CGAL 6.2 - 2D and 3D Linear Geometry Kernel: CGAL::squared_distance()

CGAL 6.2 - 2D and 3D Linear Geometry Kernel

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Functions
CGAL::squared_distance()
Reference Manual » Global Kernel Functions

##

#include <CGAL/squared_distance_2.h> //for 2D functions
#include <CGAL/squared_distance_3.h> //for 3D functions

## Functions
template<typename Kernel >
Kernel::FT | CGAL::squared_distance (Type1< Kernel > obj1, Type2< Kernel > obj2)
| computes the square of the Euclidean distance between two geometric objects.

## Function Documentation

## ◆ squared_distance()

template<typename Kernel >

Kernel::FT CGAL::squared_distance | ( | Type1< Kernel > | obj1,
|  | Type2< Kernel > | obj2
| ) |  |

`#include <CGAL/squared_distance_2.h>`

computes the square of the Euclidean distance between two geometric objects.

For arbitrary geometric objects `obj1` and `obj2` the squared distance is defined as the minimal `squared_distance(p1, p2)`, where `p1` is a point of `obj1` and `p2` is a point of `obj2`. Note that for objects that have an inside (a bounded region), this inside is part of the object. So, the squared distance from a point inside is zero, not the squared distance to the closest point on the boundary.

In 2D, the types `Type1` and `Type2` can be any of the following:

- `Point_2`
- `Line_2`
- `Ray_2`
- `Segment_2`
- `Triangle_2`

as well as any combination of `Kernel::Point_2` and `Kernel::Weighted_point_2`

In 3D, the types `Type1` and `Type2` can be any of the following:

- `Point_3`
- `Line_3`
- `Ray_3`
- `Segment_3`
- `Plane_3`

as well as the following combinations:

- `Point_3`/`Triangle_3`
- `Point_3`/`Tetrahedron_3`
- `Weighted_point_3`/`Triangle_3`
- `Weighted_point_3`/`Tetrahedron_3`
- `Triangle_3`/`Triangle_3`

See also
  `CGAL::compare_distance_to_point()`
  `CGAL::compare_signed_distance_to_line()`
  `CGAL::compare_signed_distance_to_plane()`
  `CGAL::has_larger_distance_to_point()`
  `CGAL::has_larger_signed_distance_to_line()`
  `CGAL::has_larger_signed_distance_to_plane()`
  `CGAL::has_smaller_distance_to_point()`
  `CGAL::has_smaller_signed_distance_to_line()`
  `CGAL::has_smaller_signed_distance_to_plane()`