3x1 or 1x3 vector using float32 representation. More...

Public Types
enum	Axis { X_AXIS =0, Y_AXIS =1, Z_AXIS =2, DETECT_AXIS =-1 }

Public Member Functions
	Vector3 ()
	Initializes to zero. More...

	Vector3 (DoNotInitialize dni)

	Vector3 (const Any &any)

	Vector3 (const Vector4int8 &)

	Vector3 (const Vector3uint8 &)

	Vector3 (const class Vector2 &v, float z)

	Vector3 (const class Vector3int32 &v)

	Vector3 (class BinaryInput &b)

	Vector3 (float _x, float _y, float _z)

	Vector3 (float coordinate[3])

	Vector3 (double coordinate[3])

	Vector3 (const class Vector3int16 &v)

	Vector3 (class TextInput &t)

	Vector3 (const class Color3 &c)

float	average () const

Vector3	clamp (const Vector3 &low, const Vector3 &high) const

Vector3	clamp (float low, float high) const

Vector3	cross (const Vector3 &rkVector) const
	Cross product. More...

class Matrix3	cross () const
	Returns a matrix such that v.cross() * w = v.cross(w). More...

void	deserialize (class BinaryInput &b)

void	deserialize (class TextInput &t)

Vector3	direction () const
	Returns a unit-length version of this vector. More...

Vector3	directionOrZero () const
	Returns Vector3::zero() if the length is nearly zero, otherwise returns a unit vector. More...

float	dot (const Vector3 &rkVector) const

Vector3	fastDirection () const
	Potentially less accurate but faster than direction(). More...

Vector3	fastUnit () const
	Returns a normalized vector. More...

Vector3	floor () const

bool	fuzzyEq (const Vector3 &other) const

bool	fuzzyNe (const Vector3 &other) const

void	getTangents (Vector3 &X, Vector3 &Y) const
	Creates two orthonormal tangent vectors X and Y such that if Z = this, X x Y = Z. More...

size_t	hashCode () const

bool	isFinite () const
	Returns true if this vector has finite length. More...

bool	isNaN () const
	True if any field is nan. More...

bool	isUnit () const
	Returns true if this vector has length ~= 1. More...

bool	isZero () const
	Returns true if this vector has length ~= 0. More...

float	length () const
	Same as magnitude. More...

Vector3	lerp (const Vector3 &v, float alpha) const
	Linear interpolation More...

float	magnitude () const

Vector3	max (const Vector3 &v) const

float	max () const
	Largest element. More...

Vector3	min (const Vector3 &v) const

float	min () const
	Smallest element. More...

Vector3	movedTowards (const Vector3 &goal, float maxTranslation) const
	Returns a vector that is this translated towards goal with a maximum translation of maxTranslation. More...

void	moveTowards (const Vector3 &goal, float maxTranslation)

bool	nonZero () const

bool	operator!= (const Vector3 &rkVector) const

Vector3	operator* (float s) const

Vector3	operator* (const Vector3 &v) const

Vector3 &	operator*= (float s)

Vector3 &	operator*= (const Vector3 &v)

Vector3	operator+ (const Vector3 &v) const

Vector3 &	operator+= (const Vector3 &v)

Vector3	operator- (const Vector3 &v) const

Vector3	operator- () const

Vector3 &	operator-= (const Vector3 &v)

Vector3	operator/ (float s) const

Vector3	operator/ (const Vector3 &v) const

Vector3 &	operator/= (float s)

Vector3 &	operator/= (const Vector3 &v)

Vector3 &	operator= (const Vector3 &rkVector)

Vector3 &	operator= (const Any &a)

bool	operator== (const Vector3 &rkVector) const

const float &	operator[] (int i) const

float &	operator[] (int i)

Vector3	pow (float p) const
	Raise each component of this vector to a power. More...

Axis	primaryAxis () const
	Returns the largest dimension. More...

Vector3	reflectAbout (const Vector3 &normal) const
	Reflect this vector about the (not necessarily unit) normal. More...

Vector3	reflectionDirection (const Vector3 &normal) const
	See also G3D::Ray::reflect. More...

Vector3	refractionDirection (const Vector3 &normal, float iInside, float iOutside) const
	Returns the direction of a refracted ray, where iExit is the index of refraction for the previous material and iEnter is the index of refraction for the new material. More...

Vector3	refractionDirection (const Vector3 &normal, float iRatio) const

Vector3	round () const

void	serialize (class BinaryOutput &b) const
	Format is three float32's. More...

void	serialize (class TextOutput &t) const
	Format is "(%f, %f, %f)". More...

float	squaredLength () const
	Same as squaredMagnitude. More...

float	squaredMagnitude () const

float	sum () const

Any	toAny (const String &name) const
	Converts the Vector3 to an Any, using the specified name instead of "Vector3". More...

Any	toAny () const
	Converts the Vector3 to an Any. More...

String	toString () const

Vector3	unit () const
	Synonym for direction. More...

