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 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 -> Attribute: Gets face attribute.
auto getCellAttribute(Index index) const -> 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 = IO::FileFormat::MFEM) -> MeshBase& pure virtual: Loads mesh from file.
void save(const boost::filesystem::path& filename, IO::FileFormat fmt = IO::FileFormat::MFEM) 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 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 -> Attribute pure virtual: Gets attribute of a polytope.
auto setAttribute(const std::pair<size_t, Index>& p, 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 -> Eigen::Map<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 getContext() const -> const Context::Base& pure virtual: Gets the execution context of 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

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)

Attribute Rodin::Geometry::MeshBase::getFaceAttribute(Index index) const

Gets face attribute.

Parameters
index in	Face index
Returns	Attribute value

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 = IO::FileFormat::MFEM) pure virtual

Loads mesh from file.

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

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

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, 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

Eigen::Map<const 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