Rodin::Geometry::MeshBase class
#include <Rodin/Geometry/Mesh.h>

Abstract base class for all mesh implementations.

MeshBase provides the common interface for all mesh types in Rodin, defining fundamental operations such as:

Point inclusion testing
Basic mesh properties (dimension, vertex count, etc.)
Polytope access through iterators
Mesh I/O operations
Connectivity queries

Inheritance Hierarchy

All concrete mesh implementations derive from this base class:

Mesh<Context::Local>: Sequential (non-distributed) meshes
SubMesh<Context::Local>: Submeshes representing subregions
Shard: Distributed mesh shards for parallel computing

Thread Safety

MeshBase and derived classes are not thread-safe during construction. Once finalized, read-only operations are thread-safe.

Derived classes

template<> class Mesh<Context::Local>: Represents the subdivision of some domain into faces of (possibly) different geometries.

Constructors, destructors, conversion operators

~MeshBase() defaulted virtual: Virtual destructor.

Public functions

auto operator==(const MeshBase& other) const -> bool constexpr: Equality comparison (pointer equality).
auto operator!=(const MeshBase& other) const -> bool constexpr: Inequality comparison.
auto isLocalPoint(const Point& p) const -> bool virtual: Checks whether a point is already expressed in this mesh's local indexing convention.
auto inclusion(const Point& p) const -> Optional<Point> virtual: Tests point inclusion in the mesh.
auto isEmpty() const -> bool: Checks if mesh is empty.
auto isSurface() const -> bool: Checks if mesh is a surface mesh.
auto getVertexCount() const -> size_t: Gets the number of vertices.
auto getFaceCount() const -> size_t: Gets the number of faces.
auto getCellCount() const -> size_t: Gets the number of cells.
auto getFaceAttribute(Index index) const -> Optional<Attribute>: Gets face attribute.
auto getCellAttribute(Index index) const -> Optional<Attribute>: Gets cell attribute.
auto scale(Real c) -> MeshBase& pure virtual: Scales mesh coordinates by a factor.
auto load(const boost::filesystem::path& filename, IO::FileFormat fmt) -> MeshBase& pure virtual: Loads mesh from file.
void save(const boost::filesystem::path& filename, IO::FileFormat fmt) const pure virtual: Saves mesh to file.
void flush() pure virtual: Flushes cached mesh data.
auto isSubMesh() const -> bool pure virtual: Checks if this mesh is a submesh.
auto isInterface(Index faceIdx) const -> bool pure virtual: Checks if a face is an interface between regions.
auto isBoundary(Index faceIdx) const -> bool pure virtual: Checks if a face is on the mesh boundary.
auto asSubMesh() -> SubMeshBase& pure virtual: Casts to SubMeshBase interface (mutable).
auto asSubMesh() const -> const SubMeshBase& pure virtual: Casts to SubMeshBase interface (const).
auto getDimension() const -> size_t pure virtual: Gets the topological dimension.
auto getSpaceDimension() const -> size_t pure virtual: Gets the ambient space dimension.
auto getVolume() const -> Real pure virtual: Gets the total mesh volume.
auto getVolume(Attribute attr) const -> Real pure virtual: Gets volume of cells with specified attribute.
auto getVolume(const FlatSet<Attribute>& attr) const -> Real pure virtual: Gets volume of cells with attributes in set.
auto getPerimeter() const -> Real pure virtual: Gets the total mesh perimeter.
auto getPerimeter(Attribute attr) const -> Real pure virtual: Gets perimeter of cells with specified attribute.
auto getPerimeter(const FlatSet<Attribute>& attr) const -> Real pure virtual: Gets perimeter of cells with attributes in set.
auto getArea() const -> Real pure virtual: Gets total area.
auto getArea(Attribute attr) const -> Real pure virtual: Gets area of elements with specified attribute.