Vector3	unitCross (const Vector3 &rkVector) const

Vector2	xx () const

Vector3	xxx () const

Vector4	xxxx () const

Vector4	xxxy () const

Vector4	xxxz () const

Vector3	xxy () const

Vector4	xxyx () const

Vector4	xxyy () const

Vector4	xxyz () const

Vector3	xxz () const

Vector4	xxzx () const

Vector4	xxzy () const

Vector4	xxzz () const

Vector2	xy () const

Vector3	xyx () const

Vector4	xyxx () const

Vector4	xyxy () const

Vector4	xyxz () const

Vector3	xyy () const

Vector4	xyyx () const

Vector4	xyyy () const

Vector4	xyyz () const

Vector3	xyz () const

Vector4	xyzx () const

Vector4	xyzy () const

Vector4	xyzz () const

Vector2	xz () const

Vector3	xzx () const

Vector4	xzxx () const

Vector4	xzxy () const

Vector4	xzxz () const

Vector3	xzy () const

Vector4	xzyx () const

Vector4	xzyy () const

Vector4	xzyz () const

Vector3	xzz () const

Vector4	xzzx () const

Vector4	xzzy () const

Vector4	xzzz () const

Vector2	yx () const

Vector3	yxx () const

Vector4	yxxx () const

Vector4	yxxy () const

Vector4	yxxz () const

Vector3	yxy () const

Vector4	yxyx () const

Vector4	yxyy () const

Vector4	yxyz () const

Vector3	yxz () const

Vector4	yxzx () const

Vector4	yxzy () const

Vector4	yxzz () const

Vector2	yy () const

Vector3	yyx () const

Vector4	yyxx () const

Vector4	yyxy () const

Vector4	yyxz () const

Vector3	yyy () const

Vector4	yyyx () const

Vector4	yyyy () const

Vector4	yyyz () const

Vector3	yyz () const

Vector4	yyzx () const

Vector4	yyzy () const

Vector4	yyzz () const

Vector2	yz () const

Vector3	yzx () const

Vector4	yzxx () const

Vector4	yzxy () const

Vector4	yzxz () const

Vector3	yzy () const

Vector4	yzyx () const

Vector4	yzyy () const

Vector4	yzyz () const

Vector3	yzz () const

Vector4	yzzx () const

Vector4	yzzy () const

Vector4	yzzz () const

Vector2	zx () const

Vector3	zxx () const

Vector4	zxxx () const

Vector4	zxxy () const

Vector4	zxxz () const

Vector3	zxy () const

Vector4	zxyx () const

Vector4	zxyy () const

Vector4	zxyz () const

Vector3	zxz () const

Vector4	zxzx () const

Vector4	zxzy () const

Vector4	zxzz () const

Vector2	zy () const

Vector3	zyx () const

Vector4	zyxx () const

Vector4	zyxy () const

Vector4	zyxz () const

Vector3	zyy () const

Vector4	zyyx () const

Vector4	zyyy () const

Vector4	zyyz () const

Vector3	zyz () const

Vector4	zyzx () const

Vector4	zyzy () const

Vector4	zyzz () const

Vector2	zz () const

Vector3	zzx () const

Vector4	zzxx () const

Vector4	zzxy () const

Vector4	zzxz () const

Vector3	zzy () const

Vector4	zzyx () const

Vector4	zzyy () const

Vector4	zzyz () const

Vector3	zzz () const

Vector4	zzzx () const

Vector4	zzzy () const

Vector4	zzzz () const

Static Public Member Functions
static void	cosHemiPlusCosPowHemiHemiRandom (const Vector3 &v, const Vector3 &n, const float k, float P_cosPow, Random &rng, Vector3 &w, float &pdfValue)
	Useful for sampling "lambertian + glossy" style BSDFs, even if they don't exactly match this PDF. More...

static Vector3	cosHemiRandom (const Vector3 &n, Random &r=Random::common())
	Random unit vector, distributed according to $\max(\cos \theta,0)$ . More...

static void	cosHemiRandom (const Vector3 &v, Random &rng, Vector3 &w, float &pdfValue)
	Random unit vector, distributed proportional to $\max(\hat{\omega} \cdot \hat{n},0)$ . More...

static void	cosPowHemiHemiRandom (const Vector3 &v, const Vector3 &n, const float k, Random &r, Vector3 &w, float &pdfValue)
	Random unit vector, distributed proportional to $\max(\|\hat{\omega} \cdot \hat{v}\|^k, 0) \cdot (\hat{\omega} \cdot \hat{n} \geq 0)$ . More...

static Vector3	cosPowHemiRandom (const Vector3 &v, const float k, Random &r=Random::common())
	Random unit vector, distributed proportional to $\max(\|\hat{\omega} \cdot \hat{v}\|^k, 0)$ . More...

static void	cosPowHemiRandom (const Vector3 &v, const float k, Random &r, Vector3 &w, float &pdfValue)
	Random unit vector, distributed proportional to $\max(\|\hat{\omega} \cdot \hat{v}\|^k, 0)$ . More...

static Vector3	cosSphereRandom (const Vector3 &n, Random &r=Random::common())

static void	cosSphereRandom (const Vector3 &n, Random &rng, Vector3 &w, float &pdfValue)
	Random unit vector, distributed proportional to $\|\hat{\omega} \cdot \hat{n}\|$ . More...

static Vector3	hemiRandom (const Vector3 &normal, Random &r=Random::common())
	Random vector distributed over the hemisphere about normal. More...

static void	hemiRandom (const Vector3 &v, Random &r, Vector3 &w, float &pdfValue)
	Random vector distributed over the hemisphere about v. More...

static const Vector3 &	inf ()

static const Vector3 &	maxFinite ()
	Largest representable vector. More...

