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

CGAL 4.8 - 2D and 3D Linear Geometry Kernel

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Kernel::CompareXAtY_2 Concept Reference
Kernel Function Object Concepts

## Definition

Refines:
  `AdaptableFunctor` (with three arguments)

See Also
  `CGAL::compare_x_at_y()`

## Operations
A model of this concept must provide:
Comparison_result | operator() (const Kernel::Point_2 &p, const Kernel::Line_2 &h)
| compares the \( x\)-coordinates of `p` and the horizontal projection of `p` on `h`. More...
Comparison_result | operator() (const Kernel::Point_2 &p, const Kernel::Line_2 &h1, const Kernel::Line_2 &h2)
| compares the \( x\)-coordinates of the horizontal projection of `p` on `h1` and on `h2`. More...
Comparison_result | operator() (const Kernel::Line_2 &l1, const Kernel::Line_2 &l2, const Kernel::Line_2 &h)
| Let `p` be the intersection of lines `l1` and `l2`. More...
Comparison_result | operator() (const Kernel::Line_2 &l1, const Kernel::Line_2 &l2, const Kernel::Line_2 &h1, const Kernel::Line_2 &h2)
| Let `p` be the intersection of lines `l1` and `l2`. More...

## Member Function Documentation

Comparison_result Kernel::CompareXAtY_2::operator() | ( | const Kernel::Point_2 & | p,
|  | const Kernel::Line_2 & | h
| ) |  |

compares the \( x\)-coordinates of `p` and the horizontal projection of `p` on `h`.

See Figure fig-compare_x_at_y_2 (a).

Comparison_result Kernel::CompareXAtY_2::operator() | ( | const Kernel::Point_2 & | p,
|  | const Kernel::Line_2 & | h1,
|  | const Kernel::Line_2 & | h2
| ) |  |

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

See Figure fig-compare_x_at_y_2 (b).

Comparison_result Kernel::CompareXAtY_2::operator() | ( | const Kernel::Line_2 & | l1,
|  | const Kernel::Line_2 & | l2,
|  | const Kernel::Line_2 & | h
| ) |  |

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

This function compares the \( x\)-coordinates of `p` and the horizontal projection of `p` on `h`.

See Figure fig-compare_x_at_y_2 (c).

Comparison_result Kernel::CompareXAtY_2::operator() | ( | const Kernel::Line_2 & | l1,
|  | const Kernel::Line_2 & | l2,
|  | const Kernel::Line_2 & | h1,
|  | const Kernel::Line_2 & | h2
| ) |  |

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

This function compares the \( x\)-coordinates of the horizontal projection of `p` on `h1` and on `h2`.

See Figure fig-compare_x_at_y_2 (d)).