stop = m.phi2(vit) ;
 		assert (stop != vit) ;
-		Dart vit2 = m.alpha_1(m.phi1(vit)) ;
+		Dart vit2 = m.phi12(m.phi1(vit)) ;
 		do {
 			updateHalfEdgeInfo(vit2, true) ;
 			d = m.phi2(vit2) ;
@@ -463,9 +463,9 @@ void HalfEdgeSelector_Lightfield<PFP>::updateAfterCollapse(Dart d2, Dart dd2)
 			if (d != m.phi1(vit2)) ;
 				updateHalfEdgeInfo(d, false) ;
 
-			vit2 = m.alpha_1(vit2) ;
+			vit2 = m.phi12(vit2) ;
 		} while (stop != vit2) ;
-		vit = m.alpha1(vit) ;
+		vit = m.phi2_1(vit) ;
 	} while(vit != d2) ;
 
 
@@ -694,19 +694,19 @@ void EdgeSelector_Lightfield<PFP>::updateAfterCollapse(Dart d2, Dart dd2)
 		{
 			initEdgeInfo(vit) ;							// various optimizations are applied here by
 														// treating differently :
-			Dart vit2 = m.alpha_1(m.phi1(vit)) ;		// - edges for which the criteria must be recomputed
+			Dart vit2 = m.phi12(m.phi1(vit)) ;		// - edges for which the criteria must be recomputed
 			Dart stop = m.phi2(vit) ;					// - edges that must be re-embedded
 			do											// - edges for which only the collapsibility must be re-tested
 			{
 				updateEdgeInfo(vit2, false) ;
 				updateEdgeInfo(m.phi1(vit2), false) ;
-				vit2 = m.alpha_1(vit2) ;
+				vit2 = m.phi12(vit2) ;
 			} while(vit2 != stop) ;
 		}
 		else
 			updateEdgeInfo(vit, true) ;
 
-		vit = m.alpha1(vit) ;
+		vit = m.phi2_1(vit) ;
 	} while(vit != d2) ;
 
 	cur = edges.begin() ; // set the current edge to the first one

include/Algo/Decimation/lightfieldApproximator.hpp

@@ -108,16 +108,16 @@ void Approximator_RGBfunctionsHalf<PFP>::approximate(Dart d)
 //	REAL gamma1 = ((j1 * i) > 0 ? 1 : -1) * acos( std::max(std::min(1.0f, i1 * i ), -1.0f)) ; // angle positif ssi
 	REAL gamma2 = ((j2 * i) > 0 ? 1 : -1) * acos( std::max(std::min(1.0f, i2 * i ), -1.0f)) ; // -PI/2 < angle(i,j1) < PI/2  ssi i*j1 > 0
 	// Rotation dans le sens trigo autour de l'axe i (n1->n)
-//	REAL alpha1 = ((n * j1pr) > 0 ? -1 : 1) * acos( std::max(std::min(1.0f, n * n1), -1.0f) ) ; // angle positif ssi
+//	REAL phi2_1 = ((n * j1pr) > 0 ? -1 : 1) * acos( std::max(std::min(1.0f, n * n1), -1.0f) ) ; // angle positif ssi
 	REAL alpha2 = ((n * j2pr) > 0 ? -1 : 1) * acos( std::max(std::min(1.0f, n * n2), -1.0f) ) ; // PI/2 < angle(j1',n) < -PI/2 ssi j1'*n < 0
 
 //	assert (-0.01 < gamma1 && gamma1 < 0.01) ;
-//	assert (-0.01 < alpha1 && alpha1 < 0.01) ;
+//	assert (-0.01 < phi2_1 && phi2_1 < 0.01) ;
 	REAL gamma1 = REAL(0) ;
-	REAL alpha1 = REAL(0) ;
+	REAL phi2_1 = REAL(0) ;
 
 	// Create and sum quadrics
-	m_quadricRGBfunctions[d] += QuadricRGBfunctions<REAL>(this->m_attrV[d], gamma1, alpha1) ;
+	m_quadricRGBfunctions[d] += QuadricRGBfunctions<REAL>(this->m_attrV[d], gamma1, phi2_1) ;
 	m_quadricRGBfunctions[d] += QuadricRGBfunctions<REAL>(this->m_attrV[dd], gamma2, alpha2) ;
 }
 
