Vec< T, 3 > Class Template Reference

3D specialization of vector class. More...

#include <geomc/linalg/vecdetail/Vec3.h>

Inheritance diagram for Vec< T, 3 >:

Public Types
using	elem_t
	The coordinate type of this object.
using	point_t
	The type of a point in this object's space.
typedef Vec< T, N >	self_t
	Self type. I.e., Vec<T,N> if a vector, Quat<T> if a quaternion.

Public Member Functions
constexpr	Vec ()
constexpr	Vec ()
	Construct vector with all elements set to 0.
	Vec (const std::initializer_list< T > &items)
constexpr	Vec (const T a[N])
constexpr	Vec (const T v[3])
	Construct a vector with elements copied from the 3-element array v.
constexpr	Vec (const Vec< T, M > &...vecs)
	Construct a new vector by concatenating two or more vectors.
constexpr	Vec (const Vec< U, N-1 > &v, T a)
	Vec (detail::MtxColIterator< Mx, Ref > mtx_col)
constexpr	Vec (T a)
constexpr	Vec (T a)
	Construct a vector with all elements set to a.
constexpr	Vec (T x, T y, T z)
	Construct a vector with elements (x, y, z).
template<typename U>
constexpr	Vec (Vec< U, 2 > xy, T z)
	Construct a vector with (x, y) taken from the 2D vector xy, and z as the final element.
self_t	abs () const
	Element-wise absolute value.
self_t	add (const self_t &v) const
	Vector addition.
self_t	add (const self_t &v) const
	Vector addition.
Vec< T, 3 >	add (T dx, T dy, T dz) const
self_t	align (const self_t &from, const self_t &to) const
	Apply a rotation to this which aligns the unit vectors from with to.
self_t	align (const self_t &from, const self_t &to) const
	Apply a rotation to this which aligns the unit vectors from with to.
Vec< T, 3 >	align (const Vec< T, 3 > &from, const Vec< T, 3 > &to)
T	angle_to (const self_t &v) const
	Angle between vectors.
T	angle_to (const self_t &v) const
	Angle between vectors.
index_t	argmax () const
	Return the index of the coordinate with the largest absolute value.
index_t	argmin () const
	Return the index of the coordinate with the smallest absolute value.
T *	begin ()
const T *	begin () const
self_t	bounce_on (const self_t &normal) const
	Elastic collision.
self_t	bounce_on (const self_t &normal) const
	Elastic collision.
self_t	ceil () const
	Element-wise ceiling function.
self_t	clamp (const self_t &lo, const self_t &hi) const
	Element-wise clamp.
self_t	clamp (const self_t &lo, const self_t &hi) const
	Element-wise clamp.
Vec< T, 3 >	cross (Vec< T, 3 > v) const
T	dist (const self_t &pt) const
	Distance between points.
T	dist (const self_t &pt) const
	Distance between points.
T	dist2 (const self_t &pt) const
	Distance squared to a point.
T	dist2 (const self_t &pt) const
	Distance squared to a point.
T	dot (const self_t &v) const
	Dot product.
T	dot (const self_t &v) const
	Dot product.
T	dot (T xx, T yy, T zz) const
T *	end ()
const T *	end () const
self_t	floor () const
	Element-wise floor function.
T	fraction_on (const self_t &axis) const
	Return the component of this that projects to axis, as a fraction of axis's length.
T	fraction_on (const self_t &axis) const
	Return the component of this that projects to axis, as a fraction of axis's length.
T &	get (index_t idx)
const T &	get (index_t idx) const
bool	is_finite_real () const
bool	is_zero () const
	Return true if all elements are zero.
T	mag () const
	Euclidean norm (magnitude).
T	mag2 () const
	Squared magnitude.