auto getArea(const FlatSet<Attribute>& attr) const -> Real pure virtual: Gets area of elements with attributes in set.
auto getMeasure(size_t d) const -> Real pure virtual: Gets measure of polytopes of given dimension.
auto getMeasure(size_t d, Attribute attr) const -> Real pure virtual: Gets measure of polytopes with attribute.
auto getMeasure(size_t d, const FlatSet<Attribute>& attr) const -> Real pure virtual: Gets measure of polytopes with attributes in set.
auto getBoundary() const -> FaceIterator pure virtual: Gets iterator over boundary faces.
auto getInterface() const -> FaceIterator pure virtual: Gets iterator over interface faces.
auto getPolytopeCount(size_t dimension) const -> size_t pure virtual: Gets count of polytopes of given dimension.
auto getPolytopeCount(Polytope::Type g) const -> size_t pure virtual: Gets count of polytopes of given geometry type.
auto getCell() const -> CellIterator pure virtual: Gets iterator over all cells.
auto getFace() const -> FaceIterator pure virtual: Gets iterator over all faces.
auto getVertex() const -> VertexIterator pure virtual: Gets iterator over all vertices.
auto getPolytope(size_t dimension) const -> PolytopeIterator pure virtual: Gets iterator over polytopes of given dimension.
auto getCell(Index idx) const -> CellIterator pure virtual: Gets iterator to specific cell.
auto getFace(Index idx) const -> FaceIterator pure virtual: Gets iterator to specific face.
auto getVertex(Index idx) const -> VertexIterator pure virtual: Gets iterator to specific vertex.
auto getPolytope(size_t dimension, Index idx) const -> PolytopeIterator pure virtual: Gets iterator to specific polytope.
auto getPolytopeTransformation(size_t dimension, Index idx) const -> const PolytopeTransformation& pure virtual: Gets polytope transformation.
auto getQuadrature(size_t dimension, Index idx, const QF::QuadratureFormulaBase& qf) const -> const PolytopeQuadrature& pure virtual: Gets cached quadrature for a polytope.
auto getGeometry(size_t dimension, Index idx) const -> Polytope::Type pure virtual: Gets geometry type of a polytope.
auto getAttribute(size_t dimension, Index index) const -> Optional<Attribute> pure virtual: Gets attribute of a polytope.
auto setAttribute(const std::pair<size_t, Index>& p, const Optional<Attribute>& attr) -> MeshBase& pure virtual: Sets attribute of a polytope.
auto getConnectivity() -> ConnectivityBase& pure virtual: Gets reference to mesh connectivity.
auto getConnectivity() const -> const ConnectivityBase& pure virtual: Gets a constant reference to the mesh connectivity.
auto getVertexCoordinates(Index idx) const -> Math::SpatialPoint pure virtual: Gets the space coordinates of the vertex at the given index.
auto setVertexCoordinates(Index idx, Real s, size_t i) -> MeshBase& pure virtual: Sets the space coordinate of the vertex at the given index for the given coordinate index.
auto setVertexCoordinates(Index idx, const Math::SpatialPoint& coords) -> MeshBase& pure virtual: Sets the space coordinate of the vertex at the given index for the given coordinate index.
auto setPolytopeTransformation(const std::pair<size_t, Index> p, PolytopeTransformation* trans) -> MeshBase& pure virtual: Sets the geometric transformation for a polytope.
auto getContext() const -> const Context::Base& pure virtual: Gets the execution context of the mesh.
auto getName() const -> Optional<StringView>: Gets the optional name assigned to this mesh.
auto setName(const std::string& name) -> MeshBase&: Sets a human-readable name for the mesh.

Function documentation

bool Rodin::Geometry::MeshBase::operator==(const MeshBase& other) const constexpr

Equality comparison (pointer equality).

Parameters
other in	Mesh to compare with
Returns	True if this is the same mesh object

bool Rodin::Geometry::MeshBase::operator!=(const MeshBase& other) const constexpr

Inequality comparison.

