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BaseMechanicalVisitor

The BaseMechanicalVisitor class in SOFA (Simulation Open-Framework Architecture) is an abstract class that serves as the foundation for mechanical visitors, which are used to propagate and process various mechanical properties and constraints throughout a simulation hierarchy. This component plays a crucial role in the animation pipeline of physical simulations within the SOFA framework.

abstract
`BaseMechanicalVisitor` is an abstract class for creating mechanical visitors that propagate and process mechanical properties through a hierarchical node-based framework in SOFA simulations.
sheet
# BaseMechanicalVisitor ## Overview The `BaseMechanicalVisitor` serves as the foundation for mechanical visitors, facilitating the propagation and processing of various mechanical properties and constraints throughout a hierarchical simulation structure. It interacts with nodes and their components such as ODE solvers, constraint solvers, force fields, mappings, and more. ## Parameters and Data The `BaseMechanicalVisitor` class does not expose any significant data fields but provides numerous methods for top-down (`fwdXxx`) and bottom-up (`bwdXxx`) propagation. These methods include: - **Top-Down Propagation** (`fwdXxx` Methods): - `fwdOdeSolver`: Processes ODE solvers at each node level. - `fwdConstraintSolver`: Handles constraint solvers that enforce physical constraints like contacts or joints. - `fwdMechanicalMapping`: Maps mechanical properties and forces from a parent node to its child nodes using mappings defined by the `BaseMapping` class. - `fwdMappedMechanicalState`: Applies mappings on mechanical states if they are derived from higher levels. - `fwdMechanicalState`: Processes local mechanical states that are not mapped from a parent level, directly modifying and propagating properties within the node itself. - `fwdMass`: Handles mass distribution in the simulation nodes. - `fwdForceField` and `fwdInteractionForceField`: Applies force fields to compute forces on particles or elements. Interaction force fields specifically handle interactions between different parts of the system. - `fwdProjectiveConstraintSet`, `fwdConstraintSet`, `fwdInteractionProjectiveConstraintSet`, `fwdInteractionConstraint`: Enforces constraints, including projective and interaction constraints that are applied to ensure physical consistency in the simulation. - **Bottom-Up Propagation** (`bwdXxx` Methods): - Similar methods exist for bottom-up propagation but serve a reverse function, typically aggregating results from child nodes back up to parent nodes or post-processing computed values.
name
BaseMechanicalVisitor
description
The BaseMechanicalVisitor class in SOFA (Simulation Open-Framework Architecture) is an abstract class that serves as the foundation for mechanical visitors, which are used to propagate and process various mechanical properties and constraints throughout a simulation hierarchy. This component plays a crucial role in the animation pipeline of physical simulations within the SOFA framework.
parameters
returns
None
example
None
note
  • The class defines several virtual functions that must be overridden by derived classes to perform specific tasks during the simulation process.
  • These tasks include processing ODE solvers, constraint solvers, mechanical mappings, mechanical states, masses, force fields, projective and standard constraint sets, as well as handling interaction forces and constraints between different parts of the simulation.
  • The class provides methods for both forward (fwd) and backward (bwd) processing, allowing derived classes to implement their own logic for pre-processing and post-processing tasks.
