 CGAL::Direction_d<Kernel>

Definition

A Direction_d is a vector in the d-dimensional vector space where we forget about its length. We represent directions in d-dimensional space as a tuple (h0,...,hd) of variables of type RT which we call the homogeneous coordinates of the direction. The coordinate hd must be positive. The Cartesian coordinates of a direction are ci = hi/hd for 0 i < d, which are of type FT. Two directions are equal if their Cartesian coordinates are positive multiples of each other. Directions are in one-to-one correspondence to points on the unit sphere.

Types

 Direction_d::LA the linear algebra layer. Direction_d::Delta_const_iterator a read-only iterator for the deltas of dir. Direction_d::Base_direction construction tag.

Creation

Direction_d<Kernel> dir;
introduces a variable dir of type Direction_d<Kernel>.

Direction_d<Kernel> dir ( Vector_d<Kernel> v);
introduces a variable dir of type Direction_d<Kernel> initialized to the direction of v.

template <class InputIterator>
Direction_d<Kernel> dir ( int d, InputIterator first, InputIterator last);
introduces a variable dir of type Direction_d<Kernel> in dimension d with representation tuple set [first,last).
 Precondition: d is nonnegative, [first,last) has d elements.
 Requirement: The value type of InputIterator is RT.

Direction_d<Kernel> dir ( int d, Base_direction, int i);
returns a variable dir of type Direction_d<Kernel> initialized to the direction of the i-th base vector of dimension d.
 Precondition: 0 i < d.

Direction_d<Kernel> dir ( RT x, RT y);
introduces a variable dir of type Direction_d<Kernel> in 2-dimensional space.

Direction_d<Kernel> dir ( RT x, RT y, RT z);
introduces a variable dir of type Direction_d<Kernel> in 3-dimensional space.

Operations

int dir.dimension () returns the dimension of dir.

RT dir.delta ( int i) returns the i-th component of dir.
 Precondition: 0 i < d.

RT dir [ int i ] returns the i-th delta of dir.
 Precondition: 0 i < d.

Delta_const_iterator dir.deltas_begin () returns an iterator pointing to the first delta of dir.

Delta_const_iterator dir.deltas_end () returns an iterator pointing beyond the last delta of dir.

Vector_d<Kernel> dir.vector () returns a vector pointing in direction dir.

bool dir.is_degenerate () returns true iff dir.delta(i)==0 for all 0 i < d.

Direction_d<Kernel> dir.transform ( Aff_transformation_d<Kernel> t)
returns t(p).

Direction_d<Kernel> dir.opposite () returns the direction opposite to dir.

Direction_d<Kernel> - dir returns the direction opposite to dir.

Downward compatibility

We provide the operations of the lower dimensional interface dx(), dy(), dz().

Implementation

Directions are implemented by arrays of integers as an item type. All operations like creation, initialization, tests, inversion, input and output on a direction d take time O(d.dimension()). dimension(), coordinate access and conversion take constant time. The space requirement is O(d.dimension()).