Parameters
other in	Mesh to compare with
Returns	True if not the same mesh object

bool Rodin::Geometry::MeshBase::isLocalPoint(const Point& p) const virtual

Checks whether a point is already expressed in this mesh's local indexing convention.

Ordinary meshes accept only points attached directly to themselves. Distributed meshes override this to also accept points attached to their rank-local shard.

Optional<Point> Rodin::Geometry::MeshBase::inclusion(const Point& p) const virtual

Tests point inclusion in the mesh.

Parameters
p in	Point to test
Returns	Optional point if included in mesh

Determines whether a point lies within the mesh domain and returns its representation if so.

bool Rodin::Geometry::MeshBase::isEmpty() const

Checks if mesh is empty.

Returns	True if mesh has no vertices

An empty mesh is defined as a mesh with no vertices.

bool Rodin::Geometry::MeshBase::isSurface() const

Checks if mesh is a surface mesh.

Returns	True if mesh has codimension 1

A mesh is considered a surface mesh if its codimension is 1, meaning the difference between space dimension and topological dimension equals 1.

Examples:

2D mesh embedded in 3D space (triangulated surface)
1D mesh embedded in 2D space (curve)

size_t Rodin::Geometry::MeshBase::getVertexCount() const

Gets the number of vertices.

Returns	Vertex count

size_t Rodin::Geometry::MeshBase::getFaceCount() const

Gets the number of faces.

Returns	Face count (codimension-1 polytopes)

size_t Rodin::Geometry::MeshBase::getCellCount() const

Gets the number of cells.

Returns	Cell count (maximal dimension polytopes)

Optional<Attribute> Rodin::Geometry::MeshBase::getFaceAttribute(Index index) const

Gets face attribute.

Parameters
index in	Face index
Returns	Attribute value

Optional<Attribute> Rodin::Geometry::MeshBase::getCellAttribute(Index index) const

Gets cell attribute.

Parameters
index in	Cell index
Returns	Attribute value

MeshBase& Rodin::Geometry::MeshBase::scale(Real c) pure virtual

Scales mesh coordinates by a factor.

Parameters
c in	Scaling factor
Returns	Reference to this mesh

Multiplies all vertex coordinates by .

MeshBase& Rodin::Geometry::MeshBase::load(const boost::filesystem::path& filename, IO::FileFormat fmt) pure virtual

Loads mesh from file.

Parameters
filename in	Path to mesh file
fmt in	File format (MFEM, MEDIT, etc.)
Returns	Reference to this mesh

void Rodin::Geometry::MeshBase::save(const boost::filesystem::path& filename, IO::FileFormat fmt) const pure virtual

Saves mesh to file.

Parameters
filename in	Path to output file
fmt in	File format

void Rodin::Geometry::MeshBase::flush() pure virtual

Flushes cached mesh data.

Clears any internally cached derived data (e.g., cached Jacobians).

bool Rodin::Geometry::MeshBase::isSubMesh() const pure virtual

Checks if this mesh is a submesh.

Returns	True if this is a SubMesh instance

A Mesh which is also a SubMesh may be casted down to access SubMesh-specific functionality:

if (mesh.isSubMesh())
{
  auto& submesh = static_cast<SubMesh<Context::Local>&>(mesh);
  const auto& parent = submesh.getParent();
}

bool Rodin::Geometry::MeshBase::isInterface(Index faceIdx) const pure virtual

Checks if a face is an interface between regions.

Parameters
faceIdx in	Face index
Returns	True if face connects cells with different attributes

bool Rodin::Geometry::MeshBase::isBoundary(Index faceIdx) const pure virtual

Checks if a face is on the mesh boundary.

Parameters
faceIdx in	Face index
Returns	True if face belongs to only one cell

SubMeshBase& Rodin::Geometry::MeshBase::asSubMesh() pure virtual

Casts to SubMeshBase interface (mutable).

