Ported the remaining implicit solver functions for Eigen.

Also added a couple of utility wrapper functions for Eigen types to make
interfacing with plain float arrays and blenlib math easier.

4 files changed, 912 insertions, 53 deletions

diff --git a/source/blender/physics/intern/BPH_mass_spring.cpp b/source/blender/physics/intern/BPH_mass_spring.cpp
index 72639fbfc74..6657058db48 100644
--- a/source/blender/physics/intern/BPH_mass_spring.cpp
+++ b/source/blender/physics/intern/BPH_mass_spring.cpp
@@ -519,7 +519,10 @@ static void cloth_calc_force(ClothModifierData *clmd, float UNUSED(frame), ListB
 		/* scale gravity force */
 		mul_v3_v3fl(gravity, clmd->scene->physics_settings.gravity, 0.001f * clmd->sim_parms->effector_weights->global_gravity);
 	}
-	BPH_mass_spring_force_gravity(data, gravity);
+	vert = cloth->verts;
+	for (i = 0; i < cloth->numverts; i++, vert++) {
+		BPH_mass_spring_force_gravity(data, i, vert->mass, gravity);
+	}
 #endif
 
 	cloth_calc_volume_force(clmd);
diff --git a/source/blender/physics/intern/implicit.h b/source/blender/physics/intern/implicit.h
index 4659bb010c7..287c064c1c6 100644
--- a/source/blender/physics/intern/implicit.h
+++ b/source/blender/physics/intern/implicit.h
@@ -59,6 +59,7 @@ extern "C" {
 //#define IMPLICIT_ENABLE_EIGEN_DEBUG
 
 struct Implicit_Data;
+struct ImplicitSolverInput;
 struct SimDebugData;
 
 typedef struct ImplicitSolverResult {
@@ -118,8 +119,6 @@ void BPH_mass_spring_set_velocity(struct Implicit_Data *data, int index, const f
 void BPH_mass_spring_get_motion_state(struct Implicit_Data *data, int index, float x[3], float v[3]);
 void BPH_mass_spring_set_vertex_mass(struct Implicit_Data *data, int index, float mass);
 
-int BPH_mass_spring_add_block(struct Implicit_Data *data, int v1, int v2);
-
 void BPH_mass_spring_clear_constraints(struct Implicit_Data *data);
 void BPH_mass_spring_add_constraint_ndof0(struct Implicit_Data *data, int index, const float dV[3]);
 void BPH_mass_spring_add_constraint_ndof1(struct Implicit_Data *data, int index, const float c1[3], const float c2[3], const float dV[3]);
@@ -131,9 +130,9 @@ void BPH_mass_spring_apply_result(struct Implicit_Data *data);
 /* Clear the force vector at the beginning of the time step */
 void BPH_mass_spring_clear_forces(struct Implicit_Data *data);
 /* Fictitious forces introduced by moving coordinate systems */
-void BPH_mass_spring_force_reference_frame(struct Implicit_Data *data, int index, const float acceleration[3], const float omega[3], const float domega_dt[3]);
+void BPH_mass_spring_force_reference_frame(struct Implicit_Data *data, int index, const float acceleration[3], const float omega[3], const float domega_dt[3], float mass);
 /* Simple uniform gravity force */
-void BPH_mass_spring_force_gravity(struct Implicit_Data *data, const float g[3]);
+void BPH_mass_spring_force_gravity(struct Implicit_Data *data, int index, float mass, const float g[3]);
 /* Global drag force (velocity damping) */
 void BPH_mass_spring_force_drag(struct Implicit_Data *data, float drag);
 /* Custom external force */
diff --git a/source/blender/physics/intern/implicit_blender.c b/source/blender/physics/intern/implicit_blender.c
index 75dd80ee9c0..713653ae574 100644
--- a/source/blender/physics/intern/implicit_blender.c
+++ b/source/blender/physics/intern/implicit_blender.c
@@ -754,7 +754,8 @@ void BPH_mass_spring_solver_free(Implicit_Data *id)
 
 void BPH_mass_spring_solver_debug_data(Implicit_Data *id, struct SimDebugData *debug_data)
 {
-	id->debug_data = debug_data;
+	if (id)
+		id->debug_data = debug_data;
 }
 
 /* ==== Transformation from/to root reference frames ==== */
@@ -1215,7 +1216,7 @@ void BPH_mass_spring_set_vertex_mass(Implicit_Data *data, int index, float mass)
 	mul_m3_fl(data->M[index].m, mass);
 }
 
-int BPH_mass_spring_add_block(Implicit_Data *data, int v1, int v2)
+static int BPH_mass_spring_add_block(Implicit_Data *data, int v1, int v2)
 {
 	int s = data->M[0].vcount + data->num_blocks; /* index from array start */
 	BLI_assert(s < data->M[0].vcount + data->M[0].scount);
@@ -1294,7 +1295,7 @@ void BPH_mass_spring_clear_forces(Implicit_Data *data)
 	data->num_blocks = 0;
 }
 
-void BPH_mass_spring_force_reference_frame(Implicit_Data *data, int index, const float acceleration[3], const float omega[3], const float domega_dt[3])
+void BPH_mass_spring_force_reference_frame(Implicit_Data *data, int index, const float acceleration[3], const float omega[3], const float domega_dt[3], float mass)
 {
 #ifdef CLOTH_ROOT_FRAME
 	float acc[3], w[3], dwdt[3];
@@ -1316,7 +1317,7 @@ void BPH_mass_spring_force_reference_frame(Implicit_Data *data, int index, const
 	sub_v3_v3(f, coriolis);
 	sub_v3_v3(f, centrifugal);
 	
-	mul_m3_v3(data->M[index].m, f); /* F = m * a */
+	mul_v3_fl(f, mass); /* F = m * a */
 	
 	cross_v3_identity(deuler, dwdt);
 	cross_v3_identity(dcoriolis, w);
@@ -1326,11 +1327,11 @@ void BPH_mass_spring_force_reference_frame(Implicit_Data *data, int index, const
 	
 	add_m3_m3m3(dfdx, deuler, dcentrifugal);
 	negate_m3(dfdx);
-	mul_m3_m3m3(dfdx, data->M[index].m, dfdx);
+	mul_m3_fl(dfdx, mass);
 	
 	copy_m3_m3(dfdv, dcoriolis);
 	negate_m3(dfdv);
-	mul_m3_m3m3(dfdv, data->M[index].m, dfdv);
+	mul_m3_fl(dfdv, mass);
 	
 	add_v3_v3(data->F[index], f);
 	add_m3_m3m3(data->dFdX[index].m, data->dFdX[index].m, dfdx);
@@ -1344,19 +1345,14 @@ void BPH_mass_spring_force_reference_frame(Implicit_Data *data, int index, const
 #endif
 }
 
