Rodin::Geometry::Polytope class

Base class for all geometric elements in finite element meshes.

A Polytope represents a geometric entity in a finite element mesh, ranging from vertices (0D) to cells (highest dimension). Polytopes are the building blocks of mesh topology and provide the geometric foundation for finite element computations.

Mathematical Foundation

In finite element analysis, polytopes represent:

Vertices (0D): Points
Edges (1D): Line segments connecting vertices
Faces (2D): Triangular or quadrilateral surfaces
Cells (3D): Tetrahedral, hexahedral, or other volumetric elements

Supported Element Types

Simplicial elements: Point, Segment, Triangle, Tetrahedron
Tensor-product elements: Quadrilateral, Hexahedron
Mixed elements: Wedge (prismatic) elements

Key Features

Type classification: Automatic detection of simplex vs tensor-product geometry
Dimension queries: Topological and geometric dimension access
Connectivity: Support for incidence relations between polytopes
Reference mappings: Transformations between reference and physical coordinates

Derived classes

class Cell: Class for representing polytopes of the highest dimension in the mesh, i.e. tetrahedra in 3D, triangles in 2D or lines in 1D.
class Face: Class for representing elements of codimension 1 in the mesh, i.e. triangles in 3D or lines in 2D.
class Vertex: Represents a vertex of the mesh.

Public types

enum class Type { Point, Segment, Triangle, Quadrilateral, Tetrahedron, Wedge }: Enumeration of supported polytope geometries.

Public static variables

static std::array<Type, 6> Types constexpr: Iterable of possible polytope geometry types.

Constructors, destructors, conversion operators

Polytope(size_t dimension, Index index, const MeshBase& mesh): Consructs a polytope of dimension and index belonging to the given mesh.

Public functions

auto getIndex() const -> Index: Gets the index of the simplex in the mesh.
auto getMesh() const -> const MeshBase&: Gets the associated mesh to the simplex.
auto getAttribute() const -> Attribute: Gets the attribute of the simplex.
auto getMeasure() const -> Real: Gets the measure of the polytope.

Enum documentation

enum class Rodin::Geometry::Polytope::Type

Enumeration of supported polytope geometries.

This enumeration defines the geometric types supported in Rodin's finite element framework, covering both simplicial and tensor-product element families commonly used in numerical analysis.

Enumerators
Point	0D vertex element
Segment	1D line element
Triangle	2D triangular element (simplex)
Quadrilateral	2D quadrilateral element (tensor-product)
Tetrahedron	3D tetrahedral element (simplex)
Wedge	3D prismatic element (mixed)

Function documentation

Real Rodin::Geometry::Polytope::getMeasure() const

Gets the measure of the polytope.

Returns	The measure of the polytope.

Gets the -dimensional measure of the polytope. This has different names in different dimensions. See table below.

Dimension of polytope	Measure
0	Always zero
1	Length
2	Area
3	Volume