self_t	max (const self_t &v) const
	Element-wise maximum of two Vecs.
T	max () const
	Maximum element.
self_t	max (const self_t &v) const
	Element-wise maximum of two Vecs.
self_t	min (const self_t &v) const
	Element-wise minimum of two Vecs.
T	min () const
	Minimum element.
self_t	min (const self_t &v) const
	Element-wise minimum of two Vecs.
self_t	mix (const self_t &v, T mix) const
	Linear interpolation.
self_t	mix (const self_t &v, T mix) const
	Linear interpolation.
	operator Vec< U, N > () const
	Element typecast.
bool	operator!= (const self_t &vv) const
	Inequality test.
bool	operator!= (const self_t &vv) const
	Inequality test.
self_t &	operator*= (const self_t &vv)
	Element-wise multiplication and assignment.
self_t &	operator*= (const self_t &vv)
	Element-wise multiplication and assignment.
self_t &	operator*= (T s)
	Scalar multiplication and assignment.
self_t	operator+ (const self_t &v) const
	Element-wise addition.
self_t	operator+ (const self_t &v) const
	Element-wise addition.
self_t &	operator+= (const self_t &vv)
	Element-wise addition and assignment.
self_t &	operator+= (const self_t &vv)
	Element-wise addition and assignment.
self_t	operator- (const self_t &v) const
	Element-wise subtraction.
self_t	operator- () const
	Negation.
self_t	operator- (const self_t &v) const
	Element-wise subtraction.
self_t &	operator-= (const self_t &vv)
	Subtraction and assignment.
self_t &	operator-= (const self_t &vv)
	Subtraction and assignment.
self_t &	operator/= (T s)
	Scalar division and assignment.
bool	operator== (const self_t &vv) const
	Equality test.
bool	operator== (const self_t &vv) const
	Equality test.
T &	operator[] (index_t idx)
	Vector element access.
const T &	operator[] (index_t idx) const
	Vector element access.
Vec< T, 3 >	operator^ (Vec< T, 3 > v) const
	Vector cross product.
T	product () const
	Multiply all elements together.
self_t	project_on (const self_t &axis) const
	Orthogonal projection to an axis.
self_t	project_on (const self_t &axis) const
	Orthogonal projection to an axis.
self_t	reflect_about (self_t normal) const
	Reflection about a normal.
self_t	reflect_about (self_t normal) const
	Reflection about a normal.
Vec< T, 3 >	reflected_x () const
Vec< T, 3 >	reflected_y () const
Vec< T, 3 >	reflected_z () const
PointType< T, M >::point_t	resized () const
	Resized copy of a vector.
Vec< T, 3 >	rotate (T u, T v, T w, T a, T b, T c, T radians)
Vec< T, 3 >	rotate (T u, T v, T w, T radians) const
Vec< T, 3 >	rotate (Vec< T, 3 > axis, T radians) const
Vec< T, 3 >	rotate (Vec< T, 3 > axis, Vec< T, 3 > center, T radians)
self_t	round () const
	Round each element to the nearest integer.
self_t	scale (const self_t &v) const
	Element-wise multiplication.
self_t	scale (const self_t &v) const
	Element-wise multiplication.
self_t	scale (T a) const
	Scalar multiple.
Vec< T, 3 >	scale (T a, T b, T c) const
index_t	size () const
	The number of elements in this vector. Always equal to N.
self_t	sub (const self_t &v) const
	Vector subtraction.
self_t	sub (const self_t &v) const
	Vector subtraction.
Vec< T, 3 >	sub (T dx, T dy, T dz) const
T	sum () const
	Sum the elements of the vector.
Vec< T, 3 >	to_spherical () const
self_t	unit () const
	Vector normalization.
self_t	with_length (T mag) const
	Compute a vector with the direction of this and a new magnitude mag.