static const Vector3 &	minFinite ()
	Smallest (most negative) representable vector. More...

static const Vector3 &	nan ()

static const Vector3 &	one ()

static void	orthonormalize (Vector3 akVector[3])
	Gram-Schmidt orthonormalization. More...

static Vector3	random (Random &r=Random::common())
	Random unit vector, uniformly distributed on the sphere. More...

static void	sphericalCapHemiRandom (const Vector3 &v, const Vector3 &n, const float cosHalfAngle, Random &r, Vector3 &w, float &pdfValue)
	Samples w from a pdf proportional to the spherical cap that lies within the cone about v whose apex half-angle has cosine cosHalfAngle, while restricting w to the hemisphere about n. More...

static const Vector3 &	unitX ()

static const Vector3 &	unitY ()

static const Vector3 &	unitZ ()

static const Vector3 &	zero ()

Public Attributes
float	x

float	y

float	z

Static Public Attributes
static Vector3	ignore
	For use with default output arguments. More...

Detailed Description

3x1 or 1x3 vector using float32 representation.

Typedefs use this class for Point as well.

Swizzles Vector classes have swizzle operators, e.g. v.xy(), that allow selection of arbitrary sub-fields. These cannot be used as write masks. Examples

Vector3 v(1, 2, 3);
Vector3 j;
Vector2 b;

b = v.xz();
j = b.xx();

Warning

Do not subclass– this implementation makes assumptions about the memory layout.

Member Enumeration Documentation

◆ Axis

enum G3D::Vector3::Axis

Enumerator
X_AXIS
Y_AXIS
Z_AXIS
DETECT_AXIS

Constructor & Destructor Documentation

◆ Vector3() [1/14]

G3D::Vector3::Vector3 ( )

inline

Initializes to zero.

Referenced by clamp(), cross(), direction(), fastDirection(), max(), min(), operator*(), operator+(), operator-(), operator/(), pow(), and round().

◆ Vector3() [2/14]

G3D::Vector3::Vector3 ( DoNotInitialize dni )

inline

◆ Vector3() [3/14]

G3D::Vector3::Vector3 ( const Any & any )

explicit

Parameters

any	Must either Vector3(#, #, #) or Vector3 {x = #, y = #, z = #}. Because Point3 is a typedef for Vector3 in the current implementation, this constructor accepts Point3(#, #, #), etc. as well.

◆ Vector3() [4/14]

G3D::Vector3::Vector3 ( const Vector4int8 & )

explicit

◆ Vector3() [5/14]

G3D::Vector3::Vector3 ( const Vector3uint8 & )

◆ Vector3() [6/14]

G3D::Vector3::Vector3	(	const class Vector2 &	v,
		float	z
	)

◆ Vector3() [7/14]

G3D::Vector3::Vector3 ( const class Vector3int32 & v )

◆ Vector3() [8/14]

G3D::Vector3::Vector3 ( class BinaryInput & b )

explicit

◆ Vector3() [9/14]

G3D::Vector3::Vector3	(	float	_x,
		float	_y,
		float	_z
	)

inline

◆ Vector3() [10/14]

G3D::Vector3::Vector3 ( float coordinate[3] )

inlineexplicit

◆ Vector3() [11/14]

G3D::Vector3::Vector3 ( double coordinate[3] )

inlineexplicit

◆ Vector3() [12/14]

G3D::Vector3::Vector3 ( const class Vector3int16 & v )

◆ Vector3() [13/14]

G3D::Vector3::Vector3 ( class TextInput & t )

explicit

◆ Vector3() [14/14]

G3D::Vector3::Vector3 ( const class Color3 & c )

explicit

Member Function Documentation

◆ average()

float G3D::Vector3::average ( ) const

inline

◆ clamp() [1/2]

Vector3 G3D::Vector3::clamp	(	const Vector3 &	low,
		const Vector3 &	high
	)		const

inline

Referenced by G3D::clamp(), and G3D::Plane::halfSpaceContains().

◆ clamp() [2/2]

Vector3 G3D::Vector3::clamp	(	float	low,
		float	high
	)		const

inline

◆ cosHemiPlusCosPowHemiHemiRandom()

static void G3D::Vector3::cosHemiPlusCosPowHemiHemiRandom	(	const Vector3 &	v,
		const Vector3 &	n,
		const float	k,
		float	P_cosPow,
		Random &	rng,
		Vector3 &	w,
		float &	pdfValue
	)

static

Useful for sampling "lambertian + glossy" style BSDFs, even if they don't exactly match this PDF.

Parameters

v	The lobe about which to sample the cosine-power lobe (typically `w_o.reflectAbout(n)`)
n	The normal whose hemisphere each sub-PDF is restricted to, and the vector about which to sample the cosine lobe
P_cosPow	Probability of sampling the cosPowHemi lobe about the reflection vector (1 - P_cosPow is the probability of sampling the regular cosine lobe)
k	Exponent on the cosPowHemi lobe

Assumes that P_cos + P_cosPow = 1.0

◆ cosHemiRandom() [1/2]

static Vector3 G3D::Vector3::cosHemiRandom	(	const Vector3 &	n,
		Random &	r = `Random::common()`
	)

static

Random unit vector, distributed according to $\max(\cos \theta,0)$ .

