generic laplacian computation + cotangent weights

include/Algo/Geometry/area.hpp

@@ -103,7 +103,7 @@ typename PFP::REAL vertexVoronoiArea(typename PFP::MAP& map, Dart d, const typen
 	Dart it = d ;
 	do
 	{
-		area += convexFaceArea<PFP>(map, it, position) ;
+		area += convexFaceArea<PFP>(map, it, position) / 3 ;
 		it = map.alpha1(it) ;
 	} while(it != d) ;
 	return area ;

include/Algo/Geometry/laplacian.h

@@ -40,34 +40,34 @@ namespace Algo
 namespace Geometry
 {
 
-template <typename PFP>
-typename PFP::VEC3 computeLaplacianTopoVertex(
+template <typename PFP, typename ATTR_TYPE>
+ATTR_TYPE computeLaplacianTopoVertex(
 	typename PFP::MAP& map,
 	Dart d,
-	const typename PFP::TVEC3& position) ;
+	const AttributeHandler<ATTR_TYPE>& attr) ;
 
-template <typename PFP>
-typename PFP::VEC3 computeLaplacianCotanVertex(
+template <typename PFP, typename ATTR_TYPE>
+ATTR_TYPE computeLaplacianCotanVertex(
 	typename PFP::MAP& map,
 	Dart d,
-	const typename PFP::TVEC3& position,
 	const typename PFP::TREAL& edgeWeight,
-	const typename PFP::TREAL& vertexArea) ;
+	const typename PFP::TREAL& vertexArea,
+	const AttributeHandler<ATTR_TYPE>& attr) ;
 
-template <typename PFP>
+template <typename PFP, typename ATTR_TYPE>
 void computeLaplacianTopoVertices(
 	typename PFP::MAP& map,
-	const typename PFP::TVEC3& position,
-	typename PFP::TVEC3& laplacian,
+	const AttributeHandler<ATTR_TYPE>& attr,
+	AttributeHandler<ATTR_TYPE>& laplacian,
 	const FunctorSelect& select = SelectorTrue()) ;
 
-template <typename PFP>
+template <typename PFP, typename ATTR_TYPE>
 void computeLaplacianCotanVertices(
 	typename PFP::MAP& map,
-	const typename PFP::TVEC3& position,
 	const typename PFP::TREAL& edgeWeight,
 	const typename PFP::TREAL& vertexArea,
-	typename PFP::TVEC3& laplacian,
+	const AttributeHandler<ATTR_TYPE>& attr,
+	AttributeHandler<ATTR_TYPE>& laplacian,
 	const FunctorSelect& select = SelectorTrue()) ;
 
 template <typename PFP>

include/Algo/Geometry/laplacian.hpp

@@ -33,45 +33,42 @@ namespace Algo
 namespace Geometry
 {
 
-template <typename PFP>
-typename PFP::VEC3 computeLaplacianTopoVertex(
+template <typename PFP, typename ATTR_TYPE>
+ATTR_TYPE computeLaplacianTopoVertex(
 	typename PFP::MAP& map,
 	Dart d,
-	const typename PFP::TVEC3& position)
+	const AttributeHandler<ATTR_TYPE>& attr)
 {
-	typedef typename PFP::VEC3 VEC3 ;
-	VEC3 l(0) ;
+	ATTR_TYPE l(0) ;
 	unsigned int val = 0 ;
-	Dart dd = d ;
+	Dart it = d ;
 	do
 	{
-		l += vectorOutOfDart<PFP>(map, dd, position) ;
+		l += attr[map.phi1(it)] - attr[it] ;
 		val++ ;
-		dd = map.alpha1(dd) ;
-	} while(dd != d) ;
+		it = map.alpha1(it) ;
+	} while(it != d) ;
 	l /= val ;
 	return l ;
 }
 
