CGAL 4.7 - Linear Cell Complex: Constructions for Linear Cell Complex

\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.7 - Linear Cell Complex

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Functions
Constructions for Linear Cell Complex
Linear Cell Complex Reference

##

Basic constructions.

#include <CGAL/Linear_cell_complex_constructors.h>

## Functions

template<class LCC >
LCC::Dart_handle | CGAL::import_from_plane_graph (LCC &lcc, std::istream &ais)
| Imports an embedded plane graph read from `ais` into `lcc`. More...
template<class LCC , class Polyhedron >
LCC::Dart_handle | CGAL::import_from_polyhedron_3 (LCC &lcc, const Polyhedron &apoly)
| Imports `apoly` (a `Polyhedron_3`) into `lcc`. More...
template<class LCC , class Triangulation_ >
LCC::Dart_handle | CGAL::import_from_triangulation_3 (LCC &lcc, const Triangulation_ &atr)
| Imports `atr` (a `Triangulation_3`) into `lcc`. More...

## Function Documentation

template<class LCC >

LCC::Dart_handle CGAL::import_from_plane_graph | ( | LCC & | lcc,
|  | std::istream & | ais
| ) |  |

Imports an embedded plane graph read from `ais` into `lcc`.

Objects are added in `lcc`, existing darts are not modified. Returns a dart created during the import.

Precondition
  LCC::dimension \( \geq\) 2 and LCC::ambient_dimension==2.

File format

The file format must be the following. First the number of vertices and the number of edges of the planar graph. Then, for each vertex of the planar graph, the coordinates of the \( i^{\mbox{th}}\) vertex (two numbers for \( x\) and \( y\) coordinates). The first vertex index is 0. Then for each edge of the planar graph, the two indices of the two vertices (two numbers between 0 and the number of vertices minus 1).

Here a small example:

    5 6
    1.0 3.0 0.0 2.0 2.0 2.0 0.0 0.0 2.0 0.0
    0 1 0 2 1 2 1 3 2 4 3 4

Example of import_graph reading the above file as istream.
Left: A planar graph embedded in the plane with P0=(1.0,3.0), P1=(0.0,2.0), P2=(2.0,2.0), P3=(0.0,0.0), P4=(2.0,0.0). Right: the 2D linear cell complex reconstructed.

See Also
  `CGAL::import_from_triangulation_3<LCC,Triangulation>`
  `CGAL::import_from_polyhedron_3<LCC,Polyhedron>`

`#include <CGAL/Linear_cell_complex_constructors.h>`

template<class LCC , class Polyhedron >

LCC::Dart_handle CGAL::import_from_polyhedron_3 | ( | LCC & | lcc,
|  | const Polyhedron & | apoly
| ) |  |

Imports `apoly` (a `Polyhedron_3`) into `lcc`.

Objects are added in `lcc`, existing darts are not modified. Returns a dart created during the import.

Precondition
  LCC::dimension \( \geq\) 2 and LCC::ambient_dimension==3.

See Also
  `CGAL::import_from_plane_graph<LCC>`
  `CGAL::import_from_triangulation_3<LCC,Triangulation>`

`#include <CGAL/Linear_cell_complex_constructors.h>`

template<class LCC , class Triangulation_ >

LCC::Dart_handle CGAL::import_from_triangulation_3 | ( | LCC & | lcc,
|  | const Triangulation_ & | atr
| ) |  |

Imports `atr` (a `Triangulation_3`) into `lcc`.

Objects are added in `lcc`, existing darts are not modified. Returns a dart created during the import.

Precondition
  LCC::dimension \( \geq\) 3 and LCC::ambient_dimension==3.

See Also
  `CGAL::import_from_plane_graph<LCC>`
  `CGAL::import_from_polyhedron_3<LCC,Polyhedron>`

`#include <CGAL/Linear_cell_complex_constructors.h>`