That is, so that the probability of $\vec{V}$ is proportional to $\max(\vec{v} \cdot \vec{n}, 0)$ . Useful in photon mapping for Lambertian scattering.

Distribution rendered by G3D::DirectionHistogram:

Parameters

n	Unit vector at the center of the distribution.

Referenced Code: Henrik Wann Jensen, Realistic Image Synthesis using Photon Mapping eqn 2.24

◆ cosHemiRandom() [2/2]

static void G3D::Vector3::cosHemiRandom	(	const Vector3 &	v,
		Random &	rng,
		Vector3 &	w,
		float &	pdfValue
	)

static

Random unit vector, distributed proportional to $\max(\hat{\omega} \cdot \hat{n},0)$ .

That is, so that the probability of $\vec{V}$ is proportional to $\max(\vec{w} \cdot \vec{v}, 0)$ . Useful in photon mapping for Lambertian scattering.

Distribution rendered by G3D::DirectionHistogram:

Parameters

n	Unit vector at the center of the distribution.

Referenced Code: Henrik Wann Jensen, Realistic Image Synthesis using Photon Mapping eqn 2.24

◆ cosPowHemiHemiRandom()

static void G3D::Vector3::cosPowHemiHemiRandom	(	const Vector3 &	v,
		const Vector3 &	n,
		const float	k,
		Random &	r,
		Vector3 &	w,
		float &	pdfValue
	)

static

Random unit vector, distributed proportional to $\max(|\hat{\omega} \cdot \hat{v}|^k, 0) \cdot (\hat{\omega} \cdot \hat{n} \geq 0)$ .

Parameters

k	Power lobe
v	Unit vector at the center of the distribution.
n	Unit vector defining the hemisphere to restrict the result vector to
w	$\hat{\omega}$
pdfValue	The value of the cosPowHemiHemiRandom pdf at w

See also: cosPowHemiRandom, hemiRandom, cosHemiRandom

◆ cosPowHemiRandom() [1/2]

static Vector3 G3D::Vector3::cosPowHemiRandom	(	const Vector3 &	v,
		const float	k,
		Random &	r = `Random::common()`
	)

static

Random unit vector, distributed proportional to $\max(|\hat{\omega} \cdot \hat{v}|^k, 0)$ .

Parameters

k	Power lobe
v	Unit vector at the center of the distribution.

Referenced Code: Ashikhmin and Shirley, An anisotropic Phong BRDF model, Journal of Graphics Tools, 2002

See also: cosPowHemiHemiRandom, hemiRandom, cosHemiRandom

◆ cosPowHemiRandom() [2/2]

static void G3D::Vector3::cosPowHemiRandom	(	const Vector3 &	v,
		const float	k,
		Random &	r,
		Vector3 &	w,
		float &	pdfValue
	)

static

Random unit vector, distributed proportional to $\max(|\hat{\omega} \cdot \hat{v}|^k, 0)$ .

Parameters

k	Power lobe
v	Unit vector at the center of the distribution.
w	$\hat{\omega}$
pdfValue	The value of the cosPowHemiRandom pdf at w

Referenced Code: Ashikhmin and Shirley, An anisotropic Phong BRDF model, Journal of Graphics Tools, 2002

See also: cosPowHemiHemiRandom, hemiRandom, cosHemiRandom

◆ cosSphereRandom() [1/2]

static Vector3 G3D::Vector3::cosSphereRandom	(	const Vector3 &	n,
		Random &	r = `Random::common()`
	)

static

◆ cosSphereRandom() [2/2]

static void G3D::Vector3::cosSphereRandom	(	const Vector3 &	n,
		Random &	rng,
		Vector3 &	w,
		float &	pdfValue
	)

static

Random unit vector, distributed proportional to $|\hat{\omega} \cdot \hat{n}|$ .

Parameters

n	Unit vector at the center of the distribution.

Referenced Code: Henrik Wann Jensen, Realistic Image Synthesis using Photon Mapping eqn 2.24

◆ cross() [1/2]

Vector3 G3D::Vector3::cross ( const Vector3 & rkVector ) const

inline

Cross product.

Note that two cross products in a row can be computed more cheaply: v1 x (v2 x v3) = (v1 dot v3) v2 - (v1 dot v2) v3.

Referenced by G3D::cross(), G3D::Tri::nonUnitNormal(), and G3D::Tri::tangent2().

◆ cross() [2/2]

class Matrix3 G3D::Vector3::cross ( ) const

Returns a matrix such that v.cross() * w = v.cross(w).

[ 0  -v.z  v.y ]
[ v.z  0  -v.x ]
[ -v.y v.x  0  ]

Referenced by getTangents().

◆ deserialize() [1/2]

void G3D::Vector3::deserialize ( class BinaryInput & b )

◆ deserialize() [2/2]

void G3D::Vector3::deserialize ( class TextInput & t )

◆ direction()

Vector3 G3D::Vector3::direction ( ) const

inline

Returns a unit-length version of this vector.

Returns nan if length is almost zero.

Referenced by G3D::Box::axis(), G3D::CollisionDetection::collisionTimeForMovingPointFixedTriangle(), G3D::Line::Line(), unit(), and unitCross().

◆ directionOrZero()

Vector3 G3D::Vector3::directionOrZero ( ) const

inline

Returns Vector3::zero() if the length is nearly zero, otherwise returns a unit vector.

