UniformMass
This component belongs to the category of Masses. The UniformMass is a very simplistic mass component since it does not compute the volume integration of a density term. The mass is equally spread over the number of points, thus resulting in the following diagonal mass matrix:
\[\mathbf{M}=\begin{bmatrix}m&0&\cdots&0\\&m&\cdots&0\\ \vdots&\vdots&\ddots&\vdots\\&0&\cdots&m\end{bmatrix}\]
Each diagonal term equals the nodal mass \(m=\frac{m_{\textnormal{total}}}{N}\) where \(m_{\textnormal{total}}\) is the total mass of the objet and \(N\) is the number of nodes of the object. Spreading the mass over the nodes without considering their connectivity results in this diagonal mass matrix \(\mathbf{M}\).
As all mass components, the UniformMass \(\mathbf{M}\) will contribute to the main matrix \(\mathbf{A}\) in the system \(\mathbf{A}x=b\). Depending on the type of LinearSolver used:
- for iterative solvers, the result of the multiplication between the mass matrix \(\mathbf{M}\) and an approximated solution is computed by the function:
template <class DataTypes, class MassType>
void UniformMass<DataTypes, MassType>::addMDx ( const core::MechanicalParams*, DataVecDeriv& vres, const DataVecDeriv& vdx, SReal factor)
{
helper::WriteAccessor<DataVecDeriv> res = vres;
helper::ReadAccessor<DataVecDeriv> dx = vdx;
WriteAccessor<Data<vector<int> > > indices = d_indices;
MassType m = d_vertexMass.getValue();
if ( factor != 1.0 )
m *= ( typename DataTypes::Real ) factor;
for ( unsigned int i=0; i<indices.size(); i++ )
res[indices[i]] += dx[indices[i]] * m;
}
- for direct solvers, the mass matrix \(\mathbf{M}\) is built by the function:
/// Add Mass contribution to global Matrix assembling
template <class DataTypes, class MassType>
void UniformMass<DataTypes, MassType>::addMToMatrix (const MechanicalParams *mparams, const MultiMatrixAccessor* matrix)
{
const MassType& m = d_vertexMass.getValue();
const size_t N = DataTypeInfo<Deriv>::size();
AddMToMatrixFunctor<Deriv,MassType> calc;
MultiMatrixAccessor::MatrixRef r = matrix->getMatrix(mstate);
Real mFactor = (Real)mparams->mFactorIncludingRayleighDamping(this->rayleighMass.getValue());
ReadAccessor<Data<vector<int> > > indices = d_indices;
for ( unsigned int i=0; i<indices.size(); i++ )
calc ( r.matrix, m, r.offset + N*indices[i], mFactor);
}
Usage
The UniformMass only requires a MechanicalObject to store the degrees of freedom associated to the nodes. An integration scheme and a solver are also necessary to solve the linear system at each time step.
Since the UniformMass only set a constant mass at each node without considering their connectivity, no topology is needed for the UniformMass. For this reason, the UniformMass is suitable for rigid frames.
However, the UniformMass should be carefully used if accuracy is a criterion, especially when using surface or volumetric physical models. As written above, the UniformMass does not take into account the geometry and the topology of the object since no space integration is computed.
Compute a mass equally spread over the number of nodes.
