3D specialization of vector class. More...

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

Inheritance diagram for Vec< T, 3 >:

Public Types
typedef Vec< T, 3 >	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.

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.

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

constexpr	Vec (const T v[3])
	Construct a vector with elements copied from the 3-element array `v`.

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

Vec< T, 3 >	operator^ (Vec< T, 3 > v) const
	Vector cross product.

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

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

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

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

Vec< T, 3 >	reflected_x () const

Vec< T, 3 >	reflected_y () const

Vec< T, 3 >	reflected_z () const

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

Vec< T, 3 >	to_spherical () const

Vec< T, 3 >	from_spherical () const

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

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

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

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

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

bool	is_finite_real () 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, 3 >	X_AXIS = Vec<T,3>(1,0,0)
	(1, 0, 0) constant

static const Vec< T, 3 >	Y_AXIS = Vec<T,3>(0,1,0)
	(0, 1, 0) constant

static const Vec< T, 3 >	Z_AXIS = Vec<T,3>(0,0,1)
	(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, 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 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, 3 > add	(	T	dx,
		T	dy,
		T	dz
	)		const

inline

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

◆ align()

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()

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].

◆ cross()

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

inline

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

◆ 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
	)		const

inline

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

◆ 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.

◆ from_spherical()

Vec< T, 3 > from_spherical ( ) const

inline

Convert this point, interpreted as spherical coordinates (r, elevation, azimuth), to euclidean coordinates, where r (this[0]) is the radius, eleveation (this[1]) is the angle from the +z axis, and azimuth (this[2]) is the angle about z+ from the x+ axis.

Returns: This point described by this vector interpreted as spherical coordinates as (x, y, z) euclidean coordinates.

◆ 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.

◆ is_finite_real()

bool is_finite_real ( ) const

inline

Returns: true if no elements are an infinity or NaN.

◆ 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.

◆ reflected_x()

Vec< T, 3 > reflected_x ( ) const

inline

Returns: A copy with the X component negated

◆ reflected_y()

Vec< T, 3 > reflected_y ( ) const

inline

Returns: A copy with the Y component negated

◆ reflected_z()

Vec< T, 3 > reflected_z ( ) const

inline

Returns: A copy with the Z component negated

◆ 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.

◆ rotate() [1/4]

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]

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]

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]

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() [1/3]

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, 3 > scale	(	T	a,
		T	b,
		T	c
	)		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, 3 > sub	(	T	dx,
		T	dy,
		T	dz
	)		const

inline

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

◆ to_spherical()

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

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/Vec3.h

Public Types

Public Member Functions

Static Public Attributes

Protected Attributes

Detailed Description

Member Function Documentation

◆ abs()

◆ add() [1/2]

◆ add() [2/2]

◆ align()

◆ angle_to()

◆ begin() [1/2]

◆ begin() [2/2]

◆ bounce_on()

◆ ceil()

◆ clamp()

◆ cross()

◆ dist()

◆ dist2()

◆ dot() [1/2]

◆ dot() [2/2]

◆ end() [1/2]

◆ end() [2/2]

◆ floor()

◆ fraction_on()

◆ from_spherical()

◆ get() [1/2]

◆ get() [2/2]

◆ is_finite_real()

◆ 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()

◆ reflected_x()

◆ reflected_y()

◆ reflected_z()

◆ resized()

◆ rotate() [1/4]

◆ rotate() [2/4]

◆ rotate() [3/4]

◆ rotate() [4/4]

◆ scale() [1/3]

◆ scale() [2/3]

◆ scale() [3/3]

◆ sub() [1/2]

◆ sub() [2/2]

◆ to_spherical()

◆ unit()

◆ with_length()