Referenced by G3D::ArticulatedModel::Geometry::Face::Face(), G3D::Tri::normal(), and G3D::squareMagnitude().

◆ dot()

float G3D::Vector3::dot ( const Vector3 & rkVector ) const

inline

Referenced by G3D::Ray::closestPoint(), G3D::PrecomputedRay::closestPoint(), G3D::Plane::distance(), G3D::dot(), G3D::Plane::fuzzyContains(), getTangents(), G3D::Plane::halfSpaceContains(), and G3D::Plane::halfSpaceContainsFinite().

◆ fastDirection()

Vector3 G3D::Vector3::fastDirection ( ) const

inline

Potentially less accurate but faster than direction().

Only works if System::hasSSE is true.

Referenced by fastUnit().

◆ fastUnit()

Vector3 G3D::Vector3::fastUnit ( ) const

inline

Returns a normalized vector.

May be computed with lower precision than unit

◆ floor()

Vector3 G3D::Vector3::floor ( ) const

inline

◆ fuzzyEq()

bool G3D::Vector3::fuzzyEq ( const Vector3 & other ) const

inline

◆ fuzzyNe()

bool G3D::Vector3::fuzzyNe ( const Vector3 & other ) const

inline

◆ getTangents()

void G3D::Vector3::getTangents	(	Vector3 &	X,
		Vector3 &	Y
	)		const

inline

Creates two orthonormal tangent vectors X and Y such that if Z = this, X x Y = Z.

◆ hashCode()

size_t G3D::Vector3::hashCode ( ) const

Referenced by G3D::Sphere::hashCode(), G3D::Triangle::hashCode(), HashTrait< G3D::Sphere >::hashCode(), HashTrait< G3D::CoordinateFrame >::hashCode(), G3D::ArticulatedModel::Geometry::Face::AMFaceVertexHash::hashCode(), HashTrait< G3D::Vector3 >::hashCode(), and G3D::PointHashGrid< Value, PosFunc, EqualsFunc >::PointHashGrid().

◆ hemiRandom() [1/2]

static Vector3 G3D::Vector3::hemiRandom	(	const Vector3 &	normal,
		Random &	r = `Random::common()`
	)

static

Random vector distributed over the hemisphere about normal.

Distribution rendered by G3D::DirectionHistogram:

◆ hemiRandom() [2/2]

static void G3D::Vector3::hemiRandom	(	const Vector3 &	v,
		Random &	r,
		Vector3 &	w,
		float &	pdfValue
	)

static

Random vector distributed over the hemisphere about v.

Parameters

pdfValue set to 1/pi on return, the value of a uniform PDF over the hemisphere.

Distribution rendered by G3D::DirectionHistogram:

◆ inf()

static const Vector3& G3D::Vector3::inf ( )

static

Referenced by G3D::PlaneShape::boundingAABox(), G3D::PointKDTree< T, PositionFunc, HashFunc, EqualsFunc >::computeBounds(), G3D::KDTree< T, BoundsFunc, HashFunc, EqualsFunc >::computeBounds(), G3D::PointKDTree< T, PositionFunc, HashFunc, EqualsFunc >::Node::Node(), G3D::KDTree< T, BoundsFunc, HashFunc, EqualsFunc >::Node::Node(), and G3D::PointHashGrid< Value, PosFunc, EqualsFunc >::PointHashGrid().

◆ isFinite()

bool G3D::Vector3::isFinite ( ) const

inline

Returns true if this vector has finite length.

Referenced by G3D::Plane::halfSpaceContainsFinite().

◆ isNaN()

bool G3D::Vector3::isNaN ( ) const

True if any field is nan.

Referenced by G3D::AABox::isEmpty().

◆ isUnit()

bool G3D::Vector3::isUnit ( ) const

inline

Returns true if this vector has length ~= 1.

◆ isZero()

bool G3D::Vector3::isZero ( ) const

inline

Returns true if this vector has length ~= 0.

◆ length()

float G3D::Vector3::length ( ) const

inline

Same as magnitude.

Referenced by G3D::ArrowShape::boundingSphere(), G3D::Box::extent(), and getTangents().

◆ lerp()

Vector3 G3D::Vector3::lerp	(	const Vector3 &	v,
		float	alpha
	)		const

inline

Linear interpolation

Referenced by G3D::lerp().

◆ magnitude()

float G3D::Vector3::magnitude ( ) const

inline

Referenced by G3D::RayShape::boundingSphere(), directionOrZero(), G3D::Quat::exp(), G3D::LineSegment::length(), length(), G3D::length(), and G3D::normalize().

◆ max() [1/2]

Vector3 G3D::Vector3::max ( const Vector3 & v ) const

inline

Referenced by G3D::Tri::getBounds(), G3D::max(), and G3D::PointHashGrid< Value, PosFunc, EqualsFunc >::PointHashGrid().

◆ max() [2/2]

float G3D::Vector3::max ( ) const

inline

Largest element.

◆ maxFinite()

static const Vector3& G3D::Vector3::maxFinite ( )

static

Largest representable vector.

Referenced by G3D::PointKDTree< T, PositionFunc, HashFunc, EqualsFunc >::balance(), and G3D::Plane::halfSpaceContains().

◆ min() [1/2]

Vector3 G3D::Vector3::min ( const Vector3 & v ) const

inline

Referenced by G3D::RayGridIterator::exitDistance(), G3D::RayGridIterator::exitPoint(), G3D::Tri::getBounds(), G3D::min(), and G3D::PointHashGrid< Value, PosFunc, EqualsFunc >::PointHashGrid().

