Detailed Description

This class represents a 2d quadrilateral element. The following sketch shows the node and edge numbering.

       2
 3-----------2
 |           |
 |           |
3|           |1
 |           |
 |           |
 0-----------1
       0

Definition at line 37 of file QuadRule4.h.

#include <QuadRule4.h>

Inheritance diagram for MeshLib::QuadRule4:

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Collaboration diagram for MeshLib::QuadRule4:

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Public Types
using	EdgeReturn = MeshLib::LinearEdgeReturn
	Returns the i-th edge of the element. More...

Static Public Member Functions
static bool	isPntInElement (Node const const nodes, MathLib::Point3d const &pnt, double eps)

static ElementErrorCode	validate (const Element *e)

static unsigned	identifyFace (Node const const , Node const *nodes[3])
	Returns the ID of a face given an array of nodes. More...

static double	computeVolume (Node const const _nodes)
	Calculates the volume of a convex hexahedron by partitioning it into six tetrahedra. More...

Static Public Member Functions inherited from MeshLib::FaceRule
static const Element *	getFace (const Element *e, unsigned i)
	Returns the face i of the element. More...

static bool	testElementNodeOrder (Element const &e)

static Eigen::Vector3d	getFirstSurfaceVector (Element const &e)

static Eigen::Vector3d	getSecondSurfaceVector (Element const &e)

static Eigen::Vector3d	getSurfaceNormal (Element const &e)
	Returns the surface normal of a 2D element. More...

Static Public Attributes
static const unsigned	n_base_nodes = 4u
	Constant: The number of base nodes for this element. More...

static const unsigned	n_all_nodes = 4u
	Constant: The number of all nodes for this element. More...

static const MeshElemType	mesh_elem_type = MeshElemType::QUAD
	Constant: The geometric type of the element. More...

static const CellType	cell_type = CellType::QUAD4
	Constant: The FEM type of the element. More...

static const unsigned	n_edges = 4
	Constant: The number of edges. More...

static const unsigned	n_neighbors = 4
	Constant: The number of neighbors. More...

static const unsigned	edge_nodes [4][2]
	Constant: Local node index table for edge. More...

Static Public Attributes inherited from MeshLib::FaceRule
static const unsigned	dimension = 2u
	Constant: Dimension of this mesh element. More...

static const unsigned	n_faces = 0
	Constant: The number of faces. More...

Member Typedef Documentation

◆ EdgeReturn

using MeshLib::QuadRule4::EdgeReturn = MeshLib::LinearEdgeReturn

Returns the i-th edge of the element.

Definition at line 62 of file QuadRule4.h.

Member Function Documentation

◆ computeVolume()

double MeshLib::QuadRule4::computeVolume ( Node const *const * _nodes )

static

Calculates the volume of a convex hexahedron by partitioning it into six tetrahedra.

Definition at line 25 of file QuadRule4.cpp.

 {
     return MathLib::calcTriangleArea(*_nodes[0], *_nodes[1], *_nodes[2]) +
            MathLib::calcTriangleArea(*_nodes[2], *_nodes[3], *_nodes[0]);
 }

References MathLib::calcTriangleArea().

◆ identifyFace()

unsigned MeshLib::QuadRule4::identifyFace	(	Node const const	_nodes,
		Node const *	nodes[3]
	)

static

Returns the ID of a face given an array of nodes.

Definition at line 40 of file QuadRule4.cpp.

 {
     for (unsigned i = 0; i < 4; i++)
     {
         unsigned flag(0);
         for (unsigned j = 0; j < 2; j++)
         {
             for (unsigned k = 0; k < 2; k++)
             {
                 if (_nodes[edge_nodes[i][j]] == nodes[k])
                 {
                     flag++;
                 }
             }
         }
         if (flag == 2)
         {
             return i;
         }
     }
     return std::numeric_limits<unsigned>::max();
 }

References edge_nodes.

◆ isPntInElement()

bool MeshLib::QuadRule4::isPntInElement	(	Node const const	nodes,
		MathLib::Point3d const &	pnt,
		double	eps
	)

static

Checks if a point is inside the element.