authors
  • Project SOFA
maths
The `BaseMechanicalVisitor` class in the Simulation Open-Framework Architecture (SOFA) is an abstract class designed to handle the propagation and processing of mechanical properties, constraints, and forces throughout a hierarchical simulation structure. This class plays a pivotal role in animating physical simulations by facilitating interactions between various components such as force fields, constraint sets, and mapping operators. ### Mathematical Description: #### Hierarchical Propagation: The `BaseMechanicalVisitor` operates within a hierarchical node-based framework where each node (representing an object or part of the simulation) can have its own mechanical properties, constraints, and mappings. The propagation mechanism can be described as follows: 1. **Top-Down Propagation** (`fwdXxx` Methods): - `fwdOdeSolver`: Processes Ordinary Differential Equation (ODE) solvers at each node level. - `fwdConstraintSolver`: Handles constraint solvers that enforce physical constraints like contacts or joints. - `fwdMechanicalMapping`: Maps mechanical properties and forces from a parent node to its child nodes, using mappings defined by the `BaseMapping` class. This step is crucial for transferring state between different levels of granularity in the simulation hierarchy. - `fwdMappedMechanicalState`: Applies mappings on mechanical states if they are derived from higher levels. - `fwdMechanicalState`: Processes local mechanical states that are not mapped from a parent level, directly modifying and propagating properties within the node itself. - `fwdMass`: Handles mass distribution in the simulation nodes. - `fwdForceField` and `fwdInteractionForceField`: Applies force fields to compute forces on particles or elements. Interaction force fields specifically handle interactions between different parts of the system. - `fwdProjectiveConstraintSet`, `fwdConstraintSet`, `fwdInteractionProjectiveConstraintSet`, `fwdInteractionConstraint`: Enforces constraints, including projective and interaction constraints that are applied to ensure physical consistency in the simulation. 2. **Bottom-Up Propagation** (`bwdXxx` Methods): - Similar methods exist for bottom-up propagation but serve a reverse function, typically aggregating results from child nodes back up to parent nodes or post-processing computed values. #### Mathematical Formulations: - **Force Computation**: Force fields compute forces based on physical laws. For instance, if `F` is the force vector and `x` represents positions of particles or elements, then `F = f(x)` where `f` can be a function representing various physical effects such as gravity, elasticity, or friction. - **Constraint Enforcement**: Constraint sets enforce linear or nonlinear constraints on the system. A constraint `C(x) = 0` ensures that the state vector `x` satisfies certain conditions. The projection operator `P` can be used to project a solution onto the feasible set of constraints: `x_new = P(x_old)`. - **Mapping**: Mappings, represented by matrix `M`, map properties from one level to another. For example, if `u_parent` is a state vector in the parent node and `u_child` is the corresponding state vector in the child node, then `u_child = M * u_parent`. ### Physical Description: The physical aspects of the `BaseMechanicalVisitor` revolve around simulating realistic mechanical behavior within complex systems. This involves integrating Newton's laws of motion with numerical methods for solving differential equations that describe system dynamics. The framework supports both explicit and implicit integration schemes, which can be chosen based on the specific requirements of stability and accuracy. - **Dynamics Simulation**: By propagating forces through hierarchical mappings, the visitor ensures that changes in one part of a simulation affect other parts appropriately according to physical laws. This is critical for simulating interactions such as collisions or deformations. - **Constraint Handling**: Constraints ensure that certain conditions are met during the simulation, like maintaining contacts between objects or enforcing joint movements within their defined limits. - **Animation Pipeline**: The visitor class supports the overall animation pipeline by ensuring that all mechanical properties are correctly updated and propagated at each time step of the simulation. Overall, `BaseMechanicalVisitor` provides a structured approach to processing complex mechanical systems in SOFA, leveraging mathematical formulations and physical principles to achieve realistic simulations. 