-template <typename PFP>
-typename PFP::VEC3 computeLaplacianCotanVertex(
+template <typename PFP, typename ATTR_TYPE>
+ATTR_TYPE computeLaplacianCotanVertex(
 	typename PFP::MAP& map,
 	Dart d,
-	const typename PFP::TVEC3& position,
 	const typename PFP::TREAL& edgeWeight,
-	const typename PFP::TREAL& vertexArea)
+	const typename PFP::TREAL& vertexArea,
+	const AttributeHandler<ATTR_TYPE>& attr)
 {
-	typedef typename PFP::VEC3 VEC3 ;
 	typedef typename PFP::REAL REAL ;
-	VEC3 l(0) ;
+	ATTR_TYPE l(0) ;
 	Dart it = d ;
 	REAL vArea = vertexArea[d] ;
 	REAL val = 0 ;
 	do
 	{
 		REAL w = edgeWeight[it] / vArea ;
-		VEC3 v = vectorOutOfDart<PFP>(map, it, position) * w ;
-		l += v ;
+		l += (attr[map.phi1(it)] - attr[it]) * w ;
 		val += w ;
 		it = map.alpha1(it) ;
 	} while(it != d) ;
@@ -79,12 +76,12 @@ typename PFP::VEC3 computeLaplacianCotanVertex(
 	return l ;
 }
 
-template <typename PFP>
+template <typename PFP, typename ATTR_TYPE>
 void computeLaplacianTopoVertices(
-		typename PFP::MAP& map,
-		const typename PFP::TVEC3& position,
-		typename PFP::TVEC3& laplacian,
-		const FunctorSelect& select)
+	typename PFP::MAP& map,
+	const AttributeHandler<ATTR_TYPE>& attr,
+	AttributeHandler<ATTR_TYPE>& laplacian,
+	const FunctorSelect& select)
 {
 	CellMarker marker(map, VERTEX);
 	for(Dart d = map.begin(); d != map.end(); map.next(d))
@@ -92,19 +89,19 @@ void computeLaplacianTopoVertices(
 		if(select(d) && !marker.isMarked(d))
 		{
 			marker.mark(d);
-			laplacian[d] = computeLaplacianTopoVertex<PFP>(map, d, position) ;
+			laplacian[d] = computeLaplacianTopoVertex<PFP, ATTR_TYPE>(map, d, attr) ;
 		}
 	}
 }
 
-template <typename PFP>
+template <typename PFP, typename ATTR_TYPE>
 void computeLaplacianCotanVertices(
-		typename PFP::MAP& map,
-		const typename PFP::TVEC3& position,
-		const typename PFP::TREAL& edgeWeight,
-		const typename PFP::TREAL& vertexArea,
-		typename PFP::TVEC3& laplacian,
-		const FunctorSelect& select)
+	typename PFP::MAP& map,
+	const typename PFP::TREAL& edgeWeight,
+	const typename PFP::TREAL& vertexArea,
+	const AttributeHandler<ATTR_TYPE>& attr,
+	AttributeHandler<ATTR_TYPE>& laplacian,
+	const FunctorSelect& select)
 {
 	CellMarker marker(map, VERTEX);
 	for(Dart d = map.begin(); d != map.end(); map.next(d))
@@ -112,7 +109,7 @@ void computeLaplacianCotanVertices(
 		if(select(d) && !marker.isMarked(d))
 		{
 			marker.mark(d);
-			laplacian[d] = computeLaplacianCotanVertex<PFP>(map, d, position, edgeWeight, vertexArea) ;
+			laplacian[d] = computeLaplacianCotanVertex<PFP, ATTR_TYPE>(map, d, edgeWeight, vertexArea, attr) ;
 		}
 	}
 }

include/Algo/LinearSolving/basic.h

@@ -26,6 +26,7 @@
 #define __LINEAR_SOLVING_BASIC__
 
 #include "OpenNL/linear_solver.h"
+#include "Algo/LinearSolving/variablesSetup.h"
 #include "Algo/LinearSolving/matrixSetup.h"
 
