{
  "name": "ConstraintAttachButtonSetting",
  "main": {
    "name": "ConstraintAttachButtonSetting",
    "namespace": "sofa::gui::component",
    "module": "Sofa.GUI.Component",
    "include": "sofa/gui/component/ConstraintAttachButtonSetting.h",
    "doc": "Attach an object to the mouse using lagrangian multiplier.\n\nThis component modifies the mouse picking behavior in the GUI\nand set it at the beginning to Lagrangian-based constraints\nIt doesn't have any parameter because its only presence is sufficient.",
    "inherits": [
      "MouseButtonSetting"
    ],
    "templates": [],
    "data_fields": [],
    "links": [],
    "methods": [
      {
        "name": "getOperationType",
        "return_type": "int",
        "params": [],
        "is_virtual": false,
        "is_pure_virtual": false,
        "is_static": false,
        "access": "public"
      }
    ]
  },
  "desc": {
    "description": "The `ConstraintAttachButtonSetting` is a GUI component in SOFA designed to modify mouse picking behavior, enabling the attachment of an object to the mouse using Lagrangian-based constraints. This component extends the `MouseButtonSetting` class and does not require any parameters; its presence alone is sufficient for functionality.\n\nIt interacts with other components by overriding the `getOperationType()` method, which returns a string indicating the operation type as \"ConstraintAttach\". This interaction helps in setting up specific mouse operations within the GUI environment of SOFA simulations.\n\nPractical usage involves including this component to enable the attachment behavior, facilitating interactive simulations where objects can be manipulated or attached to the cursor using constraint-based methods."
  },
  "maths": {
    "maths": "The `ConstraintAttachButtonSetting` is a GUI component in the SOFA framework that modifies mouse picking behavior to enable the attachment of an object to the mouse using Lagrangian-based constraints. This component does not directly contribute to governing equations or operators such as the mass matrix $M$, stiffness matrix $K$, internal force $f_{int}$, residual $R$, etc., but it plays a critical role in setting up specific interaction behaviors within the simulation environment.\n\n**Governing Equations / Operators:**\n- The `ConstraintAttachButtonSetting` does not implement or contribute directly to any governing equations or operators. It is primarily responsible for modifying mouse picking behavior and enabling Lagrangian-based constraints.\n\n**Constitutive / Kinematic Laws Involved:**\n- Although the component itself does not involve specific constitutive or kinematic laws, it relies on the underlying constraint mechanisms provided by SOFA. These constraints are formulated using Lagrange multipliers to enforce positional constraints between mouse and object positions. For instance, if an object is attached to a point $\\mathbf{p}$ in the simulation space via the mouse position $\\mathbf{x}_m$, the Lagrangian-based constraint would be written as:\n\n\begin{align*}\n  \\mathbf{C} = \\mathbf{p} - \\mathbf{x}(t) = 0,\n\\end{align*}\n\nwhere $\\mathbf{x}(t)$ is the position of the object at time $t$. The Lagrange multiplier method introduces a scalar value $\\lambda$ to enforce this constraint.\n\n**Role in Global FEM Pipeline:**\n- **Assembly:** This component does not directly participate in the assembly process but sets up constraints that are eventually assembled into the global system of equations.\n- **Time Integration:** The time integration schemes, such as implicit Euler or Newmark-type schemes, handle the temporal evolution of constrained systems. These schemes integrate the Lagrangian-based constraint forces over time to ensure consistent behavior.\n- **Nonlinear Solve:** The nonlinear solve phase involves solving for both the displacement and Lagrange multipliers that satisfy the constraints while maintaining equilibrium conditions in the simulation.\n- **Linear Solve:** During linearization, the system of equations involving $M$, $K$, internal force terms, and constraint forces are solved iteratively to find consistent state variables.\n\n**Numerical Methods / Discretization Choices:**\n- The component does not implement any numerical methods or discretization choices but relies on SOFA's underlying solvers for Lagrange multipliers and implicit time integration schemes.\n\n**Fit into Variational / Lagrangian Mechanics Framework:**\n- Within the broader variational / Lagrangian mechanics framework, `ConstraintAttachButtonSetting` provides a mechanism to enforce kinematic constraints in an interactive manner. These constraints are part of the larger system governed by Lagrangian mechanics principles, ensuring that the dynamics and interactions within the simulation remain consistent with physical laws.\n\n**Summary:**\nThe `ConstraintAttachButtonSetting` component modifies mouse picking behavior to enable object attachment using Lagrange multipliers for constraint enforcement. It does not directly contribute mathematical operators or equations but sets up constraints within the SOFA framework's broader variational mechanics context."
  },
  "summary": {
    "abstract": "Modifies mouse picking behavior in SOFA's GUI to enable object attachment using Lagrangian-based constraints.",
    "sheet": "# ConstraintAttachButtonSetting\n\n## Overview\nThe `ConstraintAttachButtonSetting` is a GUI component that modifies the mouse picking behavior within the SOFA framework. It enables the attachment of an object to the mouse cursor through Lagrangian-based constraints, facilitating interactive simulations where objects can be manipulated or attached to the cursor using constraint-based methods.\n\n## Mathematical Model\nThe `ConstraintAttachButtonSetting` does not directly contribute to governing equations or operators such as the mass matrix $M$, stiffness matrix $K$, internal force $f_{int}$, residual $R$, etc. However, it plays a critical role in setting up specific interaction behaviors within the simulation environment.\n\nFor instance, if an object is attached to a point $\\mathbf{p}$ in the simulation space via the mouse position $\\mathbf{x}_m$, the Lagrangian-based constraint would be written as:\n\n\begin{align*}\n  \\mathbf{C} = \\mathbf{p} - \\mathbf{x}(t) = 0,\n\\end{align*}\n\nwhere $\\mathbf{x}(t)$ is the position of the object at time $t$. The Lagrange multiplier method introduces a scalar value $\\lambda$ to enforce this constraint.\n\nThe component relies on SOFA's underlying solvers for Lagrange multipliers and implicit time integration schemes, ensuring consistent behavior in the simulation."
  }
}