4D specialization of vector class. More...

#include <geomc/linalg/vecdetail/Vec4.h>

Inheritance diagram for Vec< T, 4 >:

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 ()
	Construct vector with all elements set to 0.
constexpr	Vec (const T v[4])
	Construct a vector with elements copied from the 4-element array v.
constexpr	Vec (T a)
	Construct a vector with all elements set to a.
constexpr	Vec (T x, T y, T z, T w)
	Construct a vector with elements (x, y, z, w).
template<typename U>
constexpr	Vec (Vec< U, 2 > xy, T z, T w)
template<typename U>
constexpr	Vec (Vec< U, 3 > xyz, T w)
	Construct a vector with (x, y, z) taken from the 3D vector xyz, and w 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, 4 >	add (T dx, T dy, T dz, T dw) 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.
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.
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, T ww) 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_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.
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.
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=** (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 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.
const T &	operator[] (index_t idx) const
	Vector element access.
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.
PointType< T, M >::point_t	resized () const
	Resized copy of a vector.
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.
Vec< T, 4 >	scale (T a, T b, T c, T d) 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, 4 >	sub (T dx, T dy, T dz, T dw) const
T	sum () const
	Sum the elements of the vector.
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 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, 4 >	W_AXIS
	(0, 0, 0, 1) constant
static const Vec< T, 4 >	X_AXIS
	(1, 0, 0, 0) constant
static const Vec< T, 4 >	Y_AXIS
	(0, 1, 0, 0) constant
static const Vec< T, 4 >	Z_AXIS
	(0, 0, 1, 0) 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 >	ceil (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 >	floor (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 >	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)
Vec< T, N >	operator* (const Vec< T, N > &v, U d)
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)
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 >	sqrt (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, 4 >

4D specialization of vector class.

Vec<T,4>'s elements may be accessed under these equivalent naming schemes:

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

with x, s, and r all referring 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.

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, 4 > add	(	T	dx,
		T	dy,
		T	dz,
		T	dw ) const

inline

Returns: (dx, dy, dz, dw) added with 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].

◆ 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,
		T	ww ) const

inline

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

◆ 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.

◆ 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.

◆ 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() [1/2]

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() [2/2]

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() [1/2]

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() [2/2]

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==() [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[]()

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.

◆ 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.

◆ scale() [1/3]

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() [2/3]

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() [3/3]

template<typename T>

Vec< T, 4 > scale	(	T	a,
		T	b,
		T	c,
		T	d ) 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, 4 > sub	(	T	dx,
		T	dy,
		T	dz,
		T	dw ) const

inline

Returns: (dx, dy, dz, dw) subtracted from this

◆ 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.

◆ abs()

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

Element-wise absolute value.

◆ ceil()

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

Element-wise ceiling.

◆ cos()

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

Element-wise cosine.

◆ exp()

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

Element-wise exponentiation (e^v_i).

◆ floor()

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

Element-wise floor.

◆ log()

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

Element-wise natural log.

◆ max()

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

Element-wise maximum.

◆ min()

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

Element-wise minimum.

◆ operator*() [1/3]

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

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*() [2/3]

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

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*() [3/3]

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

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/() [1/3]

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

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/() [2/3]

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

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/() [3/3]

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

Vector division by a scalar

Parameters

v	A vector
d	Scalar value

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

◆ sin()

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

Element-wise sine.

◆ sqrt()

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

Element-wise square root.

◆ tan()

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

Element-wise tangent.

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

geomc/linalg/vecdetail/Vec4.h
geomc/linalg/Vec.h
geomc/linalg/vecdetail/VecStd.h

Public Types

Public Member Functions

Static Public Attributes

Protected Attributes

Related Symbols

Detailed Description

Member Typedef Documentation

◆ point_t

Member Function Documentation

◆ abs()

◆ add() [1/3]

◆ add() [2/3]

◆ add() [3/3]

◆ angle_to() [1/2]

◆ angle_to() [2/2]

◆ begin() [1/2]

◆ begin() [2/2]

◆ bounce_on() [1/2]

◆ bounce_on() [2/2]

◆ ceil()

◆ clamp() [1/2]

◆ clamp() [2/2]

◆ dist() [1/2]

◆ dist() [2/2]

◆ dist2() [1/2]

◆ dist2() [2/2]

◆ dot() [1/3]

◆ dot() [2/3]

◆ dot() [3/3]

◆ end() [1/2]

◆ end() [2/2]

◆ floor()

◆ fraction_on() [1/2]

◆ fraction_on() [2/2]

◆ get() [1/2]

◆ get() [2/2]

◆ mag()

◆ mag2()

◆ max() [1/2]

◆ max() [2/2]

◆ min() [1/2]

◆ min() [2/2]

◆ mix() [1/2]

◆ mix() [2/2]

◆ operator Vec< U, N >()

◆ operator!=() [1/2]

◆ operator!=() [2/2]

◆ operator==() [1/2]

◆ operator==() [2/2]

◆ operator[]()

◆ project_on() [1/2]

◆ project_on() [2/2]

◆ reflect_about() [1/2]

◆ reflect_about() [2/2]

◆ resized()

◆ scale() [1/3]

◆ scale() [2/3]

◆ scale() [3/3]

◆ sub() [1/3]

◆ sub() [2/3]

◆ sub() [3/3]

◆ unit()

◆ with_length()

Friends And Related Symbol Documentation

◆ abs()

◆ ceil()

◆ cos()

◆ exp()

◆ floor()

◆ log()

◆ max()

◆ min()

◆ operator*() [1/3]

◆ operator*() [2/3]

◆ operator*() [3/3]

◆ operator/() [1/3]

◆ operator/() [2/3]

◆ operator/() [3/3]

◆ sin()

◆ sqrt()