 namespace CGoGN
@@ -34,112 +35,9 @@ namespace CGoGN
 namespace LinearSolving
 {
 
-template <typename PFP, typename ATTR_TYPE, class SOLVER_TRAITS>
-class FunctorMeshToSolver_Scalar : public FunctorMap<typename PFP::MAP>
-{
-protected:
-	LinearSolver<SOLVER_TRAITS>* solver ;
-	CellMarker& lockingMarker ;
-	const AttributeHandler<ATTR_TYPE>& attrTable ;
-	const AttributeHandler<unsigned int>& indexTable ;
-	bool lockedVertices ;
-
-public:
-	typedef typename PFP::MAP MAP ;
-	
-	FunctorMeshToSolver_Scalar(MAP& m, LinearSolver<SOLVER_TRAITS>* s, CellMarker& lm, const AttributeHandler<ATTR_TYPE>& attr, const AttributeHandler<unsigned int> index) :
-		FunctorMap<MAP>(m), solver(s), lockingMarker(lm), attrTable(attr), indexTable(index), lockedVertices(false)
-	{}
-
-	bool operator()(Dart d)
-	{
-		solver->variable(indexTable[d]).set_value(attrTable[d]) ;
-		if(lockingMarker.isMarked(d))
-		{
-			solver->variable(indexTable[d]).lock() ;
-			lockedVertices = true ;
-		}
-		return false ;
-	}
-	bool hasLockedVertices() { return lockedVertices ; }
-} ;
-
-template <typename PFP, typename ATTR_TYPE, class SOLVER_TRAITS>
-class FunctorMeshToSolver_Vector : public FunctorMap<typename PFP::MAP>
-{
-protected:
-	LinearSolver<SOLVER_TRAITS>* solver ;
-	CellMarker& lockingMarker ;
-	const AttributeHandler<ATTR_TYPE>& attrTable ;
-	const AttributeHandler<unsigned int>& indexTable ;
-	unsigned int coord ;
-	bool lockedVertices ;
-
-public:
-	typedef typename PFP::MAP MAP ;
-	
-	FunctorMeshToSolver_Vector(MAP& m, LinearSolver<SOLVER_TRAITS>* s, CellMarker& lm, const AttributeHandler<ATTR_TYPE>& attr, unsigned int c, const AttributeHandler<unsigned int> index) :
-		FunctorMap<MAP>(m), solver(s), lockingMarker(lm), attrTable(attr), indexTable(index), coord(c), lockedVertices(false)
-	{}
-
-	bool operator()(Dart d)
-	{
-		solver->variable(indexTable[d]).set_value((attrTable[d])[coord]) ;
-		if(lockingMarker.isMarked(d))
-		{
-			solver->variable(indexTable[d]).lock() ;
-			lockedVertices = true ;
-		}
-		return false ;
-	}
-	bool hasLockedVertices() { return lockedVertices ; }
-} ;
-
-template <typename PFP, typename ATTR_TYPE, class SOLVER_TRAITS>
-class FunctorSolverToMesh_Scalar : public FunctorMap<typename PFP::MAP>
-{
-protected:
-	LinearSolver<SOLVER_TRAITS>* solver ;
-	AttributeHandler<ATTR_TYPE>& attrTable ;
-	const AttributeHandler<unsigned int>& indexTable ;
-
-public:
-	typedef typename PFP::MAP MAP ;
-	
-	FunctorSolverToMesh_Scalar(MAP& m, LinearSolver<SOLVER_TRAITS>* s, AttributeHandler<ATTR_TYPE>& attr, const AttributeHandler<unsigned int> index) :
-		FunctorMap<MAP>(m), solver(s), attrTable(attr), indexTable(index)
-	{}
-
-	bool operator()(Dart d)
-	{
-		attrTable[d] = solver->variable(indexTable[d]).value() ;
-		return false ;
-	}
-} ;
-
-template <typename PFP, typename ATTR_TYPE, class SOLVER_TRAITS>
-class FunctorSolverToMesh_Vector : public FunctorMap<typename PFP::MAP>
-{
-protected:
-	LinearSolver<SOLVER_TRAITS>* solver ;
-	AttributeHandler<ATTR_TYPE>& attrTable ;
-	const AttributeHandler<unsigned int>& indexTable ;
-	unsigned int coord ;
-
-public:
-	typedef typename PFP::MAP MAP ;
-
-	FunctorSolverToMesh_Vector(MAP& m, LinearSolver<SOLVER_TRAITS>* s, AttributeHandler<ATTR_TYPE>& attr, unsigned int c, const AttributeHandler<unsigned int> index) :
-		FunctorMap<MAP>(m), solver(s), attrTable(attr), indexTable(index), coord(c)
-	{}
-
-	bool operator()(Dart d)
-	{
-		(attrTable[d])[coord] = solver->variable(indexTable[d]).value() ;
-		return false ;
-	}
-} ;
-
+/*******************************************************************************
+ * SOLVER INIT
+ *******************************************************************************/
 
