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AttachProjectiveConstraint

This component belongs to the category of Projective Constraint. The AttachProjectiveConstraint works with a pair of objects, and it projects the degrees of freedom (e.g. position) and their derivatives (e.g. velocity), so that both objects are attached. As being a projective constraint, this projective constraints ensures a geometrical connection between both objects at the end of the time step, but it does not integrate the physics of both object (contrary to Lagrange based constraints).

Note that constraining objects using the data twoWay will project the constraint vertices of both object1 and object2 towards their average degrees of freedom and derivatives: 

Deriv corr = (dx2-dx1)*0.5*responseFactor*getConstraintFactor(index);
      dx1 += corr;
      dx2 -= corr;
- if false, the position of the object1 are projected onto the object2. Therefore, object2 only follows object1 without affecting the motion of object1 
dx2 = Deriv();

Usage

The AttachProjectiveConstraint requires two MechanicalObjects so that both degrees of freedom can be accessed and projected to the attached configuration. An integration scheme and a solver are also necessary to solve the linear system at each time step.

Attach given pair of particles, projecting the positions of the second particles to the first ones

Rigid2d

Templates:

  • Rigid2d

Target: Sofa.Component.Constraint.Projective

namespace: sofa::component::constraint::projective

parents:

  • PairInteractionProjectiveConstraintSet

Data

Name Description Default value
name object name unnamed
printLog if true, emits extra messages at runtime. 0
tags list of the subsets the objet belongs to
bbox this object bounding box
componentState The state of the component among (Dirty, Valid, Undefined, Loading, Invalid). Undefined
listening if true, handle the events, otherwise ignore the events 0
group ID of the group containing this constraint. This ID is used to specify which constraints are solved by which solver, by specifying in each solver which groups of constraints it should handle. 0
endTime The constraint stops acting after the given value. Use a negative value for infinite constraints -1
indices1 Indices of the source points on the first model
indices2 Indices of the fixed points on the second model
twoWay if true, projects the constraint vertices of both object1 and object2 towards their average degrees of freedom and derivatives. If false, the position of the object1 are projected onto the object2. Therefore, object2 only follows object1 without affecting the motion of object1 0
freeRotations true to keep rotations free (only used for Rigid DOFs) 0
lastFreeRotation true to keep rotation of the last attached point free (only used for Rigid DOFs) 0
restRotations true to use rest rotations local offsets (only used for Rigid DOFs) 0
lastPos position at which the attach constraint should become inactive
lastDir direction from lastPos at which the attach coustraint should become inactive
clamp true to clamp particles at lastPos instead of freeing them. 0
minDistance the constraint become inactive if the distance between the points attached is bigger than minDistance. -1
positionFactor IN: Factor applied to projection of position 1
velocityFactor IN: Factor applied to projection of velocity 1
responseFactor IN: Factor applied to projection of force/acceleration 1
constraintFactor Vector of factors adapting the application of the constraint per pair of points (0 -> the constraint is released. 1 -> the constraint is fully constrained)
Name Description Destination type name
context Graph Node containing this object (or BaseContext::getDefault() if no graph is used) BaseContext
slaves Sub-objects used internally by this object BaseObject
master nullptr for regular objects, or master object for which this object is one sub-objects BaseObject
mechanicalStates List of mechanical states to which this component is associated BaseMechanicalState
object1 First object associated to this component MechanicalState<Rigid2d>
object2 Second object associated to this component MechanicalState<Rigid2d>

Rigid3d

Templates:

  • Rigid3d

Target: Sofa.Component.Constraint.Projective

namespace: sofa::component::constraint::projective

parents:

