CGAL 5.6.3 - 2D Arrangements

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List of all members | Public Member Functions
CGAL::Arr_conic_traits_2< RatKernel, AlgKernel, NtTraits >::Approximate_2 Class Reference

`#include <CGAL/Arr_conic_traits_2.h>`

## Definition

template<typename RatKernel, typename AlgKernel, typename NtTraits>
class CGAL::Arr_conic_traits_2< RatKernel, AlgKernel, NtTraits >::Approximate_2

A functor that approximates a point and an \(x\)-monotone curve.

## Public Member Functions
Approximate_number_type | operator() (const Point_2 &p, int i) const
| Obtain an approximation of a point coordinate.
Approximate_point_2 | operator() (const Point_2 &p) const
| Obtain an approximation of a point.
template<typename OutputIterator >
OutputIterator | operator() (OutputIterator oi, double error, const X_monotone_curve_2 &xcv, bool l2r=true) const
| Obtain a polyline that approximates an \(x\)-monotone curve.

## Member Function Documentation

## ◆ operator()() [1/3]

template<typename RatKernel , typename AlgKernel , typename NtTraits >

Approximate_point_2 CGAL::Arr_conic_traits_2< RatKernel, AlgKernel, NtTraits >::Approximate_2::operator() | ( | const Point_2 & | p | ) | const

Obtain an approximation of a point.

Parameters

  p | The exact point.

## ◆ operator()() [2/3]

template<typename RatKernel , typename AlgKernel , typename NtTraits >

Approximate_number_type CGAL::Arr_conic_traits_2< RatKernel, AlgKernel, NtTraits >::Approximate_2::operator() | ( | const Point_2 & | p,
|  | int | i
| ) |  | const

Obtain an approximation of a point coordinate.

Parameters

  p | The exact point.
  i | The coordinate index (either 0 or 1).

Precondition
  `i` is either 0 or 1.

Returns
  An approximation of p's \(x\)-coordinate (if `i` == 0), or an approximation of p's \(y\)-coordinate (if `i` == 1).

## ◆ operator()() [3/3]

template<typename RatKernel , typename AlgKernel , typename NtTraits >
template<typename OutputIterator >

OutputIterator CGAL::Arr_conic_traits_2< RatKernel, AlgKernel, NtTraits >::Approximate_2::operator() | ( | OutputIterator | oi,
|  | double | error,
|  | const X_monotone_curve_2 & | xcv,
|  | bool | l2r = `true`
| ) |  | const

Obtain a polyline that approximates an \(x\)-monotone curve.

The polyline is defined by a range of approximate points beginning at `oi`. The type `OutputIterator` must dereference the type `Approximate_point_2`. The first and last points in the range are always the endpoints of the given arc `xcv`. The operator returns a past-the-end iterator of the destination range.

Parameters

  oi | An output iterator for the resulting polyline.
  error | The error bound of the polyline approximation. This is the Hausdorff distance between the arc and the polyline that approximates the arc.
  xcv | The exact \(x\)-monotone arc.
  l2r | A Boolean flag that indicates whether the arc direction is left to right.

Returns
  The past-the-end iterator of the output iterator.