4D specialization of vector class. More...

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

Inheritance diagram for Vec< T, 4 >:

Public Types
typedef Vec< T, 4 >	self_t
	Self type. I.e., `Vec<T,N>` if a vector, `Quat<T>` if a quaternion.

typedef T	elem_t
	Element type.

Public Member Functions
constexpr	Vec ()
	Construct vector with all elements set to 0.

constexpr	Vec (T x, T y, T z, T w)
	Construct a vector with elements `(x, y, z, w)`.

constexpr	Vec (const T v[4])
	Construct a vector with elements copied from the 4-element array `v`.

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.

constexpr	Vec (T a)
	Construct a vector with all elements set to `a`.

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

Vec< T, 4 >	sub (T dx, T dy, T dz, T dw) const

Vec< T, 4 >	scale (T a, T b, T c, T d) const

T	dot (T xx, T yy, T zz, T ww) const

const T &	operator[] (index_t idx) const
	Vector element access. More...

T &	operator[] (index_t idx)
	Vector element access. More...

	operator Vec< U, N > () const
	Element typecast. More...

bool	operator== (const self_t &vv) const
	Equality test. More...

bool	operator!= (const self_t &vv) const
	Inequality test. More...

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 &v) const
	Element-wise subtraction.

self_t	operator- () const
	Negation. More...

self_t &	operator-= (const self_t &vv)
	Subtraction and assignment.

self_t &	*operator=** (T s)
	Scalar multiplication and assignment.

self_t &	*operator=** (const self_t &vv)
	Element-wise multiplication and assignment.

self_t &	operator/= (T s)
	Scalar division and assignment.

self_t	add (const self_t &v) const
	Vector addition. More...

self_t	sub (const self_t &v) const
	Vector subtraction. More...

self_t	scale (const self_t &v) const
	Element-wise multiplication. More...

self_t	scale (T a) const
	Scalar multiple. More...

self_t	unit () const
	Vector normalization. More...

T	dot (const self_t &v) const
	Dot product. More...

T	mag () const
	Euclidean norm (magnitude). More...

T	mag2 () const
	Squared magnitude. More...

T	dist (const self_t &pt) const
	Distance between points. More...

T	dist2 (const self_t &pt) const
	Distance squared to a point. More...

self_t	reflect_about (self_t normal) const
	Reflection about a normal. More...

self_t	bounce_on (const self_t &normal) const
	Elastic collision. More...

self_t	project_on (const self_t &axis) const
	Orthogonal projection to an axis. More...

T	fraction_on (const self_t &axis) const
	Return the component of `this` that projects to `axis`, as a fraction of axis's length. More...

self_t	with_length (T mag) const
	Compute a vector with the direction of `this` and a new magnitude `mag`. More...

self_t	mix (const self_t &v, T mix) const
	Linear interpolation. More...

T	angle_to (const self_t &v) const
	Angle between vectors. More...

self_t	abs () const
	Element-wise absolute value. More...

self_t	floor () const
	Element-wise floor function. More...

self_t	ceil () const
	Element-wise ceiling function. More...

self_t	min (const self_t &v) const
	Element-wise minimum of two `Vec`s. More...

T	min () const
	Minimum element. More...

self_t	max (const self_t &v) const
	Element-wise maximum of two `Vec`s. More...

T	max () const
	Maximum element. More...

self_t	clamp (const self_t &lo, const self_t &hi) const
	Element-wise clamp. More...

self_t	round () const
	Round each element to the nearest integer.

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.

PointType< T, M >::point_t	resized () const
	Resized copy of a vector. More...

bool	is_zero () const
	Return `true` if all elements are zero.

index_t	size () const
	The number of elements in this vector. Always equal to `N`.

const T &	get (index_t idx) const

T &	get (index_t idx)

const T *	begin () const

T *	begin ()

const T *	end () const

T *	end ()

Static Public Attributes
static const Vec< T, 4 >	X_AXIS = Vec<T,4>(1,0,0,0)
	(1, 0, 0, 0) constant

static const Vec< T, 4 >	Y_AXIS = Vec<T,4>(0,1,0,0)
	(0, 1, 0, 0) constant

static const Vec< T, 4 >	Z_AXIS = Vec<T,4>(0,0,1,0)
	(0, 0, 1, 0) constant

static const Vec< T, 4 >	W_AXIS = Vec<T,4>(0,0,0,1)
	(0, 0, 0, 1) constant

static constexpr index_t	DIM
	Vector dimension.

static const self_t	ones

static const self_t	zeros

Protected Attributes
T	v [N]

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 Function Documentation

◆ abs()

self_t abs ( ) const

inlineinherited

Element-wise absolute value.

