Vec3t< T > Union Template Reference

#include <Vec3.h>

Public Member Functions
	Vec3t ()
	Default-construct to (0,0,0).
	Vec3t (T x, T y, T z)
	Construct from three component values.
	Vec3t (const Vec3t &other)
	Copy-construct from the same type.
	Vec3t (const Vec2t< T > &other, T z)
	Construct from a 2D vector and a z value.
template<typename U>
	Vec3t (const Vec3t< U > &other)
	Explicitly convert from another Vec3t with different component type.
template<typename U>
	Vec3t (const Vec2t< U > &other, T z)
	Explicitly convert from a 2D vector of a different type and a z value.
const std::string	toString () const
	String representation "[x, y, z]".
Vec3t	operator+ (const Vec3t &val) const
	Component-wise addition.
Vec3t	operator- (const Vec3t &val) const
	Component-wise subtraction.
Vec3t	operator* (const Vec3t &val) const
	Component-wise multiplication.
Vec3t	operator/ (const Vec3t &val) const
	Component-wise division.
Vec3t	operator* (const T &val) const
	Scalar multiplication.
Vec3t	operator/ (const T &val) const
	Scalar division.
Vec3t	operator+ (const T &val) const
	Add scalar to all components.
Vec3t	operator- (const T &val) const
	Subtract scalar from all components.
bool	operator== (const Vec3t &other) const
	Equality comparison (component-wise equality).
bool	operator!= (const Vec3t &other) const
	Inequality comparison (component-wise inequality).
T	length () const
	Euclidean length (magnitude).
T	sqlength () const
	Squared length (avoids sqrt).
	operator T* (void)
	Implicit pointer conversion to raw component storage.
	operator const T * (void) const
	Implicit pointer conversion to raw component storage (const).

Static Public Member Functions
static float	dot (const Vec3t &a, const Vec3t &b)
	Dot product of two vectors.
static Vec3t	cross (const Vec3t &a, const Vec3t &b)
	Cross product of two vectors.
static Vec3t	normalize (const Vec3t &a)
	Return the normalized (unit-length) version of a vector.
static Vec3t	reflect (const Vec3t &a, const Vec3t &n)
	Reflect a vector about a unit normal.
static std::optional< Vec3t >	refract (const Vec3t &a, const Vec3t &normal, const T IOR)
	Refract a vector through a surface with index-of-refraction ratio.
static Vec3t	minV (const Vec3t &a, const Vec3t &b)
	Component-wise minimum of two vectors.
static Vec3t	maxV (const Vec3t &a, const Vec3t &b)
	Component-wise maximum of two vectors.
static Vec3t< float >	random ()
	Create a vector with components sampled from [0,1).
static Vec3t< float >	randomPointInSphere ()
	Uniform random point inside the unit sphere.
static Vec3t< float >	randomPointInHemisphere ()
	Uniform random point inside the upper unit hemisphere (z>=0).
static Vec3t< float >	randomPointInDisc ()
	Uniform random point inside the unit disc on the xy-plane.
static Vec3t< float >	randomUnitVector ()
	Uniform random unit vector on the sphere.
static Vec3t< float >	clamp (const Vec3t &val, float minVal, float maxVal)
	Clamp each component to [minVal, maxVal].

Public Attributes
std::array< T, 3 >	e
	Component storage and named aliases.
struct {
T   x
T   y
T   z
};
	Cartesian aliases for components.
struct {
T   r
T   g
T   b
};
	Color aliases for components.
Vec2t< T >	xy
	2D view of the first two components.

Constructor & Destructor Documentation

Vec3t() [1/6]

template<typename T>

Vec3t< T >::Vec3t ( )

inline

Default-construct to (0,0,0).

Vec3t() [2/6]

template<typename T>

Vec3t< T >::Vec3t ( T x, T y, T z )

inline

Construct from three component values.

Parameters

x	First component.
y	Second component.
z	Third component.

Vec3t() [3/6]

template<typename T>

Vec3t< T >::Vec3t ( const Vec3t< T > & other )

inline

Copy-construct from the same type.

Parameters

other

Source vector to copy.

Vec3t() [4/6]

template<typename T>

Vec3t< T >::Vec3t ( const Vec2t< T > & other, T z )

inline

Construct from a 2D vector and a z value.

Parameters

other	Source 2D vector for x and y.
z	Third component.