Rigid2d
Templates:
- Rigid2d
Target: Sofa.Component.Mass
namespace: sofa::component::mass
parents:
- Mass
Data
| Name | Description | Default value |
|---|---|---|
| name | object name | unnamed |
| printLog | if true, emits extra messages at runtime. | 0 |
| tags | list of the subsets the object 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 |
| rayleighStiffness | Rayleigh damping - stiffness matrix coefficient | 0 |
| separateGravity | add separately gravity to velocity computation | 0 |
| rayleighMass | Rayleigh damping - mass matrix coefficient | 0 |
| vertexMass | Specify one single, positive, real value for the mass of each particle. If unspecified or wrongly set, the totalMass information is used. | 1 1 1 |
| totalMass | Specify the total mass resulting from all particles. If unspecified or wrongly set, the default value is used: totalMass = 1.0 | 1 |
| filename | File storing the mass parameters [rigid objects only]. | |
| compute_mapping_inertia | to be used if the mass is placed under a mapping | 0 |
| localRange | optional range of local DOF indices. Any computation involving only indices outside of this range are discarded (useful for parallelization using mesh partitioning) | -1 -1 |
| indices | optional local DOF indices. Any computation involving only indices outside of this list are discarded | |
| preserveTotalMass | Prevent totalMass from decreasing when removing particles. | 0 |
| Visualization | ||
| showGravityCenter | display the center of gravity of the system | 0 |
| showAxisSizeFactor | factor length of the axis displayed (only used for rigids) | 1 |
| showInitialCenterOfGravity | display the initial center of gravity of the system | 0 |
| showX0 | display the rest positions | 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.Mass
namespace: sofa::component::mass
parents:
- Mass
Data
| Name | Description | Default value |
|---|---|---|
| name | object name | unnamed |
| printLog | if true, emits extra messages at runtime. | 0 |
| tags | list of the subsets the object 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 |
| rayleighStiffness | Rayleigh damping - stiffness matrix coefficient | 0 |
| separateGravity | add separately gravity to velocity computation | 0 |
| rayleighMass | Rayleigh damping - mass matrix coefficient | 0 |
| vertexMass | Specify one single, positive, real value for the mass of each particle. If unspecified or wrongly set, the totalMass information is used. | 1 1 [1 0 0,0 1 0,0 0 1] |
| totalMass | Specify the total mass resulting from all particles. If unspecified or wrongly set, the default value is used: totalMass = 1.0 | 1 |
| filename | rigid file to load the mass parameters | |
| compute_mapping_inertia | to be used if the mass is placed under a mapping | 0 |
| localRange | optional range of local DOF indices. Any computation involving only indices outside of this range are discarded (useful for parallelization using mesh partitioning) | -1 -1 |
| indices | optional local DOF indices. Any computation involving only indices outside of this list are discarded | |
| preserveTotalMass | Prevent totalMass from decreasing when removing particles. | 0 |
| Visualization | ||
| showGravityCenter | display the center of gravity of the system | 0 |
| showAxisSizeFactor | factor length of the axis displayed (only used for rigids) | 1 |
| showInitialCenterOfGravity | display the initial center of gravity of the system | 0 |
| showX0 | display the rest positions | 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.Mass
namespace: sofa::component::mass
parents:
- Mass
Data
| Name | Description | Default value |
|---|---|---|
| name | object name | unnamed |
| printLog | if true, emits extra messages at runtime. | 0 |
| tags | list of the subsets the object 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 |
| rayleighStiffness | Rayleigh damping - stiffness matrix coefficient | 0 |
| separateGravity | add separately gravity to velocity computation | 0 |
| rayleighMass | Rayleigh damping - mass matrix coefficient | 0 |
| vertexMass | Specify one single, positive, real value for the mass of each particle. If unspecified or wrongly set, the totalMass information is used. | 1 |
| totalMass | Specify the total mass resulting from all particles. If unspecified or wrongly set, the default value is used: totalMass = 1.0 | 1 |
| filename | File storing the mass parameters [rigid objects only]. | |
| compute_mapping_inertia | to be used if the mass is placed under a mapping | 0 |
| localRange | optional range of local DOF indices. Any computation involving only indices outside of this range are discarded (useful for parallelization using mesh partitioning) | -1 -1 |
| indices | optional local DOF indices. Any computation involving only indices outside of this list are discarded | |
| preserveTotalMass | Prevent totalMass from decreasing when removing particles. | 0 |
| Visualization | ||
| showGravityCenter | display the center of gravity of the system | 0 |
