Data Fields

Methods

{
  "name": "TetrahedronSetGeometryAlgorithms",
  "namespace": "sofa::component::topology::container::dynamic",
  "module": "Sofa.Component.Topology.Container.Dynamic",
  "include": "sofa/component/topology/container/dynamic/TetrahedronSetGeometryAlgorithms.h",
  "doc": "Geometry algorithms dedicated to a tetrahedral topology.\n\nA class that provides geometry information on an TetrahedronSet.",
  "inherits": [
    "TriangleSetGeometryAlgorithms"
  ],
  "templates": [
    "sofa::defaulttype::Vec3Types"
  ],
  "data_fields": [
    {
      "name": "d_showTetrahedraIndices",
      "type": "bool"
    },
    {
      "name": "d_drawTetrahedra",
      "type": "bool"
    },
    {
      "name": "d_drawScaleTetrahedra",
      "type": "float"
    },
    {
      "name": "d_drawColorTetrahedra",
      "type": "sofa::type::RGBAColor"
    }
  ],
  "links": [],
  "methods": [
    {
      "name": "init",
      "description": "Initializes the TetrahedronSetGeometryAlgorithms instance, setting up internal data structures and performing necessary setup."
    },
    {
      "name": "draw",
      "parameters": [
        "vparams"
      ],
      "description": "Draws the tetrahedra for visualization based on the specified parameters. This method is used by Sofa's rendering pipeline to visualize the mesh.",
      "returnType": "void"
    },
    {
      "name": "computeTetrahedronAABB",
      "parameters": [
        "i",
        "minCoord",
        "maxCoord"
      ],
      "description": "Computes the axis-aligned bounding box (AABB) for a given tetrahedron index 'i'. The computed min and max coordinates are stored in 'minCoord' and 'maxCoord', respectively.",
      "returnType": "void"
    },
    {
      "name": "computeTetrahedronCenter",
      "parameters": [
        "i"
      ],
      "description": "Computes the geometric center of a given tetrahedron index 'i'. Returns a Coord object representing the computed center point.",
      "returnType": "Coord"
    },
    {
      "name": "computeTetrahedronCircumcenter",
      "parameters": [
        "i"
      ],
      "description": "Calculates the circumcenter (center of the circumscribed sphere) for tetrahedron at index 'i'. Returns a Coord object representing this point.",
      "returnType": "Coord"
    },
    {
      "name": "isPointInTetrahedron",
      "parameters": [
        "i",
        "p"
      ],
      "description": "Determines if a given 3D point 'p' is inside the tetrahedron at index 'i'. Returns true if the point lies within the tetrahedron, false otherwise.",
      "returnType": "bool"
    },
    {
      "name": "isPointInTetrahedron",
      "parameters": [
        "ind_t",
        "pTest",
        "barycentricCoordinates"
      ],
      "description": "Determines if a given 3D test point 'pTest' is inside the tetrahedron with index 'ind_t'. If true, it also computes and returns the barycentric coordinates of this point within the tetrahedron.",
      "returnType": "bool"
    },
    {
      "name": "getTetrahedronVertexCoordinates",
      "parameters": [
        "i"
      ],
      "description": "Gets the vertex coordinates for the tetrahedron at index 'i'. Returns an array of four Coord objects representing these points.",
      "returnType": "void"
    },
    {
      "name": "computeTetrahedronVolume",
      "parameters": [
        "i"
      ],
      "description": "Computes and returns the volume of the tetrahedron at index 'i'. This method calculates the volume based on the current positions of its vertices.",
      "returnType": "Real"
    }
  ],
  "description": "A class that provides geometry information on an TetrahedronSet topology container.",
  "parameters": [
    {
      "name": "d_showTetrahedraIndices",
      "description": "Debug : view Tetrahedrons indices. This parameter is used to display the indices of tetrahedra for debugging purposes.",
      "type": "bool"
    },
    {
      "name": "d_drawTetrahedra",
      "description": "Boolean indicating whether or not to draw the tetrahedra in the topology. Setting this to true will enable visualization of the tetrahedra.",
      "type": "bool"
    },
    {
      "name": "d_drawScaleTetrahedra",
      "description": "Scale factor for drawing the terahedra (between 0 and 1; if <1.0, it produces gaps between the tetrahedra). This is a float value that adjusts how the tetrahedra are rendered.",
      "type": "float"
    },
    {
      "name": "d_drawColorTetrahedra",
      "description": "RGBA code color used to draw tetrahedra in visualization. A type::RGBAColor object representing the desired RGBA color values for drawing the tetrahedra.",
      "type": "sofa::type::RGBAColor"
    }
  ],
