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_vertex_locations>
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 locations of the grid vertices are stored or not. Possible values are CGAL::Isosurfacing::Cache_vertex_locations and CGAL::Isosurfacing::Do_not_cache_vertex_locations.

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_location< 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 location 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_vertex_locations>

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_vertex_locations>

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_vertex_locations>

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_vertex_locations>

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_vertex_locations>

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.

For points on the boundary between two cells, the smaller index is returned.

Parameters

p	the point to be located

Precondition

p is inside the grid.

point()

template<typename GeomTraits , typename MemoryPolicy = Do_not_cache_vertex_locations>

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 location of the grid vertex described by its three indices.

Depending on the value of the template parameter MemoryPolicy, locations 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.