CGAL 4.7 - dD Geometry Kernel: Kernel_d::Orientation_d Concept Reference

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CGAL 4.7 - dD Geometry Kernel

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Kernel_d::Orientation_d Concept Reference
Kernel Concept

## Definition

## Operations

A model of this concept must provide:
template<class ForwardIterator >
Orientation | operator() (ForwardIterator first, ForwardIterator last)
| determines the orientation of the points of the tuple `A = tuple [first,last)` where \( A\) consists of \( d + 1\) points in \( d\)-space. More...

## Member Function Documentation

template<class ForwardIterator >

Orientation Kernel_d::Orientation_d::operator() | ( | ForwardIterator | first,
|  | ForwardIterator | last
| ) |  |

determines the orientation of the points of the tuple `A = tuple [first,last)` where \( A\) consists of \( d + 1\) points in \( d\)-space.

This is the sign of the determinant

\[ \left| \begin{array}{cccc} 1 & 1 & 1 & 1 \\ A[0] & A[1] & \dots& A[d] \end{array} \right| \]

where `A[i]` denotes the Cartesian coordinate vector of the \( i\)-th point in \( A\).

Precondition
  `size [first,last) == d+1` and `A[i].dimension() == d` \( \forall0 \leq i \leq d\).

Requires:
  The value type of `ForwardIterator` is `Kernel_d::Point_d`.