CGAL::Isosurfacing::Cartesian_grid_3< GeomTraits, MemoryPolicy > Class Template Reference

#include <CGAL/Isosurfacing_3/Cartesian_grid_3.h>

Definition

template<typename GeomTraits, typename MemoryPolicy = Do_not_cache_positions>
class CGAL::Isosurfacing::Cartesian_grid_3< GeomTraits, MemoryPolicy >

The class Cartesian_grid_3 represents a 3D Cartesian grid, that is the partition of an iso-cuboid into identical iso-cuboidal cells.

Is model of

IsosurfacingPartition_3

The class Cartesian_grid_3 is one of the possible space partitioning data structures that can be used along with value and gradient fields to make up a domain.

Template Parameters

GeomTraits	must be a model of IsosurfacingTraits_3.
MemoryPolicy	whether the geometric positions of the grid vertices are stored or not. Possible values are CGAL::Isosurfacing::Cache_positions and CGAL::Isosurfacing::Do_not_cache_positions.

See also

CGAL::Isosurfacing::Marching_cubes_domain_3()

CGAL::Isosurfacing::Dual_contouring_domain_3()

Examples

Isosurfacing_3/contouring_discrete_data.cpp, Isosurfacing_3/contouring_implicit_data.cpp, Isosurfacing_3/contouring_inrimage.cpp, Isosurfacing_3/contouring_mesh_offset.cpp, Isosurfacing_3/contouring_vtk_image.cpp, Isosurfacing_3/dual_contouring.cpp, and Isosurfacing_3/marching_cubes.cpp.

Public Types
using	Geom_traits = GeomTraits
using	FT = typename Geom_traits::FT
using	Point_3 = typename Geom_traits::Point_3
using	Vector_3 = typename Geom_traits::Vector_3
using	Iso_cuboid_3 = typename Geom_traits::Iso_cuboid_3
using	Positioner = internal::Cartesian_grid_position< GeomTraits, MemoryPolicy >

Public Member Functions
	Cartesian_grid_3 ()
	Default constructor.
	Cartesian_grid_3 (const Iso_cuboid_3 &span, const std::array< std::size_t, 3 > &dimensions, const Geom_traits &gt=Geom_traits())
	creates a Cartesian grid with dimensions[0]*dimensions[1]*dimensions[2] grid vertices.
	Cartesian_grid_3 (const Point_3 &p, const Point_3 &q, const std::array< std::size_t, 3 > &dimensions, const Geom_traits &gt=Geom_traits())
	creates a Cartesian grid with dimensions[0]*dimensions[1]*dimensions[2] grid vertices.
	Cartesian_grid_3 (const Iso_cuboid_3 &span, const Vector_3 &spacing, const Geom_traits &gt=Geom_traits())
	creates a Cartesian grid using a prescribed grid step spacing.
	Cartesian_grid_3 (const Point_3 &p, const Point_3 &q, const Vector_3 &spacing, const Geom_traits &gt=Geom_traits())
	creates a Cartesian grid using a prescribed grid step.
const Geom_traits &	geom_traits () const
	returns the geometric traits class.
const Iso_cuboid_3 &	span () const
	returns an iso-cuboid representing the geometric span of the Cartesian grid.
std::size_t	xdim () const
	returns the number of grid vertices in the x direction.
std::size_t	ydim () const
	returns the number of grid vertices in the y direction.
std::size_t	zdim () const
	returns the number of grid vertices in the z direction.
const Vector_3 &	spacing () const
	returns the spacing of the Cartesian grid, that is a vector whose coordinates are the grid steps in the x, y, and z directions, respectively.
std::size_t	linear_index (const std::size_t i, const std::size_t j, const std::size_t k) const
	returns the index of a grid cell given its indices (i.e., (k * y_dim + j) * x_dim + i).
std::array< std::size_t, 3 >	index (const Point_3 &p) const
	returns the coordinates of the grid cell that contains a given point.
decltype(auto)	point (const std::size_t i, const std::size_t j, const std::size_t k) const
	returns the geometric position of the grid vertex described by its three indices.