  • PairInteractionProjectiveConstraintSet

Data

Name Description Default value
name object name unnamed
printLog if true, emits extra messages at runtime. 0
tags list of the subsets the objet belongs to
bbox this object bounding box
componentState The state of the component among (Dirty, Valid, Undefined, Loading, Invalid). Undefined
listening if true, handle the events, otherwise ignore the events 0
group ID of the group containing this constraint. This ID is used to specify which constraints are solved by which solver, by specifying in each solver which groups of constraints it should handle. 0
endTime The constraint stops acting after the given value. Use a negative value for infinite constraints -1
indices1 Indices of the source points on the first model
indices2 Indices of the fixed points on the second model
twoWay if true, projects the constraint vertices of both object1 and object2 towards their average degrees of freedom and derivatives. If false, the position of the object1 are projected onto the object2. Therefore, object2 only follows object1 without affecting the motion of object1 0
freeRotations true to keep rotations free (only used for Rigid DOFs) 0
lastFreeRotation true to keep rotation of the last attached point free (only used for Rigid DOFs) 0
restRotations true to use rest rotations local offsets (only used for Rigid DOFs) 0
lastPos position at which the attach constraint should become inactive
lastDir direction from lastPos at which the attach coustraint should become inactive
clamp true to clamp particles at lastPos instead of freeing them. 0
minDistance the constraint become inactive if the distance between the points attached is bigger than minDistance. -1
positionFactor IN: Factor applied to projection of position 1
velocityFactor IN: Factor applied to projection of velocity 1
responseFactor IN: Factor applied to projection of force/acceleration 1
constraintFactor Vector of factors adapting the application of the constraint per pair of points (0 -> the constraint is released. 1 -> the constraint is fully constrained)
Name Description Destination type name
context Graph Node containing this object (or BaseContext::getDefault() if no graph is used) BaseContext
slaves Sub-objects used internally by this object BaseObject
master nullptr for regular objects, or master object for which this object is one sub-objects BaseObject
mechanicalStates List of mechanical states to which this component is associated BaseMechanicalState
object1 First object associated to this component MechanicalState<Rigid3d>
object2 Second object associated to this component MechanicalState<Rigid3d>

Vec1d

Templates:

  • Vec1d

Target: Sofa.Component.Constraint.Projective

namespace: sofa::component::constraint::projective

parents:

  • PairInteractionProjectiveConstraintSet

Data

Name Description Default value
name object name unnamed
printLog if true, emits extra messages at runtime. 0
tags list of the subsets the objet belongs to
bbox this object bounding box
componentState The state of the component among (Dirty, Valid, Undefined, Loading, Invalid). Undefined
listening if true, handle the events, otherwise ignore the events 0
group ID of the group containing this constraint. This ID is used to specify which constraints are solved by which solver, by specifying in each solver which groups of constraints it should handle. 0
endTime The constraint stops acting after the given value. Use a negative value for infinite constraints -1
indices1 Indices of the source points on the first model
indices2 Indices of the fixed points on the second model
twoWay if true, projects the constraint vertices of both object1 and object2 towards their average degrees of freedom and derivatives. If false, the position of the object1 are projected onto the object2. Therefore, object2 only follows object1 without affecting the motion of object1 0
freeRotations true to keep rotations free (only used for Rigid DOFs) 0
lastFreeRotation true to keep rotation of the last attached point free (only used for Rigid DOFs) 0
restRotations true to use rest rotations local offsets (only used for Rigid DOFs) 0
lastPos position at which the attach constraint should become inactive
lastDir direction from lastPos at which the attach coustraint should become inactive
clamp true to clamp particles at lastPos instead of freeing them. 0
minDistance the constraint become inactive if the distance between the points attached is bigger than minDistance. -1
positionFactor IN: Factor applied to projection of position 1
velocityFactor IN: Factor applied to projection of velocity 1
responseFactor IN: Factor applied to projection of force/acceleration 1
constraintFactor Vector of factors adapting the application of the constraint per pair of points (0 -> the constraint is released. 1 -> the constraint is fully constrained)
Name Description Destination type name
context Graph Node containing this object (or BaseContext::getDefault() if no graph is used) BaseContext
slaves Sub-objects used internally by this object BaseObject
master nullptr for regular objects, or master object for which this object is one sub-objects BaseObject
mechanicalStates List of mechanical states to which this component is associated BaseMechanicalState
object1 First object associated to this component MechanicalState<Vec1d>
object2 Second object associated to this component MechanicalState<Vec1d>

Vec2d

Templates:

  • Vec2d

Target: Sofa.Component.Constraint.Projective

namespace: sofa::component::constraint::projective

parents:

  • PairInteractionProjectiveConstraintSet

Data

Name Description Default value
name object name unnamed
printLog if true, emits extra messages at runtime. 0
tags list of the subsets the objet belongs to
bbox this object bounding box
componentState The state of the component among (Dirty, Valid, Undefined, Loading, Invalid). Undefined
listening if true, handle the events, otherwise ignore the events 0
group ID of the group containing this constraint. This ID is used to specify which constraints are solved by which solver, by specifying in each solver which groups of constraints it should handle. 0
endTime The constraint stops acting after the given value. Use a negative value for infinite constraints -1
indices1 Indices of the source points on the first model
indices2 Indices of the fixed points on the second model
twoWay if true, projects the constraint vertices of both object1 and object2 towards their average degrees of freedom and derivatives. If false, the position of the object1 are projected onto the object2. Therefore, object2 only follows object1 without affecting the motion of object1 0
freeRotations true to keep rotations free (only used for Rigid DOFs) 0
lastFreeRotation true to keep rotation of the last attached point free (only used for Rigid DOFs) 0
restRotations true to use rest rotations local offsets (only used for Rigid DOFs) 0
lastPos position at which the attach constraint should become inactive
lastDir direction from lastPos at which the attach coustraint should become inactive
clamp true to clamp particles at lastPos instead of freeing them. 0
minDistance the constraint become inactive if the distance between the points attached is bigger than minDistance. -1
positionFactor IN: Factor applied to projection of position 1
velocityFactor IN: Factor applied to projection of velocity 1
responseFactor IN: Factor applied to projection of force/acceleration 1
constraintFactor Vector of factors adapting the application of the constraint per pair of points (0 -> the constraint is released. 1 -> the constraint is fully constrained)
Name Description Destination type name
context Graph Node containing this object (or BaseContext::getDefault() if no graph is used) BaseContext
slaves Sub-objects used internally by this object BaseObject
master nullptr for regular objects, or master object for which this object is one sub-objects BaseObject
mechanicalStates List of mechanical states to which this component is associated BaseMechanicalState
object1 First object associated to this component MechanicalState<Vec2d>
object2 Second object associated to this component MechanicalState<Vec2d>

Vec3d

Templates:

  • Vec3d

Target: Sofa.Component.Constraint.Projective

namespace: sofa::component::constraint::projective

parents:

  • PairInteractionProjectiveConstraintSet

Data

Name Description Default value
name object name unnamed
printLog if true, emits extra messages at runtime. 0
tags list of the subsets the objet belongs to
bbox this object bounding box
componentState The state of the component among (Dirty, Valid, Undefined, Loading, Invalid). Undefined
listening if true, handle the events, otherwise ignore the events 0
group ID of the group containing this constraint. This ID is used to specify which constraints are solved by which solver, by specifying in each solver which groups of constraints it should handle. 0
endTime The constraint stops acting after the given value. Use a negative value for infinite constraints -1
indices1 Indices of the source points on the first model
indices2 Indices of the fixed points on the second model
twoWay if true, projects the constraint vertices of both object1 and object2 towards their average degrees of freedom and derivatives. If false, the position of the object1 are projected onto the object2. Therefore, object2 only follows object1 without affecting the motion of object1 0
freeRotations true to keep rotations free (only used for Rigid DOFs) 0
lastFreeRotation true to keep rotation of the last attached point free (only used for Rigid DOFs) 0
restRotations true to use rest rotations local offsets (only used for Rigid DOFs) 0
lastPos position at which the attach constraint should become inactive
lastDir direction from lastPos at which the attach coustraint should become inactive
clamp true to clamp particles at lastPos instead of freeing them. 0
minDistance the constraint become inactive if the distance between the points attached is bigger than minDistance. -1
positionFactor IN: Factor applied to projection of position 1
velocityFactor IN: Factor applied to projection of velocity 1
responseFactor IN: Factor applied to projection of force/acceleration 1
constraintFactor Vector of factors adapting the application of the constraint per pair of points (0 -> the constraint is released. 1 -> the constraint is fully constrained)
Name Description Destination type name
context Graph Node containing this object (or BaseContext::getDefault() if no graph is used) BaseContext
slaves Sub-objects used internally by this object BaseObject
master nullptr for regular objects, or master object for which this object is one sub-objects BaseObject
mechanicalStates List of mechanical states to which this component is associated BaseMechanicalState
object1 First object associated to this component MechanicalState<Vec3d>
object2 Second object associated to this component MechanicalState<Vec3d>

Examples

AttachProjectiveConstraint.scn

<Node name="root" dt="0.02">
    <RequiredPlugin name="Sofa.Component.Constraint.Projective"/> <!-- Needed to use components [AttachProjectiveConstraint FixedProjectiveConstraint] -->
    <RequiredPlugin name="Sofa.Component.Engine.Select"/> <!-- Needed to use components [BoxROI] -->
    <RequiredPlugin name="Sofa.Component.LinearSolver.Iterative"/> <!-- Needed to use components [CGLinearSolver] -->
    <RequiredPlugin name="Sofa.Component.Mass"/> <!-- Needed to use components [UniformMass] -->
    <RequiredPlugin name="Sofa.Component.ODESolver.Backward"/> <!-- Needed to use components [EulerImplicitSolver] -->
    <RequiredPlugin name="Sofa.Component.SolidMechanics.FEM.Elastic"/> <!-- Needed to use components [TetrahedronFEMForceField] -->
    <RequiredPlugin name="Sofa.Component.StateContainer"/> <!-- Needed to use components [MechanicalObject] -->
    <RequiredPlugin name="Sofa.Component.Topology.Container.Grid"/> <!-- Needed to use components [RegularGridTopology] -->
    <RequiredPlugin name="Sofa.Component.Visual"/> <!-- Needed to use components [VisualStyle] -->

