Data Fields

Methods

{
  "name": "ValuesFromPositions",
  "namespace": "sofa::component::engine::select",
  "module": "Sofa.Component.Engine.Select",
  "include": "sofa/component/engine/select/ValuesFromPositions.h",
  "doc": "Assign values to primitives (vertex/edge/triangle/tetrahedron) based on a linear interpolation of values along a direction.\n\nThis class find all the points/edges/triangles/tetrahedra located inside a given box.",
  "inherits": [
    "DataEngine"
  ],
  "templates": [
    "sofa::defaulttype::Rigid3Types",
    "sofa::defaulttype::Vec3Types"
  ],
  "data_fields": [
    {
      "name": "f_inputValues",
      "type": "VecReal",
      "xmlname": "inputValues",
      "help": "Input values"
    },
    {
      "name": "f_direction",
      "type": "CPos",
      "xmlname": "direction",
      "help": "Direction along which the values are interpolated"
    },
    {
      "name": "f_X0",
      "type": "VecCoord",
      "xmlname": "position",
      "help": "Rest position coordinates of the degrees of freedom"
    },
    {
      "name": "f_values",
      "type": "VecReal",
      "xmlname": "values",
      "help": "Values of the points contained in the ROI"
    },
    {
      "name": "f_edgeValues",
      "type": "VecReal",
      "xmlname": "edgeValues",
      "help": "Values of the edges contained in the ROI"
    },
    {
      "name": "f_triangleValues",
      "type": "VecReal",
      "xmlname": "triangleValues",
      "help": "Values of the triangles contained in the ROI"
    },
    {
      "name": "f_tetrahedronValues",
      "type": "VecReal",
      "xmlname": "tetrahedronValues",
      "help": "Values of the tetrahedra contained in the ROI"
    },
    {
      "name": "p_fieldType",
      "type": "sofa::helper::OptionsGroup",
      "xmlname": "fieldType",
      "help": "field type of output elements"
    },
    {
      "name": "p_drawVectors",
      "type": "bool",
      "xmlname": "drawVectors",
      "help": "draw vectors line"
    },
    {
      "name": "p_vectorLength",
      "type": "float",
      "xmlname": "drawVectorLength",
      "help": "vector length visualisation. "
    }
  ],
  "links": [],
  "methods": [
    {
      "name": "init",
      "return_type": "void",
      "params": [],
      "is_virtual": true,
      "is_pure_virtual": false,
      "is_static": false,
      "access": "public"
    },
    {
      "name": "reinit",
      "return_type": "void",
      "params": [],
      "is_virtual": true,
      "is_pure_virtual": false,
      "is_static": false,
      "access": "public"
    },
    {
      "name": "doUpdate",
      "return_type": "void",
      "params": [],
      "is_virtual": true,
      "is_pure_virtual": false,
      "is_static": false,
      "access": "public"
    },
    {
      "name": "draw",
      "return_type": "void",
      "params": [
        {
          "name": "vparams",
          "type": "const core::visual::VisualParams *"
        }
      ],
      "is_virtual": true,
      "is_pure_virtual": false,
      "is_static": false,
      "access": "public"
    },
    {
      "name": "canCreate",
      "return_type": "bool",
      "params": [
        {
          "name": "obj",
          "type": "T *&"
        },
        {
          "name": "context",
          "type": "core::objectmodel::BaseContext *"
        },
        {
          "name": "arg",
          "type": "core::objectmodel::BaseObjectDescription *"
        }
      ],
      "is_virtual": false,
      "is_pure_virtual": false,
      "is_static": true,
      "access": "public"
    },
    {
      "name": "updateValues",
      "return_type": "void",
      "params": [
        {
          "name": "_data",
          "type": "TempData &"
        }
      ],
      "is_virtual": false,
      "is_pure_virtual": false,
      "is_static": false,
      "access": "protected"
    },
    {
      "name": "valueFromPosition",
      "return_type": "Real",
      "params": [
        {
          "name": "p",
          "type": "const CPos &"
        },
        {
          "name": "data",
          "type": "const TempData &"
        }
      ],
      "is_virtual": false,
      "is_pure_virtual": false,
      "is_static": false,
      "access": "protected"
    },
    {
      "name": "valueFromPoint",
      "return_type": "Real",
      "params": [
        {
          "name": "pid",
          "type": "const PointID &"
        },
        {
          "name": "data",
          "type": "const TempData &"
        }
      ],
      "is_virtual": false,
      "is_pure_virtual": false,
      "is_static": false,
      "access": "protected"
    },
    {
      "name": "valueFromEdge",
      "return_type": "Real",
      "params": [
        {
          "name": "e",
          "type": "const Edge &"
        },
        {
          "name": "data",
          "type": "const TempData &"
        }
      ],
      "is_virtual": false,
      "is_pure_virtual": false,
      "is_static": false,
      "access": "protected"
    },
    {
      "name": "valueFromTriangle",
      "return_type": "Real",
      "params": [
        {
          "name": "t",
          "type": "const Triangle &"
        },
        {
          "name": "data",
          "type": "const TempData &"
