geomc 1.0
A c++ linear algebra template library
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Vec< T, N > Class Template Reference

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

#include <geomc/linalg/Vec.h>

Inheritance diagram for Vec< T, N >:
VecCommon< T, N, Vec< T, N > > VecBase< T, N > Dimensional< 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, Nself_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.
 
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.
 
dist (const self_t &pt) const
 Distance between points.
 
dist2 (const self_t &pt) const
 Distance squared to a point.
 
dot (const self_t &v) const
 Dot product.
 
T * end ()
 
const T * end () const
 
self_t floor () const
 Element-wise floor function.
 
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.
 
mag () const
 Euclidean norm (magnitude).
 
mag2 () const
 Squared magnitude.
 
max () const
 Maximum element.
 
self_t max (const self_t &v) const
 Element-wise maximum of two Vecs.
 
min () const
 Minimum element.
 
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.
 
 operator Vec< U, N > () const
 Element typecast.
 
bool operator!= (const self_t &vv) const
 Inequality test.
 
self_toperator*= (const self_t &vv)
 Element-wise multiplication and assignment.
 
self_toperator*= (T s)
 Scalar multiplication and assignment.
 
self_t operator+ (const self_t &v) const
 Element-wise addition.
 
self_toperator+= (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_toperator-= (const self_t &vv)
 Subtraction and assignment.
 
self_toperator/= (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.
 
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.
 
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

v [N]
 

Related Symbols

(Note that these are not member symbols.)

template<typename T, index_t N>
geom::Vec< T, Nabs (const geom::Vec< T, N > &v)
 
template<typename T, index_t N>
geom::Vec< T, Nceil (const geom::Vec< T, N > &v)
 
template<typename T, index_t N>
geom::Vec< T, Ncos (const geom::Vec< T, N > &v)
 
template<typename T, index_t N>
geom::Vec< T, Nexp (const geom::Vec< T, N > &v)
 
template<typename T, index_t N>
geom::Vec< T, Nfloor (const geom::Vec< T, N > &v)
 
template<typename T, index_t N>
geom::Vec< T, Nlog (const geom::Vec< T, N > &v)
 
template<typename T, index_t N>
geom::Vec< T, Nmax (const geom::Vec< T, N > &a, const geom::Vec< T, N > &b)
 
template<typename T, index_t N>
geom::Vec< T, Nmin (const geom::Vec< T, N > &a, const geom::Vec< T, N > &b)
 
template<typename T, index_t N>
const Vec< T, Noperator* (const Vec< T, N > &a, const Vec< T, N > &b)
 
template<typename T, index_t N, typename U>
Vec< T, Noperator* (const Vec< T, N > &v, U d)
 
template<typename T, index_t N, typename U>
Vec< T, Noperator* (U d, const Vec< T, N > &v)
 
template<typename T, index_t N>
const Vec< T, Noperator/ (const Vec< T, N > &a, const Vec< T, N > &b)
 
template<typename T, index_t N, typename U>
Vec< T, Noperator/ (const Vec< T, N > &v, U d)
 
template<typename T, index_t N, typename U>
Vec< T, Noperator/ (const Vec< T, N > &v, U d)
 
template<typename T, index_t N>
geom::Vec< T, Nsin (const geom::Vec< T, N > &v)
 
template<typename T, index_t N>
geom::Vec< T, Nsqrt (const geom::Vec< T, N > &v)
 
template<typename T, index_t N>
geom::Vec< T, Ntan (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
aScalar 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
aAn 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
vA vector of dimension N - 1
aThe 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_colA 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
itemsA 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
vAnother 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
vAnother 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
normalNormal 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
loElement-wise lower extremes.
hiElement-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
ptAnother point.
Returns
The distance between this and pt.

◆ dist2()

T dist2 ( const self_t & pt) const
inlineinherited

Distance squared to a point.

Parameters
ptAnother point.
Returns
The square of the distance between this and pt.

◆ dot()

T dot ( const self_t & v) const
inlineinherited

Dot product.

Parameters
vAnother 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
axisAn arbitrary basis vector.

◆ get() [1/2]

T & get ( index_t idx)
inlineinherited

Get the element at index idx.

Parameters
idxIndex 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
idxIndex 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
vAnother 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
vAnother 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
vAnother vector.
mixA 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
idxIndex 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
idxIndex 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
axisA 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
normalAxis 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
MDimension 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
vAnother 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
aA 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
vAnother 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)
related

Element-wise absolute value.

◆ ceil()

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

Element-wise ceiling.

◆ cos()

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

Element-wise cosine.

◆ exp()

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

Element-wise exponentiation (evi).

◆ floor()

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

Element-wise floor.

◆ log()

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

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 )
related

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 )
related

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 )
related

Element-wise vector multiplication

Parameters
aA vector
bA 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 )
related

Vector-scalar multiplication

Parameters
vA vector
dScalar 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 )
related

Vector-scalar multiplication

Parameters
dScalar value of type satisfying std::is_scalar
vA 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 )
related

Element-wise vector division

Parameters
aA vector
bA 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 )
related

Vector division by a scalar

Parameters
vA vector
dScalar 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 )
related

Scalar division by a vector

Parameters
dScalar value
vA 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)
related

Element-wise sine.

◆ sqrt()

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

Element-wise square root.

◆ tan()

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

Element-wise tangent.


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