@@ -246,12 +246,12 @@ void Approximator_RGBfunctions<PFP>::approximate(Dart d)
 	REAL gamma1 = ((j1 * i) > 0 ? 1 : -1) * acos( std::max(std::min(1.0f, i1 * i ), -1.0f)) ; // angle positif ssi
 	REAL gamma2 = ((j2 * i) > 0 ? 1 : -1) * acos( std::max(std::min(1.0f, i2 * i ), -1.0f)) ; // -PI/2 < angle(i,j1) < PI/2  ssi i*j1 > 0
 	// Rotation dans le sens trigo autour de l'axe i (n1->n)
-	REAL alpha1 = ((n * j1pr) > 0 ? -1 : 1) * acos( std::max(std::min(1.0f, n * n1), -1.0f) ) ; // angle positif ssi
+	REAL phi2_1 = ((n * j1pr) > 0 ? -1 : 1) * acos( std::max(std::min(1.0f, n * n1), -1.0f) ) ; // angle positif ssi
 	REAL alpha2 = ((n * j2pr) > 0 ? -1 : 1) * acos( std::max(std::min(1.0f, n * n2), -1.0f) ) ; // PI/2 < angle(j1',n) < -PI/2 ssi j1'*n < 0
 
 //	assert (-3.15 < gamma1 && gamma1 <= 3.15) ;
 //	assert (-3.15 < gamma2 && gamma2 <= 3.15) ;
-//	assert (-3.15 < alpha1 && alpha1 <= 3.15) ;
+//	assert (-3.15 < phi2_1 && phi2_1 <= 3.15) ;
 //	assert (-3.15 < alpha2 && alpha2 <= 3.15) ;
 
 //	MATRIX36 &f1 = this->m_attrV[d] ;
@@ -259,7 +259,7 @@ void Approximator_RGBfunctions<PFP>::approximate(Dart d)
 
 	// Create and sum quadrics
 	m_quadricRGBfunctions[d].zero() ;
-	m_quadricRGBfunctions[d] += QuadricRGBfunctions<REAL>(this->m_attrV[d], gamma1, alpha1) ;
+	m_quadricRGBfunctions[d] += QuadricRGBfunctions<REAL>(this->m_attrV[d], gamma1, phi2_1) ;
 	m_quadricRGBfunctions[d] += QuadricRGBfunctions<REAL>(this->m_attrV[dd], gamma2, alpha2) ;
 
 	// Compute new function

include/Algo/Decimation/simplifMesh.hpp

@@ -181,7 +181,7 @@ void SimplifTrian<PFP>::updateCriterias(Dart d)
 		m_protectMarker.mark(em) ;
 
 		// next edge
-		d = m_map.alpha1(d);
+		d = m_map.phi2_1(d);
 	} while (d!=dd);
 }
 
@@ -212,15 +212,15 @@ Dart SimplifTrian<PFP>::edgeCollapse(Dart d, typename PFP::VEC3& newPos)
 	{
 		CRIT* cr = getCrit(xd);
 		cr->tagDirty();
-		xd = m_map.alpha1(xd);
+		xd = m_map.phi2_1(xd);
 	} while (xd != d);
 
-	xd = m_map.alpha1(dd); // alpha1 pour ne pas repasser sur l'arete d/dd
+	xd = m_map.phi2_1(dd); // phi2_1 pour ne pas repasser sur l'arete d/dd
 	do
 	{
 		CRIT* cr = getCrit(xd);
 		cr->tagDirty();
-		xd = m_map.alpha1(xd);
+		xd = m_map.phi2_1(xd);
 	} while (xd != dd);
 
 	// store old valences

include/Algo/Geometry/stats.h

@@ -125,7 +125,7 @@ void statModele(typename PFP::MAP& map, const typename PFP::TVEC3& position)
 //			do
 //			{
 //				nbEdgePerVertex++ ;
-//				e = map.alpha1(e) ;
+//				e = map.phi2_1(e) ;
 //			}
 //			while (e != d) ;
 //		}

include/Algo/Import/importSvg.hpp

@@ -518,7 +518,7 @@ bool importSVG(typename PFP::MAP& map, const std::string& filename, typename PFP
 
 			//if the valence of one of the vertex is equal to one
 			//cut the edge to insert the quadrangular face
-			if(map.alpha1(d1)==d1)
+			if(map.phi2_1(d1)==d1)
 			{
 				map.cutEdge(d2);
 
@@ -530,7 +530,7 @@ bool importSVG(typename PFP::MAP& map, const std::string& filename, typename PFP
 				edgePlanes[map.phi_1(d1)] = Geom::Plane3D<typename PFP::REAL>(v,p1);
 			}
 