{
  "name": "BaseMechanicalVisitor",
  "main": {
    "name": "BaseMechanicalVisitor",
    "namespace": "sofa::simulation",
    "module": "Sofa.framework.Simulation.Core",
    "include": "sofa/simulation/BaseMechanicalVisitor.h",
    "doc": "Base class for easily creating new actions for mechanical simulation.\nDuring the first traversal (top-down), method processNodeTopDown(simulation::Node*) is applied to each simulation::Node.\nEach component attached to this node is processed using the appropriate method, prefixed by fwd.\nDuring the second traversal (bottom-up), method processNodeBottomUp(simulation::Node*) is applied to each simulation::Node.\nEach component attached to this node is processed using the appropriate method, prefixed by bwd.\nThe default behavior of the fwd* and bwd* is to do nothing.\nDerived actions typically overload these methods to implement the desired processing.",
    "inherits": [
      "Visitor"
    ],
    "templates": [],
    "data_fields": [],
    "links": [],
    "methods": [
      {
        "name": "processNodeTopDown",
        "return_type": "Result",
        "params": [
          {
            "name": "node",
            "type": "simulation::Node *"
          },
          {
            "name": "ctx",
            "type": "VisitorContext *"
          }
        ],
        "is_virtual": true,
        "is_pure_virtual": false,
        "is_static": false,
        "access": "protected"
      },
      {
        "name": "processNodeBottomUp",
        "return_type": "void",
        "params": [
          {
            "name": "node",
            "type": "simulation::Node *"
          },
          {
            "name": "ctx",
            "type": "VisitorContext *"
          }
        ],
        "is_virtual": true,
        "is_pure_virtual": false,
        "is_static": false,
        "access": "protected"
      },
      {
        "name": "processNodeTopDown",
        "return_type": "Result",
        "params": [
          {
            "name": "node",
            "type": "simulation::Node *"
          }
        ],
        "is_virtual": true,
        "is_pure_virtual": false,
        "is_static": false,
        "access": "public"
      },
      {
        "name": "fwdOdeSolver",
        "return_type": "Result",
        "params": [
          {
            "name": "",
            "type": "simulation::Node *"
          },
          {
            "name": "",
            "type": "sofa::core::behavior::OdeSolver *"
          }
        ],
        "is_virtual": true,
        "is_pure_virtual": false,
        "is_static": false,
        "access": "public"
      },
      {
        "name": "fwdOdeSolver",
        "return_type": "Result",
        "params": [
          {
            "name": "ctx",
            "type": "VisitorContext *"
          },
          {
            "name": "solver",
            "type": "sofa::core::behavior::OdeSolver *"
          }
        ],
        "is_virtual": true,
        "is_pure_virtual": false,
        "is_static": false,
        "access": "public"
      },
      {
        "name": "fwdConstraintSolver",
        "return_type": "Result",
        "params": [
          {
            "name": "",
            "type": "simulation::Node *"
          },
          {
            "name": "",
            "type": "sofa::core::behavior::ConstraintSolver *"
          }
        ],
        "is_virtual": true,
        "is_pure_virtual": false,
        "is_static": false,
        "access": "public"
      },
      {
        "name": "fwdConstraintSolver",
        "return_type": "Result",
        "params": [
          {
            "name": "ctx",
            "type": "VisitorContext *"
          },
          {
            "name": "solver",
            "type": "sofa::core::behavior::ConstraintSolver *"
          }
        ],
        "is_virtual": true,
        "is_pure_virtual": false,
        "is_static": false,
        "access": "public"
      },
      {
        "name": "fwdMechanicalMapping",
        "return_type": "Result",
        "params": [
          {
            "name": "",
            "type": "simulation::Node *"
          },
          {
            "name": "",
            "type": "sofa::core::BaseMapping *"
          }
        ],
        "is_virtual": true,
        "is_pure_virtual": false,
        "is_static": false,
        "access": "public"
      },
      {
        "name": "fwdMechanicalMapping",
        "return_type": "Result",
        "params": [
          {
            "name": "ctx",
            "type": "VisitorContext *"
          },
          {
            "name": "map",
            "type": "sofa::core::BaseMapping *"
          }
        ],
        "is_virtual": true,