-void BPH_mass_spring_force_gravity(Implicit_Data *data, const float g[3])
+void BPH_mass_spring_force_gravity(Implicit_Data *data, int index, float mass, const float g[3])
 {
-	int i, numverts = data->M[0].vcount;
-	/* multiply F with mass matrix
-	 * force = mass * acceleration (in this case: gravity)
-	 */
-	for (i = 0; i < numverts; i++) {
-		float f[3];
-		world_to_root_v3(data, i, f, g);
-		mul_m3_v3(data->M[i].m, f);
-		
-		add_v3_v3(data->F[i], f);
-	}
+	/* force = mass * acceleration (in this case: gravity) */
+	float f[3];
+	world_to_root_v3(data, index, f, g);
+	mul_v3_fl(f, mass);
+	
+	add_v3_v3(data->F[index], f);
 }
 
 void BPH_mass_spring_force_drag(Implicit_Data *data, float drag)
diff --git a/source/blender/physics/intern/implicit_eigen.cpp b/source/blender/physics/intern/implicit_eigen.cpp
index 402ffcb64d7..a6148b65816 100644
--- a/source/blender/physics/intern/implicit_eigen.cpp
+++ b/source/blender/physics/intern/implicit_eigen.cpp
@@ -111,7 +111,7 @@ public:
 			coeffRef(k) = v[k];
 	}
 	
-	fVector &operator = (const ctype &v)
+	fVector& operator = (const ctype &v)
 	{
 		for (int k = 0; k < 3; ++k)
 			coeffRef(k) = v[k];
@@ -142,7 +142,7 @@ public:
 				coeffRef(l, k) = v[k][l];
 	}
 	
-	fMatrix &operator = (const ctype &v)
+	fMatrix& operator = (const ctype &v)
 	{
 		for (int k = 0; k < 3; ++k)
 			for (int l = 0; l < 3; ++l)
@@ -156,27 +156,63 @@ public:
 	}
 };
 
-typedef Eigen::VectorXf lVector;
+/* Extension of dense Eigen vectors,
+ * providing 3-float block access for blenlib math functions
+ */
+class lVector : public Eigen::VectorXf {
+public:
+	typedef Eigen::VectorXf base_t;
+	
+	lVector()
+	{
+	}
+	
+	template <typename T>
+	lVector& operator = (T rhs)
+	{
+		base_t::operator=(rhs);
+		return *this;
+	}
+	
+	float* v3(int vertex)
+	{
+		return &coeffRef(3 * vertex);
+	}
+	
+	const float* v3(int vertex) const
+	{
+		return &coeffRef(3 * vertex);
+	}
+};
 
 typedef Eigen::Triplet<Scalar> Triplet;
 typedef std::vector<Triplet> TripletList;
 
 typedef Eigen::SparseMatrix<Scalar> lMatrix;
 
+/* Constructor type that provides more convenient handling of Eigen triplets
+ * for efficient construction of sparse 3x3 block matrices.
+ * This should be used for building lMatrix instead of writing to such lMatrix directly (which is very inefficient).
+ * After all elements have been defined using the set() method, the actual matrix can be filled using construct().
+ */
 struct lMatrixCtor {
-	lMatrixCtor(int numverts) :
-	    m_numverts(numverts)
+	lMatrixCtor()
+	{
+	}
+	
+	void reset()
+	{
+		m_trips.clear();
+	}
+	
+	void reserve(int numverts)
 	{
 		/* reserve for diagonal entries */
 		m_trips.reserve(numverts * 9);
 	}
 	
-	int numverts() const { return m_numverts; }
-	
-	void set(int i, int j, const fMatrix &m)
+	void add(int i, int j, const fMatrix &m)
 	{
-		BLI_assert(i >= 0 && i < m_numverts);
-		BLI_assert(j >= 0 && j < m_numverts);
 		i *= 3;
 		j *= 3;
 		for (int k = 0; k < 3; ++k)
@@ -184,15 +220,22 @@ struct lMatrixCtor {
 				m_trips.push_back(Triplet(i + k, j + l, m.coeff(l, k)));
 	}
 	
-	inline lMatrix construct() const
+	void sub(int i, int j, const fMatrix &m)
+	{
+		i *= 3;
+		j *= 3;
+		for (int k = 0; k < 3; ++k)
+			for (int l = 0; l < 3; ++l)
+				m_trips.push_back(Triplet(i + k, j + l, -m.coeff(l, k)));
+	}
+	
+	inline void construct(lMatrix &m)
 	{
-		lMatrix m(m_numverts, m_numverts);
 		m.setFromTriplets(m_trips.begin(), m_trips.end());
-		return m;
+		m_trips.clear();
 	}
 	
 private:
-	const int m_numverts;
 	TripletList m_trips;
 };
 
@@ -247,6 +290,7 @@ BLI_INLINE const float *lVector_v3(const lVector &v, int vertex)
 	return v.data() + 3 * vertex;
 }
 
+#if 0
 BLI_INLINE void triplets_m3(TripletList &tlist, float m[3][3], int i, int j)
 {
 	i *= 3;
@@ -289,6 +333,7 @@ BLI_INLINE void lMatrix_sub_triplets(lMatrix &r, const TripletList &tlist)
 	t.setFromTriplets(tlist.begin(), tlist.end());
 	r -= t;
 }
+#endif
 
 BLI_INLINE void outerproduct(float r[3][3], const float a[3], const float b[3])
 {
@@ -297,11 +342,50 @@ BLI_INLINE void outerproduct(float r[3][3], const float a[3], const float b[3])
 	mul_v3_v3fl(r[2], a, b[2]);
 }
 
