Real-Valued Vectors ( real_vector )

Definition

An instance of data type real_vector is a vector of variables of type real.

#include < LEDA/numbers/real_vector.h >

Creation

real_vector	v	creates an instance v of type real_vector; v is initialized to the zero-dimensional vector.
real_vector	v(int d)	creates an instance v of type real_vector; v is initialized to the zero vector of dimension d.
real_vector	v(real a, real b)	creates an instance v of type real_vector; v is initialized to the two-dimensional vector (a, b).
real_vector	v(real a, real b, real c)	creates an instance v of type real_vector; v is initialized to the three-dimensional vector (a, b, c).
real_vector	v(double a, double b)	creates an instance v of type real_vector; v is initialized to the two-dimensional vector (a, b).
real_vector	v(double a, double b, double c)
		creates an instance v of type real_vector; v is initialized to the three-dimensional vector (a, b, c).

Operations

int	v.dim()	returns the dimension of v.
real&	v[int i]	returns i-th component of v. Precondition 0 < = i < = v.dim()-1.
real	v.hcoord(int i)	for compatibility with rat_vector.
real	v.coord(int i)	for compatibility with rat_vector.
real	v.sqr_length()	returns the square of the Euclidean length of v.
real	v.length()	returns the Euclidean length of v.
real_vector	v.norm()	returns v normalized.
real_vector	v.rotate90(int i=1)	returns v by an angle of i x 90 degrees. If i > 0 the rotation is counter-clockwise otherwise it is clockwise. Precondition v.dim() = 2
real_vector	v + const real_vector& v1	Addition. Precondition v.dim() = v1.dim().
real_vector	v - const real_vector& v1	Subtraction. Precondition v.dim() = v1.dim().
real	v * const real_vector& v1	Scalar multiplication. Precondition v.dim() = v1.dim().
real_vector&	v *= real r	multiplies all coordinates by r.
real_vector	v * real r	Componentwise multiplication with real r.
bool	v == const real_vector& w	Test for equality.
bool	v != const real_vector& w	Test for inequality.
void	v.print(ostream& O)	prints v componentwise to ostream O.
void	v.print()	prints v to cout.
void	v.read(istream& I)	reads d = v.dim() numbers from input stream I and writes them into v[0]...v[d - 1].
void	v.read()	reads v from cin.
ostream&	ostream& O « const real_vector& v
		writes v componentwise to the output stream O.
istream&	istream& I » real_vector& v
		reads v componentwise from the input stream I.
vector	v.to_float()	returns a floating point approximation of v.

Additional Operations for vectors in two and three-dimensional space

real	v.xcoord()	returns the zero-th cartesian coordinate of v.
real	v.ycoord()	returns the first cartesian coordinate of v.
real	v.zcoord()	returns the second cartesian coordinate of v.
int	compare_by_angle(const real_vector& v1, const real_vector& v2)
		For a non-zero vector v let $\alpha$(v) be the angle by which the positive x-axis has to be turned counter-clockwise until it aligns with v. The function compares the angles defined by v1 and v2, respectively. The zero-vector precedes all non-zero vectors in the angle-order.
real_vector	cross_product(const real_vector& v1, const real_vector& v2)
		returns the cross product of the three-dimensional vectors v1 and v2.

Implementation

Vectors are implemented by arrays of real numbers. All operations on a vector v take O(v.dim()) real-number operations, except for dim and [ ] which take constant time. The space requirement depends on the size of the representations of the coordinates.