    <VisualStyle displayFlags="showBehaviorModels showForceFields" />
    <DefaultAnimationLoop/>
    <Node name="Single">
        <EulerImplicitSolver name="cg_odesolver" printLog="false"  rayleighStiffness="0.1" rayleighMass="0.1" />
        <CGLinearSolver iterations="25" name="linear solver" tolerance="1.0e-9" threshold="1.0e-9" />
        <Node name="M1">
            <MechanicalObject showObject="1"/>
            <UniformMass vertexMass="1" />
            <RegularGridTopology nx="4" ny="4" nz="28" xmin="-9" xmax="-6" ymin="0" ymax="3" zmin="0" zmax="27" />
            <BoxConstraint box="-9.1 -0.1 -0.1 -5.9 3.1 0.1" />
            <!--<BoxConstraint box="-9.1 -0.1 26.9 -5.9 3.1 27.1" />-->
            <TetrahedronFEMForceField name="FEM" youngModulus="4000" poissonRatio="0.3" />
        </Node>
    </Node>
    <Node name="AttachOneWay">
        <EulerImplicitSolver name="cg_odesolver" printLog="false" />
        <CGLinearSolver iterations="25" name="linear solver" tolerance="1.0e-9" threshold="1.0e-9" />
        <Node name="M1">
            <MechanicalObject />
            <UniformMass vertexMass="1" />
            <RegularGridTopology nx="4" ny="4" nz="10" xmin="-4" xmax="-1" ymin="0" ymax="3" zmin="0" zmax="9" />
            <BoxConstraint box="-4.1 -0.1 -0.1 -0.9 3.1 0.1" />
            <TetrahedronFEMForceField name="FEM" youngModulus="4000" poissonRatio="0.3" />
        </Node>
        <Node name="M2">
            <EulerImplicitSolver name="cg_odesolver" printLog="false" />
            <CGLinearSolver iterations="25" name="linear solver" tolerance="1.0e-9" threshold="1.0e-9" />
            <MechanicalObject />
            <UniformMass vertexMass="1" />
            <RegularGridTopology nx="4" ny="4" nz="10" xmin="-4" xmax="-1" ymin="0" ymax="3" zmin="9" zmax="18" />
            <TetrahedronFEMForceField name="FEM" youngModulus="4000" poissonRatio="0.3" />
        </Node>
        <Node name="M3">
            <EulerImplicitSolver name="cg_odesolver" printLog="false" />
            <CGLinearSolver iterations="25" name="linear solver" tolerance="1.0e-9" threshold="1.0e-9" />
            <MechanicalObject />
            <UniformMass vertexMass="1" />
            <RegularGridTopology nx="4" ny="4" nz="10" xmin="-4" xmax="-1" ymin="0" ymax="3" zmin="18" zmax="27" />
            <!--<BoxConstraint box="-4.1 -0.1 26.9 -0.9 3.1 27.1" />-->
            <TetrahedronFEMForceField name="FEM" youngModulus="4000" poissonRatio="0.3" />
        </Node>
        <AttachProjectiveConstraint object1="@M1" object2="@M2" indices1="144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159" indices2="0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15" constraintFactor="1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1"/>
        <AttachProjectiveConstraint object1="@M2" object2="@M3" indices1="144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159" indices2="0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15" constraintFactor="1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1"/>
    </Node>
    <Node name="AttachTwoWay">
        <EulerImplicitSolver name="cg_odesolver" printLog="false" />
        <CGLinearSolver iterations="25" name="linear solver" tolerance="1.0e-9" threshold="1.0e-9" />
        <Node name="M1">
            <MechanicalObject />
            <UniformMass vertexMass="1" />
            <RegularGridTopology nx="4" ny="4" nz="10" xmin="1" xmax="4" ymin="0" ymax="3" zmin="0" zmax="9" />
            <BoxConstraint box="0.9 -0.1 -0.1 4.1 3.1 0.1" />
            <TetrahedronFEMForceField name="FEM" youngModulus="4000" poissonRatio="0.3" />
        </Node>
        <Node name="M2">
            <EulerImplicitSolver name="cg_odesolver" printLog="false" />
            <CGLinearSolver iterations="25" name="linear solver" tolerance="1.0e-9" threshold="1.0e-9" />
            <MechanicalObject />
            <UniformMass vertexMass="1" />
            <RegularGridTopology nx="4" ny="4" nz="10" xmin="1" xmax="4" ymin="0" ymax="3" zmin="9" zmax="18" />
            <TetrahedronFEMForceField name="FEM" youngModulus="4000" poissonRatio="0.3" />
        </Node>
        <Node name="M3">
            <EulerImplicitSolver name="cg_odesolver" printLog="false" />
            <CGLinearSolver iterations="25" name="linear solver" tolerance="1.0e-9" threshold="1.0e-9" />
            <MechanicalObject />
            <UniformMass vertexMass="1" />
            <RegularGridTopology nx="4" ny="4" nz="10" xmin="1" xmax="4" ymin="0" ymax="3" zmin="18" zmax="27" />
            <!--<BoxConstraint box="0.9 -0.1 26.9 4.1 3.1 27.1" />-->
            <TetrahedronFEMForceField name="FEM" youngModulus="4000" poissonRatio="0.3" />
        </Node>
        <AttachProjectiveConstraint object1="@M1" object2="@M2" twoWay="true" indices1="144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159" indices2="0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15" constraintFactor="1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1"/>
        <AttachProjectiveConstraint object1="@M2" object2="@M3" twoWay="true" indices1="144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159" indices2="0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15"/>
    </Node>
</Node>