  "maths": "## Mathematical Description\n\nThe TetrahedronSetGeometryAlgorithms class in the SOFA framework provides geometric information and operations for a tetrahedral mesh, which is a type of 3D mesh where every element is a tetrahedron (a polyhedron with four triangular faces). This description covers various methods related to the geometry of these elements.\n\n### Basic Geometric Operations\n- **Compute Tetrahedron Center**: The center of the tetrahedron can be computed as the arithmetic mean of its vertices. For a tetrahedron with vertices \\(v_1, v_2, v_3,\\) and \\(v_4\\), the center is given by:\n  \n    \\[ C = \\frac{1}{4} (v_1 + v_2 + v_3 + v_4) \\]\n\n- **Compute Circumcenter**: The circumcenter of a tetrahedron is the point equidistant from all its vertices, and it can be found using linear algebra techniques involving the coordinates of the vertices.\n\n- **Volume Computation**: The volume \\(V\\) of a tetrahedron with vertices at \\((x_1,y_1,z_1), (x_2,y_2,z_2), (x_3,y_3,z_3),\\) and \\((x_4,y_4,z_4)\\) can be calculated using the determinant of a matrix formed by these points. The formula is:\n  \n    \\[ V = \\frac{1}{6} | det(M) | \\]\n  where \\(M\\) is the matrix with rows given by the vectors from one vertex to the other three, augmented with a column of ones.\n\n### Bounding Volume Hierarchies (BVH)\n- **Get Tetra in Ball**: This method identifies all tetrahedrons within a specified radius around a given point. It involves distance computations and may use bounding spheres or boxes for efficiency.\n\n### Topological Operations\n- **Check Node Sequence**: Ensures that the nodes of a tetrahedron are ordered correctly by verifying cross products between edges, which helps in maintaining consistent orientation across all elements.\n\n- **Dihedral Angle Calculation**: Computes the dihedral angle (angle between two planes) for each edge of the tetrahedron. The calculation involves finding normal vectors to the faces sharing an edge and then computing their dot product.\n  \n    \\[ cos(\\theta) = n_1 \\cdot n_2 / ||n_1|| ||n_2|| \\]\n\n### Numerical Integration\n- **Cubature Points**: Provides integration points (cubature points) for numerical integration over the tetrahedron, which is important for finite element methods and other computational techniques.\n\n## Physical Description\n\nThe TetrahedronSetGeometryAlgorithms component operates on a mesh composed of tetrahedral elements. These are used in many physical simulations because they can conform to complex shapes and provide a solid foundation for numerical analysis.\n\n- **Mesh Representation**: Each tetrahedron is defined by its four vertices, which form the basis for all geometric calculations performed within this class.\n\n- **Simulation Requirements**: The component provides tools necessary for finite element methods (FEM) and other physical simulations that require precise spatial information. For example, computing the center or volume of a tetrahedron can be crucial in force calculation or material property evaluation.\n\n- **Validation Checks**: Methods like checking node sequence or dihedral angles ensure that the mesh remains well-formed and physically realistic throughout the simulation, preventing issues such as inverted elements which could lead to numerical instabilities.\n\nThis class is essential for ensuring the integrity of a tetrahedral mesh used in physical simulations within the SOFA framework.",
  "abstract": "The TetrahedronSetGeometryAlgorithms class provides geometric information and operations for tetrahedral meshes in SOFA simulations, including center computation, volume calculation, and validation checks.",
  "sheet": "# TetrahedronSetGeometryAlgorithms\n\n## Overview\nTetrahedronSetGeometryAlgorithms is a component that handles geometric computations on tetrahedral meshes within the SOFA framework. It inherits from TriangleSetGeometryAlgorithms and provides methods for computing various geometric properties of tetrahedra, such as centers, circumcenters, volumes, and dihedral angles.\n\n## Mathematical Model\n### Basic Geometric Operations\n- **Compute Tetrahedron Center**: The center of a tetrahedron with vertices \\(v_1, v_2, v_3,\\) and \\(v_4\\) is given by:\n  \n    \\[ C = \\frac{1}{4} (v_1 + v_2 + v_3 + v_4) \\]\n\n- **Compute Circumcenter**: The circumcenter of a tetrahedron can be found using linear algebra techniques involving the coordinates of the vertices.\n\n- **Volume Computation**: The volume \\(V\\) of a tetrahedron with vertices at \\((x_1,y_1,z_1), (x_2,y_2,z_2), (x_3,y_3,z_3),\\) and \\((x_4,y_4,z_4)\\) is given by:\n  \n    \\[ V = \\frac{1}{6} | \\det(M) | \\]\n  where \\(M\\) is the matrix with rows given by the vectors from one vertex to the other three, augmented with a column of ones.\n\n### Dihedral Angle Calculation\n- **Dihedral Angle**: The dihedral angle between two faces sharing an edge can be computed using normal vectors to these faces:\n  \n    \\[ \\cos(\\theta) = \\frac{n_1 \\cdot n_2}{||n_1|| ||n_2||} \\]\n\n## Parameters and Data\n- **d_showTetrahedraIndices**: Boolean flag to show tetrahedron indices (default: false).\n- **d_drawTetrahedra**: Boolean flag to draw tetrahedra (default: false).\n- **d_drawScaleTetrahedra**: Scale factor for drawing tetrahedra (default: 1.0).\n- **d_drawColorTetrahedra**: Color used for drawing tetrahedra (default: white)."
}