+BLI_INLINE void cross_m3_v3m3(float r[3][3], const float v[3], float m[3][3])
+{
+	cross_v3_v3v3(r[0], v, m[0]);
+	cross_v3_v3v3(r[1], v, m[1]);
+	cross_v3_v3v3(r[2], v, m[2]);
+}
+
+BLI_INLINE void cross_v3_identity(float r[3][3], const float v[3])
+{
+	r[0][0] = 0.0f;		r[1][0] = v[2];		r[2][0] = -v[1];
+	r[0][1] = -v[2];	r[1][1] = 0.0f;		r[2][1] = v[0];
+	r[0][2] = v[1];		r[1][2] = -v[0];	r[2][2] = 0.0f;
+}
+
+BLI_INLINE void madd_m3_m3fl(float r[3][3], float m[3][3], float f)
+{
+	r[0][0] += m[0][0] * f;
+	r[0][1] += m[0][1] * f;
+	r[0][2] += m[0][2] * f;
+	r[1][0] += m[1][0] * f;
+	r[1][1] += m[1][1] * f;
+	r[1][2] += m[1][2] * f;
+	r[2][0] += m[2][0] * f;
+	r[2][1] += m[2][1] * f;
+	r[2][2] += m[2][2] * f;
+}
+
+BLI_INLINE void madd_m3_m3m3fl(float r[3][3], float a[3][3], float b[3][3], float f)
+{
+	r[0][0] = a[0][0] + b[0][0] * f;
+	r[0][1] = a[0][1] + b[0][1] * f;
+	r[0][2] = a[0][2] + b[0][2] * f;
+	r[1][0] = a[1][0] + b[1][0] * f;
+	r[1][1] = a[1][1] + b[1][1] * f;
+	r[1][2] = a[1][2] + b[1][2] * f;
+	r[2][0] = a[2][0] + b[2][0] * f;
+	r[2][1] = a[2][1] + b[2][1] * f;
+	r[2][2] = a[2][2] + b[2][2] * f;
+}
+
 struct Implicit_Data {
 	typedef std::vector<fMatrix> fMatrixVector;
 	
-	Implicit_Data(int numverts) :
-	    M(numverts)
+	Implicit_Data(int numverts)
 	{
 		resize(numverts);
 	}
@@ -311,8 +395,10 @@ struct Implicit_Data {
 		this->numverts = numverts;
 		int tot = 3 * numverts;
 		
-		dFdV.resize(tot, tot);
+		M.resize(tot, tot);
+		F.resize(tot);
 		dFdX.resize(tot, tot);
+		dFdV.resize(tot, tot);
 		
 		tfm.resize(numverts, I);
 		
@@ -320,22 +406,26 @@ struct Implicit_Data {
 		Xnew.resize(tot);
 		V.resize(tot);
 		Vnew.resize(tot);
-		F.resize(tot);
 		
-		B.resize(tot);
 		A.resize(tot, tot);
+		B.resize(tot);
 		
 		dV.resize(tot);
 		z.resize(tot);
 		S.resize(tot, tot);
+		
+		iM.reserve(numverts);
+		idFdX.reserve(numverts);
+		idFdV.reserve(numverts);
+		iS.reserve(numverts);
 	}
 	
 	int numverts;
 	
 	/* inputs */
-	lMatrixCtor M;				/* masses */
+	lMatrix M;					/* masses */
 	lVector F;					/* forces */
-	lMatrix dFdV, dFdX;			/* force jacobians */
+	lMatrix dFdX, dFdV;			/* force jacobians */
 	
 	fMatrixVector tfm;			/* local coordinate transform */
 	
@@ -351,9 +441,40 @@ struct Implicit_Data {
 	lVector z;					/* target velocity in constrained directions */
 	lMatrix S;					/* filtering matrix for constraints */
 	
+	/* temporary constructors */
+	lMatrixCtor iM;				/* masses */
+	lMatrixCtor idFdX, idFdV;	/* force jacobians */
+	lMatrixCtor iS;				/* filtering matrix for constraints */
+	
 	struct SimDebugData *debug_data;
 };
 
+Implicit_Data *BPH_mass_spring_solver_create(int numverts, int numsprings)
+{
+	Implicit_Data *id = new Implicit_Data(numverts);
+	return id;
+}
+
+void BPH_mass_spring_solver_free(Implicit_Data *id)
+{
+	if (id)
+		delete id;
+}
+
+int BPH_mass_spring_solver_numvert(Implicit_Data *id)
+{
+	if (id)
+		return id->numverts;
+	else
+		return 0;
+}
+
+void BPH_mass_spring_solver_debug_data(Implicit_Data *id, struct SimDebugData *debug_data)
+{
+	if (id)
+		id->debug_data = debug_data;
+}
+
 /* ==== Transformation from/to root reference frames ==== */
 
 BLI_INLINE void world_to_root_v3(Implicit_Data *data, int index, float r[3], const float v[3])
@@ -405,8 +526,12 @@ bool BPH_mass_spring_solve(Implicit_Data *data, float dt, ImplicitSolverResult *
 	cg.setMaxIterations(100);
 	cg.setTolerance(0.01f);
 	
-	lMatrix M = data->M.construct();
-	data->A = M - dt * data->dFdV - dt*dt * data->dFdX;
+	data->iM.construct(data->M);
+	data->idFdX.construct(data->dFdX);
+	data->idFdV.construct(data->dFdV);
+	data->iS.construct(data->S);
+	
+	data->A = data->M - dt * data->dFdV - dt*dt * data->dFdX;
 	cg.compute(data->A);
 	cg.filter() = data->S;
 	
@@ -465,24 +590,24 @@ void BPH_mass_spring_set_rest_transform(Implicit_Data *data, int index, float tf
 
 void BPH_mass_spring_set_motion_state(Implicit_Data *data, int index, const float x[3], const float v[3])
 {
-	world_to_root_v3(data, index, lVector_v3(data->X, index), x);
-	world_to_root_v3(data, index, lVector_v3(data->V, index), v);
+	world_to_root_v3(data, index, data->X.v3(index), x);
+	world_to_root_v3(data, index, data->V.v3(index), v);
 }
 
 void BPH_mass_spring_set_position(Implicit_Data *data, int index, const float x[3])
 {
-	world_to_root_v3(data, index, lVector_v3(data->X, index), x);
+	world_to_root_v3(data, index, data->X.v3(index), x);
 }
 
 void BPH_mass_spring_set_velocity(Implicit_Data *data, int index, const float v[3])
 {
-	world_to_root_v3(data, index, lVector_v3(data->V, index), v);
+	world_to_root_v3(data, index, data->V.v3(index), v);
 }
 
 void BPH_mass_spring_get_motion_state(struct Implicit_Data *data, int index, float x[3], float v[3])
 {
-	if (x) root_to_world_v3(data, index, x, lVector_v3(data->X, index));
-	if (v) root_to_world_v3(data, index, v, lVector_v3(data->V, index));
+	if (x) root_to_world_v3(data, index, x, data->X.v3(index));
+	if (v) root_to_world_v3(data, index, v, data->V.v3(index));
 }
 
