FixedProjectiveConstraint
This component belongs to the category of Projective Constraint. The FixedProjectiveConstraint projects a constant velocity. If the fixed points have a zero velocity at the simulation start, they will keep a zero velocity i.e. be fixed.
As introduced in the page about the Projective Constraint, the FixedProjectiveConstraint corresponds to a projection matrix noted \(\mathbf{P}\) which will multiply the system matrix \(\mathbf{A}\) so that: \(\mathbf{P}^T\mathbf{A}\mathbf{P}\Deltav=\mathbf{P}^Tb\). This projection matrix \(\mathbf{P}\) is the identity matrix in which the diagonal value corresponding to the indices of the fixed points equals zero. These lines and columns equals 0. As a consequence, when the integration scheme (ODESolver) will call the projectResponse() or projectVelocity() the constraint will be applied, ensuring that the desired degrees of freedom remain fixed.
Example of a system of size 6, with a fixed constraint at the index 5:
\[
\mathbf{P}=\begin{bmatrix}1&0&0&0&0&0\\0&1&0&0&0&0\\0&0&1&0&0&0\\0&0&0&1&0&0\\0&0&0&0&\mathbf{0}&0\\0&0&0&0&0&1\end{bmatrix}
\]
By projecting this \(\mathbf{P}\) matrix on the right hand side vector we have \(\mathbf{P}^Tb\). This ensures to have the projection \(b[5]=0\), thus preventing any time evolution of the fifth degree of freedom. In such case, we function projectResponse():
template <class DataTypes>
void FixedProjectiveConstraint<DataTypes>::projectResponse(const core::MechanicalParams* mparams, DataVecDeriv& resData)
{
SOFA_UNUSED(mparams);
helper::WriteAccessor<DataVecDeriv> res (resData );
const SetIndexArray & indices = d_indices.getValue();
if( d_fixAll.getValue() )
{
// fix everything
typename VecDeriv::iterator it;
for( it = res.begin(); it != res.end(); ++it )
{
*it = Deriv();
}
}
else
{
for (SetIndexArray::const_iterator it = indices.begin(); it != indices.end(); ++it)
{
res[*it] = Deriv();
}
}
}
Usage
The FixedProjectiveConstraint requires a MechanicalObject to store the degrees of freedom associated to the nodes, as well as a Mass so that the system matrix is not null. An integration scheme and a solver are also necessary to solve the linear system at each time step.
Note that if only a part of the degrees of freedom must be constraint, you can use the PartialFixedProjectiveConstraint working in the same way as the FixedProjectiveConstraint.
Attach given particles to their initial positions
Rigid2d
Templates:
- Rigid2d
Target: Sofa.Component.Constraint.Projective
namespace: sofa::component::constraint::projective
parents:
- ProjectiveConstraintSet
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 |
| indices | Indices of the fixed points | |
| fixAll | filter all the DOF to implement a fixed object | 0 |
| activate_projectVelocity | if true, projects not only a constant but a zero velocity | 0 |
| Visualization | ||
| showObject | draw or not the fixed constraints | 1 |
| drawSize | Size of the rendered particles (0 -> point based rendering, >0 -> radius of spheres) | 0 |
Links
| 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 |
| mstate | MechanicalState used by this component | MechanicalState<Rigid2d> |
| topology | link to the topology container | BaseMeshTopology |
Rigid3d
Templates:
- Rigid3d
Target: Sofa.Component.Constraint.Projective
namespace: sofa::component::constraint::projective
parents:
- ProjectiveConstraintSet
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 |
| indices | Indices of the fixed points | |
| fixAll | filter all the DOF to implement a fixed object | 0 |
| activate_projectVelocity | if true, projects not only a constant but a zero velocity | 0 |
| Visualization | ||
| showObject | draw or not the fixed constraints | 1 |
| drawSize | Size of the rendered particles (0 -> point based rendering, >0 -> radius of spheres) | 0 |
Links
| 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 |
| mstate | MechanicalState used by this component | MechanicalState<Rigid3d> |
| topology | link to the topology container | BaseMeshTopology |
Vec1d
Templates:
- Vec1d
Target: Sofa.Component.Constraint.Projective
namespace: sofa::component::constraint::projective
parents:
- ProjectiveConstraintSet
