#include <deal.II/grid/grid_tools.h>

Public Types
using	value_type = typename VectorType::value_type

Public Member Functions
	MarchingCubeAlgorithm (const Mapping< dim, dim > &mapping, const FiniteElement< dim, dim > &fe, const unsigned int n_subdivisions=1, const double tolerance=1e-10)

void	process (const DoFHandler< dim > &background_dof_handler, const VectorType &ls_vector, const double iso_level, std::vector< Point< dim > > &vertices, std::vector< CellData< dim==1 ? 1 :dim - 1 > > &cells) const

void	process (const DoFHandler< dim > &background_dof_handler, const VectorType &ls_vector, const double iso_level, std::vector< Point< dim > > &vertices) const

void	process_cell (const typename DoFHandler< dim >::active_cell_iterator &cell, const VectorType &ls_vector, const double iso_level, std::vector< Point< dim > > &vertices, std::vector< CellData< dim==1 ? 1 :dim - 1 > > &cells) const

void	process_cell (const typename DoFHandler< dim >::active_cell_iterator &cell, const VectorType &ls_vector, const double iso_level, std::vector< Point< dim > > &vertices) const

Private Member Functions
void	process_cell (std::vector< value_type > &ls_values, const std::vector< Point< dim > > &points, const double iso_level, std::vector< Point< dim > > &vertices, std::vector< CellData< dim==1 ? 1 :dim - 1 > > &cells, const bool write_back_cell_data=true) const

void	process_sub_cell (const std::vector< value_type > &, const std::vector< Point< 1 > > &, const std::vector< unsigned int > &, const double, std::vector< Point< 1 > > &, std::vector< CellData< 1 > > &, const bool) const

void	process_sub_cell (const std::vector< value_type > &ls_values, const std::vector< Point< 2 > > &points, const std::vector< unsigned int > &mask, const double iso_level, std::vector< Point< 2 > > &vertices, std::vector< CellData< 1 > > &cells, const bool write_back_cell_data) const

void	process_sub_cell (const std::vector< value_type > &ls_values, const std::vector< Point< 3 > > &points, const std::vector< unsigned int > &mask, const double iso_level, std::vector< Point< 3 > > &vertices, std::vector< CellData< 2 > > &cells, const bool write_back_cell_data) const

Static Private Member Functions
static Quadrature< dim >	create_quadrature_rule (const unsigned int n_subdivisions)

Private Attributes
const unsigned int	n_subdivisions

const double	tolerance

FEValues< dim >	fe_values

Detailed Description

template<int dim, typename VectorType>
class GridTools::MarchingCubeAlgorithm< dim, VectorType >

An implementation of the marching-square (2d) and marching-cube algorithm for creating data structures (vectors of Point and CellData) to create a linear/bilinear surface mesh on the iso line/contour of a scalar field.

To improve the approximation of the iso line/contour and the resulting linear surface mesh, one increases the number of subdivision so that the algorithm is not run on a cell but on subcells with vertex values having been interpolated from the cell values.

Note: The resulting mesh will contain lines in 2d and triangles in 3d.; The resulting mesh will not be of high quality, since it might contain cells with very small diameters if the mesh is cut close to a vertex.; Iso lines/contours as a saddle point within a subcell is not detected by the implemented algorithm.

Definition at line 2871 of file grid_tools.h.

Member Typedef Documentation

◆ value_type

template<int dim, typename VectorType >

using GridTools::MarchingCubeAlgorithm< dim, VectorType >::value_type = typename VectorType::value_type

Value type of vector.

Definition at line 2877 of file grid_tools.h.

Constructor & Destructor Documentation

◆ MarchingCubeAlgorithm()

template<int dim, typename VectorType >

GridTools::MarchingCubeAlgorithm< dim, VectorType >::MarchingCubeAlgorithm	(	const Mapping< dim, dim > &	mapping,
		const FiniteElement< dim, dim > &	fe,
		const unsigned int	n_subdivisions = `1`,
		const double	tolerance = `1e-10`
	)

Constructor.

Definition at line 5002 of file grid_tools.cc.

Member Function Documentation

◆ process() [1/2]

template<int dim, typename VectorType >

void GridTools::MarchingCubeAlgorithm< dim, VectorType >::process	(	const DoFHandler< dim > &	background_dof_handler,
		const VectorType &	ls_vector,
		const double	iso_level,
		std::vector< Point< dim > > &	vertices,
		std::vector< CellData< dim==1 ? 1 :dim - 1 > > &	cells
	)		const

Process all locally-owned cells and fill vertices and cells for all cells that are cut.

Note: This function is only implemented for dim>1. Use process(background_dof_handler, ls_vector, iso_level, vertices) for dim==1.; Duplicate vertices are not deleted.

Definition at line 5054 of file grid_tools.cc.

◆ process() [2/2]

template<int dim, typename VectorType >

void GridTools::MarchingCubeAlgorithm< dim, VectorType >::process	(	const DoFHandler< dim > &	background_dof_handler,
		const VectorType &	ls_vector,
		const double	iso_level,
		std::vector< Point< dim > > &	vertices
	)		const

Process all locally-owned cells and fill vertices for all cells that are cut.

Definition at line 5074 of file grid_tools.cc.