 template <class SOLVER_TRAITS>
 void initSolver(LinearSolver<SOLVER_TRAITS>* s, unsigned int nb_variables, bool least_squares, bool direct)
@@ -159,81 +57,208 @@ void initSolver(LinearSolver<SOLVER_TRAITS>* s, unsigned int nb_variables, bool
 	s->set_direct(direct) ;
 }
 
+/*******************************************************************************
+ * VARIABLES SETUP
+ *******************************************************************************/
+
 template <typename PFP, typename ATTR_TYPE, class SOLVER_TRAITS>
-void setupVariables(typename PFP::MAP& m, LinearSolver<SOLVER_TRAITS>* s, CellMarker& lm, const AttributeHandler<ATTR_TYPE>& attr, const AttributeHandler<unsigned int> index)
+void setupVariables(
+	typename PFP::MAP& m,
+	LinearSolver<SOLVER_TRAITS>* s,
+	const AttributeHandler<unsigned int> index,
+	CellMarker& lm,
+	const AttributeHandler<ATTR_TYPE>& attr)
 {
-	FunctorMeshToSolver_Scalar<PFP, ATTR_TYPE, SOLVER_TRAITS> fmts(m, s, lm, attr, index) ;
+	FunctorMeshToSolver_Scalar<PFP, ATTR_TYPE, SOLVER_TRAITS> fmts(s, index, lm, attr) ;
 	m.foreach_orbit(VERTEX, fmts) ;
 }
 
 template <typename PFP, typename ATTR_TYPE, class SOLVER_TRAITS>
-void setupVariables(typename PFP::MAP& m, LinearSolver<SOLVER_TRAITS>* s, CellMarker& lm, const AttributeHandler<ATTR_TYPE>& attr, unsigned int coord, const AttributeHandler<unsigned int> index)
+void setupVariables(
+	typename PFP::MAP& m,
+	LinearSolver<SOLVER_TRAITS>* s,
+	const AttributeHandler<unsigned int> index,
+	CellMarker& lm,
+	const AttributeHandler<ATTR_TYPE>& attr,
+	unsigned int coord)
 {
-	FunctorMeshToSolver_Vector<PFP, ATTR_TYPE, SOLVER_TRAITS> fmts(m, s, lm, attr, coord, index) ;
+	FunctorMeshToSolver_Vector<PFP, ATTR_TYPE, SOLVER_TRAITS> fmts(s, index, lm, attr, coord) ;
 	m.foreach_orbit(VERTEX, fmts) ;
 }
 
+/*******************************************************************************
+ * START MATRIX DEFINITION
+ *******************************************************************************/
+
 template <class SOLVER_TRAITS>
 void startMatrix(LinearSolver<SOLVER_TRAITS>* s)
 {
 	s->begin_system() ;
 }
 