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 |
| indices | Indices of the fixed points | |
| fixAll | filter all the DOF to implement a fixed object | 0 |
| activate_projectVelocity | if true, projects not only a constant but a zero velocity | 0 |
| Visualization | ||
| showObject | draw or not the fixed constraints | 1 |
| drawSize | Size of the rendered particles (0 -> point based rendering, >0 -> radius of spheres) | 0 |
Links
| 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 |
| mstate | MechanicalState used by this component | MechanicalState<Vec1d> |
| topology | link to the topology container | BaseMeshTopology |
Vec2d
Templates:
- Vec2d
Target: Sofa.Component.Constraint.Projective
namespace: sofa::component::constraint::projective
parents:
- ProjectiveConstraintSet
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 |
| indices | Indices of the fixed points | |
| fixAll | filter all the DOF to implement a fixed object | 0 |
| activate_projectVelocity | if true, projects not only a constant but a zero velocity | 0 |
| Visualization | ||
| showObject | draw or not the fixed constraints | 1 |
| drawSize | Size of the rendered particles (0 -> point based rendering, >0 -> radius of spheres) | 0 |
Links
| 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 |
| mstate | MechanicalState used by this component | MechanicalState<Vec2d> |
| topology | link to the topology container | BaseMeshTopology |
Vec3d
Templates:
- Vec3d
Target: Sofa.Component.Constraint.Projective
namespace: sofa::component::constraint::projective
parents:
- ProjectiveConstraintSet
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 |
| indices | Indices of the fixed points | |
| fixAll | filter all the DOF to implement a fixed object | 0 |
| activate_projectVelocity | if true, projects not only a constant but a zero velocity | 0 |
| Visualization | ||
| showObject | draw or not the fixed constraints | 1 |
| drawSize | Size of the rendered particles (0 -> point based rendering, >0 -> radius of spheres) | 0 |
Links
| 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 |
| mstate | MechanicalState used by this component | MechanicalState<Vec3d> |
| topology | link to the topology container | BaseMeshTopology |
Vec6d
Templates:
- Vec6d
Target: Sofa.Component.Constraint.Projective
namespace: sofa::component::constraint::projective
parents:
- ProjectiveConstraintSet
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 |
| indices | Indices of the fixed points | |
| fixAll | filter all the DOF to implement a fixed object | 0 |
| activate_projectVelocity | if true, projects not only a constant but a zero velocity | 0 |
| Visualization | ||
| showObject | draw or not the fixed constraints | 1 |
| drawSize | Size of the rendered particles (0 -> point based rendering, >0 -> radius of spheres) | 0 |
Links
| 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 |
| mstate | MechanicalState used by this component | MechanicalState<Vec6d> |
| topology | link to the topology container | BaseMeshTopology |
Examples
FixedProjectiveConstraint.scn
<Node name="root" dt="0.02">
<RequiredPlugin name="Sofa.Component.Collision.Detection.Algorithm"/> <!-- Needed to use components [BVHNarrowPhase BruteForceBroadPhase CollisionPipeline] -->
<RequiredPlugin name="Sofa.Component.Collision.Detection.Intersection"/> <!-- Needed to use components [DiscreteIntersection] -->
<RequiredPlugin name="Sofa.Component.Collision.Geometry"/> <!-- Needed to use components [SphereCollisionModel] -->
<RequiredPlugin name="Sofa.Component.Collision.Response.Contact"/> <!-- Needed to use components [CollisionResponse] -->
<RequiredPlugin name="Sofa.Component.Constraint.Projective"/> <!-- Needed to use components [FixedProjectiveConstraint] -->
<RequiredPlugin name="Sofa.Component.IO.Mesh"/> <!-- Needed to use components [MeshGmshLoader MeshOBJLoader SphereLoader] -->
<RequiredPlugin name="Sofa.Component.LinearSolver.Iterative"/> <!-- Needed to use components [CGLinearSolver] -->
<RequiredPlugin name="Sofa.Component.Mapping.Linear"/> <!-- Needed to use components [BarycentricMapping] -->