        "is_pure_virtual": false,
        "is_static": false,
        "access": "public"
      },
      {
        "name": "fwdMappedMechanicalState",
        "return_type": "Result",
        "params": [
          {
            "name": "",
            "type": "simulation::Node *"
          },
          {
            "name": "",
            "type": "sofa::core::behavior::BaseMechanicalState *"
          }
        ],
        "is_virtual": true,
        "is_pure_virtual": false,
        "is_static": false,
        "access": "public"
      },
      {
        "name": "fwdMappedMechanicalState",
        "return_type": "Result",
        "params": [
          {
            "name": "ctx",
            "type": "VisitorContext *"
          },
          {
            "name": "mm",
            "type": "sofa::core::behavior::BaseMechanicalState *"
          }
        ],
        "is_virtual": true,
        "is_pure_virtual": false,
        "is_static": false,
        "access": "public"
      },
      {
        "name": "fwdMechanicalState",
        "return_type": "Result",
        "params": [
          {
            "name": "",
            "type": "simulation::Node *"
          },
          {
            "name": "",
            "type": "sofa::core::behavior::BaseMechanicalState *"
          }
        ],
        "is_virtual": true,
        "is_pure_virtual": false,
        "is_static": false,
        "access": "public"
      },
      {
        "name": "fwdMechanicalState",
        "return_type": "Result",
        "params": [
          {
            "name": "ctx",
            "type": "VisitorContext *"
          },
          {
            "name": "mm",
            "type": "sofa::core::behavior::BaseMechanicalState *"
          }
        ],
        "is_virtual": true,
        "is_pure_virtual": false,
        "is_static": false,
        "access": "public"
      },
      {
        "name": "fwdMass",
        "return_type": "Result",
        "params": [
          {
            "name": "",
            "type": "simulation::Node *"
          },
          {
            "name": "",
            "type": "sofa::core::behavior::BaseMass *"
          }
        ],
        "is_virtual": true,
        "is_pure_virtual": false,
        "is_static": false,
        "access": "public"
      },
      {
        "name": "fwdMass",
        "return_type": "Result",
        "params": [
          {
            "name": "ctx",
            "type": "VisitorContext *"
          },
          {
            "name": "mass",
            "type": "sofa::core::behavior::BaseMass *"
          }
        ],
        "is_virtual": true,
        "is_pure_virtual": false,
        "is_static": false,
        "access": "public"
      },
      {
        "name": "fwdForceField",
        "return_type": "Result",
        "params": [
          {
            "name": "",
            "type": "simulation::Node *"
          },
          {
            "name": "",
            "type": "sofa::core::behavior::BaseForceField *"
          }
        ],
        "is_virtual": true,
        "is_pure_virtual": false,
        "is_static": false,
        "access": "public"
      },
      {
        "name": "fwdForceField",
        "return_type": "Result",
        "params": [
          {
            "name": "ctx",
            "type": "VisitorContext *"
          },
          {
            "name": "ff",
            "type": "sofa::core::behavior::BaseForceField *"
          }
        ],
        "is_virtual": true,
        "is_pure_virtual": false,
        "is_static": false,
        "access": "public"
      },
      {
        "name": "fwdInteractionForceField",
        "return_type": "Result",
        "params": [
          {
            "name": "node",
            "type": "simulation::Node *"
          },
          {
            "name": "ff",
            "type": "sofa::core::behavior::BaseInteractionForceField *"
          }
        ],
        "is_virtual": true,
        "is_pure_virtual": false,
        "is_static": false,
        "access": "public"
      },
      {
        "name": "fwdInteractionForceField",
        "return_type": "Result",
        "params": [
          {
            "name": "ctx",
            "type": "VisitorContext *"
          },
          {
            "name": "ff",
            "type": "sofa::core::behavior::BaseInteractionForceField *"
          }
        ],
        "is_virtual": true,
        "is_pure_virtual": false,
        "is_static": false,
        "access": "public"
      },
      {
        "name": "fwdProjectiveConstraintSet",
        "return_type": "Result",
        "params": [
          {
            "name": "",
            "type": "simulation::Node *"
          },
