Rodin::Geometry::Polytope class
#include <Rodin/Geometry/Polytope.h>

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

Each polytope in a mesh has:

A dimension (0 for vertices, 1 for edges, etc.)
An index unique within its dimension
An associated reference element
A transformation mapping reference to physical coordinates

Hierarchy

The Polytope class serves as the base for specialized classes:

Cell: Highest-dimensional elements (e.g., tetrahedra in 3D, triangles in 2D)
Face: Codimension-1 elements (e.g., triangles in 3D, edges in 2D)
Vertex: 0-dimensional points

Usage

Polytopes are typically obtained through iterators:

for (auto it = mesh.getCell(); it; ++it)
{
  const Cell& cell = *it;
  std::cout << "Cell " << cell.getIndex() 
            << " has measure " << cell.getMeasure() << std::endl;
}

Derived classes

class Cell: Represents a cell (highest-dimensional element) in a mesh.
class Face: Represents a face (codimension-1 element) in a mesh.
class Vertex: Represents a vertex (0-dimensional element) in a mesh.

Public types

struct Project: Projection operations for polytope sub-entities.
struct Traits: Geometric traits for polytope 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: Array of all supported polytope types.

Constructors, destructors, conversion operators

Polytope(size_t dimension, Index index, const MeshBase& mesh): Constructs a polytope with given dimension and index.
Polytope(const Polytope& other): Copy constructor.
Polytope(Polytope&& other): Move constructor.
~Polytope() defaulted virtual: Virtual destructor.

Public functions

auto operator=(const Polytope& other) -> Polytope&: Copy assignment operator.
auto operator=(Polytope&& other) -> Polytope&: Move assignment operator.
auto getIndex() const -> Index: Gets the polytope's index within its dimension.
auto getDimension() const -> size_t: Gets the topological dimension.
auto getMesh() const -> const MeshBase&: Gets the containing mesh.
auto getAttribute() const -> Attribute: Gets the attribute (marker) of this polytope.
auto getMeasure() const -> Real: Gets the geometric measure of this polytope.
auto getTransformation() const -> const PolytopeTransformation&: Gets the geometric transformation for this polytope.
auto getVertex() const -> VertexIterator: Gets an iterator over the vertices of this polytope.
auto getVertices() const -> const Array<Index>&: Gets the vertex indices defining this polytope.
auto getAdjacent() const -> PolytopeIterator: Gets an iterator over polytopes adjacent to this one.
auto getGeometry() const -> Type: Gets the geometry type of this polytope.
auto isCell() const -> bool: Checks if this is a cell (maximal dimension).
auto isFace() const -> bool: Checks if this is a face (codimension 1).
auto isVertex() const -> bool: Checks if this is a vertex (dimension 0).
auto setAttribute() -> Polytope&: Sets the attribute for this 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
Quadrilateral	2D quadrilateral element
Tetrahedron	3D tetrahedral element
Wedge	3D prismatic element (triangular prism)

Function documentation

Rodin::Geometry::Polytope::Polytope(size_t dimension, Index index, const MeshBase& mesh)

Constructs a polytope with given dimension and index.

Parameters
dimension in	Topological dimension
index in	Index within the mesh
mesh in	Reference to the containing mesh

Index Rodin::Geometry::Polytope::getIndex() const

Gets the polytope's index within its dimension.

Returns	Index of this polytope

size_t Rodin::Geometry::Polytope::getDimension() const

Gets the topological dimension.

Returns	Dimension of this polytope

const MeshBase& Rodin::Geometry::Polytope::getMesh() const

Gets the containing mesh.

Returns	Reference to the mesh this polytope belongs to

Attribute Rodin::Geometry::Polytope::getAttribute() const

Gets the attribute (marker) of this polytope.

Returns	Attribute value

Attributes are typically used to mark material regions, boundary conditions, or other domain-specific properties.

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

Gets the geometric measure of this polytope.

Returns	The measure (length/area/volume) of the polytope

Computes the -dimensional measure of the polytope:

Dimension	Measure
0	Always 0
1	Length
2	Area
3	Volume

const PolytopeTransformation& Rodin::Geometry::Polytope::getTransformation() const

Gets the geometric transformation for this polytope.

Returns	Reference to the transformation

VertexIterator Rodin::Geometry::Polytope::getVertex() const

Gets an iterator over the vertices of this polytope.

Returns	Iterator over all vertices

const Array<Index>& Rodin::Geometry::Polytope::getVertices() const

Gets the vertex indices defining this polytope.

Returns	Array of vertex indices

PolytopeIterator Rodin::Geometry::Polytope::getAdjacent() const

Gets an iterator over polytopes adjacent to this one.

Returns	Iterator over adjacent polytopes

Type Rodin::Geometry::Polytope::getGeometry() const

Gets the geometry type of this polytope.

Returns	Geometry type (Triangle, Tetrahedron, etc.)

bool Rodin::Geometry::Polytope::isCell() const

Checks if this is a cell (maximal dimension).

Returns	True if this polytope is a cell, false otherwise

bool Rodin::Geometry::Polytope::isFace() const

Checks if this is a face (codimension 1).

Returns	True if this polytope is a face, false otherwise

bool Rodin::Geometry::Polytope::isVertex() const

Checks if this is a vertex (dimension 0).

Returns	True if this polytope is a vertex, false otherwise

Polytope& Rodin::Geometry::Polytope::setAttribute()

Sets the attribute for this polytope.

Returns	Reference to this polytope for method chaining

Variable documentation

static std::array<Type, 6> Rodin::Geometry::Polytope::Types constexpr

Array of all supported polytope types.

Useful for iterating over all geometry types at compile time.