Vec3t() [5/6]

template<typename T>

template<typename U>

Vec3t< T >::Vec3t ( const Vec3t< U > & other )

inlineexplicit

Explicitly convert from another Vec3t with different component type.

Template Parameters

U	Source component type.

Parameters

other

Source vector to convert from.

Vec3t() [6/6]

template<typename T>

template<typename U>

Vec3t< T >::Vec3t ( const Vec2t< U > & other, T z )

inlineexplicit

Explicitly convert from a 2D vector of a different type and a z value.

Template Parameters

U	Source component type.

Parameters

other	Source 2D vector for x and y.
z	Third component.

Member Function Documentation

clamp()

template<typename T>

Vec3t< float > Vec3t< T >::clamp ( const Vec3t< T > & val, float minVal, float maxVal )

inlinestatic

Clamp each component to [minVal, maxVal].

Parameters

val	Input vector.
minVal	Lower bound.
maxVal	Upper bound.

Returns

New vector with components clamped to the given range.

cross()

template<typename T>

Vec3t Vec3t< T >::cross ( const Vec3t< T > & a, const Vec3t< T > & b )

inlinestatic

Cross product of two vectors.

Parameters

a	First vector.
b	Second vector.

Returns

a × b.

Here is the caller graph for this function:

dot()

template<typename T>

float Vec3t< T >::dot ( const Vec3t< T > & a, const Vec3t< T > & b )

inlinestatic

Dot product of two vectors.

Parameters

a	First vector.
b	Second vector.

Returns

a·b.

Here is the caller graph for this function:

length()

template<typename T>

T Vec3t< T >::length ( ) const

inline

Euclidean length (magnitude).

Returns

sqrt(x*x + y*y + z*z).

Here is the caller graph for this function:

maxV()

template<typename T>

Vec3t Vec3t< T >::maxV ( const Vec3t< T > & a, const Vec3t< T > & b )

inlinestatic

Component-wise maximum of two vectors.

Parameters

a	First vector.
b	Second vector.

Returns

{max(a.x,b.x), max(a.y,b.y), max(a.z,b.z)}.

minV()

template<typename T>

Vec3t Vec3t< T >::minV ( const Vec3t< T > & a, const Vec3t< T > & b )

inlinestatic

Component-wise minimum of two vectors.

Parameters

a	First vector.
b	Second vector.

Returns

{min(a.x,b.x), min(a.y,b.y), min(a.z,b.z)}.

normalize()

template<typename T>

Vec3t Vec3t< T >::normalize ( const Vec3t< T > & a )

inlinestatic

Return the normalized (unit-length) version of a vector.

Parameters

a	Input vector.

Returns

a / |a| if |a| != 0, otherwise (0,0,0).

Here is the caller graph for this function:

operator const T *()

template<typename T>

Vec3t< T >::operator const T * ( void ) const

inline

Implicit pointer conversion to raw component storage (const).

Returns

Pointer to first component (const overload).

operator T*()

template<typename T>

Vec3t< T >::operator T* ( void )

inline

Implicit pointer conversion to raw component storage.

Returns

Pointer to first component (non-const overload).

Warning

Raw pointer exposes internal layout; use with care.

operator!=()

template<typename T>

bool Vec3t< T >::operator!= ( const Vec3t< T > & other ) const

inline

Inequality comparison (component-wise inequality).

Parameters

other

Vector to compare against.

Returns

True if any component differs.

operator*() [1/2]

template<typename T>

Vec3t Vec3t< T >::operator* ( const T & val ) const

inline

Scalar multiplication.

Parameters

val	Scalar factor.

Returns

Result of this * val.

operator*() [2/2]

template<typename T>

Vec3t Vec3t< T >::operator* ( const Vec3t< T > & val ) const

inline

Component-wise multiplication.

Parameters

val	Vector to multiply component-wise.

Returns

Result of this * val.

operator+() [1/2]

template<typename T>

Vec3t Vec3t< T >::operator+ ( const T & val ) const

inline

Add scalar to all components.

Parameters

val	Scalar to add.

Returns

Result of this + val.

operator+() [2/2]

template<typename T>

Vec3t Vec3t< T >::operator+ ( const Vec3t< T > & val ) const

inline

Component-wise addition.

Parameters

val	Vector to add.

Returns

Result of this + val.

operator-() [1/2]

template<typename T>

Vec3t Vec3t< T >::operator- ( const T & val ) const

inline

Subtract scalar from all components.