Static Public Member Functions
static Vec< T, 3 >	from_spherical (T r, T elev, T azi)

Static Public Attributes
static constexpr index_t	N
	The dimension of this object.
static const self_t	ones
static const self_t	unit_x
static const Vec< T, 3 >	X_AXIS
	(1, 0, 0) constant
static const Vec< T, 3 >	Y_AXIS
	(0, 1, 0) constant
static const Vec< T, 3 >	Z_AXIS
	(0, 0, 1) constant
static const self_t	zeros

Protected Attributes
T	v [N]

Related Symbols
(Note that these are not member symbols.)
geom::Vec< T, N >	abs (const geom::Vec< T, N > &v)
geom::Vec< T, N >	abs (const geom::Vec< T, N > &v)
geom::Vec< T, N >	ceil (const geom::Vec< T, N > &v)
geom::Vec< T, N >	ceil (const geom::Vec< T, N > &v)
geom::Vec< T, N >	cos (const geom::Vec< T, N > &v)
geom::Vec< T, N >	cos (const geom::Vec< T, N > &v)
geom::Vec< T, N >	exp (const geom::Vec< T, N > &v)
geom::Vec< T, N >	exp (const geom::Vec< T, N > &v)
geom::Vec< T, N >	floor (const geom::Vec< T, N > &v)
geom::Vec< T, N >	floor (const geom::Vec< T, N > &v)
geom::Vec< T, N >	log (const geom::Vec< T, N > &v)
geom::Vec< T, N >	log (const geom::Vec< T, N > &v)
geom::Vec< T, N >	max (const geom::Vec< T, N > &a, const geom::Vec< T, N > &b)
geom::Vec< T, N >	max (const geom::Vec< T, N > &a, const geom::Vec< T, N > &b)
geom::Vec< T, N >	min (const geom::Vec< T, N > &a, const geom::Vec< T, N > &b)
geom::Vec< T, N >	min (const geom::Vec< T, N > &a, const geom::Vec< T, N > &b)
const Vec< T, N >	operator* (const Vec< T, N > &a, const Vec< T, N > &b)
const Vec< T, N >	operator* (const Vec< T, N > &a, const Vec< T, N > &b)
Vec< T, N >	operator* (const Vec< T, N > &v, U d)
Vec< T, N >	operator* (const Vec< T, N > &v, U d)
Vec< T, N >	operator* (U d, const Vec< T, N > &v)
Vec< T, N >	operator* (U d, const Vec< T, N > &v)
const Vec< T, N >	operator/ (const Vec< T, N > &a, const Vec< T, N > &b)
const Vec< T, N >	operator/ (const Vec< T, N > &a, const Vec< T, N > &b)
Vec< T, N >	operator/ (const Vec< T, N > &v, U d)
Vec< T, N >	operator/ (const Vec< T, N > &v, U d)
Vec< T, N >	operator/ (const Vec< T, N > &v, U d)
Vec< T, N >	operator/ (const Vec< T, N > &v, U d)
geom::Vec< T, N >	sin (const geom::Vec< T, N > &v)
geom::Vec< T, N >	sin (const geom::Vec< T, N > &v)
geom::Vec< T, N >	sqrt (const geom::Vec< T, N > &v)
geom::Vec< T, N >	sqrt (const geom::Vec< T, N > &v)
geom::Vec< T, N >	tan (const geom::Vec< T, N > &v)
geom::Vec< T, N >	tan (const geom::Vec< T, N > &v)

Detailed Description

template<typename T>
class geom::Vec< T, 3 >

3D specialization of vector class.

Vec<T,3>'s elements may be accessed under these equivalent naming schemes:

v.{x,y,z} // conventional Euclidean coordinate names
v.{s,t,u} // conventional parameterization coordinate names
v.{r,g,b} // conventional color tuple coordinate names

x, s, and r all refer to the same element.

Member Typedef Documentation

point_t

using point_t

The type of a point in this object's space.

An N-vector of T if N > 1, otherwise a T.

Constructor & Destructor Documentation

Vec() [1/6]

Vec ( )

inlineconstexpr

Construct a new vector with all elements set to zero.

Vec() [2/6]

Vec ( T a )

inlineconstexpr

Construct a new vector with all elements set to the value of a.

Parameters

a	Scalar value

Vec() [3/6]

Vec ( const T a[N] )

inlineconstexpr

Construct a new vector with elements copied from a.

Parameters

a	An array of length N.

Vec() [4/6]

Vec ( const Vec< U, N-1 > & v, T a )

inlineconstexpr

Construct a new vector with the elements from v, with a as the last element.

Parameters

v	A vector of dimension N - 1
a	The value of the last element

Vec() [5/6]

Vec ( detail::MtxColIterator< Mx, Ref > mtx_col )

inline

Construct a vector from a column of a matrix.