+/*******************************************************************************
+ * MATRIX SETUP : EQUALITY
+ *******************************************************************************/
+
+template <typename PFP, typename ATTR_TYPE, class SOLVER_TRAITS>
+void addRowsRHS_Equality(
+	typename PFP::MAP& m,
+	LinearSolver<SOLVER_TRAITS>* s,
+	const AttributeHandler<unsigned int> index,
+	const AttributeHandler<ATTR_TYPE>& attr,
+	float amount)
+{
+	FunctorEquality_Scalar<PFP, ATTR_TYPE, SOLVER_TRAITS> ec(s, index, attr, amount) ;
+	m.foreach_orbit(VERTEX, ec) ;
+}
+
+template <typename PFP, typename ATTR_TYPE, class SOLVER_TRAITS>
+void addRowsRHS_Equality(
+	typename PFP::MAP& m,
+	LinearSolver<SOLVER_TRAITS>* s,
+	const AttributeHandler<unsigned int> index,
+	const AttributeHandler<ATTR_TYPE>& attr,
+	float amount,
+	unsigned int coord)
+{
+	FunctorEquality_Vector<PFP, ATTR_TYPE, SOLVER_TRAITS> ec(s, index, attr, amount, coord) ;
+	m.foreach_orbit(VERTEX, ec) ;
+}
+
+/*******************************************************************************
+ * MATRIX SETUP : LAPLACIAN TOPO
+ *******************************************************************************/
+
 template <typename PFP, class SOLVER_TRAITS>
-void addRows_Laplacian_Topo(typename PFP::MAP& m, LinearSolver<SOLVER_TRAITS>* s, const AttributeHandler<unsigned int> index)
+void addRows_Laplacian_Topo(
+	typename PFP::MAP& m,
+	LinearSolver<SOLVER_TRAITS>* s,
+	const AttributeHandler<unsigned int> index)
+{
+	FunctorLaplacianTopo<PFP, SOLVER_TRAITS> flt(m, s, index) ;
+	m.foreach_orbit(VERTEX, flt) ;
+}
+
+template <typename PFP, typename ATTR_TYPE, class SOLVER_TRAITS>
+void addRowsRHS_Laplacian_Topo(
+	typename PFP::MAP& m,
+	LinearSolver<SOLVER_TRAITS>* s,
+	const AttributeHandler<unsigned int> index,
+	const AttributeHandler<ATTR_TYPE>& attr)
 {
-	FunctorLaplacianTopo<PFP, SOLVER_TRAITS> lt(m, s, index) ;
-	m.foreach_orbit(VERTEX, lt) ;
+	FunctorLaplacianTopoRHS_Scalar<PFP, ATTR_TYPE, SOLVER_TRAITS> flt(m, s, index, attr) ;
+	m.foreach_orbit(VERTEX, flt) ;
 }
 
+template <typename PFP, typename ATTR_TYPE, class SOLVER_TRAITS>
+void addRowsRHS_Laplacian_Topo(
+	typename PFP::MAP& m,
+	LinearSolver<SOLVER_TRAITS>* s,
+	const AttributeHandler<unsigned int> index,
+	const AttributeHandler<ATTR_TYPE>& attr,
+	unsigned int coord)
+{
+	FunctorLaplacianTopoRHS_Vector<PFP, ATTR_TYPE, SOLVER_TRAITS> flt(m, s, index, attr, coord) ;
+	m.foreach_orbit(VERTEX, flt) ;
+}
+
+/*******************************************************************************
+ * MATRIX SETUP : LAPLACIAN COTAN
+ *******************************************************************************/
+
 template <typename PFP, class SOLVER_TRAITS>
-void addRows_Laplacian_Cotan(typename PFP::MAP& m, LinearSolver<SOLVER_TRAITS>* s, const AttributeHandler<unsigned int> index, const typename PFP::TREAL& edgeWeight, const typename PFP::TREAL& vertexArea)
+void addRows_Laplacian_Cotan(
+	typename PFP::MAP& m,
+	LinearSolver<SOLVER_TRAITS>* s,
+	const AttributeHandler<unsigned int> index,
+	const typename PFP::TREAL& edgeWeight,
+	const typename PFP::TREAL& vertexArea)
 {
-	FunctorLaplacianCotan<PFP, SOLVER_TRAITS> lt(m, s, index, edgeWeight, vertexArea) ;
-	m.foreach_orbit(VERTEX, lt) ;
+	FunctorLaplacianCotan<PFP, SOLVER_TRAITS> flc(m, s, index, edgeWeight, vertexArea) ;
+	m.foreach_orbit(VERTEX, flc) ;
 }
 