 void BPH_mass_spring_set_vertex_mass(Implicit_Data *data, int index, float mass)
@@ -490,7 +615,743 @@ void BPH_mass_spring_set_vertex_mass(Implicit_Data *data, int index, float mass)
 	float m[3][3];
 	copy_m3_m3(m, I);
 	mul_m3_fl(m, mass);
-	data->M.set(index, index, m);
+	data->iM.add(index, index, m);
+}
+
+void BPH_mass_spring_clear_constraints(Implicit_Data *data)
+{
+	int numverts = data->numverts;
+	for (int i = 0; i < numverts; ++i) {
+		data->iS.add(i, i, I);
+		zero_v3(data->z.v3(i));
+	}
+}
+
+void BPH_mass_spring_add_constraint_ndof0(Implicit_Data *data, int index, const float dV[3])
+{
+	data->iS.sub(index, index, I);
+	
+	world_to_root_v3(data, index, data->z.v3(index), dV);
+}
+
+void BPH_mass_spring_add_constraint_ndof1(Implicit_Data *data, int index, const float c1[3], const float c2[3], const float dV[3])
+{
+	float m[3][3], p[3], q[3], u[3], cmat[3][3];
+	
+	world_to_root_v3(data, index, p, c1);
+	outerproduct(cmat, p, p);
+	copy_m3_m3(m, cmat);
+	
+	world_to_root_v3(data, index, q, c2);
+	outerproduct(cmat, q, q);
+	add_m3_m3m3(m, m, cmat);
+	
+	/* XXX not sure but multiplication should work here */
+	data->iS.sub(index, index, m);
+//	mul_m3_m3m3(data->S[index].m, data->S[index].m, m);
+	
+	world_to_root_v3(data, index, u, dV);
+	add_v3_v3(data->z.v3(index), u);
+}
+
+void BPH_mass_spring_add_constraint_ndof2(Implicit_Data *data, int index, const float c1[3], const float dV[3])
+{
+	float m[3][3], p[3], u[3], cmat[3][3];
+	
+	world_to_root_v3(data, index, p, c1);
+	outerproduct(cmat, p, p);
+	copy_m3_m3(m, cmat);
+	
+	data->iS.sub(index, index, m);
+//	mul_m3_m3m3(data->S[index].m, data->S[index].m, m);
+	
+	world_to_root_v3(data, index, u, dV);
+	add_v3_v3(data->z.v3(index), u);
+}
+
+void BPH_mass_spring_clear_forces(Implicit_Data *data)
+{
+	data->F.setZero();
+	data->dFdX.setZero();
+	data->dFdV.setZero();
+}
+
+void BPH_mass_spring_force_reference_frame(Implicit_Data *data, int index, const float acceleration[3], const float omega[3], const float domega_dt[3], float mass)
+{
+#ifdef CLOTH_ROOT_FRAME
+	float acc[3], w[3], dwdt[3];
+	float f[3], dfdx[3][3], dfdv[3][3];
+	float euler[3], coriolis[3], centrifugal[3], rotvel[3];
+	float deuler[3][3], dcoriolis[3][3], dcentrifugal[3][3], drotvel[3][3];
+	
+	world_to_root_v3(data, index, acc, acceleration);
+	world_to_root_v3(data, index, w, omega);
+	world_to_root_v3(data, index, dwdt, domega_dt);
+	
+	cross_v3_v3v3(euler, dwdt, data->X.v3(index));
+	cross_v3_v3v3(coriolis, w, data->V.v3(index));
+	mul_v3_fl(coriolis, 2.0f);
+	cross_v3_v3v3(rotvel, w, data->X.v3(index));
+	cross_v3_v3v3(centrifugal, w, rotvel);
+	
+	sub_v3_v3v3(f, acc, euler);
+	sub_v3_v3(f, coriolis);
+	sub_v3_v3(f, centrifugal);
+	
+	mul_v3_fl(f, mass); /* F = m * a */
+	
+	cross_v3_identity(deuler, dwdt);
+	cross_v3_identity(dcoriolis, w);
+	mul_m3_fl(dcoriolis, 2.0f);
+	cross_v3_identity(drotvel, w);
+	cross_m3_v3m3(dcentrifugal, w, drotvel);
+	
+	add_m3_m3m3(dfdx, deuler, dcentrifugal);
+	negate_m3(dfdx);
+	mul_m3_fl(dfdx, mass);
+	
+	copy_m3_m3(dfdv, dcoriolis);
+	negate_m3(dfdv);
+	mul_m3_fl(dfdv, mass);
+	
+	add_v3_v3(data->F.v3(index), f);
+	data->idFdX.add(index, index, dfdx);
+	data->idFdV.add(index, index, dfdv);
+#else
+	(void)data;
+	(void)index;
+	(void)acceleration;
+	(void)omega;
+	(void)domega_dt;
+#endif
+}
+
+void BPH_mass_spring_force_gravity(Implicit_Data *data, int index, float mass, const float g[3])
+{
+	/* force = mass * acceleration (in this case: gravity) */
+	float f[3];
+	world_to_root_v3(data, index, f, g);
+	mul_v3_fl(f, mass);
+	
+	add_v3_v3(data->F.v3(index), f);
+}
+
+void BPH_mass_spring_force_drag(Implicit_Data *data, float drag)
+{
+	int numverts = data->numverts;
+	for (int i = 0; i < numverts; i++) {
+		float tmp[3][3];
+		
+		/* NB: uses root space velocity, no need to transform */
+		madd_v3_v3fl(data->F.v3(i), data->V.v3(i), -drag);
+		
+		copy_m3_m3(tmp, I);
+		mul_m3_fl(tmp, -drag);
+		data->idFdV.add(i, i, tmp);
+	}
+}
+
+void BPH_mass_spring_force_extern(struct Implicit_Data *data, int i, const float f[3], float dfdx[3][3], float dfdv[3][3])
+{
+	float tf[3], tdfdx[3][3], tdfdv[3][3];
+	world_to_root_v3(data, i, tf, f);
+	world_to_root_m3(data, i, tdfdx, dfdx);
+	world_to_root_m3(data, i, tdfdv, dfdv);
+	
+	add_v3_v3(data->F.v3(i), tf);
+	data->idFdX.add(i, i, tdfdx);
+	data->idFdV.add(i, i, tdfdv);
+}
+
+static float calc_nor_area_tri(float nor[3], const float v1[3], const float v2[3], const float v3[3])
+{
+	float n1[3], n2[3];
+	
+	sub_v3_v3v3(n1, v1, v2);
+	sub_v3_v3v3(n2, v2, v3);
+	