Parameters

mtx_col

A matrix column iterator (obtained via mtx.col(i)).

Vec() [6/6]

Vec ( const std::initializer_list< T > & items )

inline

Construct a vector from a brace-initialization list.

Example: Vec<int,3> v = {2, 5, 8};

Parameters

items

A brace-initializer list.

Member Function Documentation

abs()

self_t abs ( ) const

inline

Element-wise absolute value.

Returns

A new vector x such that x[i] = abs(this[i]).

add() [1/3]

self_t add ( const self_t & v ) const

inlineinherited

Vector addition.

Parameters

v	Another vector.

Returns

A new vector x such that x[i] = this[i] + v[i].

add() [2/3]

self_t add ( const self_t & v ) const

inline

Vector addition.

Parameters

v	Another vector.

Returns

A new vector x such that x[i] = this[i] + v[i].

add() [3/3]

template<typename T>

Vec< T, 3 > add ( T dx, T dy, T dz ) const

inline

Returns

(dx, dy, dz) added with this

align()

template<typename T>

Vec< T, 3 > align ( const Vec< T, 3 > & from, const Vec< T, 3 > & to )

inline

Compute a transform aligning from with to and apply it to this.

angle_to() [1/2]

T angle_to ( const self_t & v ) const

inlineinherited

Angle between vectors.

Parameters

v	Another vector.

Returns

Angle in radians between this and v, between 0 and pi.

angle_to() [2/2]

T angle_to ( const self_t & v ) const

inline

Angle between vectors.

Parameters

v	Another vector.

Returns

Angle in radians between this and v, between 0 and pi.

begin() [1/2]

T * begin ( )

inline

Returns

A writeable iterator pointing at the first element.

begin() [2/2]

const T * begin ( ) const

inline

Returns

A read-only iterator pointing at the first element.

bounce_on() [1/2]

self_t bounce_on ( const self_t & normal ) const

inlineinherited

Elastic collision.

Treat this as a velocity vector or incident ray; this function returns the velocity reflected off of a surface with normal normal. Convenience for -reflect_about(normal).

Parameters

normal

Normal of surface to "bounce" on.

Returns

The "bounced" direction vector.

bounce_on() [2/2]

self_t bounce_on ( const self_t & normal ) const

inline

Elastic collision.

Treat this as a velocity vector or incident ray; this function returns the velocity reflected off of a surface with normal normal. Convenience for -reflect_about(normal).

Parameters

normal

Normal of surface to "bounce" on.

Returns

The "bounced" direction vector.

ceil()

self_t ceil ( ) const

inline

Element-wise ceiling function.

Returns

A new vector x such that x[i] = ceil(this[i]).

clamp() [1/2]

self_t clamp ( const self_t & lo, const self_t & hi ) const

inlineinherited

Element-wise clamp.

Parameters

lo	Element-wise lower extremes.
hi	Element-wise upper extremes.

Returns

A new vector such that each element x[i] is clamped between lo[i] and hi[i].

clamp() [2/2]

self_t clamp ( const self_t & lo, const self_t & hi ) const

inline

Element-wise clamp.

Parameters

lo	Element-wise lower extremes.
hi	Element-wise upper extremes.

Returns

A new vector such that each element x[i] is clamped between lo[i] and hi[i].

cross()

template<typename T>

Vec< T, 3 > cross ( Vec< T, 3 > v ) const

inline

Returns

Cross product of this by v, in the order shown.

dist() [1/2]

T dist ( const self_t & pt ) const

inlineinherited

Distance between points.

Parameters

pt	Another point.

Returns

The distance between this and pt.

dist() [2/2]

T dist ( const self_t & pt ) const

inline

Distance between points.

Parameters

pt	Another point.

Returns

The distance between this and pt.

dist2() [1/2]

T dist2 ( const self_t & pt ) const

inlineinherited

Distance squared to a point.

Parameters

pt	Another point.

Returns

The square of the distance between this and pt.

dist2() [2/2]

T dist2 ( const self_t & pt ) const

inline

Distance squared to a point.