          {
            "name": "",
            "type": "sofa::core::behavior::BaseProjectiveConstraintSet *"
          }
        ],
        "is_virtual": true,
        "is_pure_virtual": false,
        "is_static": false,
        "access": "public"
      },
      {
        "name": "fwdConstraintSet",
        "return_type": "Result",
        "params": [
          {
            "name": "",
            "type": "simulation::Node *"
          },
          {
            "name": "",
            "type": "sofa::core::behavior::BaseConstraintSet *"
          }
        ],
        "is_virtual": true,
        "is_pure_virtual": false,
        "is_static": false,
        "access": "public"
      },
      {
        "name": "fwdProjectiveConstraintSet",
        "return_type": "Result",
        "params": [
          {
            "name": "ctx",
            "type": "VisitorContext *"
          },
          {
            "name": "c",
            "type": "sofa::core::behavior::BaseProjectiveConstraintSet *"
          }
        ],
        "is_virtual": true,
        "is_pure_virtual": false,
        "is_static": false,
        "access": "public"
      },
      {
        "name": "fwdConstraintSet",
        "return_type": "Result",
        "params": [
          {
            "name": "ctx",
            "type": "VisitorContext *"
          },
          {
            "name": "c",
            "type": "sofa::core::behavior::BaseConstraintSet *"
          }
        ],
        "is_virtual": true,
        "is_pure_virtual": false,
        "is_static": false,
        "access": "public"
      },
      {
        "name": "fwdInteractionProjectiveConstraintSet",
        "return_type": "Result",
        "params": [
          {
            "name": "",
            "type": "simulation::Node *"
          },
          {
            "name": "",
            "type": "sofa::core::behavior::BaseInteractionProjectiveConstraintSet *"
          }
        ],
        "is_virtual": true,
        "is_pure_virtual": false,
        "is_static": false,
        "access": "public"
      },
      {
        "name": "fwdInteractionConstraint",
        "return_type": "Result",
        "params": [
          {
            "name": "",
            "type": "simulation::Node *"
          },
          {
            "name": "",
            "type": "sofa::core::behavior::BaseInteractionConstraint *"
          }
        ],
        "is_virtual": true,
        "is_pure_virtual": false,
        "is_static": false,
        "access": "public"
      },
      {
        "name": "fwdInteractionProjectiveConstraintSet",
        "return_type": "Result",
        "params": [
          {
            "name": "ctx",
            "type": "VisitorContext *"
          },
          {
            "name": "c",
            "type": "sofa::core::behavior::BaseInteractionProjectiveConstraintSet *"
          }
        ],
        "is_virtual": true,
        "is_pure_virtual": false,
        "is_static": false,
        "access": "public"
      },
      {
        "name": "fwdInteractionConstraint",
        "return_type": "Result",
        "params": [
          {
            "name": "ctx",
            "type": "VisitorContext *"
          },
          {
            "name": "c",
            "type": "sofa::core::behavior::BaseInteractionConstraint *"
          }
        ],
        "is_virtual": true,
        "is_pure_virtual": false,
        "is_static": false,
        "access": "public"
      },
      {
        "name": "processNodeBottomUp",
        "return_type": "void",
        "params": [
          {
            "name": "node",
            "type": "simulation::Node *"
          }
        ],
        "is_virtual": true,
        "is_pure_virtual": false,
        "is_static": false,
        "access": "public"
      },
      {
        "name": "bwdMechanicalState",
        "return_type": "void",
        "params": [
          {
            "name": "",
            "type": "simulation::Node *"
          },
          {
            "name": "",
            "type": "sofa::core::behavior::BaseMechanicalState *"
          }
        ],
        "is_virtual": true,
        "is_pure_virtual": false,
        "is_static": false,
        "access": "public"
      },
      {
        "name": "bwdMechanicalState",
        "return_type": "void",
        "params": [
          {
            "name": "ctx",
            "type": "VisitorContext *"
          },
          {
            "name": "mm",
            "type": "sofa::core::behavior::BaseMechanicalState *"
          }
        ],
        "is_virtual": true,
        "is_pure_virtual": false,
        "is_static": false,
        "access": "public"
      },
      {