+	cross_v3_v3v3(nor, n1, n2);
+	return normalize_v3(nor);
+}
+
+static float calc_nor_area_quad(float nor[3], const float v1[3], const float v2[3], const float v3[3], const float v4[3])
+{
+	float n1[3], n2[3];
+	
+	sub_v3_v3v3(n1, v1, v3);
+	sub_v3_v3v3(n2, v2, v4);
+	
+	cross_v3_v3v3(nor, n1, n2);
+	return normalize_v3(nor);
+}
+
+/* XXX does not support force jacobians yet, since the effector system does not provide them either */
+void BPH_mass_spring_force_face_wind(Implicit_Data *data, int v1, int v2, int v3, int v4, const float (*winvec)[3])
+{
+	const float effector_scale = 0.02f;
+	float win[3], nor[3], area;
+	float factor;
+	
+	// calculate face normal and area
+	if (v4) {
+		area = calc_nor_area_quad(nor, data->X.v3(v1), data->X.v3(v2), data->X.v3(v3), data->X.v3(v4));
+		factor = effector_scale * area * 0.25f;
+	}
+	else {
+		area = calc_nor_area_tri(nor, data->X.v3(v1), data->X.v3(v2), data->X.v3(v3));
+		factor = effector_scale * area / 3.0f;
+	}
+	
+	world_to_root_v3(data, v1, win, winvec[v1]);
+	madd_v3_v3fl(data->F.v3(v1), nor, factor * dot_v3v3(win, nor));
+	
+	world_to_root_v3(data, v2, win, winvec[v2]);
+	madd_v3_v3fl(data->F.v3(v2), nor, factor * dot_v3v3(win, nor));
+	
+	world_to_root_v3(data, v3, win, winvec[v3]);
+	madd_v3_v3fl(data->F.v3(v3), nor, factor * dot_v3v3(win, nor));
+	
+	if (v4) {
+		world_to_root_v3(data, v4, win, winvec[v4]);
+		madd_v3_v3fl(data->F.v3(v4), nor, factor * dot_v3v3(win, nor));
+	}
+}
+
+void BPH_mass_spring_force_edge_wind(Implicit_Data *data, int v1, int v2, const float (*winvec)[3])
+{
+	const float effector_scale = 0.01;
+	float win[3], dir[3], nor[3], length;
+	
+	sub_v3_v3v3(dir, data->X.v3(v1), data->X.v3(v2));
+	length = normalize_v3(dir);
+	
+	world_to_root_v3(data, v1, win, winvec[v1]);
+	madd_v3_v3v3fl(nor, win, dir, -dot_v3v3(win, dir));
+	madd_v3_v3fl(data->F.v3(v1), nor, effector_scale * length);
+	
+	world_to_root_v3(data, v2, win, winvec[v2]);
+	madd_v3_v3v3fl(nor, win, dir, -dot_v3v3(win, dir));
+	madd_v3_v3fl(data->F.v3(v2), nor, effector_scale * length);
+}
+
+BLI_INLINE void dfdx_spring(float to[3][3], const float dir[3], float length, float L, float k)
+{
+	// dir is unit length direction, rest is spring's restlength, k is spring constant.
+	//return  ( (I-outerprod(dir, dir))*Min(1.0f, rest/length) - I) * -k;
+	outerproduct(to, dir, dir);
+	sub_m3_m3m3(to, I, to);
+	
+	mul_m3_fl(to, (L/length)); 
+	sub_m3_m3m3(to, to, I);
+	mul_m3_fl(to, k);
+}
+
+/* unused */
+#if 0
+BLI_INLINE void dfdx_damp(float to[3][3], const float dir[3], float length, const float vel[3], float rest, float damping)
+{
+	// inner spring damping   vel is the relative velocity  of the endpoints.  
+	// 	return (I-outerprod(dir, dir)) * (-damping * -(dot(dir, vel)/Max(length, rest)));
+	mul_fvectorT_fvector(to, dir, dir);
+	sub_fmatrix_fmatrix(to, I, to);
+	mul_fmatrix_S(to,  (-damping * -(dot_v3v3(dir, vel)/MAX2(length, rest))));
+}
+#endif
+
+BLI_INLINE void dfdv_damp(float to[3][3], const float dir[3], float damping)
+{
+	// derivative of force wrt velocity
+	outerproduct(to, dir, dir);
+	mul_m3_fl(to, -damping);
+}
+
+BLI_INLINE float fb(float length, float L)
+{
+	float x = length / L;
+	return (-11.541f * powf(x, 4) + 34.193f * powf(x, 3) - 39.083f * powf(x, 2) + 23.116f * x - 9.713f);
+}
+
+BLI_INLINE float fbderiv(float length, float L)
+{
+	float x = length/L;
+
+	return (-46.164f * powf(x, 3) + 102.579f * powf(x, 2) - 78.166f * x + 23.116f);
+}
+
+BLI_INLINE float fbstar(float length, float L, float kb, float cb)
+{
+	float tempfb_fl = kb * fb(length, L);
+	float fbstar_fl = cb * (length - L);
+	
+	if (tempfb_fl < fbstar_fl)
+		return fbstar_fl;
+	else
+		return tempfb_fl;
+}
+
+// function to calculae bending spring force (taken from Choi & Co)
+BLI_INLINE float fbstar_jacobi(float length, float L, float kb, float cb)
+{
+	float tempfb_fl = kb * fb(length, L);
+	float fbstar_fl = cb * (length - L);
+
+	if (tempfb_fl < fbstar_fl) {
+		return -cb;
+	}
+	else {
+		return -kb * fbderiv(length, L);
+	}
+}
+
+/* calculate elonglation */
+BLI_INLINE bool spring_length(Implicit_Data *data, int i, int j, float r_extent[3], float r_dir[3], float *r_length, float r_vel[3])
+{
+	sub_v3_v3v3(r_extent, data->X.v3(j), data->X.v3(i));
+	sub_v3_v3v3(r_vel, data->V.v3(j), data->V.v3(i));
+	*r_length = len_v3(r_extent);
+	
+	if (*r_length > ALMOST_ZERO) {
+		/*
+		if (length>L) {
+			if ((clmd->sim_parms->flags & CSIMSETT_FLAG_TEARING_ENABLED) &&
+			    ( ((length-L)*100.0f/L) > clmd->sim_parms->maxspringlen )) {
+				// cut spring!
+				s->flags |= CSPRING_FLAG_DEACTIVATE;
