Methods

{
  "name": "MechanicalProjectPositionVisitor",
  "namespace": "sofa::simulation::mechanicalvisitor",
  "module": "Sofa.framework.Simulation.Core",
  "include": "sofa/simulation/mechanicalvisitor/MechanicalProjectPositionVisitor.h",
  "doc": "",
  "inherits": [
    "MechanicalVisitor"
  ],
  "templates": [],
  "data_fields": [],
  "links": [],
  "methods": [
    {
      "name": "fwdMechanicalMapping",
      "return_type": "Result",
      "params": [
        {
          "name": "",
          "type": "simulation::Node *"
        },
        {
          "name": "map",
          "type": "sofa::core::BaseMapping *"
        }
      ],
      "is_virtual": true,
      "is_pure_virtual": false,
      "is_static": false,
      "access": "public"
    },
    {
      "name": "fwdProjectiveConstraintSet",
      "return_type": "Result",
      "params": [
        {
          "name": "",
          "type": "simulation::Node *"
        },
        {
          "name": "c",
          "type": "sofa::core::behavior::BaseProjectiveConstraintSet *"
        }
      ],
      "is_virtual": true,
      "is_pure_virtual": false,
      "is_static": false,
      "access": "public"
    },
    {
      "name": "getInfos",
      "return_type": "int",
      "params": [],
      "is_virtual": false,
      "is_pure_virtual": false,
      "is_static": false,
      "access": "public"
    },
    {
      "name": "isThreadSafe",
      "return_type": "bool",
      "params": [],
      "is_virtual": true,
      "is_pure_virtual": false,
      "is_static": false,
      "access": "public"
    }
  ],
  "description": "<p>The <code>MechanicalProjectPositionVisitor</code> is a visitor class within the SOFA simulation framework, specifically designed to handle mechanical projective constraints and mappings in the context of mechanical simulations.</p>\n\n<p>This class inherits from <code>MechanicalVisitor</code>, which indicates its role in the simulation pipeline for processing various mechanical operations. Its primary purpose is to project positions based on constraints defined within the simulation environment, ensuring that these constraints are accurately applied during the simulation process.</p>\n\n<p>The visitor interacts with other SOFA components through method overrides:</p>\n<ul>\n<li><code>fwdMechanicalMapping</code>: This method handles mechanical mappings by returning a result indicating how the node should be processed (e.g., <code>RESULT_PRUNE</code>).</li>\n<li><code>fwdProjectiveConstraintSet</code>: This method projects positions based on projective constraints and returns a continue flag to indicate that processing should proceed.</li>\n<li><code>getInfos</code>: Provides information about the visitor, which can be useful for debugging or logging purposes.</li>\n<li><code>isThreadSafe</code>: Indicates whether this visitor is thread-safe, allowing it to be used in parallel processing scenarios.</li>\n</ul>\n\n<p>The <code>MechanicalProjectPositionVisitor</code> class initializes with parameters such as mechanical parameters and time, and optionally a position identifier. It also specifies read-write vectors for debugging purposes through the <code>setReadWriteVectors</code> method.</p>",
  "maths": "The `MechanicalProjectPositionVisitor` class in the SOFA framework is designed to handle mechanical projective constraints and mappings within a simulation. Its primary role is to ensure that position constraints are accurately applied during the simulation process, contributing to the overall constraint handling phase of the FEM pipeline.\n\n### Governing Equations or Operators\n- **Project Position**: This visitor projects positions based on projective constraints, which can be represented as linear transformations or more complex mappings. The projection step is critical for enforcing boundary conditions and maintaining physical consistency in deformable systems.\n  - Mathematically, this can be expressed as: \\\\[ \\mathbf{x}_{proj} = P(\\mathbf{x}) \\\\] where \\(P\\) represents the projective constraint or mapping function applied to the position vector \\(\b‌​f x\").\n- **Mechanical Mapping**: The `fwdMechanicalMapping` method handles mechanical mappings, which are transformations between different coordinate systems (e.g., from slave to master nodes in multi-resolution coupling scenarios).