def createScene(root_node):

   root = root_node.addChild('root', dt="0.02")

   root.addObject('RequiredPlugin', name="Sofa.Component.Constraint.Projective")
   root.addObject('RequiredPlugin', name="Sofa.Component.Engine.Select")
   root.addObject('RequiredPlugin', name="Sofa.Component.LinearSolver.Iterative")
   root.addObject('RequiredPlugin', name="Sofa.Component.Mass")
   root.addObject('RequiredPlugin', name="Sofa.Component.ODESolver.Backward")
   root.addObject('RequiredPlugin', name="Sofa.Component.SolidMechanics.FEM.Elastic")
   root.addObject('RequiredPlugin', name="Sofa.Component.StateContainer")
   root.addObject('RequiredPlugin', name="Sofa.Component.Topology.Container.Grid")
   root.addObject('RequiredPlugin', name="Sofa.Component.Visual")
   root.addObject('VisualStyle', displayFlags="showBehaviorModels showForceFields")
   root.addObject('DefaultAnimationLoop', )

   single = root.addChild('Single')

   single.addObject('EulerImplicitSolver', name="cg_odesolver", printLog="false", rayleighStiffness="0.1", rayleighMass="0.1")
   single.addObject('CGLinearSolver', iterations="25", name="linear solver", tolerance="1.0e-9", threshold="1.0e-9")

   m1 = Single.addChild('M1')

   m1.addObject('MechanicalObject', showObject="1")
   m1.addObject('UniformMass', vertexMass="1")
   m1.addObject('RegularGridTopology', nx="4", ny="4", nz="28", xmin="-9", xmax="-6", ymin="0", ymax="3", zmin="0", zmax="27")
   m1.addObject('BoxConstraint', box="-9.1 -0.1 -0.1 -5.9 3.1 0.1")
   m1.addObject('TetrahedronFEMForceField', name="FEM", youngModulus="4000", poissonRatio="0.3")

   attach_one_way = root.addChild('AttachOneWay')

   attach_one_way.addObject('EulerImplicitSolver', name="cg_odesolver", printLog="false")
   attach_one_way.addObject('CGLinearSolver', iterations="25", name="linear solver", tolerance="1.0e-9", threshold="1.0e-9")

   m1 = AttachOneWay.addChild('M1')

   m1.addObject('MechanicalObject', )
   m1.addObject('UniformMass', vertexMass="1")
   m1.addObject('RegularGridTopology', nx="4", ny="4", nz="10", xmin="-4", xmax="-1", ymin="0", ymax="3", zmin="0", zmax="9")
   m1.addObject('BoxConstraint', box="-4.1 -0.1 -0.1 -0.9 3.1 0.1")
   m1.addObject('TetrahedronFEMForceField', name="FEM", youngModulus="4000", poissonRatio="0.3")

   m2 = AttachOneWay.addChild('M2')

   m2.addObject('EulerImplicitSolver', name="cg_odesolver", printLog="false")
   m2.addObject('CGLinearSolver', iterations="25", name="linear solver", tolerance="1.0e-9", threshold="1.0e-9")
   m2.addObject('MechanicalObject', )
   m2.addObject('UniformMass', vertexMass="1")
   m2.addObject('RegularGridTopology', nx="4", ny="4", nz="10", xmin="-4", xmax="-1", ymin="0", ymax="3", zmin="9", zmax="18")
   m2.addObject('TetrahedronFEMForceField', name="FEM", youngModulus="4000", poissonRatio="0.3")