+				return false;
+			}
+		}
+		*/
+		mul_v3_v3fl(r_dir, r_extent, 1.0f/(*r_length));
+	}
+	else {
+		zero_v3(r_dir);
+	}
+	
+	return true;
+}
+
+BLI_INLINE void apply_spring(Implicit_Data *data, int i, int j, const float f[3], float dfdx[3][3], float dfdv[3][3])
+{
+	add_v3_v3(data->F.v3(i), f);
+	sub_v3_v3(data->F.v3(j), f);
+	
+	data->idFdX.add(i, i, dfdx);
+	data->idFdX.add(j, j, dfdx);
+	data->idFdX.sub(i, j, dfdx);
+	data->idFdX.sub(j, i, dfdx);
+	
+	data->idFdV.add(i, i, dfdv);
+	data->idFdV.add(j, j, dfdv);
+	data->idFdV.sub(i, j, dfdv);
+	data->idFdV.sub(j, i, dfdv);
+}
+
+bool BPH_mass_spring_force_spring_linear(Implicit_Data *data, int i, int j, float restlen,
+                                         float stiffness, float damping, bool no_compress, float clamp_force,
+                                         float r_f[3], float r_dfdx[3][3], float r_dfdv[3][3])
+{
+	float extent[3], length, dir[3], vel[3];
+	
+	// calculate elonglation
+	spring_length(data, i, j, extent, dir, &length, vel);
+	
+	if (length > restlen || no_compress) {
+		float stretch_force, f[3], dfdx[3][3], dfdv[3][3];
+		
+		stretch_force = stiffness * (length - restlen);
+		if (clamp_force > 0.0f && stretch_force > clamp_force) {
+			stretch_force = clamp_force;
+		}
+		mul_v3_v3fl(f, dir, stretch_force);
+		
+		// Ascher & Boxman, p.21: Damping only during elonglation
+		// something wrong with it...
+		madd_v3_v3fl(f, dir, damping * dot_v3v3(vel, dir));
+		
+		dfdx_spring(dfdx, dir, length, restlen, stiffness);
+		dfdv_damp(dfdv, dir, damping);
+		
+		apply_spring(data, i, j, f, dfdx, dfdv);
+		
+		if (r_f) copy_v3_v3(r_f, f);
+		if (r_dfdx) copy_m3_m3(r_dfdx, dfdx);
+		if (r_dfdv) copy_m3_m3(r_dfdv, dfdv);
+		
+		return true;
+	}
+	else {
+		if (r_f) zero_v3(r_f);
+		if (r_dfdx) zero_m3(r_dfdx);
+		if (r_dfdv) zero_m3(r_dfdv);
+		
+		return false;
+	}
+}
+
+/* See "Stable but Responsive Cloth" (Choi, Ko 2005) */
+bool BPH_mass_spring_force_spring_bending(Implicit_Data *data, int i, int j, float restlen,
+                                          float kb, float cb,
+                                          float r_f[3], float r_dfdx[3][3], float r_dfdv[3][3])
+{
+	float extent[3], length, dir[3], vel[3];
+	
+	// calculate elonglation
+	spring_length(data, i, j, extent, dir, &length, vel);
+	
+	if (length < restlen) {
+		float f[3], dfdx[3][3], dfdv[3][3];
+		
+		mul_v3_v3fl(f, dir, fbstar(length, restlen, kb, cb));
+		
+		outerproduct(dfdx, dir, dir);
+		mul_m3_fl(dfdx, fbstar_jacobi(length, restlen, kb, cb));
+		
+		/* XXX damping not supported */
+		zero_m3(dfdv);
+		
+		apply_spring(data, i, j, f, dfdx, dfdv);
+		
+		if (r_f) copy_v3_v3(r_f, f);
+		if (r_dfdx) copy_m3_m3(r_dfdx, dfdx);
+		if (r_dfdv) copy_m3_m3(r_dfdv, dfdv);
+		
+		return true;
+	}
+	else {
+		if (r_f) zero_v3(r_f);
+		if (r_dfdx) zero_m3(r_dfdx);
+		if (r_dfdv) zero_m3(r_dfdv);
+		
+		return false;
+	}
+}
+
+/* Jacobian of a direction vector.
+ * Basically the part of the differential orthogonal to the direction,
+ * inversely proportional to the length of the edge.
+ * 
+ * dD_ij/dx_i = -dD_ij/dx_j = (D_ij * D_ij^T - I) / len_ij
+ */
+BLI_INLINE void spring_grad_dir(Implicit_Data *data, int i, int j, float edge[3], float dir[3], float grad_dir[3][3])
+{
+	float length;
+	
+	sub_v3_v3v3(edge, data->X.v3(j), data->X.v3(i));
+	length = normalize_v3_v3(dir, edge);
+	
+	if (length > ALMOST_ZERO) {
+		outerproduct(grad_dir, dir, dir);
+		sub_m3_m3m3(grad_dir, I, grad_dir);
+		mul_m3_fl(grad_dir, 1.0f / length);
+	}
+	else {
+		zero_m3(grad_dir);
+	}
+}
+
+BLI_INLINE void spring_angbend_forces(Implicit_Data *data, int i, int j, int k,
+                                      const float goal[3],
+                                      float stiffness, float damping,
+                                      int q, const float dx[3], const float dv[3],
+                                      float r_f[3])
+{
+	float edge_ij[3], dir_ij[3];
+	float edge_jk[3], dir_jk[3];
+	float vel_ij[3], vel_jk[3], vel_ortho[3];
+	float f_bend[3], f_damp[3];
+	float fk[3];
+	float dist[3];
+	
+	zero_v3(fk);
+	
+	sub_v3_v3v3(edge_ij, data->X.v3(j), data->X.v3(i));
+	if (q == i) sub_v3_v3(edge_ij, dx);
+	if (q == j) add_v3_v3(edge_ij, dx);
+	normalize_v3_v3(dir_ij, edge_ij);
+	
+	sub_v3_v3v3(edge_jk, data->X.v3(k), data->X.v3(j));
+	if (q == j) sub_v3_v3(edge_jk, dx);
+	if (q == k) add_v3_v3(edge_jk, dx);
+	normalize_v3_v3(dir_jk, edge_jk);
+	
+	sub_v3_v3v3(vel_ij, data->V.v3(j), data->V.v3(i));
+	if (q == i) sub_v3_v3(vel_ij, dv);
+	if (q == j) add_v3_v3(vel_ij, dv);