\n  - This is typically a matrix-based transformation: \\\\[ \\mathbf{x}_s = F(\\mathbf{x}_m) \\\\] where \\(\b‌​f x_s\") and \\(\b‌​f x_m\"). are the slave and master positions, respectively.\n\n### Constitutive or Kinematic Laws Involved\n- **Projective Constraints**: These constraints can be kinematic (position-based) or involve more complex constitutive laws. For example, in a hyperelastic material model: \\\\[ \\sigma = f(\\varepsilon) \\\\] where \\(\b‌​f \"). and \\(\b‌​f \") are the stress and strain tensors.\n- **Mapping Constraints**: The mappings can involve linear or nonlinear transformations depending on the specific application, such as in corotational methods: \\\\[ F = R Ε_{rel} R^T \\\\] where \\(R\"). is the rotation matrix and \\(Ε_{rel}\"). is the relative deformation gradient.\n\n### Role in the Global FEM Pipeline\n- **Assembly Phase**: The visitor plays a role during the assembly phase by ensuring that projective constraints are applied correctly. This includes projecting positions to satisfy these constraints before further operations (e.g., stiffness matrix assembly).\n- **Nonlinear Resolution**: During nonlinear resolution, position projections help maintain consistency in the Newton-Raphson iteration process, ensuring that each step adheres to the imposed constraints.\n\n### Numerical Methods or Discretization Choices\n- The visitor uses an implicit projection method where positions are adjusted based on projective constraints. This is a form of constraint enforcement commonly used in iterative solvers and nonlinear mechanics simulations.\n\n### Integration into Variational / Lagrangian Mechanics Framework\n- **Variational Formulation**: Projecting positions is consistent with the variational framework as it enforces admissible motion within the space defined by projective constraints. This ensures that the solution remains physically valid and respects boundary conditions.\n- **Lagrangian Mechanics**: By ensuring position consistency, the visitor aids in maintaining the integrity of Lagrangian mechanics principles, particularly in enforcing holonomic or non-holonomic constraints that may arise from specific physical scenarios (e.g., contact interactions).\n\n### Summary\nThe `MechanicalProjectPositionVisitor` component is a critical part of the SOFA framework's constraint handling mechanism. It ensures positions are accurately projected according to defined projective constraints and mappings, contributing to the overall stability and consistency of deformable body simulations.",
  "abstract": "The `MechanicalProjectPositionVisitor` projects positions according to defined projective constraints and mappings within SOFA simulations, ensuring accurate constraint enforcement during the simulation process.",
  "sheet": "# MechanicalProjectPositionVisitor\n\n## Overview\n\nThe `MechanicalProjectPositionVisitor` is a visitor class that handles mechanical projective constraints and mappings. It inherits from `MechanicalVisitor`, indicating its role in processing various mechanical operations within SOFA simulations, particularly projecting positions based on defined constraints.\n\n## Mathematical Model\n\n### Project Position\n\nThis visitor projects positions based on projective constraints, which can be represented as linear transformations or more complex mappings. The projection step is critical for enforcing boundary conditions and maintaining physical consistency in deformable systems. Mathematically, this can be expressed as:\n\n\\[ \\mathbf{x}_{proj} = P(\\mathbf{x}) \\]\n\nwhere \\(P\\) represents the projective constraint or mapping function applied to the position vector \\({ x }\").\n\n### Mechanical Mapping\n\nThe `fwdMechanicalMapping` method handles mechanical mappings, which are transformations between different coordinate systems (e.g., from slave to master nodes in multi-resolution coupling scenarios). This is typically a matrix-based transformation:\n\n\\[ \\mathbf{x}_s = F(\\mathbf{x}_m) \\]\n\nwhere \\({ x_s }\"). and \\({ x_m }\"). are the slave and master positions, respectively.\n\n## Practical Notes\n\nThe `MechanicalProjectPositionVisitor` ensures that position constraints are accurately applied during the simulation process. It is critical for maintaining stability and consistency in deformable body simulations by enforcing projective constraints and mappings."
}