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

CGAL 4.8 - 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` \( \forall0 \leq i \leq d\).

Template Parameters

  ForwardIterator | has `Kernel_d::Point_d` as value type.