Kernel_d::Orientation_d Concept Reference

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.

Member Function Documentation

operator()()

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.