        }
      ],
      "is_virtual": false,
      "is_pure_virtual": false,
      "is_static": false,
      "access": "protected"
    },
    {
      "name": "valueFromTetrahedron",
      "return_type": "Real",
      "params": [
        {
          "name": "t",
          "type": "const Tetra &"
        },
        {
          "name": "data",
          "type": "const TempData &"
        }
      ],
      "is_virtual": false,
      "is_pure_virtual": false,
      "is_static": false,
      "access": "protected"
    },
    {
      "name": "updateVectors",
      "return_type": "void",
      "params": [
        {
          "name": "_data",
          "type": "TempData &"
        }
      ],
      "is_virtual": false,
      "is_pure_virtual": false,
      "is_static": false,
      "access": "protected"
    },
    {
      "name": "vectorFromPosition",
      "return_type": "Vec3",
      "params": [
        {
          "name": "p",
          "type": "const CPos &"
        },
        {
          "name": "data",
          "type": "const TempData &"
        }
      ],
      "is_virtual": false,
      "is_pure_virtual": false,
      "is_static": false,
      "access": "protected"
    },
    {
      "name": "vectorFromPoint",
      "return_type": "Vec3",
      "params": [
        {
          "name": "pid",
          "type": "const PointID &"
        },
        {
          "name": "data",
          "type": "const TempData &"
        }
      ],
      "is_virtual": false,
      "is_pure_virtual": false,
      "is_static": false,
      "access": "protected"
    },
    {
      "name": "vectorFromEdge",
      "return_type": "Vec3",
      "params": [
        {
          "name": "e",
          "type": "const Edge &"
        },
        {
          "name": "data",
          "type": "const TempData &"
        }
      ],
      "is_virtual": false,
      "is_pure_virtual": false,
      "is_static": false,
      "access": "protected"
    },
    {
      "name": "vectorFromTriangle",
      "return_type": "Vec3",
      "params": [
        {
          "name": "t",
          "type": "const Triangle &"
        },
        {
          "name": "data",
          "type": "const TempData &"
        }
      ],
      "is_virtual": false,
      "is_pure_virtual": false,
      "is_static": false,
      "access": "protected"
    },
    {
      "name": "vectorFromTetrahedron",
      "return_type": "Vec3",
      "params": [
        {
          "name": "t",
          "type": "const Tetra &"
        },
        {
          "name": "data",
          "type": "const TempData &"
        }
      ],
      "is_virtual": false,
      "is_pure_virtual": false,
      "is_static": false,
      "access": "protected"
    }
  ],
  "description": "The `ValuesFromPositions` component in the SOFA framework is designed to assign values to geometric primitives (points, edges, triangles, tetrahedra) based on linear interpolation along a specified direction. It operates by interpolating input values provided along a given direction and mapping these values to specific elements within a defined region of interest (ROI). The component can generate both scalar and vector output fields for the assigned elements.\n\n### Interactions with Other Components\n- **Mechanical State and Topology**: `ValuesFromPositions` relies on the mechanical state and mesh topology provided by other components in the simulation graph. It specifically uses rest position coordinates (`f_X0`) and topological data (edges, triangles, tetrahedra) to perform its operations.\n- **Data Engine**: As a subclass of `core::DataEngine`, it inherits methods for initialization (`init`), reinitialization (`reinit`), and updating the computed values (`doUpdate`). It also implements drawing functionality (`draw`) for visualizing vectors if enabled.\n\n### Data Fields\n- **Input Fields**:\n  - `f_inputValues`: Input scalar values to be interpolated along a direction.\n  - `f_direction`: Direction vector along which interpolation is performed.\n  - `f_X0`: Rest position coordinates of the geometric elements.\n  - `f_edges`, `f_triangles`, `f_tetrahedra`: Topological data for edges, triangles, and tetrahedra.\n- **Output Fields**:\n  - `f_values`, `f_edgeValues`, `f_triangleValues`, `f_tetrahedronValues`: Output scalar values assigned to points, edges, triangles, and tetrahedra respectively.\n  - `f_pointVectors`, `f_edgeVectors`, `f_triangleVectors`, `f_tetrahedronVectors`: Output vector fields for the respective geometric primitives if vector output is selected.\n- **Parameters**:\n  - `p_fieldType`: Selects whether to compute scalar or vector values.\n  - `p_drawVectors`: Toggles visualization of computed vectors.\n  - `p_vectorLength`: Sets the length of visualized vectors.\n\n### Practical Usage Guidance\nThe component is useful for assigning scalar or vector values to geometric primitives based on linear interpolation. It can be configured by setting input values and a direction, and it updates these values based on topology data from other components in the simulation graph. The `p_fieldType` parameter determines whether to compute scalars or vectors, while `p_drawVectors` controls the visualization of computed vectors with adjustable length.",