        "name": "bwdMappedMechanicalState",
        "return_type": "void",
        "params": [
          {
            "name": "",
            "type": "simulation::Node *"
          },
          {
            "name": "",
            "type": "sofa::core::behavior::BaseMechanicalState *"
          }
        ],
        "is_virtual": true,
        "is_pure_virtual": false,
        "is_static": false,
        "access": "public"
      },
      {
        "name": "bwdMappedMechanicalState",
        "return_type": "void",
        "params": [
          {
            "name": "ctx",
            "type": "VisitorContext *"
          },
          {
            "name": "mm",
            "type": "sofa::core::behavior::BaseMechanicalState *"
          }
        ],
        "is_virtual": true,
        "is_pure_virtual": false,
        "is_static": false,
        "access": "public"
      },
      {
        "name": "bwdMechanicalMapping",
        "return_type": "void",
        "params": [
          {
            "name": "",
            "type": "simulation::Node *"
          },
          {
            "name": "",
            "type": "sofa::core::BaseMapping *"
          }
        ],
        "is_virtual": true,
        "is_pure_virtual": false,
        "is_static": false,
        "access": "public"
      },
      {
        "name": "bwdMechanicalMapping",
        "return_type": "void",
        "params": [
          {
            "name": "ctx",
            "type": "VisitorContext *"
          },
          {
            "name": "map",
            "type": "sofa::core::BaseMapping *"
          }
        ],
        "is_virtual": true,
        "is_pure_virtual": false,
        "is_static": false,
        "access": "public"
      },
      {
        "name": "bwdOdeSolver",
        "return_type": "void",
        "params": [
          {
            "name": "",
            "type": "simulation::Node *"
          },
          {
            "name": "",
            "type": "sofa::core::behavior::OdeSolver *"
          }
        ],
        "is_virtual": true,
        "is_pure_virtual": false,
        "is_static": false,
        "access": "public"
      },
      {
        "name": "bwdOdeSolver",
        "return_type": "void",
        "params": [
          {
            "name": "ctx",
            "type": "VisitorContext *"
          },
          {
            "name": "solver",
            "type": "sofa::core::behavior::OdeSolver *"
          }
        ],
        "is_virtual": true,
        "is_pure_virtual": false,
        "is_static": false,
        "access": "public"
      },
      {
        "name": "bwdConstraintSolver",
        "return_type": "void",
        "params": [
          {
            "name": "",
            "type": "simulation::Node *"
          },
          {
            "name": "",
            "type": "sofa::core::behavior::ConstraintSolver *"
          }
        ],
        "is_virtual": true,
        "is_pure_virtual": false,
        "is_static": false,
        "access": "public"
      },
      {
        "name": "bwdConstraintSolver",
        "return_type": "void",
        "params": [
          {
            "name": "ctx",
            "type": "VisitorContext *"
          },
          {
            "name": "solver",
            "type": "sofa::core::behavior::ConstraintSolver *"
          }
        ],
        "is_virtual": true,
        "is_pure_virtual": false,
        "is_static": false,
        "access": "public"
      },
      {
        "name": "bwdProjectiveConstraintSet",
        "return_type": "void",
        "params": [
          {
            "name": "",
            "type": "simulation::Node *"
          },
          {
            "name": "",
            "type": "sofa::core::behavior::BaseProjectiveConstraintSet *"
          }
        ],
        "is_virtual": true,
        "is_pure_virtual": false,
        "is_static": false,
        "access": "public"
      },
      {
        "name": "bwdConstraintSet",
        "return_type": "void",
        "params": [
          {
            "name": "",
            "type": "simulation::Node *"
          },
          {
            "name": "",
            "type": "sofa::core::behavior::BaseConstraintSet *"
          }
        ],
        "is_virtual": true,
        "is_pure_virtual": false,
        "is_static": false,
        "access": "public"
      },
      {
        "name": "bwdProjectiveConstraintSet",
        "return_type": "void",
        "params": [
          {
            "name": "ctx",
            "type": "VisitorContext *"
          },
          {
            "name": "c",
            "type": "sofa::core::behavior::BaseProjectiveConstraintSet *"
          }
        ],
        "is_virtual": true,
