CGAL 4.7 - 2D and 3D Linear Geometry Kernel: CGAL::compare_y_at_x()

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

CGAL 4.7 - 2D and 3D Linear Geometry Kernel

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Functions
CGAL::compare_y_at_x()
Global Kernel Functions

##

See Also
  `CGAL::compare_xy()`
  `CGAL::compare_xyz()`
  `CGAL::compare_x()`
  `CGAL::compare_y()`
  `CGAL::compare_yx()`
  `CGAL::compare_x_at_y()`
  `CGAL::compare_z()`

## Functions

template<typename Kernel >
Comparison_result | CGAL::compare_y_at_x (const CGAL::Point_2< Kernel > &p, const CGAL::Line_2< Kernel > &h)
| compares the \( y\)-coordinates of `p` and the vertical projection of `p` on `h`. More...
template<typename Kernel >
Comparison_result | CGAL::compare_y_at_x (const CGAL::Point_2< Kernel > &p, const CGAL::Line_2< Kernel > &h1, const CGAL::Line_2< Kernel > &h2)
| compares the \( y\)-coordinates of the vertical projection of `p` on `h1` and on `h2`. More...
template<typename Kernel >
Comparison_result | CGAL::compare_y_at_x (const CGAL::Line_2< Kernel > &l1, const CGAL::Line_2< Kernel > &l2, const CGAL::Line_2< Kernel > &h)
| Let `p` be the `intersection` of lines `l1` and `l2`. More...
template<typename Kernel >
Comparison_result | CGAL::compare_y_at_x (const CGAL::Line_2< Kernel > &l1, const CGAL::Line_2< Kernel > &l2, const CGAL::Line_2< Kernel > &h1, const CGAL::Line_2< Kernel > &h2)
| Let `p` be the `intersection` of lines `l1` and `l2`. More...
template<typename Kernel >
Comparison_result | CGAL::compare_y_at_x (const CGAL::Point_2< Kernel > &p, const CGAL::Segment_2< Kernel > &s)
| compares the \( y\)-coordinates of `p` and the vertical projection of `p` on `s`. More...
template<typename Kernel >
Comparison_result | CGAL::compare_y_at_x (const CGAL::Point_2< Kernel > &p, const CGAL::Segment_2< Kernel > &s1, const CGAL::Segment_2< Kernel > &s2)
| compares the \( y\)-coordinates of the vertical projection of `p` on `s1` and on `s2`. More...

## With the 2D Circular Kernel

See 2D Circular Geometry Kernel. #include <CGAL/global_functions_circular_kernel_2.h>
template<typename CircularKernel >
Comparison_result | CGAL::compare_y_at_x (const CGAL::Circular_arc_point_2< CircularKernel > &p, const CGAL::Circular_arc_2< CircularKernel > &a)
| Same as above, for a point and a circular arc.
template<typename CircularKernel >
Comparison_result | CGAL::compare_y_at_x (const CGAL::Circular_arc_point_2< CircularKernel > &p, const CGAL::Line_arc_2< CircularKernel > &a)
| Same as above, for a point and a line segment.

## Function Documentation

template<typename Kernel >

Comparison_result CGAL::compare_y_at_x | ( | const CGAL::Point_2< Kernel > & | p,
|  | const CGAL::Line_2< Kernel > & | h
| ) |  |

compares the \( y\)-coordinates of `p` and the vertical projection of `p` on `h`.

See Figure figcompareyatx (d).

Precondition
  `h` is not vertical.

`#include <CGAL/global_functions.h>`

template<typename Kernel >

Comparison_result CGAL::compare_y_at_x | ( | const CGAL::Point_2< Kernel > & | p,
|  | const CGAL::Line_2< Kernel > & | h1,
|  | const CGAL::Line_2< Kernel > & | h2
| ) |  |

compares the \( y\)-coordinates of the vertical projection of `p` on `h1` and on `h2`.

See Figure figcompareyatx (e).

Precondition
  `h1` and `h2` are not vertical.

`#include <CGAL/global_functions.h>`

template<typename Kernel >

Comparison_result CGAL::compare_y_at_x | ( | const CGAL::Line_2< Kernel > & | l1,
|  | const CGAL::Line_2< Kernel > & | l2,
|  | const CGAL::Line_2< Kernel > & | h
| ) |  |

Let `p` be the `intersection` of lines `l1` and `l2`.

This function compares the \( y\)-coordinates of `p` and the vertical projection of `p` on `h` See Figure figcompareyatx (f).

Precondition
  `l1`, `l2` intersect and `h` is not vertical.

`#include <CGAL/global_functions.h>`

template<typename Kernel >

Comparison_result CGAL::compare_y_at_x | ( | const CGAL::Line_2< Kernel > & | l1,
|  | const CGAL::Line_2< Kernel > & | l2,
|  | const CGAL::Line_2< Kernel > & | h1,
|  | const CGAL::Line_2< Kernel > & | h2
| ) |  |

Let `p` be the `intersection` of lines `l1` and `l2`.

This function compares the \( y\)-coordinates of the vertical projection of `p` on `h1` and on `h2`. See Figure figcompareyatx (g).

Precondition
  `l1` and `l2` intersect; `h1` and `h2` are not vertical.

`#include <CGAL/global_functions.h>`

template<typename Kernel >

Comparison_result CGAL::compare_y_at_x | ( | const CGAL::Point_2< Kernel > & | p,
|  | const CGAL::Segment_2< Kernel > & | s
| ) |  |

compares the \( y\)-coordinates of `p` and the vertical projection of `p` on `s`.

If `s` is vertical, then return `CGAL::EQUAL` when `p` lies on `s`, `CGAL::SMALLER` when `p` lies under {s}, and `CGAL::LARGER` otherwise.

Precondition
  `p` is within the x range of `s`.

`#include <CGAL/global_functions.h>`

template<typename Kernel >

Comparison_result CGAL::compare_y_at_x | ( | const CGAL::Point_2< Kernel > & | p,
|  | const CGAL::Segment_2< Kernel > & | s1,
|  | const CGAL::Segment_2< Kernel > & | s2
| ) |  |

compares the \( y\)-coordinates of the vertical projection of `p` on `s1` and on `s2`.

If `s1` or `s2` is vertical, then return `CGAL::EQUAL` if they intersect, otherwise return `CGAL::SMALLER` if `s1` lies below `s2`, and return `CGAL::LARGER` otherwise.

Precondition
  `p` is within the x range of `s1` and `s2`.

`#include <CGAL/global_functions.h>`