   m3 = AttachOneWay.addChild('M3')

   m3.addObject('EulerImplicitSolver', name="cg_odesolver", printLog="false")
   m3.addObject('CGLinearSolver', iterations="25", name="linear solver", tolerance="1.0e-9", threshold="1.0e-9")
   m3.addObject('MechanicalObject', )
   m3.addObject('UniformMass', vertexMass="1")
   m3.addObject('RegularGridTopology', nx="4", ny="4", nz="10", xmin="-4", xmax="-1", ymin="0", ymax="3", zmin="18", zmax="27")
   m3.addObject('TetrahedronFEMForceField', name="FEM", youngModulus="4000", poissonRatio="0.3")

   attach_one_way.addObject('AttachProjectiveConstraint', object1="@M1", object2="@M2", indices1="144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159", indices2="0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15", constraintFactor="1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1")
   attach_one_way.addObject('AttachProjectiveConstraint', object1="@M2", object2="@M3", indices1="144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159", indices2="0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15", constraintFactor="1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1")

   attach_two_way = root.addChild('AttachTwoWay')

   attach_two_way.addObject('EulerImplicitSolver', name="cg_odesolver", printLog="false")
   attach_two_way.addObject('CGLinearSolver', iterations="25", name="linear solver", tolerance="1.0e-9", threshold="1.0e-9")

   m1 = AttachTwoWay.addChild('M1')

   m1.addObject('MechanicalObject', )
   m1.addObject('UniformMass', vertexMass="1")
   m1.addObject('RegularGridTopology', nx="4", ny="4", nz="10", xmin="1", xmax="4", ymin="0", ymax="3", zmin="0", zmax="9")
   m1.addObject('BoxConstraint', box="0.9 -0.1 -0.1 4.1 3.1 0.1")
   m1.addObject('TetrahedronFEMForceField', name="FEM", youngModulus="4000", poissonRatio="0.3")

   m2 = AttachTwoWay.addChild('M2')

   m2.addObject('EulerImplicitSolver', name="cg_odesolver", printLog="false")
   m2.addObject('CGLinearSolver', iterations="25", name="linear solver", tolerance="1.0e-9", threshold="1.0e-9")
   m2.addObject('MechanicalObject', )
   m2.addObject('UniformMass', vertexMass="1")
   m2.addObject('RegularGridTopology', nx="4", ny="4", nz="10", xmin="1", xmax="4", ymin="0", ymax="3", zmin="9", zmax="18")
   m2.addObject('TetrahedronFEMForceField', name="FEM", youngModulus="4000", poissonRatio="0.3")

   m3 = AttachTwoWay.addChild('M3')

   m3.addObject('EulerImplicitSolver', name="cg_odesolver", printLog="false")
   m3.addObject('CGLinearSolver', iterations="25", name="linear solver", tolerance="1.0e-9", threshold="1.0e-9")
   m3.addObject('MechanicalObject', )
   m3.addObject('UniformMass', vertexMass="1")
   m3.addObject('RegularGridTopology', nx="4", ny="4", nz="10", xmin="1", xmax="4", ymin="0", ymax="3", zmin="18", zmax="27")
   m3.addObject('TetrahedronFEMForceField', name="FEM", youngModulus="4000", poissonRatio="0.3")

   attach_two_way.addObject('AttachProjectiveConstraint', object1="@M1", object2="@M2", twoWay="true", indices1="144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159", indices2="0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15", constraintFactor="1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1")
   attach_two_way.addObject('AttachProjectiveConstraint', object1="@M2", object2="@M3", twoWay="true", indices1="144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159", indices2="0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15")