  "maths": "### Mathematical and Physical Description of `ValuesFromPositions`\n\nThe `ValuesFromPositions` component in the SOFA framework is designed to interpolate input values along a specified direction for various geometric primitives such as points, edges, triangles, and tetrahedra. This interpolation process generates scalar or vector output fields based on the selected configuration.\n\n#### Governing Equations and Operators\n\n1. **Linear Interpolation of Scalar Values**:\n   The component performs linear interpolation of input values along a specified direction `\\mathbf{d}`. Given a set of input values \\( V = [v_0, v_1, \\ldots, v_n] \\) and the corresponding positions along the direction vector \\( P = [p_0, p_1, \\ldots, p_n] \\), the interpolated value at any position \\( x \\) can be computed as:\n   \n   \\[ v(x) = v_i + (v_{i+1} - v_i) \\frac{x - p_i}{p_{i+1} - p_i}, \\quad \\text{for } p_i \\leq x < p_{i+1} \\]\n\n2. **Direction Vector and Interpolation**:\n   The direction vector \\(\\mathbf{d}\\) is specified by the user, and the interpolation is performed along this direction.\n\n#### Constitutive or Kinematic Laws Involved\n\n- **Linear Interpolation**: \n  - Given a point position \\( p_i \\), its value \\( v(p_i) \\) is determined using linear interpolation based on the nearest input values. The interpolation formula is given above.\n\n3. **Vector Output**:\n   If vector output is selected, the direction vector \\(\\mathbf{d}\\) is assigned to each geometric primitive's position.\n\n#### Role in the Global FEM Pipeline\n\n- **Assembly Phase**: \n  - The component reads rest positions (`f_X0`), edge, triangle, and tetrahedron topologies from the simulation graph. It then computes scalar or vector values for each element based on the interpolation formula.\n- **Nonlinear Resolution**: Not applicable as this component does not contribute to nonlinear residual computation.\n- **Linear Solve**: Not applicable since no linear system is solved by this component.\n\n#### Numerical Methods and Discretization Choices\n\n1. **Interpolation of Scalar Values**:\n   - For each geometric primitive (point, edge, triangle, tetrahedron), the value at its centroid or representative position is computed using linear interpolation along the direction \\(\\mathbf{d}\\).\n2. **Vector Output**: \n   - The direction vector \\(\\mathbf{d}\\) is assigned to each geometric primitive's position.\n\n#### Broad Variational / Lagrangian Mechanics Framework Context\n\nWhile this component does not directly contribute to the variational or Lagrangian mechanics framework, it can be used as part of a broader simulation pipeline. For example, scalar values computed by `ValuesFromPositions` could represent material properties such as stiffness coefficients that are interpolated based on spatial coordinates.\n\n### Summary\n\nThe `ValuesFromPositions` component in SOFA performs linear interpolation of input values along a specified direction for points, edges, triangles, and tetrahedra. It generates scalar or vector output fields depending on the configuration and is useful for assigning material properties or other scalar/vector fields to geometric primitives based on spatial coordinates.",
  "abstract": "The `ValuesFromPositions` component interpolates input values along a specified direction for points, edges, triangles, and tetrahedra, generating scalar or vector output fields based on linear interpolation.",
  "sheet": "# ValuesFromPositions\n\n## Overview\nThe `ValuesFromPositions` component is an engine that assigns values to geometric primitives (points, edges, triangles, tetrahedra) by interpolating input values along a specified direction. It operates within the SOFA framework and inherits from `DataEngine`, providing methods for initialization (`init`), reinitialization (`reinit`), updating computed values (`doUpdate`), and drawing vectors if visualization is enabled.\n\n## Mathematical Model\nThe component performs linear interpolation of input values along a specified direction vector \\(\\mathbf{d}\\). Given a set of input values \\(V = [v_0, v_1, \\ldots, v_n]\\) at positions \\(P = [p_0, p_1, \\ldots, p_n]\\), the interpolated value at any position \\(x\\) is computed as:\n\n\\[ v(x) = v_i + (v_{i+1} - v_i) \\frac{x - p_i}{p_{i+1} - p_i}, \\quad \\text{for } p_i \\leq x < p_{i+1}. \\]\n\nFor vector output, the direction vector \\(\\mathbf{d}\\) is assigned to each geometric primitive's position.\n\n## Parameters and Data\n- **Input Fields**:\n  - `f_inputValues`: Input scalar values to be interpolated along a direction.\n  - `f_direction`: Direction vector along which interpolation is performed.\n  - `f_X0`: Rest position coordinates of the geometric elements.\n- **Output Fields**:\n  - `f_values`, `f_edgeValues`, `f_triangleValues`, `f_tetrahedronValues`: Output scalar values assigned to points, edges, triangles, and tetrahedra respectively.\n  - `p_fieldType`: Selects whether to compute scalar or vector values.\n  - `p_drawVectors`: Toggles visualization of computed vectors.\n  - `p_vectorLength`: Sets the length of visualized vectors."
}