Parameters

val	Scalar to subtract.

Returns

Result of this - val.

operator-() [2/2]

template<typename T>

Vec3t Vec3t< T >::operator- ( const Vec3t< T > & val ) const

inline

Component-wise subtraction.

Parameters

val	Vector to subtract.

Returns

Result of this - val.

operator/() [1/2]

template<typename T>

Vec3t Vec3t< T >::operator/ ( const T & val ) const

inline

Scalar division.

Parameters

val	Scalar divisor.

Returns

Result of this / val.

operator/() [2/2]

template<typename T>

Vec3t Vec3t< T >::operator/ ( const Vec3t< T > & val ) const

inline

Component-wise division.

Parameters

val	Vector to divide by component-wise.

Returns

Result of this / val.

operator==()

template<typename T>

bool Vec3t< T >::operator== ( const Vec3t< T > & other ) const

inline

Equality comparison (component-wise equality).

Parameters

other

Vector to compare against.

Returns

True iff all components are equal.

random()

template<typename T>

Vec3t< float > Vec3t< T >::random ( )

inlinestatic

Create a vector with components sampled from [0,1).

Returns

Random vector (x,y,z) in [0,1) each.

Note

Depends on a global/namespace-scope RNG named staticRand provided by Rand.h .

randomPointInDisc()

template<typename T>

Vec3t< float > Vec3t< T >::randomPointInDisc ( )

inlinestatic

Uniform random point inside the unit disc on the xy-plane.

Returns

Random point with x^2 + y^2 <= 1 and z = 0.

randomPointInHemisphere()

template<typename T>

Vec3t< float > Vec3t< T >::randomPointInHemisphere ( )

inlinestatic

Uniform random point inside the upper unit hemisphere (z>=0).

Returns

Random point with |p| <= 1 and z >= 0.

randomPointInSphere()

template<typename T>

Vec3t< float > Vec3t< T >::randomPointInSphere ( )

inlinestatic

Uniform random point inside the unit sphere.

Returns

Random point with |p| <= 1.

randomUnitVector()

template<typename T>

Vec3t< float > Vec3t< T >::randomUnitVector ( )

inlinestatic

Uniform random unit vector on the sphere.

Returns

Unit-length random direction.

reflect()

template<typename T>

Vec3t Vec3t< T >::reflect ( const Vec3t< T > & a, const Vec3t< T > & n )

inlinestatic

Reflect a vector about a unit normal.

Parameters

a	Incident vector.
n	Unit surface normal (assumed normalized).

Returns

Reflected vector r = a - 2(n·a)n.

refract()

template<typename T>

std::optional< Vec3t > Vec3t< T >::refract ( const Vec3t< T > & a, const Vec3t< T > & normal, const T IOR )

inlinestatic

Refract a vector through a surface with index-of-refraction ratio.

Computes the transmitted direction using Snell's law. If total internal reflection occurs, returns an empty optional.

Parameters

a	Incident vector (assumed pointing towards the surface).
normal	Surface normal (assumed normalized, pointing away from surface).
IOR	Index-of-refraction of the material (n_material / n_outside).

Returns

Transmitted direction if refraction is possible; otherwise empty.

sqlength()

template<typename T>

T Vec3t< T >::sqlength ( ) const

inline

Squared length (avoids sqrt).

Returns

x*x + y*y + z*z.

Here is the caller graph for this function:

toString()

template<typename T>

const std::string Vec3t< T >::toString ( ) const

inline

String representation "[x, y, z]".

Returns

A new std::string describing the vector.

Here is the caller graph for this function:

Member Data Documentation

[struct]

struct { ... } Vec3t< T >

Cartesian aliases for components.

[struct]

struct { ... } Vec3t< T >

Color aliases for components.

b

template<typename T>

T Vec3t< T >::b

e

template<typename T>

std::array<T, 3> Vec3t< T >::e

Component storage and named aliases.

Indexed access: e[0], e[1], e[2].

g

template<typename T>

T Vec3t< T >::g

r

template<typename T>

T Vec3t< T >::r

x

template<typename T>

T Vec3t< T >::x

xy

template<typename T>

Vec2t<T> Vec3t< T >::xy

2D view of the first two components.

y

template<typename T>

T Vec3t< T >::y

z

template<typename T>

T Vec3t< T >::z

---

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

• Vec3.h