Parameters

pnt	a 3D MathLib::Point3d object
eps	tolerance for numerical algorithm used or computing the property

Returns: true if the point is not outside the element, false otherwise

Parameters

nodes the nodes of the element.

Definition at line 31 of file QuadRule4.cpp.

 {
     return (
         MathLib::isPointInTriangle(pnt, *nodes[0], *nodes[1], *nodes[2], eps) ||
         MathLib::isPointInTriangle(pnt, *nodes[0], *nodes[2], *nodes[3], eps));
 }

References MathLib::isPointInTriangle().

◆ validate()

ElementErrorCode MeshLib::QuadRule4::validate ( const Element * e )

static

Tests if the element is geometrically valid.

Definition at line 64 of file QuadRule4.cpp.

 {
     ElementErrorCode error_code;
     error_code[ElementErrorFlag::ZeroVolume] = hasZeroVolume(*e);
     Node const* const* _nodes = e->getNodes();
     error_code[ElementErrorFlag::NonCoplanar] =
         (!MathLib::isCoplanar(*_nodes[0], *_nodes[1], *_nodes[2], *_nodes[3]));
     // for collapsed quads (i.e. reduced to a line) this test might result
     // "false" as all four points are actually located on a line.
     if (!error_code[ElementErrorFlag::ZeroVolume])
     {
         error_code[ElementErrorFlag::NonConvex] =
             (!(MathLib::dividedByPlane(
                    *_nodes[0], *_nodes[2], *_nodes[1], *_nodes[3]) &&
                MathLib::dividedByPlane(
                    *_nodes[1], *_nodes[3], *_nodes[0], *_nodes[2])));
     }
     error_code[ElementErrorFlag::NodeOrder] = !e->testElementNodeOrder();
     return error_code;
 }

References MathLib::dividedByPlane(), MeshLib::Element::getNodes(), MeshLib::hasZeroVolume(), MathLib::isCoplanar(), NodeOrder, NonConvex, NonCoplanar, MeshLib::Element::testElementNodeOrder(), and ZeroVolume.

Member Data Documentation

◆ cell_type

const CellType MeshLib::QuadRule4::cell_type = CellType::QUAD4

static

Constant: The FEM type of the element.

Definition at line 50 of file QuadRule4.h.

◆ edge_nodes

const unsigned MeshLib::QuadRule4::edge_nodes

static

Initial value:

= {
    {0, 1},  
    {1, 2},  
    {2, 3},  
    {3, 0}   
}

Constant: Local node index table for edge.

Definition at line 59 of file QuadRule4.h.

Referenced by identifyFace().

◆ mesh_elem_type

const MeshElemType MeshLib::QuadRule4::mesh_elem_type = MeshElemType::QUAD

static

Constant: The geometric type of the element.

Definition at line 47 of file QuadRule4.h.

◆ n_all_nodes

const unsigned MeshLib::QuadRule4::n_all_nodes = 4u

static

Constant: The number of all nodes for this element.

Definition at line 44 of file QuadRule4.h.

◆ n_base_nodes

const unsigned MeshLib::QuadRule4::n_base_nodes = 4u

static

Constant: The number of base nodes for this element.

Definition at line 41 of file QuadRule4.h.

◆ n_edges

const unsigned MeshLib::QuadRule4::n_edges = 4

static

Constant: The number of edges.

Definition at line 53 of file QuadRule4.h.

◆ n_neighbors

const unsigned MeshLib::QuadRule4::n_neighbors = 4

static

Constant: The number of neighbors.

Definition at line 56 of file QuadRule4.h.

The documentation for this class was generated from the following files:

MeshLib/Elements/QuadRule4.h
MeshLib/Elements/QuadRule4.cpp

Detailed Description

Public Types

Static Public Member Functions

Static Public Attributes

Member Typedef Documentation

◆ EdgeReturn

Member Function Documentation

◆ computeVolume()

◆ identifyFace()

◆ isPntInElement()

◆ validate()

Member Data Documentation

◆ cell_type

◆ edge_nodes

◆ mesh_elem_type

◆ n_all_nodes

◆ n_base_nodes

◆ n_edges

◆ n_neighbors