Constructor & Destructor Documentation

Cartesian_grid_3() [1/4]

template<typename GeomTraits , typename MemoryPolicy = Do_not_cache_positions>

CGAL::Isosurfacing::Cartesian_grid_3< GeomTraits, MemoryPolicy >::Cartesian_grid_3	(	const Iso_cuboid_3 &	span,
		const std::array< std::size_t, 3 > &	dimensions,
		const Geom_traits &	gt = Geom_traits()
	)

creates a Cartesian grid with dimensions[0]*dimensions[1]*dimensions[2] grid vertices.

The grid covers the space described by the iso-cuboid span.

Parameters

span	the geometric span of the grid
dimensions	the number of grid vertices in the x, y, and z directions
gt	the geometric traits

Precondition

all dimensions are (strictly) positive.

Cartesian_grid_3() [2/4]

template<typename GeomTraits , typename MemoryPolicy = Do_not_cache_positions>

CGAL::Isosurfacing::Cartesian_grid_3< GeomTraits, MemoryPolicy >::Cartesian_grid_3	(	const Point_3 &	p,
		const Point_3 &	q,
		const std::array< std::size_t, 3 > &	dimensions,
		const Geom_traits &	gt = Geom_traits()
	)

creates a Cartesian grid with dimensions[0]*dimensions[1]*dimensions[2] grid vertices.

The grid covers the space described by the iso-cuboid span, itself described through two diagonal corners p and q.

Parameters

p	the lexicographically smallest corner of the iso-cuboid
q	the lexicographically largest corner of the iso-cuboid
dimensions	the number of grid vertices in the x, y, and z directions
gt	the geometric traits

Precondition

p is lexicographically (strictly) smaller than q

all dimensions are (strictly) positive.

Cartesian_grid_3() [3/4]

template<typename GeomTraits , typename MemoryPolicy = Do_not_cache_positions>

CGAL::Isosurfacing::Cartesian_grid_3< GeomTraits, MemoryPolicy >::Cartesian_grid_3	(	const Iso_cuboid_3 &	span,
		const Vector_3 &	spacing,
		const Geom_traits &	gt = Geom_traits()
	)

creates a Cartesian grid using a prescribed grid step spacing.

The grid covers the space described by the iso-cuboid span.

Parameters

span	the geometric span of the grid
spacing	the dimension of the paving cell, in the x, y, and z directions
gt	the geometric traits

Precondition

the diagonal of span has length a multiple of spacing

Cartesian_grid_3() [4/4]

template<typename GeomTraits , typename MemoryPolicy = Do_not_cache_positions>

CGAL::Isosurfacing::Cartesian_grid_3< GeomTraits, MemoryPolicy >::Cartesian_grid_3	(	const Point_3 &	p,
		const Point_3 &	q,
		const Vector_3 &	spacing,
		const Geom_traits &	gt = Geom_traits()
	)

creates a Cartesian grid using a prescribed grid step.

The grid covers the space described by an iso-cuboid, itself described through two diagonal corners.

Parameters

p	the lexicographically smallest corner of the iso-cuboid
q	the lexicographically largest corner of the iso-cuboid
spacing	the dimension of the paving cell, in the x, y, and z directions, respectively.
gt	the geometric traits

Precondition

p is lexicographically (strictly) smaller than q

the diagonal of the iso-cuboid has length a multiple of spacing

Member Function Documentation

index()

template<typename GeomTraits , typename MemoryPolicy = Do_not_cache_positions>

std::array< std::size_t, 3 > CGAL::Isosurfacing::Cartesian_grid_3< GeomTraits, MemoryPolicy >::index

(

const Point_3 &

p

)

const

returns the coordinates of the grid cell that contains a given point.

Parameters

p	the point to be located

Precondition

p is inside the grid.

point()

template<typename GeomTraits , typename MemoryPolicy = Do_not_cache_positions>

decltype(auto) CGAL::Isosurfacing::Cartesian_grid_3< GeomTraits, MemoryPolicy >::point	(	const std::size_t	i,
		const std::size_t	j,
		const std::size_t	k
	)		const

returns the geometric position of the grid vertex described by its three indices.

Depending on the value of the template parameter cache_points, positions might not be stored but calculated on-the-fly.

Parameters

i	the index in the x direction
j	the index in the y direction
k	the index in the z direction

Precondition

i < xdim() and j < ydim() and k < zdim()

Returns

a const reference or a newly constructed point, depending on the caching policy.