CGAL 5.6.3 - 2D Straight Skeleton and Polygon Offsetting

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Functions
Skeleton Extrusion
2D Straight Skeleton and Polygon Offsetting Reference

##

The following functions are used to construct the skeleton extrusion of a polygon.

## Functions
template<typename Polygon , typename FT , typename PolygonMesh , typename NamedParameters = parameters::Default_named_parameters>
bool | CGAL::extrude_skeleton (const Polygon &polygon, PolygonMesh &out, const NamedParameters &np=parameters::default_values())
| constructs the straight skeleton-based extrusion of a polygon with holes.

## Function Documentation

## ◆ extrude_skeleton()

template<typename Polygon , typename FT , typename PolygonMesh , typename NamedParameters = parameters::Default_named_parameters>

bool CGAL::extrude_skeleton | ( | const Polygon & | polygon,
|  | PolygonMesh & | out,
|  | const NamedParameters & | np = `parameters::default_values()`
| ) |  |

`#include <CGAL/extrude_skeleton.h>`

constructs the straight skeleton-based extrusion of a polygon with holes.

Given a polygon with holes and a set of weights (or angles) associated to its edges, the skeleton extrusion is a volume constructed from the weighted straight skeleton by associating a height to the vertices of the skeleton, which corresponds to the time at the vertex. The input polygon is placed at `z = 0`.

The result is a closed, 2-manifold surface triangle mesh. Note that this mesh can have non-local self-intersections if a maximal height is provided due to possible (geometric) non-manifold occurences.

It is possible to crop the extruded skeleton at a maximum height using the optional `maximum_height()` named parameter. A maximum height must be specified if the weights (or angles) associated to the edges of the input polygon correspond an outward extrusion, i.e. if no weight is greater than zero (or no angle is smaller than `90` degrees).

Template Parameters

  Polygon | must be a model of `SequenceContainer` with value type `InK::Point_2` (e.g. `Polygon_2<InK>`) or a model of `GeneralPolygonWithHoles_2` (e.g. `Polygon_with_holes_2<InK>`).
  PolygonMesh | a model of `MutableFaceGraph`
  NamedParameters | a sequence of Named Parameters

Parameters

  polygon | the polygon with holes
  out | the output polygon mesh
  np | an optional sequence of Named Parameters among the ones listed below

Optional Named Parameters

  a range of weights, one for each edge of the input polygon Type: a model of `Range` whose value type is a model of `Range` whose value type is `FT` Default: an empty range (uniform weights are used) Extra: Weights should be finite and all of the same sign. Negative weights are used to signify exterior extrusion. Contrary to weighted skeleton functions, a weight `0` can here be used to signify a vertical extrusion of this edge. Extra: If neither `weights` nor `angles` are provided, uniform weights are used. |
  a range of angles, one for each edge of the input polygon. For each contour edge, the angle is the dihedral angle between the `z=0` plane and the desired extrusion plane. Type: a model of `Range` whose value type is a model of `Range` whose value type is `FT` Default: an empty range (uniform weights are used) Extra: Angles are measured in degrees and should be strictly within `0` and `180` degrees and should be either all acute (inward extrusion) or all obtuse (outward extrusion). Extra: This parameter is ignored if the `weights` parameter is provided. Extra: The conversion to weights involves trigonometry and will be inexact, even when using a number type with exact square roots. |
  the maximum height of the extrusion Type: `FT`, a model of `FieldNumberType` convertible to the kernel type of the polygon. Default: unused Extra: This parameter should not be null, but can be negative; in this case, the polygon is extruded downwards. |
  Whether information about the extrusion process should be printed to `std::cout` Type: Boolean Default: `false` |
  an instance of a geometric traits class Type: a class model of `Kernel` Default: a CGAL Kernel deduced from the polygon's point type, using `CGAL::Kernel_traits` |
  a property map associating points to the vertices of `out` Type: a class model of `ReadWritePropertyMap` with `boost::graph_traits<PolygonMesh>::vertex_descriptor` as key type and `InK::Point_2` as value type. Default: the internal property map for `CGAL::vertex_point_t` of `out` |

Returns
  `true` if the construction was successful, `false` otherwise.

Precondition
  `polygon` is a weakly simple polygon with holes.
  Holes are weakly simple polygons that do not intersect each other or the outer boundary.

See also
  `CGAL::create_interior_weighted_skeleton_and_offset_polygons_with_holes_2()`
  `CGAL::Straight_skeleton_2`

Examples
  Straight_skeleton_2/extrude_skeleton.cpp.