◆ min() [2/2]

float G3D::Vector3::min ( ) const

inline

Smallest element.

◆ minFinite()

static const Vector3& G3D::Vector3::minFinite ( )

static

Smallest (most negative) representable vector.

Referenced by G3D::PointKDTree< T, PositionFunc, HashFunc, EqualsFunc >::balance(), and G3D::Plane::halfSpaceContains().

◆ movedTowards()

Vector3 G3D::Vector3::movedTowards	(	const Vector3 &	goal,
		float	maxTranslation
	)		const

Returns a vector that is this translated towards goal with a maximum translation of maxTranslation.

◆ moveTowards()

void G3D::Vector3::moveTowards	(	const Vector3 &	goal,
		float	maxTranslation
	)

◆ nan()

static const Vector3& G3D::Vector3::nan ( )

static

Referenced by G3D::RayShape::getRandomSurfacePoint(), G3D::ArrowShape::getRandomSurfacePoint(), G3D::AxesShape::getRandomSurfacePoint(), G3D::PlaneShape::getRandomSurfacePoint(), G3D::GazeTracker::headSpaceCalibrationPoint(), and G3D::PlaneShape::randomInteriorPoint().

◆ nonZero()

bool G3D::Vector3::nonZero ( ) const

inline

◆ one()

static const Vector3& G3D::Vector3::one ( )

static

◆ operator!=()

bool G3D::Vector3::operator!= ( const Vector3 & rkVector ) const

inline

◆ operator*() [1/2]

Vector3 G3D::Vector3::operator* ( float s ) const

inline

◆ operator*() [2/2]

Vector3 G3D::Vector3::operator* ( const Vector3 & v ) const

inline

◆ operator*=() [1/2]

Vector3 & G3D::Vector3::operator*= ( float s )

inline

◆ operator*=() [2/2]

Vector3 & G3D::Vector3::operator*= ( const Vector3 & v )

inline

◆ operator+()

Vector3 G3D::Vector3::operator+ ( const Vector3 & v ) const

inline

◆ operator+=()

Vector3 & G3D::Vector3::operator+= ( const Vector3 & v )

inline

◆ operator-() [1/2]

Vector3 G3D::Vector3::operator- ( const Vector3 & v ) const

inline

◆ operator-() [2/2]

Vector3 G3D::Vector3::operator- ( ) const

inline

◆ operator-=()

Vector3 & G3D::Vector3::operator-= ( const Vector3 & v )

inline

◆ operator/() [1/2]

Vector3 G3D::Vector3::operator/ ( float s ) const

inline

◆ operator/() [2/2]

Vector3 G3D::Vector3::operator/ ( const Vector3 & v ) const

inline

◆ operator/=() [1/2]

Vector3& G3D::Vector3::operator/= ( float s )

inline

◆ operator/=() [2/2]

Vector3 & G3D::Vector3::operator/= ( const Vector3 & v )

inline

◆ operator=() [1/2]

Vector3 & G3D::Vector3::operator= ( const Vector3 & rkVector )

inline

◆ operator=() [2/2]

Vector3& G3D::Vector3::operator= ( const Any & a )

◆ operator==()

bool G3D::Vector3::operator== ( const Vector3 & rkVector ) const

inline

◆ operator[]() [1/2]

const float & G3D::Vector3::operator[] ( int i ) const

inline

◆ operator[]() [2/2]

float & G3D::Vector3::operator[] ( int i )

inline

◆ orthonormalize()

static void G3D::Vector3::orthonormalize ( Vector3 akVector[3] )

static

Gram-Schmidt orthonormalization.

◆ pow()

Vector3 G3D::Vector3::pow ( float p ) const

inline

Raise each component of this vector to a power.

◆ primaryAxis()

Axis G3D::Vector3::primaryAxis ( ) const

Returns the largest dimension.

Particularly convenient for determining which plane to project a triangle onto for point-in-polygon tests.

Referenced by G3D::PointKDTree< T, PositionFunc, HashFunc, EqualsFunc >::makeNode().

◆ random()

static Vector3 G3D::Vector3::random ( Random & r = Random::common() )

static

Random unit vector, uniformly distributed on the sphere.

Distribution rendered by G3D::DirectionHistogram:

◆ reflectAbout()

Vector3 G3D::Vector3::reflectAbout ( const Vector3 & normal ) const

Reflect this vector about the (not necessarily unit) normal.

Assumes that both the before and after vectors point away from the base of the normal.

Note that if used for a collision or ray reflection you must negate the resulting vector to get a direction pointing away from the collision.

  V'    N      V

    r   ^   -,
     \  |  /
       |/

◆ reflectionDirection()

Vector3 G3D::Vector3::reflectionDirection ( const Vector3 & normal ) const

◆ refractionDirection() [1/2]

Vector3 G3D::Vector3::refractionDirection	(	const Vector3 &	normal,
		float	iInside,
		float	iOutside
	)		const

Returns the direction of a refracted ray, where iExit is the index of refraction for the previous material and iEnter is the index of refraction for the new material.

Like Vector3::reflectionDirection, the result has length 1 and is pointed away from the intersection.

Returns Vector3::zero() in the case of total internal refraction.