AttachProjectiveConstraintMatrix.scn

<Node name="root" dt="0.02">
    <RequiredPlugin name="Sofa.Component.Constraint.Projective"/> <!-- Needed to use components [AttachProjectiveConstraint FixedProjectiveConstraint] -->
    <RequiredPlugin name="Sofa.Component.Engine.Select"/> <!-- Needed to use components [BoxROI] -->
    <RequiredPlugin name="Sofa.Component.LinearSolver.Direct"/> <!-- Needed to use components [EigenSimplicialLDLT] -->
    <RequiredPlugin name="Sofa.Component.LinearSolver.Iterative"/> <!-- Needed to use components [CGLinearSolver] -->
    <RequiredPlugin name="Sofa.Component.Mass"/> <!-- Needed to use components [UniformMass] -->
    <RequiredPlugin name="Sofa.Component.ODESolver.Backward"/> <!-- Needed to use components [EulerImplicitSolver] -->
    <RequiredPlugin name="Sofa.Component.SolidMechanics.FEM.Elastic"/> <!-- Needed to use components [TetrahedronFEMForceField] -->
    <RequiredPlugin name="Sofa.Component.StateContainer"/> <!-- Needed to use components [MechanicalObject] -->
    <RequiredPlugin name="Sofa.Component.Topology.Container.Grid"/> <!-- Needed to use components [RegularGridTopology] -->
    <RequiredPlugin name="Sofa.Component.Visual"/> <!-- Needed to use components [VisualStyle] -->

    <VisualStyle displayFlags="showBehaviorModels showForceFields" />
    <DefaultAnimationLoop/>
    <Node name="AttachOneWay">
        <EulerImplicitSolver name="cg_odesolver" printLog="false"  rayleighStiffness="0.1" rayleighMass="0.1" />
        <CGLinearSolver iterations="25" name="linear solver" tolerance="1.0e-9" threshold="1.0e-9" />
        <Node name="M1">
            <MechanicalObject showObject="1"/>
            <UniformMass vertexMass="1" />
            <RegularGridTopology nx="4" ny="4" nz="10" xmin="1" xmax="4" ymin="0" ymax="3" zmin="0" zmax="9" />
            <BoxConstraint box="0.9 -0.1 -0.1 4.1 3.1 0.1" />
            <TetrahedronFEMForceField name="FEM" youngModulus="4000" poissonRatio="0.3" />
        </Node>
        <Node name="M2">
            <MechanicalObject />
            <UniformMass vertexMass="1" />
            <RegularGridTopology nx="4" ny="4" nz="10" xmin="1" xmax="4" ymin="0" ymax="3" zmin="9" zmax="18" />
            <TetrahedronFEMForceField name="FEM" youngModulus="4000" poissonRatio="0.3" />
        </Node>
        <!--
        <Node name="M3">
            <EulerImplicitSolver name="cg_odesolver" printLog="false"/>
            <CGLinearSolver iterations="25" name="linear solver" tolerance="1.0e-9" threshold="1.0e-9"/>
            <MechanicalObject/>
            <UniformMass vertexMass="1"/>
            <RegularGridTopology nx="4" ny="4" nz="10" xmin="1" xmax="4" ymin="0" ymax="3" zmin="18" zmax="27"/>
            <TetrahedronFEMForceField name="FEM" youngModulus="4000" poissonRatio="0.3"/>
        </Node>
        -->
        <AttachProjectiveConstraint object1="@M1" object2="@M2" indices1="144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159" indices2="0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15"/>
        <!--    <AttachProjectiveConstraint object1="@M2" object2="@M3" radius="0.1" indices1="144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159" indices2="0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15" constraintFactor="1"/> -->
    </Node>
    <Node name="AttachOneWay2">
        <EulerImplicitSolver name="cg_odesolver" printLog="false" />
        <EigenSimplicialLDLT template="CompressedRowSparseMatrixMat3x3"/>
        <Node name="M1">
            <MechanicalObject />
            <UniformMass vertexMass="1" />
            <RegularGridTopology nx="4" ny="4" nz="10" xmin="-4" xmax="-1" ymin="0" ymax="3" zmin="0" zmax="9" />
            <BoxConstraint box="-4.1 -0.9 -0.1 4.1 3.1 0.1" />
            <TetrahedronFEMForceField name="FEM" youngModulus="4000" poissonRatio="0.3" />
        </Node>
        <Node name="M2">
            <MechanicalObject />
            <UniformMass vertexMass="1" />
            <RegularGridTopology nx="4" ny="4" nz="10" xmin="-4" xmax="-1" ymin="0" ymax="3" zmin="9" zmax="18" />
            <TetrahedronFEMForceField name="FEM" youngModulus="4000" poissonRatio="0.3" />
        </Node>
        <!--
        <Node name="M3">
            <EulerImplicitSolver name="cg_odesolver" printLog="false"/>
            <CGLinearSolver iterations="25" name="linear solver" tolerance="1.0e-9" threshold="1.0e-9"/>
            <MechanicalObject/>
            <UniformMass vertexMass="1"/>
            <RegularGridTopology nx="4" ny="4" nz="10" xmin="-4" xmax="-1" ymin="0" ymax="3" zmin="18" zmax="27"/>
            <TetrahedronFEMForceField name="FEM" youngModulus="4000" poissonRatio="0.3"/>
        </Node>
        -->
        <AttachProjectiveConstraint object1="@M1" object2="@M2" indices1="144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159" indices2="0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15"/>
        <!--    <AttachProjectiveConstraint object1="@M2" object2="@M3" radius="0.1" indices1="144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159" indices2="0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15" constraintFactor="1"/> -->
    </Node>
</Node>

