A tuple of N elements of type T. More...

#include <geomc/linalg/Vec.h>

Inheritance diagram for Vec< T, N >:

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 ()

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

constexpr	Vec (const T a[N])

template<index_t... M> requires ((M + ...) == N) and (sizeof...(M) > 1)
constexpr	Vec (const Vec< T, M > &...vecs)
	Construct a new vector by concatenating two or more vectors.

template<typename U>
constexpr	Vec (const Vec< U, N-1 > &v, T a)

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

constexpr	Vec (T a)

self_t	abs () const
	Element-wise absolute value.

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

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.

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	ceil () const
	Element-wise ceiling function.

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

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

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 &	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.

T	max () const
	Maximum element.

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

T	min () const
	Minimum element.

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

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.

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 &vv)
	Element-wise addition and assignment.

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/= (T s)
	Scalar division and assignment.

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.

T	product () const
	Multiply all elements together.

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.

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 (T a) const
	Scalar multiple.

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.

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 self_t	zeros

Protected Attributes
T	v [N]

Related Symbols
(Note that these are not member symbols.)
template<typename T, index_t N>
geom::Vec< T, N >	abs (const geom::Vec< T, N > &v)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Detailed Description

template<typename T, index_t N>
class geom::Vec< T, N >

A tuple of N elements of type T.

Vectors are lightweight and generally perform as well as a bare array of their element type.

Geomc makes no type distinction between vectors, points, or normals; the distinction is to be made by the programmer based on usage.

Declaring a 3-dimensional vector of doubles:

Vec<double,3> v;

Basic arithmetic:

v3 = v1 + v2;   // addition
v3 = v1 - v2;   // subtraction
v3 = -v1;       // negation
v3 = 2.71 * v1; // scalar mult
v3 = 1.61 / v1; // scalar div
v3 = v1 / 1.41; // scalar div

Element-wise multiplication / division:

v3 = v1 * v2;
v3 = v2 / v1;

Element access:

double z = v[2];
z = v.get(2);

Access to / iteration over internal array:

for (double *p = v.begin(); p != v.end(); p++) {
    double a = f(*p, ...);
}

Cross product (3D only):

v3 = v1 ^ v2;

Compatibility with std:

// element-wise operations
std::min(v1, v2);
std::max(v1, v2);
std::abs(v1);
std::floor(v1);
std::ceil(v1);

Resizing:

Vec<double,3> v3d;
Vec<double,2> v2d = v3d.resized<2>(); // truncate the last coordinate
Vec<double,4> v4d = v3d.resized<4>(); // last coordinate is zero

Member Typedef Documentation

◆ point_t

using point_t

inherited

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]

template<typename T, index_t N>

Vec ( )

inlineconstexpr

Construct a new vector with all elements set to zero.

◆ Vec() [2/6]

template<typename T, index_t N>

Vec ( T a )

inlineconstexpr

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

Parameters

a	Scalar value

◆ Vec() [3/6]

template<typename T, index_t N>

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]

template<typename T, index_t N>

template<typename U>

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]

template<typename T, index_t N>

template<typename Mx, typename Ref>

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]

template<typename T, index_t N>

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

inlineinherited

Element-wise absolute value.

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

◆ add()

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].

◆ 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()

T dot ( const self_t & v ) const

inlineinherited

Dot product.

Parameters

v	Another vector.

Returns: The dot product of this with v.

◆ 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() [1/2]

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() [2/2]

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.

◆ sub()

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].

◆ 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.

Friends And Related Symbol Documentation

◆ abs()

template<typename T, index_t N>

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

Element-wise absolute value.

◆ ceil()

template<typename T, index_t N>

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

Element-wise ceiling.

◆ cos()

template<typename T, index_t N>

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

Element-wise cosine.

◆ exp()

template<typename T, index_t N>

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

Element-wise exponentiation (e^v_i).

◆ floor()

template<typename T, index_t N>

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

Element-wise floor.

◆ log()

template<typename T, index_t N>

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

Element-wise natural log.

◆ max()

template<typename T, index_t N>

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

Element-wise maximum.

◆ min()

template<typename T, index_t N>

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

Element-wise minimum.

◆ operator*() [1/3]

template<typename T, index_t N>

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]

template<typename T, index_t N, typename U>

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]

template<typename T, index_t N, typename U>

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]

template<typename T, index_t N>

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]

template<typename T, index_t N, typename U>

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

◆ operator/() [3/3]

template<typename T, index_t N, typename U>

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]

◆ sin()

template<typename T, index_t N>

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

Element-wise sine.

◆ sqrt()

template<typename T, index_t N>

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

Element-wise square root.

◆ tan()

template<typename T, index_t N>

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/LinalgTypes.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

Constructor & Destructor Documentation

◆ Vec() [1/6]

◆ Vec() [2/6]

◆ Vec() [3/6]

◆ Vec() [4/6]

◆ Vec() [5/6]

◆ Vec() [6/6]

Member Function Documentation

◆ abs()

◆ add()

◆ angle_to()

◆ begin() [1/2]

◆ begin() [2/2]

◆ bounce_on()

◆ ceil()

◆ clamp()

◆ dist()

◆ dist2()

◆ dot()

◆ 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() [1/2]

◆ scale() [2/2]

◆ sub()

◆ 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()

◆ tan()