◆ process_cell() [1/3]

template<int dim, typename VectorType >

void GridTools::MarchingCubeAlgorithm< dim, VectorType >::process_cell	(	const typename DoFHandler< dim >::active_cell_iterator &	cell,
		const VectorType &	ls_vector,
		const double	iso_level,
		std::vector< Point< dim > > &	vertices,
		std::vector< CellData< dim==1 ? 1 :dim - 1 > > &	cells
	)		const

Process the provided cell and fill vertices and cells for all cells that are cut.

Note: The resulting vectors are empty if the cell is not cut.; This function is only implemented for dim>1. Use process_cell(cell, ls_vector, iso_level, vertices) for dim==1.

Definition at line 5090 of file grid_tools.cc.

◆ process_cell() [2/3]

template<int dim, typename VectorType >

void GridTools::MarchingCubeAlgorithm< dim, VectorType >::process_cell	(	const typename DoFHandler< dim >::active_cell_iterator &	cell,
		const VectorType &	ls_vector,
		const double	iso_level,
		std::vector< Point< dim > > &	vertices
	)		const

Process the provided cell and fill vertices for all cells that are cut.

Note: The resulting vector is empty if the cell is not cut.

Definition at line 5114 of file grid_tools.cc.

◆ create_quadrature_rule()

template<int dim, typename VectorType >

Quadrature< dim > GridTools::MarchingCubeAlgorithm< dim, VectorType >::create_quadrature_rule ( const unsigned int n_subdivisions )

staticprivate

Internal function to create a quadrature rule with n_subdivisions+1 equally-positioned quadrature points.

Definition at line 5019 of file grid_tools.cc.

◆ process_cell() [3/3]

template<int dim, typename VectorType >

void GridTools::MarchingCubeAlgorithm< dim, VectorType >::process_cell	(	std::vector< value_type > &	ls_values,
		const std::vector< Point< dim > > &	points,
		const double	iso_level,
		std::vector< Point< dim > > &	vertices,
		std::vector< CellData< dim==1 ? 1 :dim - 1 > > &	cells,
		const bool	write_back_cell_data = `true`
	)		const

private

Process a cell.

Definition at line 5140 of file grid_tools.cc.

◆ process_sub_cell() [1/3]

template<int dim, typename VectorType >

void GridTools::MarchingCubeAlgorithm< dim, VectorType >::process_sub_cell	(	const std::vector< value_type > &	,
		const std::vector< Point< 1 > > &	,
		const std::vector< unsigned int > &	,
		const double	,
		std::vector< Point< 1 > > &	,
		std::vector< CellData< 1 > > &	,
		const bool
	)		const

inlineprivate

Dummy function for 1d processing a sub-cell.

Definition at line 2963 of file grid_tools.h.

◆ process_sub_cell() [2/3]

template<int dim, typename VectorType >

void GridTools::MarchingCubeAlgorithm< dim, VectorType >::process_sub_cell	(	const std::vector< value_type > &	ls_values,
		const std::vector< Point< 2 > > &	points,
		const std::vector< unsigned int > &	mask,
		const double	iso_level,
		std::vector< Point< 2 > > &	vertices,
		std::vector< CellData< 1 > > &	cells,
		const bool	write_back_cell_data
	)		const

private

Process a sub-cell (2d).

Note: Subcells with saddle points are ignored. Please increase the number of subdivisions in this case.

Definition at line 5230 of file grid_tools.cc.

◆ process_sub_cell() [3/3]

template<int dim, typename VectorType >

void GridTools::MarchingCubeAlgorithm< dim, VectorType >::process_sub_cell	(	const std::vector< value_type > &	ls_values,
		const std::vector< Point< 3 > > &	points,
		const std::vector< unsigned int > &	mask,
		const double	iso_level,
		std::vector< Point< 3 > > &	vertices,
		std::vector< CellData< 2 > > &	cells,
		const bool	write_back_cell_data
	)		const

private

Process a sub-cell (3d).

Definition at line 5313 of file grid_tools.cc.

Member Data Documentation

◆ n_subdivisions

template<int dim, typename VectorType >

const unsigned int GridTools::MarchingCubeAlgorithm< dim, VectorType >::n_subdivisions

private

Number of subdivisions each cell is subdivided into in each direction to improve the approximation.

Definition at line 3005 of file grid_tools.h.

◆ tolerance

template<int dim, typename VectorType >

const double GridTools::MarchingCubeAlgorithm< dim, VectorType >::tolerance

private

Absolute tolerance specifying the minimum distance between a vertex and the cut point so that a line is considered cut.

Definition at line 3011 of file grid_tools.h.

◆ fe_values

template<int dim, typename VectorType >

FEValues<dim> GridTools::MarchingCubeAlgorithm< dim, VectorType >::fe_values

mutableprivate

FEValues used internally and set up with a quadrature rule with the correct number of subdivisions.

Definition at line 3017 of file grid_tools.h.

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

include/deal.II/grid/grid_tools.h
source/grid/grid_tools.cc

Public Types

Public Member Functions

Private Member Functions

Static Private Member Functions

Private Attributes

Detailed Description

Member Typedef Documentation

◆ value_type

Constructor & Destructor Documentation

◆ MarchingCubeAlgorithm()

Member Function Documentation

◆ process() [1/2]

◆ process() [2/2]

◆ process_cell() [1/3]

◆ process_cell() [2/3]

◆ create_quadrature_rule()

◆ process_cell() [3/3]

◆ process_sub_cell() [1/3]

◆ process_sub_cell() [2/3]

◆ process_sub_cell() [3/3]

Member Data Documentation

◆ n_subdivisions

◆ tolerance

◆ fe_values