| showAxisSizeFactor | factor length of the axis displayed (only used for rigids) | 1 |
| showInitialCenterOfGravity | display the initial center of gravity of the system | 0 |
| showX0 | display the rest positions | 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.Mass
namespace: sofa::component::mass
parents:
- Mass
Data
| Name | Description | Default value |
|---|---|---|
| name | object name | unnamed |
| printLog | if true, emits extra messages at runtime. | 0 |
| tags | list of the subsets the object 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 |
| rayleighStiffness | Rayleigh damping - stiffness matrix coefficient | 0 |
| separateGravity | add separately gravity to velocity computation | 0 |
| rayleighMass | Rayleigh damping - mass matrix coefficient | 0 |
| vertexMass | Specify one single, positive, real value for the mass of each particle. If unspecified or wrongly set, the totalMass information is used. | 1 |
| totalMass | Specify the total mass resulting from all particles. If unspecified or wrongly set, the default value is used: totalMass = 1.0 | 1 |
| filename | File storing the mass parameters [rigid objects only]. | |
| compute_mapping_inertia | to be used if the mass is placed under a mapping | 0 |
| localRange | optional range of local DOF indices. Any computation involving only indices outside of this range are discarded (useful for parallelization using mesh partitioning) | -1 -1 |
| indices | optional local DOF indices. Any computation involving only indices outside of this list are discarded | |
| preserveTotalMass | Prevent totalMass from decreasing when removing particles. | 0 |
| Visualization | ||
| showGravityCenter | display the center of gravity of the system | 0 |
| showAxisSizeFactor | factor length of the axis displayed (only used for rigids) | 1 |
| showInitialCenterOfGravity | display the initial center of gravity of the system | 0 |
| showX0 | display the rest positions | 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.Mass
namespace: sofa::component::mass
parents:
- Mass
Data
| Name | Description | Default value |
|---|---|---|
| name | object name | unnamed |
| printLog | if true, emits extra messages at runtime. | 0 |
| tags | list of the subsets the object 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 |
| rayleighStiffness | Rayleigh damping - stiffness matrix coefficient | 0 |
| separateGravity | add separately gravity to velocity computation | 0 |
| rayleighMass | Rayleigh damping - mass matrix coefficient | 0 |
| vertexMass | Specify one single, positive, real value for the mass of each particle. If unspecified or wrongly set, the totalMass information is used. | 1 |
| totalMass | Specify the total mass resulting from all particles. If unspecified or wrongly set, the default value is used: totalMass = 1.0 | 1 |
| filename | File storing the mass parameters [rigid objects only]. | |
| compute_mapping_inertia | to be used if the mass is placed under a mapping | 0 |
| localRange | optional range of local DOF indices. Any computation involving only indices outside of this range are discarded (useful for parallelization using mesh partitioning) | -1 -1 |
| indices | optional local DOF indices. Any computation involving only indices outside of this list are discarded | |
| preserveTotalMass | Prevent totalMass from decreasing when removing particles. | 0 |
| Visualization | ||
| showGravityCenter | display the center of gravity of the system | 0 |
| showAxisSizeFactor | factor length of the axis displayed (only used for rigids) | 1 |
| showInitialCenterOfGravity | display the initial center of gravity of the system | 0 |
| showX0 | display the rest positions | 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.Mass
namespace: sofa::component::mass
parents:
- Mass
Data
| Name | Description | Default value |
|---|---|---|
| name | object name | unnamed |
| printLog | if true, emits extra messages at runtime. | 0 |
| tags | list of the subsets the object 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 |
| rayleighStiffness | Rayleigh damping - stiffness matrix coefficient | 0 |
| separateGravity | add separately gravity to velocity computation | 0 |
| rayleighMass | Rayleigh damping - mass matrix coefficient | 0 |
| vertexMass | Specify one single, positive, real value for the mass of each particle. If unspecified or wrongly set, the totalMass information is used. | 1 |
| totalMass | Specify the total mass resulting from all particles. If unspecified or wrongly set, the default value is used: totalMass = 1.0 | 1 |
| filename | File storing the mass parameters [rigid objects only]. | |
| compute_mapping_inertia | to be used if the mass is placed under a mapping | 0 |
| localRange | optional range of local DOF indices. Any computation involving only indices outside of this range are discarded (useful for parallelization using mesh partitioning) | -1 -1 |
| indices | optional local DOF indices. Any computation involving only indices outside of this list are discarded | |