 template <typename PFP, typename ATTR_TYPE, class SOLVER_TRAITS>
-void addRows_Equality(typename PFP::MAP& m, LinearSolver<SOLVER_TRAITS>* s, const AttributeHandler<ATTR_TYPE>& attr, const AttributeHandler<unsigned int> index, float amount)
+void addRowsRHS_Laplacian_Cotan(
+	typename PFP::MAP& m,
+	LinearSolver<SOLVER_TRAITS>* s,
+	const AttributeHandler<unsigned int> index,
+	const typename PFP::TREAL& edgeWeight,
+	const typename PFP::TREAL& vertexArea,
+	const AttributeHandler<ATTR_TYPE>& attr)
 {
-	setupEqualityMatrix<PFP, ATTR_TYPE, SOLVER_TRAITS>(m, s, attr, index, amount) ;
+	FunctorLaplacianCotanRHS_Scalar<PFP, ATTR_TYPE, SOLVER_TRAITS> flc(m, s, index, edgeWeight, vertexArea, attr) ;
+	m.foreach_orbit(VERTEX, flc) ;
 }
 
 template <typename PFP, typename ATTR_TYPE, class SOLVER_TRAITS>
-void addRows_Equality(typename PFP::MAP& m, LinearSolver<SOLVER_TRAITS>* s, const AttributeHandler<ATTR_TYPE>& attr, unsigned int coord, const AttributeHandler<unsigned int> index, float amount)
+void addRowsRHS_Laplacian_Cotan(
+	typename PFP::MAP& m,
+	LinearSolver<SOLVER_TRAITS>* s,
+	const AttributeHandler<unsigned int> index,
+	const typename PFP::TREAL& edgeWeight,
+	const typename PFP::TREAL& vertexArea,
+	const AttributeHandler<ATTR_TYPE>& attr,
+	unsigned int coord)
 {
-	setupEqualityMatrix<PFP, ATTR_TYPE, SOLVER_TRAITS>(m, s, attr, coord, index, amount) ;
+	FunctorLaplacianCotanRHS_Vector<PFP, ATTR_TYPE, SOLVER_TRAITS> flc(m, s, index, edgeWeight, vertexArea, attr, coord) ;
+	m.foreach_orbit(VERTEX, flc) ;
 }
 
+/*******************************************************************************
+ * END MATRIX DEFINITION
+ *******************************************************************************/
+
 template <class SOLVER_TRAITS>
 void endMatrix(LinearSolver<SOLVER_TRAITS>* s)
 {
 	s->end_system() ;
 }
 
+/*******************************************************************************
+ * SOLVE SYSTEM
+ *******************************************************************************/
+
 template <class SOLVER_TRAITS>
 void solve(LinearSolver<SOLVER_TRAITS>* s)
 {
 	s->solve() ;
 }
 
+/*******************************************************************************
+ * RESET SOLVER
+ *******************************************************************************/
+
 template <class SOLVER_TRAITS>
 void resetSolver(LinearSolver<SOLVER_TRAITS>* s, bool keepMatrix)
 {
 	s->reset(keepMatrix) ;
 }
 
+/*******************************************************************************
+ * GET RESULTS
+ *******************************************************************************/
+
 template <typename PFP, typename ATTR_TYPE, class SOLVER_TRAITS>
-void getResult(typename PFP::MAP& m, LinearSolver<SOLVER_TRAITS>* s, AttributeHandler<ATTR_TYPE>& attr, const AttributeHandler<unsigned int> index)
+void getResult(
+	typename PFP::MAP& m,
+	LinearSolver<SOLVER_TRAITS>* s,
+	const AttributeHandler<unsigned int> index,
+	AttributeHandler<ATTR_TYPE>& attr)
 {
-	FunctorSolverToMesh_Scalar<PFP, ATTR_TYPE, SOLVER_TRAITS> fstm(m, s, attr, index) ;
+	FunctorSolverToMesh_Scalar<PFP, ATTR_TYPE, SOLVER_TRAITS> fstm(s, index, attr) ;
 	m.foreach_orbit(VERTEX, fstm) ;
 }
 
