CGAL 4.12 - Principal Component Analysis

The function centroid() computes the (uniform) center of mass of a set of 2D or 3D bounded objects.

In 2D these objects include points, segments, triangles, iso rectangles, circles and disks. In 3D these objects include points, segments, triangles, iso cuboids, spheres, balls and tetrahedra.

The user can also optionally pass an explicit kernel, in case the default based on Kernel_traits is not sufficient. The default dimension tag is deduced automatically, although the user can pass a tag specifying the dimension of the objects to be considered for the centroid computation. For example, the default dimension of a tetrahedron is 3, but specifying a dimension 0 computes the centroid of the tetrahedron vertices (3D points), specifying a dimension 1 computes the centroid of the tetrahedron edges (3D segments) and specifying a dimension 2 computes the centroid of the tetrahedron facets (3D triangles).

CGAL::barycenter()
CGAL::centroid() (Linear Kernel)

## Functions

template<typename InputIterator , typename Tag >
Deduced CGAL::centroid (InputIterator first, InputIterator beyond, const Tag &t)
computes the centroid of a non-empty set of 2D or 3D objects. More...

template<typename InputIterator , typename K , typename Tag >
Deduced CGAL::centroid (InputIterator first, InputIterator beyond, const K &k, const Tag &t)
computes the centroid of a non-empty set of 2D or 3D objects. More...

## ◆ centroid() [1/2]

template<typename InputIterator , typename Tag >
 Deduced CGAL::centroid ( InputIterator first, InputIterator beyond, const Tag & t )

#include <CGAL/centroid.h>

computes the centroid of a non-empty set of 2D or 3D objects.

The tag is used to specify the dimension to be considered from the objects.

Precondition
first != beyond.
Returns
The return type is either K::Point_2 or K::Point_3, depending on the dimension of the input objects, where K is
CGAL::Kernel_traits<std::iterator_traits<InputIterator>::value_type>::Kernel

Two Dimensional Input

The value type must be either K::Point_2, K::Segment_2, K::Triangle_2, K::Rectangle_2 or K::Circle_2. To fit a set of disks the user must call the function with value type K::Circle_2 and with dimension tag of 2. The tag must range between Dimension_tag<0> and Dimension_tag<2>.

Three Dimensional Input

The value type must be either K::Point_3, K::Segment_3, K::Triangle_3, K::Cuboid_3, K::Sphere_3 or K::Tetrahedron_3. To fit a set of balls the user must call the function with value type K::Sphere_3 and with dimension tag of 3. The tag must range between Dimension_tag<0> and Dimension_tag<3>.

## ◆ centroid() [2/2]

template<typename InputIterator , typename K , typename Tag >
 Deduced CGAL::centroid ( InputIterator first, InputIterator beyond, const K & k, const Tag & t )

#include <CGAL/centroid.h>

computes the centroid of a non-empty set of 2D or 3D objects.

The tag is used to specify the dimension to be considered from the objects.

Precondition
first != beyond.
Returns
The return type is either K::Point_2 or K::Point_3, depending on the dimension of the input objects.

Two Dimensional Input

The value type must be either K::Point_2, K::Segment_2, K::Triangle_2, K::Rectangle_2 or K::Circle_2. To fit a set of disks the user must call the function with value type K::Circle_2 and with dimension tag of 2. The tag must range between Dimension_tag<0> and Dimension_tag<2>.

Three Dimensional Input

The value type must be either K::Point_3, K::Segment_3, K::Triangle_3, K::Cuboid_3, K::Sphere_3 or K::Tetrahedron_3. To fit a set of balls the user must call the function with value type K::Sphere_3 and with dimension tag of 3. The tag must range between Dimension_tag<0> and Dimension_tag<3>.