+	
+	sub_v3_v3v3(vel_jk, data->V.v3(k), data->V.v3(j));
+	if (q == j) sub_v3_v3(vel_jk, dv);
+	if (q == k) add_v3_v3(vel_jk, dv);
+	
+	/* bending force */
+	sub_v3_v3v3(dist, goal, edge_jk);
+	mul_v3_v3fl(f_bend, dist, stiffness);
+	
+	add_v3_v3(fk, f_bend);
+	
+	/* damping force */
+	madd_v3_v3v3fl(vel_ortho, vel_jk, dir_jk, -dot_v3v3(vel_jk, dir_jk));
+	mul_v3_v3fl(f_damp, vel_ortho, damping);
+	
+	sub_v3_v3(fk, f_damp);
+	
+	copy_v3_v3(r_f, fk);
+}
+
+/* Finite Differences method for estimating the jacobian of the force */
+BLI_INLINE void spring_angbend_estimate_dfdx(Implicit_Data *data, int i, int j, int k,
+                                             const float goal[3],
+                                             float stiffness, float damping,
+                                             int q, float dfdx[3][3])
+{
+	const float delta = 0.00001f; // TODO find a good heuristic for this
+	float dvec_null[3][3], dvec_pos[3][3], dvec_neg[3][3];
+	float f[3];
+	int a, b;
+	
+	zero_m3(dvec_null);
+	unit_m3(dvec_pos);
+	mul_m3_fl(dvec_pos, delta * 0.5f);
+	copy_m3_m3(dvec_neg, dvec_pos);
+	negate_m3(dvec_neg);
+	
+	/* XXX TODO offset targets to account for position dependency */
+	
+	for (a = 0; a < 3; ++a) {
+		spring_angbend_forces(data, i, j, k, goal, stiffness, damping,
+		                      q, dvec_pos[a], dvec_null[a], f);
+		copy_v3_v3(dfdx[a], f);
+		
+		spring_angbend_forces(data, i, j, k, goal, stiffness, damping,
+		                      q, dvec_neg[a], dvec_null[a], f);
+		sub_v3_v3(dfdx[a], f);
+		
+		for (b = 0; b < 3; ++b) {
+			dfdx[a][b] /= delta;
+		}
+	}
+}
+
+/* Finite Differences method for estimating the jacobian of the force */
+BLI_INLINE void spring_angbend_estimate_dfdv(Implicit_Data *data, int i, int j, int k,
+                                             const float goal[3],
+                                             float stiffness, float damping,
+                                             int q, float dfdv[3][3])
+{
+	const float delta = 0.00001f; // TODO find a good heuristic for this
+	float dvec_null[3][3], dvec_pos[3][3], dvec_neg[3][3];
+	float f[3];
+	int a, b;
+	
+	zero_m3(dvec_null);
+	unit_m3(dvec_pos);
+	mul_m3_fl(dvec_pos, delta * 0.5f);
+	copy_m3_m3(dvec_neg, dvec_pos);
+	negate_m3(dvec_neg);
+	
+	/* XXX TODO offset targets to account for position dependency */
+	
+	for (a = 0; a < 3; ++a) {
+		spring_angbend_forces(data, i, j, k, goal, stiffness, damping,
+		                      q, dvec_null[a], dvec_pos[a], f);
+		copy_v3_v3(dfdv[a], f);
+		
+		spring_angbend_forces(data, i, j, k, goal, stiffness, damping,
+		                      q, dvec_null[a], dvec_neg[a], f);
+		sub_v3_v3(dfdv[a], f);
+		
+		for (b = 0; b < 3; ++b) {
+			dfdv[a][b] /= delta;
+		}
+	}
+}
+
+/* Angular spring that pulls the vertex toward the local target
+ * See "Artistic Simulation of Curly Hair" (Pixar technical memo #12-03a)
+ */
+bool BPH_mass_spring_force_spring_bending_angular(Implicit_Data *data, int i, int j, int k,
+                                                  const float target[3], float stiffness, float damping)
+{
+	float goal[3];
+	float fj[3], fk[3];
+	float dfj_dxi[3][3], dfj_dxj[3][3], dfk_dxi[3][3], dfk_dxj[3][3], dfk_dxk[3][3];
+	float dfj_dvi[3][3], dfj_dvj[3][3], dfk_dvi[3][3], dfk_dvj[3][3], dfk_dvk[3][3];
+	
+	const float vecnull[3] = {0.0f, 0.0f, 0.0f};
+	
+	world_to_root_v3(data, j, goal, target);
+	
+	spring_angbend_forces(data, i, j, k, goal, stiffness, damping, k, vecnull, vecnull, fk);
+	negate_v3_v3(fj, fk); /* counterforce */
+	
+	spring_angbend_estimate_dfdx(data, i, j, k, goal, stiffness, damping, i, dfk_dxi);
+	spring_angbend_estimate_dfdx(data, i, j, k, goal, stiffness, damping, j, dfk_dxj);
+	spring_angbend_estimate_dfdx(data, i, j, k, goal, stiffness, damping, k, dfk_dxk);
+	copy_m3_m3(dfj_dxi, dfk_dxi); negate_m3(dfj_dxi);
+	copy_m3_m3(dfj_dxj, dfk_dxj); negate_m3(dfj_dxj);
+	
+	spring_angbend_estimate_dfdv(data, i, j, k, goal, stiffness, damping, i, dfk_dvi);
+	spring_angbend_estimate_dfdv(data, i, j, k, goal, stiffness, damping, j, dfk_dvj);
+	spring_angbend_estimate_dfdv(data, i, j, k, goal, stiffness, damping, k, dfk_dvk);
+	copy_m3_m3(dfj_dvi, dfk_dvi); negate_m3(dfj_dvi);
+	copy_m3_m3(dfj_dvj, dfk_dvj); negate_m3(dfj_dvj);
+	
+	/* add forces and jacobians to the solver data */
+	
+	add_v3_v3(data->F.v3(j), fj);
+	add_v3_v3(data->F.v3(k), fk);
+	
+	data->idFdX.add(j, j, dfj_dxj);
+	data->idFdX.add(k, k, dfk_dxk);
+	
+	data->idFdX.add(i, j, dfj_dxi);
+	data->idFdX.add(j, i, dfj_dxi);
+	data->idFdX.add(j, k, dfk_dxj);