-			if(map.alpha1(d2)==d2)
+			if(map.phi2_1(d2)==d2)
 			{
 				map.cutEdge(d1);
 				brokenL.mark(map.phi1(d1));

include/Algo/LinearSolving/matrixSetup.h

@@ -327,7 +327,7 @@ public:
 			REAL aij = edgeWeight[it] / vArea ;
 			aii += aij ;
 			solver->add_coefficient(indexTable[this->m_map.phi1(it)], aij) ;
-			it = this->m_map.alpha1(it) ;
+			it = this->m_map.phi2_1(it) ;
 		} while(it != d) ;
 		solver->add_coefficient(indexTable[d], -aii) ;
 		solver->normalize_row() ;

include/Algo/Modelisation/extrusion.hpp

@@ -287,7 +287,7 @@ Dart extrudeFace(typename PFP::MAP& the_map, typename PFP::TVEC3& positions, Dar
 	do
 	{
 		the_map.cutEdge(cc);
-		cc = the_map.alpha1(cc);
+		cc = the_map.phi2_1(cc);
 	}while (cc != c);
 
 	// cut faces
@@ -296,7 +296,7 @@ Dart extrudeFace(typename PFP::MAP& the_map, typename PFP::TVEC3& positions, Dar
 		Dart d1 = the_map.phi1(cc);
 		Dart d2 = the_map.phi_1(cc);
 		the_map.splitFace(d1,d2);
-		cc = the_map.alpha1(cc);
+		cc = the_map.phi2_1(cc);
 	}while (cc != c);
 
 	// delete the central vertex

include/Algo/Modelisation/subdivision.hpp

@@ -73,7 +73,7 @@ void trianguleFaces(typename PFP::MAP& map, EMBV& attributs, const FunctorSelect
 		do
 		{
 			t.mark(fit);
-			fit = map.alpha1(fit);
+			fit = map.phi2_1(fit);
 		} while(fit != cd);
 	}
 }
@@ -102,7 +102,7 @@ void trianguleFaces(
 		do
 		{
 			t.mark(fit);
-			fit = map.alpha1(fit);
+			fit = map.phi2_1(fit);
 		} while(fit != cd);
 	}
 }
@@ -163,7 +163,7 @@ void quadranguleFaces(typename PFP::MAP& map, EMBV& attributs, const FunctorSele
 			do
 			{
 				mf.markOrbit(FACE, e);
-				e = map.alpha1(e);
+				e = map.phi2_1(e);
 			} while (e != cf);
 		}
 	}
@@ -286,7 +286,7 @@ void CatmullClarkSubdivision(typename PFP::MAP& map, EMBV& attributs, const Func
 			temp2 += attributs[v];
 
 			++n;
-			x = map.alpha1(x);
+			x = map.phi2_1(x);
 		} while (x != *vert);
 
 		EMB emcp = attributs[*vert];
@@ -403,7 +403,7 @@ void LoopSubdivision(typename PFP::MAP& map, EMBV& attributs, const FunctorSelec
 			Dart y = map.phi1(map.phi1(x));
 			temp += attributs[y];
 			++n;
-			x = map.alpha1(x);
+			x = map.phi2_1(x);
 		} while ((x != *vert));
 		EMB emcp = attributs[*vert];
 		if (n == 6)
@@ -548,7 +548,7 @@ void computeDual(typename PFP::MAP& map, const FunctorSelect& selected)
 
 	for(Dart d = map.begin(); d != map.end(); map.next(d))
 	{
-		Dart dd = map.alpha_1(d) ;
+		Dart dd = map.phi12(d) ;
 		new_phi1[d] = dd ;
 		new_phi_1[dd] = d ;
 	}
@@ -621,7 +621,7 @@ void Sqrt3Subdivision(typename PFP::MAP& map, typename PFP::TVEC3& position, con
 			{
 				newP += position[map.phi2(vit)] ;
 				++val ;
-				vit = map.alpha1(vit) ;
+				vit = map.phi2_1(vit) ;
 			} while(vit != d) ;
 			REAL K = sqrt3_K(val) ;
 			newP *= REAL(3) ;

include/Algo/MovingObjects/particle_cell_2D.hpp

@@ -75,24 +75,24 @@ void ParticleCell2D<PFP>::vertexState(const VEC3& current)
 	{
 		//orientation step
 		if(m_positions[d][0] == m_positions[m.phi1(d)][0] && m_positions[d][1] == m_positions[m.phi1(d)][1])
-			d = m.alpha1(d);
-		if(getOrientationEdge(current,m.alpha1(d)) != Geom::RIGHT)
+			d = m.phi2_1(d);
+		if(getOrientationEdge(current,m.phi2_1(d)) != Geom::RIGHT)
 		{
 			Dart dd_vert = d;
 			do
 			{
-				d = m.alpha1(d);
+				d = m.phi2_1(d);
 				if(m_positions[d][0] == m_positions[m.phi1(d)][0] && m_positions[d][1] == m_positions[m.phi1(d)][1])