Exceptions
Returns	Reference to SubMeshBase interface
Exception	if mesh is not a submesh

const SubMeshBase& Rodin::Geometry::MeshBase::asSubMesh() const pure virtual

Casts to SubMeshBase interface (const).

Exceptions
Returns	Const reference to SubMeshBase interface
Exception	if mesh is not a submesh

size_t Rodin::Geometry::MeshBase::getDimension() const pure virtual

Gets the topological dimension.

Returns	Mesh dimension (highest polytope dimension)

size_t Rodin::Geometry::MeshBase::getSpaceDimension() const pure virtual

Gets the ambient space dimension.

Returns	Space dimension in which mesh is embedded

For example, a 2D triangulated surface in 3D space has:

getDimension() = 2
getSpaceDimension() = 3

Real Rodin::Geometry::MeshBase::getVolume() const pure virtual

Gets the total mesh volume.

Returns	Sum of all cell volumes

Real Rodin::Geometry::MeshBase::getVolume(Attribute attr) const pure virtual

Gets volume of cells with specified attribute.

Parameters
attr in	Attribute value
Returns	Sum of volumes of cells with attribute `attr`

Real Rodin::Geometry::MeshBase::getVolume(const FlatSet<Attribute>& attr) const pure virtual

Gets volume of cells with attributes in set.

Parameters
attr in	Set of attribute values
Returns	Sum of volumes

Real Rodin::Geometry::MeshBase::getPerimeter() const pure virtual

Gets the total mesh perimeter.

Returns	Sum of all cell perimeters

Real Rodin::Geometry::MeshBase::getPerimeter(Attribute attr) const pure virtual

Gets perimeter of cells with specified attribute.

Parameters
attr in	Attribute value
Returns	Sum of perimeters

Real Rodin::Geometry::MeshBase::getPerimeter(const FlatSet<Attribute>& attr) const pure virtual

Gets perimeter of cells with attributes in set.

Parameters
attr in	Set of attribute values
Returns	Sum of perimeters

Real Rodin::Geometry::MeshBase::getArea() const pure virtual

Gets total area.

Returns	Sum of all element areas

Real Rodin::Geometry::MeshBase::getArea(Attribute attr) const pure virtual

Gets area of elements with specified attribute.

Parameters
attr in	Attribute value
Returns	Sum of areas

Real Rodin::Geometry::MeshBase::getArea(const FlatSet<Attribute>& attr) const pure virtual

Gets area of elements with attributes in set.

Parameters
attr in	Set of attribute values
Returns	Sum of areas

Real Rodin::Geometry::MeshBase::getMeasure(size_t d) const pure virtual

Gets measure of polytopes of given dimension.

Parameters
d in	Polytope dimension
Returns	Total measure

Real Rodin::Geometry::MeshBase::getMeasure(size_t d, Attribute attr) const pure virtual

Gets measure of polytopes with attribute.

Parameters
d in	Polytope dimension
attr in	Attribute value
Returns	Total measure

Real Rodin::Geometry::MeshBase::getMeasure(size_t d, const FlatSet<Attribute>& attr) const pure virtual

Gets measure of polytopes with attributes in set.

Parameters
d in	Polytope dimension
attr in	Set of attribute values
Returns	Total measure

FaceIterator Rodin::Geometry::MeshBase::getBoundary() const pure virtual

Gets iterator over boundary faces.

Returns	FaceIterator for boundary faces

FaceIterator Rodin::Geometry::MeshBase::getInterface() const pure virtual

Gets iterator over interface faces.

Returns	FaceIterator for interface faces

size_t Rodin::Geometry::MeshBase::getPolytopeCount(size_t dimension) const pure virtual

Gets count of polytopes of given dimension.

Parameters
dimension in	Polytope dimension
Returns	Number of polytopes

size_t Rodin::Geometry::MeshBase::getPolytopeCount(Polytope::Type g) const pure virtual

Gets count of polytopes of given geometry type.