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

◆ add() [1/2]

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() [2/2]

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

inline

Returns: (dx, dy, dz, dw) added with this

◆ angle_to()

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.

◆ begin() [1/2]

T * begin ( )

inlineinherited

Returns: A writeable iterator pointing at the first element.

◆ begin() [2/2]

const T * begin ( ) const

inlineinherited

Returns: A read-only iterator pointing at the first element.

◆ bounce_on()

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.

◆ ceil()

self_t ceil ( ) const

inlineinherited

Element-wise ceiling function.

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

◆ clamp()

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].

◆ dist()

T dist ( const self_t & pt ) const

inlineinherited

Distance between points.

Parameters

pt	Another point.

Returns: The distance between this and pt.

◆ dist2()

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.

◆ dot() [1/2]

T dot ( const self_t & v ) const

inlineinherited

Dot product.

Parameters

v	Another vector.

Returns: The dot product of this with v.

◆ dot() [2/2]

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 ( )

inlineinherited

Returns: A writeable iterator pointing just beyond the last element.

◆ end() [2/2]

const T * end ( ) const

inlineinherited

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

◆ floor()

self_t floor ( ) const

inlineinherited

Element-wise floor function.

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

◆ fraction_on()

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.

◆ get() [1/2]

T & get ( index_t idx )

inlineinherited

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

inlineinherited

Get the element at index idx.

Parameters

idx	Index of element.

Returns: A const reference to the element at idx.

◆ mag()

T mag ( ) const

inlineinherited

Euclidean norm (magnitude).

Returns: The Euclidean magnitude (geometric length) of this vector.

◆ mag2()

T mag2 ( ) const

inlineinherited

Squared magnitude.

Returns: The square of the magnitude of this vector.

◆ max() [1/2]

T max ( ) const

inlineinherited

Maximum element.

Returns: The value of the component with the highest value.

◆ max() [2/2]

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]).

◆ min() [1/2]

T min ( ) const

inlineinherited

Minimum element.

Returns: The value of the component with the lowest value.

◆ min() [2/2]

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]).

◆ mix()

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.

◆ operator Vec< U, N >()

operator Vec< U, N > ( ) const

inlineexplicitinherited

Element typecast.

Returns: A new vector with all elements cast to type U.

◆ operator!=()

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-()

self_t operator- ( ) const

inlineinherited

Negation.

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

◆ operator==()

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[]() [1/2]

T & operator[] ( index_t idx )

inlineinherited

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

inlineinherited

Vector element access.

Parameters

idx	Index of element to retrieve.

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

◆ project_on()

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.

◆ reflect_about()

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.

◆ resized()

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

inlineinherited

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 ( T a ) const

inlineinherited

Scalar multiple.

Parameters

a	A constant scale factor.

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

◆ scale() [3/3]

Vec< T, 4 > scale	(	T	a,
		T	b,
		T	c,
		T	d
	)		const

inline

Returns: Element-wise scaled copy

◆ sub() [1/2]

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() [2/2]

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

inlineinherited

Vector normalization.

Returns: A copy of this vector with unit length.

◆ with_length()

self_t with_length ( T mag ) const

inlineinherited

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

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

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

geomc/linalg/vecdetail/Vec4.h

Public Types

Public Member Functions

Static Public Attributes

Protected Attributes

Detailed Description

Member Function Documentation

◆ abs()

◆ add() [1/2]

◆ add() [2/2]

◆ angle_to()

◆ begin() [1/2]

◆ begin() [2/2]

◆ bounce_on()

◆ ceil()

◆ clamp()

◆ dist()

◆ dist2()

◆ dot() [1/2]

◆ dot() [2/2]

◆ end() [1/2]

◆ end() [2/2]

◆ floor()

◆ fraction_on()

◆ get() [1/2]

◆ get() [2/2]

◆ mag()

◆ mag2()

◆ max() [1/2]

◆ max() [2/2]

◆ min() [1/2]

◆ min() [2/2]

◆ mix()

◆ operator Vec< U, N >()

◆ operator!=()

◆ operator-()

◆ operator==()

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ project_on()

◆ reflect_about()

◆ resized()

◆ scale() [1/3]

◆ scale() [2/3]

◆ scale() [3/3]

◆ sub() [1/2]

◆ sub() [2/2]

◆ unit()

◆ with_length()