<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.Constant"/> <!-- Needed to use components [MeshTopology] -->
<RequiredPlugin name="Sofa.Component.Visual"/> <!-- Needed to use components [VisualStyle] -->
<RequiredPlugin name="Sofa.GL.Component.Rendering3D"/> <!-- Needed to use components [OglModel] -->
<DefaultAnimationLoop/>
<VisualStyle displayFlags="showBehaviorModels" />
<CollisionPipeline verbose="0" name="CollisionPipeline" />
<BruteForceBroadPhase/>
<BVHNarrowPhase/>
<CollisionResponse response="PenalityContactForceField" name="collision response" />
<DiscreteIntersection />
<Node name="Liver">
<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" />
<MeshGmshLoader name="loader" filename="mesh/liver.msh" />
<MeshTopology src="@loader" />
<MechanicalObject src="@loader" name="dofs" />
<UniformMass name="mass" vertexMass="0.05" />
<TetrahedronFEMForceField name="FEM" youngModulus="500" poissonRatio="0.3" computeGlobalMatrix="false" method="large" />
<FixedProjectiveConstraint name="FixedProjectiveConstraint" indices="3 39 64" />
<Node name="Visu">
<MeshOBJLoader name="meshLoader_0" filename="mesh/liver-smooth.obj" handleSeams="1" />
<OglModel name="VisualModel" src="@meshLoader_0" color="red" />
<BarycentricMapping input="@.." output="@VisualModel" name="visual mapping" />
</Node>
<Node name="Surf">
<SphereLoader filename="mesh/liver.sph" />
<MechanicalObject position="@[-1].position" />
<SphereCollisionModel name="CollisionModel" listRadius="@[-2].listRadius" />
<BarycentricMapping name="sphere mapping" />
</Node>
</Node>
</Node>
def createScene(root_node):
root = root_node.addChild('root', dt="0.02")
root.addObject('RequiredPlugin', name="Sofa.Component.Collision.Detection.Algorithm")
root.addObject('RequiredPlugin', name="Sofa.Component.Collision.Detection.Intersection")
root.addObject('RequiredPlugin', name="Sofa.Component.Collision.Geometry")
root.addObject('RequiredPlugin', name="Sofa.Component.Collision.Response.Contact")
root.addObject('RequiredPlugin', name="Sofa.Component.Constraint.Projective")
root.addObject('RequiredPlugin', name="Sofa.Component.IO.Mesh")
root.addObject('RequiredPlugin', name="Sofa.Component.LinearSolver.Iterative")
root.addObject('RequiredPlugin', name="Sofa.Component.Mapping.Linear")
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.Constant")
root.addObject('RequiredPlugin', name="Sofa.Component.Visual")
root.addObject('RequiredPlugin', name="Sofa.GL.Component.Rendering3D")
root.addObject('DefaultAnimationLoop', )
root.addObject('VisualStyle', displayFlags="showBehaviorModels")
root.addObject('CollisionPipeline', verbose="0", name="CollisionPipeline")
root.addObject('BruteForceBroadPhase', )
root.addObject('BVHNarrowPhase', )
root.addObject('CollisionResponse', response="PenalityContactForceField", name="collision response")
root.addObject('DiscreteIntersection', )
liver = root.addChild('Liver')
liver.addObject('EulerImplicitSolver', name="cg_odesolver", printLog="false", rayleighStiffness="0.1", rayleighMass="0.1")
liver.addObject('CGLinearSolver', iterations="25", name="linear solver", tolerance="1.0e-9", threshold="1.0e-9")
liver.addObject('MeshGmshLoader', name="loader", filename="mesh/liver.msh")
liver.addObject('MeshTopology', src="@loader")
liver.addObject('MechanicalObject', src="@loader", name="dofs")
liver.addObject('UniformMass', name="mass", vertexMass="0.05")
liver.addObject('TetrahedronFEMForceField', name="FEM", youngModulus="500", poissonRatio="0.3", computeGlobalMatrix="false", method="large")
liver.addObject('FixedProjectiveConstraint', name="FixedProjectiveConstraint", indices="3 39 64")
visu = Liver.addChild('Visu')
visu.addObject('MeshOBJLoader', name="meshLoader_0", filename="mesh/liver-smooth.obj", handleSeams="1")
visu.addObject('OglModel', name="VisualModel", src="@meshLoader_0", color="red")
visu.addObject('BarycentricMapping', input="@..", output="@VisualModel", name="visual mapping")
surf = Liver.addChild('Surf')
surf.addObject('SphereLoader', filename="mesh/liver.sph")
surf.addObject('MechanicalObject', position="@[-1].position")
surf.addObject('SphereCollisionModel', name="CollisionModel", listRadius="@[-2].listRadius")
surf.addObject('BarycentricMapping', name="sphere mapping")