Parameters
g in	Polytope geometry type
Returns	Number of polytopes

CellIterator Rodin::Geometry::MeshBase::getCell() const pure virtual

Gets iterator over all cells.

Returns	CellIterator

FaceIterator Rodin::Geometry::MeshBase::getFace() const pure virtual

Gets iterator over all faces.

Returns	FaceIterator

VertexIterator Rodin::Geometry::MeshBase::getVertex() const pure virtual

Gets iterator over all vertices.

Returns	VertexIterator

PolytopeIterator Rodin::Geometry::MeshBase::getPolytope(size_t dimension) const pure virtual

Gets iterator over polytopes of given dimension.

Parameters
dimension in	Polytope dimension
Returns	PolytopeIterator

CellIterator Rodin::Geometry::MeshBase::getCell(Index idx) const pure virtual

Gets iterator to specific cell.

Parameters
idx in	Cell index
Returns	CellIterator positioned at cell

FaceIterator Rodin::Geometry::MeshBase::getFace(Index idx) const pure virtual

Gets iterator to specific face.

Parameters
idx in	Face index
Returns	FaceIterator positioned at face

VertexIterator Rodin::Geometry::MeshBase::getVertex(Index idx) const pure virtual

Gets iterator to specific vertex.

Parameters
idx in	Vertex index
Returns	VertexIterator positioned at vertex

PolytopeIterator Rodin::Geometry::MeshBase::getPolytope(size_t dimension, Index idx) const pure virtual

Gets iterator to specific polytope.

Parameters
dimension in	Polytope dimension
idx in	Polytope index
Returns	PolytopeIterator positioned at polytope

const PolytopeTransformation& Rodin::Geometry::MeshBase::getPolytopeTransformation(size_t dimension, Index idx) const pure virtual

Gets polytope transformation.

Parameters
dimension in	Polytope dimension
idx in	Polytope index
Returns	Reference to transformation

Polytope::Type Rodin::Geometry::MeshBase::getGeometry(size_t dimension, Index idx) const pure virtual

Gets geometry type of a polytope.

Parameters
dimension in	Polytope dimension
idx in	Polytope index
Returns	Geometry type

Optional<Attribute> Rodin::Geometry::MeshBase::getAttribute(size_t dimension, Index index) const pure virtual

Gets attribute of a polytope.

Parameters
dimension in	Polytope dimension
index in	Polytope index
Returns	Attribute value

MeshBase& Rodin::Geometry::MeshBase::setAttribute(const std::pair<size_t, Index>& p, const Optional<Attribute>& attr) pure virtual

Sets attribute of a polytope.

Parameters
p in	Pair of (dimension, index)
attr in	New attribute value
Returns	Reference to this mesh

ConnectivityBase& Rodin::Geometry::MeshBase::getConnectivity() pure virtual

Gets reference to mesh connectivity.

Returns	Const reference to Connectivity object

Math::SpatialPoint Rodin::Geometry::MeshBase::getVertexCoordinates(Index idx) const pure virtual

Gets the space coordinates of the vertex at the given index.

Parameters
idx in	Vertex index

MeshBase& Rodin::Geometry::MeshBase::setVertexCoordinates(Index idx, Real s, size_t i) pure virtual

Sets the space coordinate of the vertex at the given index for the given coordinate index.

Parameters
idx in	Vertex index
s in	New coordinate
i in	Coordinate index

For example, the following code sets the coordinates of the 0-vertex to in a mesh embedded in three dimensional space.

Mesh mesh;
// Add vertices...
mesh.setVertexCoordinates(0, 0.0, 0);
mesh.setVertexCoordinates(0, 5.0, 1);
mesh.setVertexCoordinates(0, 10.0, 2);

MeshBase& Rodin::Geometry::MeshBase::setVertexCoordinates(Index idx, const Math::SpatialPoint& coords) pure virtual