| preserveTotalMass | Prevent totalMass from decreasing when removing particles. | 0 |
| Visualization | ||
| showGravityCenter | display the center of gravity of the system | 0 |
| showAxisSizeFactor | factor length of the axis displayed (only used for rigids) | 1 |
| showInitialCenterOfGravity | display the initial center of gravity of the system | 0 |
| showX0 | display the rest positions | 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
UniformMass.scn
<?xml version="1.0" ?>
<Node name="root" dt="0.005">
<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 [TetrahedralCorotationalFEMForceField] -->
<RequiredPlugin name="Sofa.Component.StateContainer"/> <!-- Needed to use components [MechanicalObject] -->
<RequiredPlugin name="Sofa.Component.Topology.Container.Dynamic"/> <!-- Needed to use components [TetrahedronSetGeometryAlgorithms TetrahedronSetTopologyContainer] -->
<RequiredPlugin name="Sofa.Component.Visual"/> <!-- Needed to use components [InteractiveCamera] -->
<RequiredPlugin name="Sofa.GL.Component.Rendering3D"/> <!-- Needed to use components [OglModel] -->
<CollisionPipeline verbose="0" name="CollisionPipeline" />
<BruteForceBroadPhase/>
<BVHNarrowPhase/>
<CollisionResponse response="PenalityContactForceField" name="collision response" />
<DiscreteIntersection />
<DefaultAnimationLoop/>
<InteractiveCamera position="-2 2.6 17.9" orientation="0 0 0 1" distance="17.9" />
<MeshGmshLoader name="loader" filename="mesh/liver.msh" />
<MeshOBJLoader name="meshLoader_0" filename="mesh/liver-smooth.obj" handleSeams="1" />
<Node name="Liver" depend="topo dofs">
<EulerImplicitSolver name="integration scheme" />
<CGLinearSolver name="linear solver" iterations="1000" tolerance="1e-9" threshold="1e-9"/>
<MechanicalObject name="dofs" src="@../loader" />
<!-- Container for the tetrahedra-->
<TetrahedronSetTopologyContainer name="TetraTopo" src="@../loader" />
<TetrahedronSetGeometryAlgorithms name="GeomAlgo" />
<UniformMass totalMass="60" name="uniformlyConstantMass" printLog="1"/>
<TetrahedralCorotationalFEMForceField template="Vec3" name="FEM" method="large" poissonRatio="0.45" youngModulus="5000" />
<FixedProjectiveConstraint name="FixedProjectiveConstraint" indices="3 39 64" />
<Node name="Visu">
<OglModel name="VisualModel" src="@../../meshLoader_0" color="yellow" />
<BarycentricMapping name="VisualMapping" input="@../dofs" output="@VisualModel" />
</Node>
<Node name="Surf">
<SphereLoader filename="mesh/liver.sph" />
<MechanicalObject name="spheres" position="@[-1].position" />
<SphereCollisionModel name="CollisionModel" listRadius="@[-2].listRadius" />
<BarycentricMapping name="CollisionMapping" input="@../dofs" output="@spheres" />
</Node>
</Node>
</Node>
def createScene(root_node):
root = root_node.addChild('root', dt="0.005")
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.Dynamic")
root.addObject('RequiredPlugin', name="Sofa.Component.Visual")
root.addObject('RequiredPlugin', name="Sofa.GL.Component.Rendering3D")
root.addObject('CollisionPipeline', verbose="0", name="CollisionPipeline")
root.addObject('BruteForceBroadPhase', )
root.addObject('BVHNarrowPhase', )
root.addObject('CollisionResponse', response="PenalityContactForceField", name="collision response")
root.addObject('DiscreteIntersection', )
root.addObject('DefaultAnimationLoop', )
root.addObject('InteractiveCamera', position="-2 2.6 17.9", orientation="0 0 0 1", distance="17.9")
root.addObject('MeshGmshLoader', name="loader", filename="mesh/liver.msh")
root.addObject('MeshOBJLoader', name="meshLoader_0", filename="mesh/liver-smooth.obj", handleSeams="1")
liver = root.addChild('Liver', depend="topo dofs")
liver.addObject('EulerImplicitSolver', name="integration scheme")
liver.addObject('CGLinearSolver', name="linear solver", iterations="1000", tolerance="1e-9", threshold="1e-9")
liver.addObject('MechanicalObject', name="dofs", src="@../loader")
liver.addObject('TetrahedronSetTopologyContainer', name="TetraTopo", src="@../loader")
liver.addObject('TetrahedronSetGeometryAlgorithms', name="GeomAlgo")
liver.addObject('UniformMass', totalMass="60", name="uniformlyConstantMass", printLog="1")
liver.addObject('TetrahedralCorotationalFEMForceField', template="Vec3", name="FEM", method="large", poissonRatio="0.45", youngModulus="5000")
liver.addObject('FixedProjectiveConstraint', name="FixedProjectiveConstraint", indices="3 39 64")
visu = Liver.addChild('Visu')
visu.addObject('OglModel', name="VisualModel", src="@../../meshLoader_0", color="yellow")
visu.addObject('BarycentricMapping', name="VisualMapping", input="@../dofs", output="@VisualModel")
surf = Liver.addChild('Surf')
surf.addObject('SphereLoader', filename="mesh/liver.sph")
surf.addObject('MechanicalObject', name="spheres", position="@[-1].position")
surf.addObject('SphereCollisionModel', name="CollisionModel", listRadius="@[-2].listRadius")
surf.addObject('BarycentricMapping', name="CollisionMapping", input="@../dofs", output="@spheres")