        "is_pure_virtual": false,
        "is_static": false,
        "access": "public"
      },
      {
        "name": "bwdConstraintSet",
        "return_type": "void",
        "params": [
          {
            "name": "ctx",
            "type": "VisitorContext *"
          },
          {
            "name": "c",
            "type": "sofa::core::behavior::BaseConstraintSet *"
          }
        ],
        "is_virtual": true,
        "is_pure_virtual": false,
        "is_static": false,
        "access": "public"
      },
      {
        "name": "getCategoryName",
        "return_type": "const char *",
        "params": [],
        "is_virtual": true,
        "is_pure_virtual": false,
        "is_static": false,
        "access": "public"
      },
      {
        "name": "stopAtMechanicalMapping",
        "return_type": "bool",
        "params": [
          {
            "name": "",
            "type": "simulation::Node *"
          },
          {
            "name": "map",
            "type": "sofa::core::BaseMapping *"
          }
        ],
        "is_virtual": true,
        "is_pure_virtual": false,
        "is_static": false,
        "access": "public"
      }
    ]
  },
  "desc": {
    "name": "BaseMechanicalVisitor",
    "description": "The BaseMechanicalVisitor class in SOFA (Simulation Open-Framework Architecture) is an abstract class that serves as the foundation for mechanical visitors, which are used to propagate and process various mechanical properties and constraints throughout a simulation hierarchy. This component plays a crucial role in the animation pipeline of physical simulations within the SOFA framework.",
    "parameters": [],
    "returns": null,
    "example": null,
    "note": [
      "The class defines several virtual functions that must be overridden by derived classes to perform specific tasks during the simulation process.",
      "These tasks include processing ODE solvers, constraint solvers, mechanical mappings, mechanical states, masses, force fields, projective and standard constraint sets, as well as handling interaction forces and constraints between different parts of the simulation.",
      "The class provides methods for both forward (fwd) and backward (bwd) processing, allowing derived classes to implement their own logic for pre-processing and post-processing tasks."
    ],
    "authors": [
      "Project SOFA"
    ]
  },
  "maths": {
    "maths": "The `BaseMechanicalVisitor` class in the Simulation Open-Framework Architecture (SOFA) is an abstract class designed to handle the propagation and processing of mechanical properties, constraints, and forces throughout a hierarchical simulation structure. This class plays a pivotal role in animating physical simulations by facilitating interactions between various components such as force fields, constraint sets, and mapping operators.\n\n### Mathematical Description:\n\n#### Hierarchical Propagation:\nThe `BaseMechanicalVisitor` operates within a hierarchical node-based framework where each node (representing an object or part of the simulation) can have its own mechanical properties, constraints, and mappings. The propagation mechanism can be described as follows:\n\n1. **Top-Down Propagation** (`fwdXxx` Methods):\n   - `fwdOdeSolver`: Processes Ordinary Differential Equation (ODE) solvers at each node level.\n   - `fwdConstraintSolver`: Handles constraint solvers that enforce physical constraints like contacts or joints.\n   - `fwdMechanicalMapping`: Maps mechanical properties and forces from a parent node to its child nodes, using mappings defined by the `BaseMapping` class. This step is crucial for transferring state between different levels of granularity in the simulation hierarchy.\n   - `fwdMappedMechanicalState`: Applies mappings on mechanical states if they are derived from higher levels.\n   - `fwdMechanicalState`: Processes local mechanical states that are not mapped from a parent level, directly modifying and propagating properties within the node itself.\n   - `fwdMass`: Handles mass distribution in the simulation nodes.\n   - `fwdForceField` and `fwdInteractionForceField`: Applies force fields to compute forces on particles or elements. Interaction force fields specifically handle interactions between different parts of the system.\n   - `fwdProjectiveConstraintSet`, `fwdConstraintSet`, `fwdInteractionProjectiveConstraintSet`, `fwdInteractionConstraint`: Enforces constraints, including projective and interaction constraints that are applied to ensure physical consistency in the simulation.