Parameters

iOutside	The index of refraction (eta) outside (on the positive normal side) of the surface.
iInside	The index of refraction (eta) inside (on the negative normal side) of the surface.

◆ refractionDirection() [2/2]

Vector3 G3D::Vector3::refractionDirection	(	const Vector3 &	normal,
		float	iRatio
	)		const

◆ round()

Vector3 G3D::Vector3::round ( ) const

inline

◆ serialize() [1/2]

void G3D::Vector3::serialize ( class BinaryOutput & b ) const

Format is three float32's.

◆ serialize() [2/2]

void G3D::Vector3::serialize ( class TextOutput & t ) const

Format is "(%f, %f, %f)".

◆ sphericalCapHemiRandom()

static void G3D::Vector3::sphericalCapHemiRandom	(	const Vector3 &	v,
		const Vector3 &	n,
		const float	cosHalfAngle,
		Random &	r,
		Vector3 &	w,
		float &	pdfValue
	)

static

Samples w from a pdf proportional to the spherical cap that lies within the cone about v whose apex half-angle has cosine cosHalfAngle, while restricting w to the hemisphere about n.

◆ squaredLength()

float G3D::Vector3::squaredLength ( ) const

inline

Same as squaredMagnitude.

Referenced by G3D::squareMagnitude().

◆ squaredMagnitude()

float G3D::Vector3::squaredMagnitude ( ) const

inline

Referenced by direction(), fuzzyEq(), fuzzyNe(), isUnit(), and squaredLength().

◆ sum()

float G3D::Vector3::sum ( ) const

inline

Referenced by average().

◆ toAny() [1/2]

Any G3D::Vector3::toAny ( const String & name ) const

Converts the Vector3 to an Any, using the specified name instead of "Vector3".

◆ toAny() [2/2]

Any G3D::Vector3::toAny ( ) const

Converts the Vector3 to an Any.

◆ toString()

String G3D::Vector3::toString ( ) const

Referenced by G3D::KDTree< T, BoundsFunc, HashFunc, EqualsFunc >::Node::verifyNode().

◆ unit()

Vector3 G3D::Vector3::unit ( ) const

inline

Synonym for direction.

◆ unitCross()

Vector3 G3D::Vector3::unitCross ( const Vector3 & rkVector ) const

inline

◆ unitX()

static const Vector3& G3D::Vector3::unitX ( )

static

Referenced by getTangents(), G3D::Matrix4::pitchDegrees(), G3D::PrecomputedRay::PrecomputedRay(), and G3D::Ray::Ray().

◆ unitY()

static const Vector3& G3D::Vector3::unitY ( )

static

Referenced by G3D::PointShape::getRandomSurfacePoint(), getTangents(), and G3D::Matrix4::yawDegrees().

◆ unitZ()

static const Vector3& G3D::Vector3::unitZ ( )

static

Referenced by G3D::Matrix4::rollDegrees().

◆ xx()

Vector2 G3D::Vector3::xx ( ) const

◆ xxx()

Vector3 G3D::Vector3::xxx ( ) const

◆ xxxx()

Vector4 G3D::Vector3::xxxx ( ) const

◆ xxxy()

Vector4 G3D::Vector3::xxxy ( ) const

◆ xxxz()

Vector4 G3D::Vector3::xxxz ( ) const

◆ xxy()

Vector3 G3D::Vector3::xxy ( ) const

◆ xxyx()

Vector4 G3D::Vector3::xxyx ( ) const

◆ xxyy()

Vector4 G3D::Vector3::xxyy ( ) const

◆ xxyz()

Vector4 G3D::Vector3::xxyz ( ) const

◆ xxz()

Vector3 G3D::Vector3::xxz ( ) const

◆ xxzx()

Vector4 G3D::Vector3::xxzx ( ) const

◆ xxzy()

Vector4 G3D::Vector3::xxzy ( ) const

◆ xxzz()

Vector4 G3D::Vector3::xxzz ( ) const

◆ xy()

Vector2 G3D::Vector3::xy ( ) const

◆ xyx()

Vector3 G3D::Vector3::xyx ( ) const

◆ xyxx()

Vector4 G3D::Vector3::xyxx ( ) const

◆ xyxy()

Vector4 G3D::Vector3::xyxy ( ) const

◆ xyxz()

Vector4 G3D::Vector3::xyxz ( ) const

◆ xyy()

Vector3 G3D::Vector3::xyy ( ) const

◆ xyyx()

Vector4 G3D::Vector3::xyyx ( ) const

◆ xyyy()

Vector4 G3D::Vector3::xyyy ( ) const

◆ xyyz()

Vector4 G3D::Vector3::xyyz ( ) const

◆ xyz()

Vector3 G3D::Vector3::xyz ( ) const

Referenced by G3D::PointShape::center().

