CGAL 4.7 - 2D and 3D Linear Geometry Kernel: Kernel::CompareXAtY_2 Concept Reference

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CGAL 4.7 - 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)).