\n\n2. **Bottom-Up Propagation** (`bwdXxx` Methods):\n   - Similar methods exist for bottom-up propagation but serve a reverse function, typically aggregating results from child nodes back up to parent nodes or post-processing computed values.\n\n#### Mathematical Formulations:\n- **Force Computation**: Force fields compute forces based on physical laws. For instance, if `F` is the force vector and `x` represents positions of particles or elements, then `F = f(x)` where `f` can be a function representing various physical effects such as gravity, elasticity, or friction.\n- **Constraint Enforcement**: Constraint sets enforce linear or nonlinear constraints on the system. A constraint `C(x) = 0` ensures that the state vector `x` satisfies certain conditions. The projection operator `P` can be used to project a solution onto the feasible set of constraints: `x_new = P(x_old)`.\n- **Mapping**: Mappings, represented by matrix `M`, map properties from one level to another. For example, if `u_parent` is a state vector in the parent node and `u_child` is the corresponding state vector in the child node, then `u_child = M * u_parent`.\n\n### Physical Description:\nThe physical aspects of the `BaseMechanicalVisitor` revolve around simulating realistic mechanical behavior within complex systems. This involves integrating Newton's laws of motion with numerical methods for solving differential equations that describe system dynamics. The framework supports both explicit and implicit integration schemes, which can be chosen based on the specific requirements of stability and accuracy.\n\n- **Dynamics Simulation**: By propagating forces through hierarchical mappings, the visitor ensures that changes in one part of a simulation affect other parts appropriately according to physical laws. This is critical for simulating interactions such as collisions or deformations.\n- **Constraint Handling**: Constraints ensure that certain conditions are met during the simulation, like maintaining contacts between objects or enforcing joint movements within their defined limits.\n- **Animation Pipeline**: The visitor class supports the overall animation pipeline by ensuring that all mechanical properties are correctly updated and propagated at each time step of the simulation.\n\nOverall, `BaseMechanicalVisitor` provides a structured approach to processing complex mechanical systems in SOFA, leveraging mathematical formulations and physical principles to achieve realistic simulations."
  },
  "summary": {
    "abstract": "`BaseMechanicalVisitor` is an abstract class for creating mechanical visitors that propagate and process mechanical properties through a hierarchical node-based framework in SOFA simulations.",
    "sheet": "# BaseMechanicalVisitor\n\n## Overview\nThe `BaseMechanicalVisitor` serves as the foundation for mechanical visitors, facilitating the propagation and processing of various mechanical properties and constraints throughout a hierarchical simulation structure. It interacts with nodes and their components such as ODE solvers, constraint solvers, force fields, mappings, and more.\n\n## Parameters and Data\nThe `BaseMechanicalVisitor` class does not expose any significant data fields but provides numerous methods for top-down (`fwdXxx`) and bottom-up (`bwdXxx`) propagation. These methods include:\n- **Top-Down Propagation** (`fwdXxx` Methods):\n  - `fwdOdeSolver`: Processes ODE solvers at each node level.\n  - `fwdConstraintSolver`: Handles constraint solvers that enforce physical constraints like contacts or joints.\n  - `fwdMechanicalMapping`: Maps mechanical properties and forces from a parent node to its child nodes using mappings defined by the `BaseMapping` class.\n  - `fwdMappedMechanicalState`: Applies mappings on mechanical states if they are derived from higher levels.\n  - `fwdMechanicalState`: Processes local mechanical states that are not mapped from a parent level, directly modifying and propagating properties within the node itself.\n  - `fwdMass`: Handles mass distribution in the simulation nodes.\n  - `fwdForceField` and `fwdInteractionForceField`: Applies force fields to compute forces on particles or elements. Interaction force fields specifically handle interactions between different parts of the system.\n  - `fwdProjectiveConstraintSet`, `fwdConstraintSet`, `fwdInteractionProjectiveConstraintSet`, `fwdInteractionConstraint`: Enforces constraints, including projective and interaction constraints that are applied to ensure physical consistency in the simulation.\n- **Bottom-Up Propagation** (`bwdXxx` Methods):\n  - Similar methods exist for bottom-up propagation but serve a reverse function, typically aggregating results from child nodes back up to parent nodes or post-processing computed values."
  }
}