CGAL 4.14 - 2D and 3D Linear Geometry Kernel
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#include <CGAL/Vector_3.h>
An object of the class Vector_3
is a vector in the three-dimensional vector space \( \mathbb{R}^3\).
Geometrically spoken a vector is the difference of two points \( p_2\), \( p_1\) and denotes the direction and the distance from \( p_1\) to \( p_2\).
CGAL defines a symbolic constant NULL_VECTOR. We will explicitly state where you can pass this constant as an argument instead of a vector initialized with zeros.
Public Member Functions | |
Kernel::FT | squared_length () const |
returns the squared length of v . | |
Vector_3< Kernel > | operator* (const Vector_3< Kernel > &v, const Kernel::RT &s) |
Multiplication with a scalar from the right. | |
Vector_3< Kernel > | operator* (const Vector_3< Kernel > &v, const Kernel::FT &s) |
Multiplication with a scalar from the right. | |
Vector_3< Kernel > | operator* (const Kernel::RT &s, const Vector_3< Kernel > &v) |
Multiplication with a scalar from the left. | |
Vector_3< Kernel > | operator* (const Kernel::FT &s, const Vector_3< Kernel > &v) |
Multiplication with a scalar from the left. | |
Types | |
typedef unspecified_type | Cartesian_const_iterator |
An iterator for enumerating the Cartesian coordinates of a vector. | |
Creation | |
Vector_3 (const Point_3< Kernel > &a, const Point_3< Kernel > &b) | |
introduces the vector b-a . | |
Vector_3 (const Segment_3< Kernel > &s) | |
introduces the vector s.target()-s.source() . | |
Vector_3 (const Ray_3< Kernel > &r) | |
introduces a vector having the same direction as r . | |
Vector_3 (const Line_3< Kernel > &l) | |
introduces a vector having the same direction as l . | |
Vector_3 (const Null_vector &NULL_VECTOR) | |
introduces a null vector v . | |
Vector_3 (int x, int y, int z) | |
introduces a vector v initialized to (x, y, z) . | |
Vector_3 (double x, double y, double z) | |
introduces a vector v initialized to `(x, y, z). | |
Vector_3 (const Kernel::RT &hx, const Kernel::RT &hy, const Kernel::RT &hz, const Kernel::RT &hw=RT(1)) | |
introduces a vector v initialized to `(hx/hw, hy/hw, hz/hw). | |
Vector_3 (const Kernel::FT &x, const Kernel::FT &y, const Kernel::FT &z) | |
introduces a vector v initialized to (x, y, z) . | |
Coordinate Access | |
There are two sets of coordinate access functions, namely to the homogeneous and to the Cartesian coordinates. They can be used independently from the chosen kernel model. Note that you do not loose information with the homogeneous representation, because the | |
Kernel::RT | hx () const |
returns the homogeneous \( x\) coordinate. | |
Kernel::RT | hy () const |
returns the homogeneous \( y\) coordinate. | |
Kernel::RT | hz () const |
returns the homogeneous \( z\) coordinate. | |
Kernel::RT | hw () const |
returns the homogenizing coordinate. | |
Kernel::FT | x () const |
returns the x -coordinate of v , that is hx() /hw() . | |
Kernel::FT | y () const |
returns the y -coordinate of v , that is hy() /hw() . | |
Kernel::FT | z () const |
returns the z coordinate of v , that is hz() /hw() . | |
Convenience Operations | |
The following operations are for convenience and for compatibility with higher dimensional vectors. Again they come in a Cartesian and homogeneous flavor. | |
Kernel::RT | homogeneous (int i) const |
returns the i'th homogeneous coordinate of v . More... | |
Kernel::FT | cartesian (int i) const |
returns the i'th Cartesian coordinate of v . More... | |
Kernel::FT | operator[] (int i) const |
returns cartesian(i) . More... | |
Cartesian_const_iterator | cartesian_begin () const |
returns an iterator to the Cartesian coordinates of v , starting with the 0th coordinate. | |
Cartesian_const_iterator | cartesian_end () const |
returns an off the end iterator to the Cartesian coordinates of v . | |
int | dimension () const |
returns the dimension (the constant 3). | |
Vector_3< Kernel > | transform (const Aff_transformation_3< Kernel > &t) const |
returns the vector obtained by applying t on v . | |
Direction_3< Kernel > | direction () const |
returns the direction of v . | |
Operators | |
bool | operator== (const Vector_3< Kernel > &w) const |
Test for equality: two vectors are equal, iff their \( x\), \( y\) and \( z\) coordinates are equal. More... | |
bool | operator!= (const Vector_3< Kernel > &w) const |
Test for inequality. More... | |
Vector_3< Kernel > | operator+ (const Vector_3< Kernel > &w) const |
Addition. | |
Vector_3< Kernel > & | operator+= (const Vector_3< Kernel > &w) |
Addition. | |
Vector_3< Kernel > | operator- (const Vector_3< Kernel > &w) const |
Subtraction. | |
Vector_3< Kernel > & | operator-= (const Vector_3< Kernel > &w) |
Subtraction. | |
Vector_3< Kernel > | operator- () const |
Returns the opposite vector. | |
Vector_3< Kernel > | operator/ (const Kernel::RT &s) const |
Division by a scalar. | |
Vector_3< Kernel > & | operator/= (const Kernel::RT &s) |
Division by a scalar. | |
Kernel::FT | operator* (const Vector_3< Kernel > &w) const |
returns the scalar product (= inner product) of the two vectors. | |
Vector_3< Kernel > & | operator*= (const Kernel::FT &s) |
Multiplication by a scalar. | |
Kernel::FT CGAL::Vector_3< Kernel >::cartesian | ( | int | i | ) | const |
returns the i'th Cartesian coordinate of v
.
Kernel::RT CGAL::Vector_3< Kernel >::homogeneous | ( | int | i | ) | const |
returns the i'th homogeneous coordinate of v
.
bool CGAL::Vector_3< Kernel >::operator!= | ( | const Vector_3< Kernel > & | w | ) | const |
Test for inequality.
You can compare a vector with the NULL_VECTOR
.
bool CGAL::Vector_3< Kernel >::operator== | ( | const Vector_3< Kernel > & | w | ) | const |
Test for equality: two vectors are equal, iff their \( x\), \( y\) and \( z\) coordinates are equal.
You can compare a vector with the NULL_VECTOR
.
Kernel::FT CGAL::Vector_3< Kernel >::operator[] | ( | int | i | ) | const |
returns cartesian(i)
.