Parameters

pt	Another point.

Returns

The square of the distance between this and pt.

dot() [1/3]

T dot ( const self_t & v ) const

inlineinherited

Dot product.

Parameters

v	Another vector.

Returns

The dot product of this with v.

dot() [2/3]

T dot ( const self_t & v ) const

inline

Dot product.

Parameters

v	Another vector.

Returns

The dot product of this with v.

dot() [3/3]

template<typename T>

T dot ( T xx, T yy, T zz ) const

inline

Returns

Dot product of this with the vector (xx, yy, zz)

end() [1/2]

T * end ( )

inline

Returns

A writeable iterator pointing just beyond the last element.

end() [2/2]

const T * end ( ) const

inline

Returns

A read-only iterator pointing just beyond the last element.

floor()

self_t floor ( ) const

inline

Element-wise floor function.

Returns

A new vector x such that x[i] = floor(this[i]).

fraction_on() [1/2]

T fraction_on ( const self_t & axis ) const

inlineinherited

Return the component of this that projects to axis, as a fraction of axis's length.

Parameters

axis	An arbitrary basis vector.

fraction_on() [2/2]

T fraction_on ( const self_t & axis ) const

inline

Return the component of this that projects to axis, as a fraction of axis's length.

Parameters

axis	An arbitrary basis vector.

from_spherical()

template<typename T>

static Vec< T, 3 > from_spherical ( T r, T elev, T azi )

inlinestatic

Construct a point from spherical coordinates (r, elevation, azimuth), to euclidean coordinates, where r is the radius, eleveation is the angle from the +z axis, and azimuth is the angle about z+ from the x+ axis.

Returns

A euclidean point constructed from spherical coordinates.

get() [1/2]

T & get ( index_t idx )

inline

Get the element at index idx.

Parameters

idx	Index of element.

Returns

A reference to the element at idx.

get() [2/2]

const T & get ( index_t idx ) const

inline

Get the element at index idx.

Parameters

idx	Index of element.

Returns

A const reference to the element at idx.

is_finite_real()

template<typename T>

bool is_finite_real ( ) const

inline

Returns

true if no elements are an infinity or NaN.

mag()

T mag ( ) const

inline

Euclidean norm (magnitude).

Returns

The Euclidean magnitude (geometric length) of this vector.

mag2()

T mag2 ( ) const

inline

Squared magnitude.

Returns

The square of the magnitude of this vector.

max() [1/3]

self_t max ( const self_t & v ) const

inlineinherited

Element-wise maximum of two Vecs.

Parameters

v	Another vector.

Returns

A new vector x such that x[i] = max(this[i], v[i]).

max() [2/3]

T max ( ) const

inline

Maximum element.

Returns

The value of the component with the highest value.

max() [3/3]

self_t max ( const self_t & v ) const

inline

Element-wise maximum of two Vecs.

Parameters

v	Another vector.

Returns

A new vector x such that x[i] = max(this[i], v[i]).

min() [1/3]

self_t min ( const self_t & v ) const

inlineinherited

Element-wise minimum of two Vecs.

Parameters

v	Another vector.

Returns

A new vector x such that x[i] = min(this[i], v[i]).

min() [2/3]

T min ( ) const

inline

Minimum element.

Returns

The value of the component with the lowest value.

min() [3/3]

self_t min ( const self_t & v ) const

inline

Element-wise minimum of two Vecs.

Parameters

v	Another vector.

Returns

A new vector x such that x[i] = min(this[i], v[i]).

mix() [1/2]

self_t mix ( const self_t & v, T mix ) const

inlineinherited

Linear interpolation.

A mix parameter of 0 evaluates to this, while 1 is v.

Parameters

v	Another vector.
mix	A mixing factor between 0 and 1.

Returns

A linear mixing of this with v.

mix() [2/2]

self_t mix ( const self_t & v, T mix ) const

inline

Linear interpolation.

A mix parameter of 0 evaluates to this, while 1 is v.

Parameters

v	Another vector.
mix	A mixing factor between 0 and 1.