+	data->idFdX.add(k, j, dfk_dxj);
+	data->idFdX.add(i, k, dfk_dxi);
+	data->idFdX.add(k, i, dfk_dxi);
+	
+	data->idFdV.add(j, j, dfj_dvj);
+	data->idFdV.add(k, k, dfk_dvk);
+	
+	data->idFdV.add(i, j, dfj_dvi);
+	data->idFdV.add(j, i, dfj_dvi);
+	data->idFdV.add(j, k, dfk_dvj);
+	data->idFdV.add(k, j, dfk_dvj);
+	data->idFdV.add(i, k, dfk_dvi);
+	data->idFdV.add(k, i, dfk_dvi);
+
+	/* XXX analytical calculation of derivatives below is incorrect.
+	 * This proved to be difficult, but for now just using the finite difference method for
+	 * estimating the jacobians should be sufficient.
+	 */
+#if 0
+	float edge_ij[3], dir_ij[3], grad_dir_ij[3][3];
+	float edge_jk[3], dir_jk[3], grad_dir_jk[3][3];
+	float dist[3], vel_jk[3], vel_jk_ortho[3], projvel[3];
+	float target[3];
+	float tmp[3][3];
+	float fi[3], fj[3], fk[3];
+	float dfi_dxi[3][3], dfj_dxi[3][3], dfj_dxj[3][3], dfk_dxi[3][3], dfk_dxj[3][3], dfk_dxk[3][3];
+	float dfdvi[3][3];
+	
+	// TESTING
+	damping = 0.0f;
+	
+	zero_v3(fi);
+	zero_v3(fj);
+	zero_v3(fk);
+	zero_m3(dfi_dxi);
+	zero_m3(dfj_dxi);
+	zero_m3(dfk_dxi);
+	zero_m3(dfk_dxj);
+	zero_m3(dfk_dxk);
+	
+	/* jacobian of direction vectors */
+	spring_grad_dir(data, i, j, edge_ij, dir_ij, grad_dir_ij);
+	spring_grad_dir(data, j, k, edge_jk, dir_jk, grad_dir_jk);
+	
+	sub_v3_v3v3(vel_jk, data->V[k], data->V[j]);
+	
+	/* bending force */
+	mul_v3_v3fl(target, dir_ij, restlen);
+	sub_v3_v3v3(dist, target, edge_jk);
+	mul_v3_v3fl(fk, dist, stiffness);
+	
+	/* damping force */
+	madd_v3_v3v3fl(vel_jk_ortho, vel_jk, dir_jk, -dot_v3v3(vel_jk, dir_jk));
+	madd_v3_v3fl(fk, vel_jk_ortho, damping);
+	
+	/* XXX this only holds true as long as we assume straight rest shape!
+	 * eventually will become a bit more involved since the opposite segment
+	 * gets its own target, under condition of having equal torque on both sides.
+	 */
+	copy_v3_v3(fi, fk);
+	
+	/* counterforce on the middle point */
+	sub_v3_v3(fj, fi);
+	sub_v3_v3(fj, fk);
+	
+	/* === derivatives === */
+	
+	madd_m3_m3fl(dfk_dxi, grad_dir_ij, stiffness * restlen);
+	
+	madd_m3_m3fl(dfk_dxj, grad_dir_ij, -stiffness * restlen);
+	madd_m3_m3fl(dfk_dxj, I, stiffness);
+	
+	madd_m3_m3fl(dfk_dxk, I, -stiffness);
+	
+	copy_m3_m3(dfi_dxi, dfk_dxk);
+	negate_m3(dfi_dxi);
+	
+	/* dfj_dfi == dfi_dfj due to symmetry,
+	 * dfi_dfj == dfk_dfj due to fi == fk
+	 * XXX see comment above on future bent rest shapes
+	 */
+	copy_m3_m3(dfj_dxi, dfk_dxj);
+	
+	/* dfj_dxj == -(dfi_dxj + dfk_dxj) due to fj == -(fi + fk) */
+	sub_m3_m3m3(dfj_dxj, dfj_dxj, dfj_dxi);
+	sub_m3_m3m3(dfj_dxj, dfj_dxj, dfk_dxj);
+	
+	/* add forces and jacobians to the solver data */
+	add_v3_v3(data->F[i], fi);
+	add_v3_v3(data->F[j], fj);
+	add_v3_v3(data->F[k], fk);
+	
+	add_m3_m3m3(data->dFdX[i].m, data->dFdX[i].m, dfi_dxi);
+	add_m3_m3m3(data->dFdX[j].m, data->dFdX[j].m, dfj_dxj);
+	add_m3_m3m3(data->dFdX[k].m, data->dFdX[k].m, dfk_dxk);
+	
+	add_m3_m3m3(data->dFdX[block_ij].m, data->dFdX[block_ij].m, dfj_dxi);
+	add_m3_m3m3(data->dFdX[block_jk].m, data->dFdX[block_jk].m, dfk_dxj);
+	add_m3_m3m3(data->dFdX[block_ik].m, data->dFdX[block_ik].m, dfk_dxi);
+#endif
+	
+	return true;
+}
+
+bool BPH_mass_spring_force_spring_goal(Implicit_Data *data, int i, const float goal_x[3], const float goal_v[3],
+                                       float stiffness, float damping,
+                                       float r_f[3], float r_dfdx[3][3], float r_dfdv[3][3])
+{
+	float root_goal_x[3], root_goal_v[3], extent[3], length, dir[3], vel[3];
+	float f[3], dfdx[3][3], dfdv[3][3];
+	
+	/* goal is in world space */
+	world_to_root_v3(data, i, root_goal_x, goal_x);
+	world_to_root_v3(data, i, root_goal_v, goal_v);
+	
+	sub_v3_v3v3(extent, root_goal_x, data->X.v3(i));
+	sub_v3_v3v3(vel, root_goal_v, data->V.v3(i));
+	length = normalize_v3_v3(dir, extent);
+	
+	if (length > ALMOST_ZERO) {
+		mul_v3_v3fl(f, dir, stiffness * length);
+		
+		// Ascher & Boxman, p.21: Damping only during elonglation
+		// something wrong with it...
+		madd_v3_v3fl(f, dir, damping * dot_v3v3(vel, dir));
+		
+		dfdx_spring(dfdx, dir, length, 0.0f, stiffness);
+		dfdv_damp(dfdv, dir, damping);
+		
+		add_v3_v3(data->F.v3(i), f);
+		data->idFdX.add(i, i, dfdx);
+		data->idFdV.add(i, i, dfdv);
+		
+		if (r_f) copy_v3_v3(r_f, f);
+		if (r_dfdx) copy_m3_m3(r_dfdx, dfdx);
+		if (r_dfdv) copy_m3_m3(r_dfdv, dfdv);
+		
+		return true;
+	}
+	else {
+		if (r_f) zero_v3(r_f);
+		if (r_dfdx) zero_m3(r_dfdx);
+		if (r_dfdv) zero_m3(r_dfdv);
+		
+		return false;
+	}
 }
 
 #endif /* IMPLICIT_SOLVER_EIGEN */