2D specialization of vector class. More...

#include <geomc/linalg/vecdetail/Vec2.h>

Inheritance diagram for Vec< T, 2 >:

Public Types
typedef Vec< T, 2 >	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 both elements set to 0.

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

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

constexpr	Vec (const T v[2])
	Construct a vector with elements copied from the 2-element array `v`.

Vec< T, 2 >	add (T dx, T dy) const
	Addition. Convenience function with separate args for `x` and `y`.

Vec< T, 2 >	sub (T dx, T dy) const
	Subtraction. Convenience function with separate args for `x` and `y`.

Vec< T, 2 >	scale (T sx, T sy) const
	Scalar multiplication. Convenience function with separate args for `x` and `y`.

T	dot (T x1, T y1) const
	Dot product with the vector `(x1, y1)`.

Vec< T, 2 >	reflected_x () const

Vec< T, 2 >	reflected_y () const

bool	is_finite_real () const

Vec< T, 2 >	left_perpendicular () const

Vec< T, 2 >	right_perpendicular () const

Vec< T, 2 >	rotate (T radians) const

Vec< T, 2 >	rotate (Vec< T, 2 > center, T radians) const

Vec< T, 2 >	to_polar () const

Vec< T, 2 >	from_polar () const

T	get_angle () 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, 2 >	X_AXIS = Vec<T,2>(1,0)
	(1, 0) vector constant

static const Vec< T, 2 >	Y_AXIS = Vec<T,2>(0,1)
	(0, 1) vector 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, 2 >

2D specialization of vector class.

Vec<T,2>'s elements may be accessed under these equivalent naming schemes:

v.{x,y}     // conventional Euclidean coordinate names
v.{s,t}     // conventional parameterization coordinate names
v.{row,col} // matrix coordinate names

with the latter scheme intended for use as matrix coordinates. x, s, and row all refer to the same element.

Take special note that, in accordance with convention, row refers to the vertical position of a matrix element, despite being the first coordinate. This means that row, a vertical coordinate, aliases x, a traditionally horizontal coordinate. For this reason it is inadviseable to interchange usage of the "matrix coordinate" and "Euclidean" naming schemes.

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.

◆ from_polar()

Vec< T, 2 > from_polar ( ) const

inline

Returns: The cartesian (x, y) coordinates of this point interpreted as polar coordinates, with this[0] = r and this[1] = radians.

◆ 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.

◆ get_angle()

T get_angle ( ) const

inline

Returns: The angle in radians to this vector from the x-axis, between 0 and 2 * pi.

◆ is_finite_real()

bool is_finite_real ( ) const

inline

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

◆ left_perpendicular()

Vec< T, 2 > left_perpendicular ( ) const

inline

Returns: A vector perpendicular to this, created by a rotation of 90 degrees counterclockwise.

◆ 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, 2 > reflected_x ( ) const

inline

Returns: A new vector with the X component reflected.

◆ reflected_y()

Vec< T, 2 > reflected_y ( ) const

inline

Returns: A new vector with the Y component reflected.

◆ 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.

◆ right_perpendicular()

Vec< T, 2 > right_perpendicular ( ) const

inline

Returns: A vector perpendicular to this, created by a rotation of 90 degrees clockwise.

◆ rotate() [1/2]

Vec< T, 2 > rotate ( T radians ) const

inline

Returns: A vector rotated counterclockwise by the angle radians.

Parameters

radians Rotation angle in radians

◆ rotate() [2/2]

Vec< T, 2 > rotate	(	Vec< T, 2 >	center,
		T	radians
	)		const

inline

Returns: A vector rotated counterclockwise by the angle radians about the point center.

Parameters

center	Center of rotation.
radians	Angle of rotation.

◆ 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].

◆ to_polar()

Vec< T, 2 > to_polar ( ) const

inline

Returns: The polar coordinates (r, angle) for this cartesian point, with angle in radians.

◆ 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/Vec2.h

Public Types

Public Member Functions

Static Public Attributes

Protected Attributes

Detailed Description

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()

◆ from_polar()

◆ get() [1/2]

◆ get() [2/2]

◆ get_angle()

◆ is_finite_real()

◆ left_perpendicular()

◆ 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()

◆ resized()

◆ right_perpendicular()

◆ rotate() [1/2]

◆ rotate() [2/2]

◆ scale() [1/2]

◆ scale() [2/2]

◆ sub()

◆ to_polar()

◆ unit()

◆ with_length()