Returns

A linear mixing of this with v.

operator Vec< U, N >()

operator Vec< U, N > ( ) const

inlineexplicit

Element typecast.

Returns

A new vector with all elements cast to type U.

operator!=() [1/2]

bool operator!= ( const self_t & vv ) const

inlineinherited

Inequality test.

Returns

true if any corresponding elements of this and vv are unequal, false otherwise.

operator!=() [2/2]

bool operator!= ( const self_t & vv ) const

inline

Inequality test.

Returns

true if any corresponding elements of this and vv are unequal, false otherwise.

operator-()

self_t operator- ( ) const

inline

Negation.

Returns

A copy of this vector with all elements negated (i.e. a vector pointing in the opposite direction).

operator==() [1/2]

bool operator== ( const self_t & vv ) const

inlineinherited

Equality test.

Returns

true if all corresponding elements of this and vv are equal, false otherwise.

operator==() [2/2]

bool operator== ( const self_t & vv ) const

inline

Equality test.

Returns

true if all corresponding elements of this and vv are equal, false otherwise.

operator[]() [1/2]

T & operator[] ( index_t idx )

inline

Vector element access.

Parameters

idx	Index of element to retrieve.

Returns

A reference to the element at index idx.

operator[]() [2/2]

const T & operator[] ( index_t idx ) const

inline

Vector element access.

Parameters

idx	Index of element to retrieve.

Returns

A read-only reference to the element at index idx.

project_on() [1/2]

self_t project_on ( const self_t & axis ) const

inlineinherited

Orthogonal projection to an axis.

Parameters

axis	A direction vector.

Returns

A vector in direction axis with magnitude equal to the component of this aligned with axis.

project_on() [2/2]

self_t project_on ( const self_t & axis ) const

inline

Orthogonal projection to an axis.

Parameters

axis	A direction vector.

Returns

A vector in direction axis with magnitude equal to the component of this aligned with axis.

reflect_about() [1/2]

self_t reflect_about ( self_t normal ) const

inlineinherited

Reflection about a normal.

Parameters

normal

Axis of reflection.

Returns

A copy of this vector reflected across the given axis.

reflect_about() [2/2]

self_t reflect_about ( self_t normal ) const

inline

Reflection about a normal.

Parameters

normal

Axis of reflection.

Returns

A copy of this vector reflected across the given axis.

reflected_x()

template<typename T>

Vec< T, 3 > reflected_x ( ) const

inline

Returns

A copy with the X component negated

reflected_y()

template<typename T>

Vec< T, 3 > reflected_y ( ) const

inline

Returns

A copy with the Y component negated

reflected_z()

template<typename T>

Vec< T, 3 > reflected_z ( ) const

inline

Returns

A copy with the Z component negated

resized()

PointType< T, M >::point_t resized ( ) const

inline

Resized copy of a vector.

Template Parameters

M	Dimension of new vector.

Returns

A new vector with size M. If M is larger than N, the new elements will be set to zero. If M is 1, then the return type is T.

rotate() [1/4]

template<typename T>

Vec< T, 3 > rotate ( T u, T v, T w, T a, T b, T c, T radians )

inline

Returns

A copy of this vector rotated by angle radians about the axis (u, v, w), and centerpoint (a, b, c).

rotate() [2/4]

template<typename T>

Vec< T, 3 > rotate ( T u, T v, T w, T radians ) const

inline

Returns

A copy of this vector rotated by angle radians about the axis (u, v, w).

rotate() [3/4]

template<typename T>

Vec< T, 3 > rotate ( Vec< T, 3 > axis, T radians ) const

inline

Returns

A copy of this vector rotated by angle radians about axis.

rotate() [4/4]

template<typename T>

Vec< T, 3 > rotate ( Vec< T, 3 > axis, Vec< T, 3 > center, T radians )

inline

Returns

A copy of this vector rotated by angle radians about rotation axis axis and centerpoint center.

scale() [1/4]

self_t scale ( const self_t & v ) const

inlineinherited

Element-wise multiplication.

Parameters

v	Another vector.

