CGAL 6.1.1 - 2D Straight Skeleton and Polygon Offsetting

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CGAL::Polygon_offset_builder_2< StraightSkeleton_, Traits_, Container_ > Class Template Reference
Reference Manual » Classes

`#include <CGAL/Polygon_offset_builder_2.h>`

## Definition

template<typename StraightSkeleton_, typename Traits_, typename Container_>
class CGAL::Polygon_offset_builder_2< StraightSkeleton_, Traits_, Container_ >

The class `Polygon_offset_builder_2` encapsulates the construction of inward offset contours of a 2D simple polygon with holes.

The construction is based on the straight skeleton of the interior of the polygon.

Template Parameters

  StraightSkeleton_ | must be a model of the `StraightSkeleton_2`.
  Traits_ | must be a model of the `StraightSkeletonBuilderTraits_2`.
  Container_ | must be a model of the `SequenceContainer`.

See also
  `PolygonOffsetBuilderTraits_2`
  `Polygon_offset_builder_traits_2`

Examples
  Straight_skeleton_2/Low_level_API.cpp.

## Types
typedef StraightSkeleton_ | Ss
| The straight skeleton (first template parameter)
typedef Container_ | Container
| The container of 2D vertices that represents each offset contour generated by the algorithm (third template parameter)
typedef Traits::FT | FT
| The model of `FieldWithSqrt` used to specify the desired offset distance, provided by the geometric traits `Traits`.

## Creation
| Polygon_offset_builder_2 (const Ss &ss, const Traits &traits=Traits())
| Constructs the builder class using the given Straight Skeleton instance.

## Methods
template<class OutputIterator >
OutputIterator | construct_offset_contours (FT t, OutputIterator out)
| Given the straight skeleton passed in the constructor which corresponds to the interior of a non-degenerate strictly-simple polygon with holes P, returns all the offset contours of P at the Euclidean distance `t`.

## Member Function Documentation

## ◆ construct_offset_contours()

template<typename StraightSkeleton_ , typename Traits_ , typename Container_ >
template<class OutputIterator >

OutputIterator CGAL::Polygon_offset_builder_2< StraightSkeleton_, Traits_, Container_ >::construct_offset_contours | ( | FT | t,
|  | OutputIterator | out
| ) |  |

Given the straight skeleton passed in the constructor which corresponds to the interior of a non-degenerate strictly-simple polygon with holes P, returns all the offset contours of P at the Euclidean distance `t`.

Such offset contours are polygons in the interior of `P`. Provided exact constructions are used, these polygons are strictly simple. For any offset distance `t` there are `0`, `1`, or more offset contours.

For any given input polygon, its offset polygons at a certain distance are composed of several contours. This method returns all such contours in an unspecified order and with no parental relationship between them (that is why it is called `construct_offset_contours()` and not `construct_offset_polygons()`).

Those offset contours in the resulting sequence which are oriented counterclockwise are outer contours and those oriented clockwise are holes. It is up to the user to match each hole to its parent in order to reconstruct the parent-hole relationship of the conceptual output. It is sufficient to test each hole against each parent as there won't be a hole inside a hole, a parent inside any other contour, or a hole inside more than one parent. The recommended insideness test is to perform a regularized Boolean set operation. The function `do_intersect()` from Chapter 2D Regularized Boolean Set-Operations will work fine in our case since it is guaranteed that no hole would cross halfway outside any parent (in the presence of such cases, subtracting the parent from the hole works better as it correctly rejects halfway holes).

You can call `construct_offset_contours()` with different offset distances (there is no need to construct the builder again). If you call it with an offset distance so large that there are no offset contours at that distance, no contour is inserted into the output sequence and the returned iterator will be equal to `out`.

If there are degenerate, or nearly degenerate vertices; that is, vertices whose internal or external angle approaches `0`, numerical overflow may prevent some of the polygon contours to be constructed. If that happens, the failed contour just won't be added into the resulting sequence.

Template Parameters

  OutputIterator | must be a model of the OutputIterator category whose `value_type` is a `std::shared_ptr` holding the dynamically allocated instances of type `Container`.

Parameters

  t | the offset value
  out | an output iterator. For each resulting offset contour, a default constructed instance of `Container` type, is dynamically allocated and each offset vertex is added to it. A `std::shared_ptr` holding onto the dynamically allocated container is inserted into the output sequence via the OutputIterator `out`.

Returns
  an `OutputIterator` past-the-end of the resulting sequence, which contains each offset contour generated.

Precondition
  `t > 0`