def createScene(root_node):

   root = root_node.addChild('root', dt="0.02")

   root.addObject('RequiredPlugin', name="Sofa.Component.Constraint.Projective")
   root.addObject('RequiredPlugin', name="Sofa.Component.Engine.Select")
   root.addObject('RequiredPlugin', name="Sofa.Component.LinearSolver.Direct")
   root.addObject('RequiredPlugin', name="Sofa.Component.LinearSolver.Iterative")
   root.addObject('RequiredPlugin', name="Sofa.Component.Mass")
   root.addObject('RequiredPlugin', name="Sofa.Component.ODESolver.Backward")
   root.addObject('RequiredPlugin', name="Sofa.Component.SolidMechanics.FEM.Elastic")
   root.addObject('RequiredPlugin', name="Sofa.Component.StateContainer")
   root.addObject('RequiredPlugin', name="Sofa.Component.Topology.Container.Grid")
   root.addObject('RequiredPlugin', name="Sofa.Component.Visual")
   root.addObject('VisualStyle', displayFlags="showBehaviorModels showForceFields")
   root.addObject('DefaultAnimationLoop', )

   attach_one_way = root.addChild('AttachOneWay')

   attach_one_way.addObject('EulerImplicitSolver', name="cg_odesolver", printLog="false", rayleighStiffness="0.1", rayleighMass="0.1")
   attach_one_way.addObject('CGLinearSolver', iterations="25", name="linear solver", tolerance="1.0e-9", threshold="1.0e-9")

   m1 = AttachOneWay.addChild('M1')

   m1.addObject('MechanicalObject', showObject="1")
   m1.addObject('UniformMass', vertexMass="1")
   m1.addObject('RegularGridTopology', nx="4", ny="4", nz="10", xmin="1", xmax="4", ymin="0", ymax="3", zmin="0", zmax="9")
   m1.addObject('BoxConstraint', box="0.9 -0.1 -0.1 4.1 3.1 0.1")
   m1.addObject('TetrahedronFEMForceField', name="FEM", youngModulus="4000", poissonRatio="0.3")

   m2 = AttachOneWay.addChild('M2')

   m2.addObject('MechanicalObject', )
   m2.addObject('UniformMass', vertexMass="1")
   m2.addObject('RegularGridTopology', nx="4", ny="4", nz="10", xmin="1", xmax="4", ymin="0", ymax="3", zmin="9", zmax="18")
   m2.addObject('TetrahedronFEMForceField', name="FEM", youngModulus="4000", poissonRatio="0.3")

   attach_one_way.addObject('AttachProjectiveConstraint', object1="@M1", object2="@M2", indices1="144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159", indices2="0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15")

   attach_one_way2 = root.addChild('AttachOneWay2')

   attach_one_way2.addObject('EulerImplicitSolver', name="cg_odesolver", printLog="false")
   attach_one_way2.addObject('EigenSimplicialLDLT', template="CompressedRowSparseMatrixMat3x3")

   m1 = AttachOneWay2.addChild('M1')

   m1.addObject('MechanicalObject', )
   m1.addObject('UniformMass', vertexMass="1")
   m1.addObject('RegularGridTopology', nx="4", ny="4", nz="10", xmin="-4", xmax="-1", ymin="0", ymax="3", zmin="0", zmax="9")
   m1.addObject('BoxConstraint', box="-4.1 -0.9 -0.1 4.1 3.1 0.1")
   m1.addObject('TetrahedronFEMForceField', name="FEM", youngModulus="4000", poissonRatio="0.3")

   m2 = AttachOneWay2.addChild('M2')

   m2.addObject('MechanicalObject', )
   m2.addObject('UniformMass', vertexMass="1")
   m2.addObject('RegularGridTopology', nx="4", ny="4", nz="10", xmin="-4", xmax="-1", ymin="0", ymax="3", zmin="9", zmax="18")
   m2.addObject('TetrahedronFEMForceField', name="FEM", youngModulus="4000", poissonRatio="0.3")

   attach_one_way2.addObject('AttachProjectiveConstraint', object1="@M1", object2="@M2", indices1="144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159", indices2="0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15")