Returns

A new vector x such that x[i] = this[i] * v[i].

scale() [2/4]

self_t scale ( const self_t & v ) const

inline

Element-wise multiplication.

Parameters

v	Another vector.

Returns

A new vector x such that x[i] = this[i] * v[i].

scale() [3/4]

self_t scale ( T a ) const

inline

Scalar multiple.

Parameters

a	A constant scale factor.

Returns

A new vector x such that x[i] = this[i] * a.

scale() [4/4]

template<typename T>

Vec< T, 3 > scale ( T a, T b, T c ) const

inline

Returns

Element-wise scaled copy

sub() [1/3]

self_t sub ( const self_t & v ) const

inlineinherited

Vector subtraction.

Parameters

v	Another vector.

Returns

A new vector x such that x[i] = this[i] - v[i].

sub() [2/3]

self_t sub ( const self_t & v ) const

inline

Vector subtraction.

Parameters

v	Another vector.

Returns

A new vector x such that x[i] = this[i] - v[i].

sub() [3/3]

template<typename T>

Vec< T, 3 > sub ( T dx, T dy, T dz ) const

inline

Returns

(dx, dy, dz) subtracted from this

to_spherical()

template<typename T>

Vec< T, 3 > to_spherical ( ) const

inline

Convert this euclidean point to spherical coordinates (r, elevation, azimuth), with both angles in radians. Elevation is the angle from the +z axis in the range (0, pi), and azimuth is the angle about +z from the +x axis in the range (-pi, pi).

Returns

This euclidean point converted to spherical coordinates.

unit()

self_t unit ( ) const

inline

Vector normalization.

Returns

A copy of this vector with unit length.

with_length()

self_t with_length ( T mag ) const

inline

Compute a vector with the direction of this and a new magnitude mag.

If this is the zero vector, it will remain unchanged.

Friends And Related Symbol Documentation

abs() [1/2]

geom::Vec< T, N > abs ( const geom::Vec< T, N > & v )

related

Element-wise absolute value.

abs() [2/2]

geom::Vec< T, N > abs ( const geom::Vec< T, N > & v )

related

Element-wise absolute value.

ceil() [1/2]

geom::Vec< T, N > ceil ( const geom::Vec< T, N > & v )

related

Element-wise ceiling.

ceil() [2/2]

geom::Vec< T, N > ceil ( const geom::Vec< T, N > & v )

related

Element-wise ceiling.

cos() [1/2]

geom::Vec< T, N > cos ( const geom::Vec< T, N > & v )

related

Element-wise cosine.

cos() [2/2]

geom::Vec< T, N > cos ( const geom::Vec< T, N > & v )

related

Element-wise cosine.

exp() [1/2]

geom::Vec< T, N > exp ( const geom::Vec< T, N > & v )

related

Element-wise exponentiation (e^v_i).

exp() [2/2]

geom::Vec< T, N > exp ( const geom::Vec< T, N > & v )

related

Element-wise exponentiation (e^v_i).

floor() [1/2]

geom::Vec< T, N > floor ( const geom::Vec< T, N > & v )

related

Element-wise floor.

floor() [2/2]

geom::Vec< T, N > floor ( const geom::Vec< T, N > & v )

related

Element-wise floor.

log() [1/2]

geom::Vec< T, N > log ( const geom::Vec< T, N > & v )

related

Element-wise natural log.

log() [2/2]

geom::Vec< T, N > log ( const geom::Vec< T, N > & v )

related

Element-wise natural log.

max() [1/2]

geom::Vec< T, N > max ( const geom::Vec< T, N > & a, const geom::Vec< T, N > & b )

related

Element-wise maximum.

max() [2/2]

geom::Vec< T, N > max ( const geom::Vec< T, N > & a, const geom::Vec< T, N > & b )

related

Element-wise maximum.

min() [1/2]

geom::Vec< T, N > min ( const geom::Vec< T, N > & a, const geom::Vec< T, N > & b )

related

Element-wise minimum.

min() [2/2]

geom::Vec< T, N > min ( const geom::Vec< T, N > & a, const geom::Vec< T, N > & b )

related

Element-wise minimum.