 template <typename PFP, typename ATTR_TYPE, class SOLVER_TRAITS>
-void getResult(typename PFP::MAP& m, LinearSolver<SOLVER_TRAITS>* s, AttributeHandler<ATTR_TYPE>& attr, unsigned int coord, const AttributeHandler<unsigned int> index)
+void getResult(
+	typename PFP::MAP& m,
+	LinearSolver<SOLVER_TRAITS>* s,
+	const AttributeHandler<unsigned int> index,
+	AttributeHandler<ATTR_TYPE>& attr,
+	unsigned int coord)
 {
-	FunctorSolverToMesh_Vector<PFP, ATTR_TYPE, SOLVER_TRAITS> fstm(m, s, attr, coord, index) ;
+	FunctorSolverToMesh_Vector<PFP, ATTR_TYPE, SOLVER_TRAITS> fstm(s, index, attr, coord) ;
 	m.foreach_orbit(VERTEX, fstm) ;
 }
 

include/Algo/LinearSolving/matrixSetup.h

@@ -22,10 +22,8 @@
 *                                                                              *
 *******************************************************************************/
 
-#ifndef __LINEAR_SOLVING_CONSTRAINTS__
-#define __LINEAR_SOLVING_CONSTRAINTS__
-
-#include "Algo/LinearSolving/Laplacian/matrixSetup.h"
+#ifndef __LINEAR_SOLVING_MATRIX_SETUP__
+#define __LINEAR_SOLVING_MATRIX_SETUP__
 
 namespace CGoGN
 {
@@ -33,77 +31,355 @@ namespace CGoGN
 namespace LinearSolving
 {
 
+/*******************************************************************************
+ * EQUALITY MATRIX : right-hand-side SCALAR
+ *******************************************************************************/
+
 template<typename PFP, typename ATTR_TYPE, class SOLVER_TRAITS>
-class EqualityConstraint_Scalar : public FunctorMap<typename PFP::MAP>
+class FunctorEquality_Scalar : public FunctorType
 {
 protected:
 	LinearSolver<SOLVER_TRAITS>* solver ;
+	const AttributeHandler<unsigned int>& indexTable ;
 	const AttributeHandler<ATTR_TYPE>& attrTable ;
+	float weight ;
+
+public:
+	FunctorEquality_Scalar(
+		LinearSolver<SOLVER_TRAITS>* s,
+		const AttributeHandler<unsigned int>& index,
+		const AttributeHandler<ATTR_TYPE>& attr,
+		float w
+	) :	solver(s), indexTable(index), attrTable(attr), weight(w)
+	{}
+
+	bool operator()(Dart d)
+	{
+		solver->begin_row() ;
+		solver->add_coefficient(indexTable[d], 1) ;
+		solver->set_right_hand_side(attrTable[d]) ;
+		solver->normalize_row(weight) ;
+		solver->end_row() ;
+		return false ;
+	}
+} ;
+
+/*******************************************************************************
+ * EQUALITY MATRIX : right-hand-side VECTOR + coordinate
+ *******************************************************************************/
+
+template<typename PFP, typename ATTR_TYPE, class SOLVER_TRAITS>
+class FunctorEquality_Vector : public FunctorType
+{
+protected:
+	LinearSolver<SOLVER_TRAITS>* solver ;
 	const AttributeHandler<unsigned int>& indexTable ;
+	const AttributeHandler<ATTR_TYPE>& attrTable ;
 	float weight ;
+	unsigned int coord ;
+
+public:
+	FunctorEquality_Vector(
+		LinearSolver<SOLVER_TRAITS>* s,
+		const AttributeHandler<unsigned int>& index,
+		const AttributeHandler<ATTR_TYPE>& attr,
+		float w,
+		unsigned int c
+	) :	solver(s), indexTable(index), attrTable(attr), weight(w), coord(c)
+	{}
+
+	bool operator()(Dart d)
+	{
+		solver->begin_row() ;
+		solver->add_coefficient(indexTable[d], 1) ;
+		solver->set_right_hand_side((attrTable[d])[coord]) ;
+		solver->normalize_row(weight) ;
+		solver->end_row() ;
+		return false ;
+	}
+} ;
+
+/*******************************************************************************
+ * LAPLACIAN TOPO MATRIX : right-hand-side 0
+ *********