operator*() [1/6]

const Vec< T, N > operator* ( const Vec< T, N > & a, const Vec< T, N > & b )

related

Element-wise vector multiplication

Parameters

a	A vector
b	A vector

Returns

A new vector x such that x[i] = a[i] * b[i]

operator*() [2/6]

const Vec< T, N > operator* ( const Vec< T, N > & a, const Vec< T, N > & b )

related

Element-wise vector multiplication

Parameters

a	A vector
b	A vector

Returns

A new vector x such that x[i] = a[i] * b[i]

operator*() [3/6]

Vec< T, N > operator* ( const Vec< T, N > & v, U d )

related

Vector-scalar multiplication

Parameters

v	A vector
d	Scalar value of type satisfying std::is_scalar

Returns

A new vector x such that x[i] = v[i] * d

operator*() [4/6]

Vec< T, N > operator* ( const Vec< T, N > & v, U d )

related

Vector-scalar multiplication

Parameters

v	A vector
d	Scalar value of type satisfying std::is_scalar

Returns

A new vector x such that x[i] = v[i] * d

operator*() [5/6]

Vec< T, N > operator* ( U d, const Vec< T, N > & v )

related

Vector-scalar multiplication

Parameters

d	Scalar value of type satisfying std::is_scalar
v	A vector

Returns

A new vector x such that x[i] = d * v[i]

operator*() [6/6]

Vec< T, N > operator* ( U d, const Vec< T, N > & v )

related

Vector-scalar multiplication

Parameters

d	Scalar value of type satisfying std::is_scalar
v	A vector

Returns

A new vector x such that x[i] = d * v[i]

operator/() [1/6]

const Vec< T, N > operator/ ( const Vec< T, N > & a, const Vec< T, N > & b )

related

Element-wise vector division

Parameters

a	A vector
b	A vector

Returns

A new vector x such that x[i] = a[i] / b[i]

operator/() [2/6]

const Vec< T, N > operator/ ( const Vec< T, N > & a, const Vec< T, N > & b )

related

Element-wise vector division

Parameters

a	A vector
b	A vector

Returns

A new vector x such that x[i] = a[i] / b[i]

operator/() [3/6]

Vec< T, N > operator/ ( const Vec< T, N > & v, U d )

related

Vector division by a scalar

Parameters

v	A vector
d	Scalar value

Returns

A new vector x such that x[i] = v[i] / d

operator/() [4/6]

Vec< T, N > operator/ ( const Vec< T, N > & v, U d )

related

Vector division by a scalar

Parameters

v	A vector
d	Scalar value

Returns

A new vector x such that x[i] = v[i] / d

operator/() [5/6]

Vec< T, N > operator/ ( const Vec< T, N > & v, U d )

related

Scalar division by a vector

Parameters

d	Scalar value
v	A vector

Returns

A new vector x such that x[i] = d / v[i]

operator/() [6/6]

Vec< T, N > operator/ ( const Vec< T, N > & v, U d )

related

Scalar division by a vector

Parameters

d	Scalar value
v	A vector

Returns

A new vector x such that x[i] = d / v[i]

sin() [1/2]

geom::Vec< T, N > sin ( const geom::Vec< T, N > & v )

related

Element-wise sine.

sin() [2/2]

geom::Vec< T, N > sin ( const geom::Vec< T, N > & v )

related

Element-wise sine.

sqrt() [1/2]

geom::Vec< T, N > sqrt ( const geom::Vec< T, N > & v )

related

Element-wise square root.

sqrt() [2/2]

geom::Vec< T, N > sqrt ( const geom::Vec< T, N > & v )

related

Element-wise square root.

tan() [1/2]

geom::Vec< T, N > tan ( const geom::Vec< T, N > & v )

related

Element-wise tangent.

tan() [2/2]

geom::Vec< T, N > tan ( const geom::Vec< T, N > & v )

related

Element-wise tangent.

---

The documentation for this class was generated from the following files:

• geomc/linalg/vecdetail/Vec3.h
• geomc/linalg/Vec.h
• geomc/linalg/vecdetail/VecStd.h