◆ xyzx()

Vector4 G3D::Vector3::xyzx ( ) const

◆ xyzy()

Vector4 G3D::Vector3::xyzy ( ) const

◆ xyzz()

Vector4 G3D::Vector3::xyzz ( ) const

◆ xz()

Vector2 G3D::Vector3::xz ( ) const

◆ xzx()

Vector3 G3D::Vector3::xzx ( ) const

◆ xzxx()

Vector4 G3D::Vector3::xzxx ( ) const

◆ xzxy()

Vector4 G3D::Vector3::xzxy ( ) const

◆ xzxz()

Vector4 G3D::Vector3::xzxz ( ) const

◆ xzy()

Vector3 G3D::Vector3::xzy ( ) const

◆ xzyx()

Vector4 G3D::Vector3::xzyx ( ) const

◆ xzyy()

Vector4 G3D::Vector3::xzyy ( ) const

◆ xzyz()

Vector4 G3D::Vector3::xzyz ( ) const

◆ xzz()

Vector3 G3D::Vector3::xzz ( ) const

◆ xzzx()

Vector4 G3D::Vector3::xzzx ( ) const

◆ xzzy()

Vector4 G3D::Vector3::xzzy ( ) const

◆ xzzz()

Vector4 G3D::Vector3::xzzz ( ) const

◆ yx()

Vector2 G3D::Vector3::yx ( ) const

◆ yxx()

Vector3 G3D::Vector3::yxx ( ) const

◆ yxxx()

Vector4 G3D::Vector3::yxxx ( ) const

◆ yxxy()

Vector4 G3D::Vector3::yxxy ( ) const

◆ yxxz()

Vector4 G3D::Vector3::yxxz ( ) const

◆ yxy()

Vector3 G3D::Vector3::yxy ( ) const

◆ yxyx()

Vector4 G3D::Vector3::yxyx ( ) const

◆ yxyy()

Vector4 G3D::Vector3::yxyy ( ) const

◆ yxyz()

Vector4 G3D::Vector3::yxyz ( ) const

◆ yxz()

Vector3 G3D::Vector3::yxz ( ) const

◆ yxzx()

Vector4 G3D::Vector3::yxzx ( ) const

◆ yxzy()

Vector4 G3D::Vector3::yxzy ( ) const

◆ yxzz()

Vector4 G3D::Vector3::yxzz ( ) const

◆ yy()

Vector2 G3D::Vector3::yy ( ) const

◆ yyx()

Vector3 G3D::Vector3::yyx ( ) const

◆ yyxx()

Vector4 G3D::Vector3::yyxx ( ) const

◆ yyxy()

Vector4 G3D::Vector3::yyxy ( ) const

◆ yyxz()

Vector4 G3D::Vector3::yyxz ( ) const

◆ yyy()

Vector3 G3D::Vector3::yyy ( ) const

◆ yyyx()

Vector4 G3D::Vector3::yyyx ( ) const

◆ yyyy()

Vector4 G3D::Vector3::yyyy ( ) const

◆ yyyz()

Vector4 G3D::Vector3::yyyz ( ) const

◆ yyz()

Vector3 G3D::Vector3::yyz ( ) const

◆ yyzx()

Vector4 G3D::Vector3::yyzx ( ) const

◆ yyzy()

Vector4 G3D::Vector3::yyzy ( ) const

◆ yyzz()

Vector4 G3D::Vector3::yyzz ( ) const

◆ yz()

Vector2 G3D::Vector3::yz ( ) const

◆ yzx()

Vector3 G3D::Vector3::yzx ( ) const

◆ yzxx()

Vector4 G3D::Vector3::yzxx ( ) const

◆ yzxy()

Vector4 G3D::Vector3::yzxy ( ) const

◆ yzxz()

Vector4 G3D::Vector3::yzxz ( ) const

◆ yzy()

Vector3 G3D::Vector3::yzy ( ) const

◆ yzyx()

Vector4 G3D::Vector3::yzyx ( ) const

◆ yzyy()

Vector4 G3D::Vector3::yzyy ( ) const

◆ yzyz()

Vector4 G3D::Vector3::yzyz ( ) const

◆ yzz()

Vector3 G3D::Vector3::yzz ( ) const

◆ yzzx()

Vector4 G3D::Vector3::yzzx ( ) const

◆ yzzy()

Vector4 G3D::Vector3::yzzy ( ) const

◆ yzzz()

Vector4 G3D::Vector3::yzzz ( ) const

◆ zero()

static const Vector3& G3D::Vector3::zero ( )

static

Referenced by directionOrZero(), G3D::PointKDTree< T, PositionFunc, HashFunc, EqualsFunc >::getIntersectingMembers(), G3D::KDTree< T, BoundsFunc, HashFunc, EqualsFunc >::getIntersectingMembers(), G3D::FogVolumeSurface::getObjectSpaceBoundingSphere(), G3D::ControlPointEditor::ControlPointSurface::getObjectSpaceBoundingSphere(), G3D::PrecomputedRay::PrecomputedRay(), and G3D::Ray::Ray().

◆ zx()

Vector2 G3D::Vector3::zx ( ) const

◆ zxx()

Vector3 G3D::Vector3::zxx ( ) const

◆ zxxx()

Vector4 G3D::Vector3::zxxx ( ) const

◆ zxxy()

Vector4 G3D::Vector3::zxxy ( ) const

◆ zxxz()

Vector4 G3D::Vector3::zxxz ( ) const

◆ zxy()

Vector3 G3D::Vector3::zxy ( ) const

◆ zxyx()

Vector4 G3D::Vector3::zxyx ( ) const

◆ zxyy()

Vector4 G3D::Vector3::zxyy ( ) const

◆ zxyz()

Vector4 G3D::Vector3::zxyz ( ) const

◆ zxz()

Vector3 G3D::Vector3::zxz ( ) const

◆ zxzx()

Vector4 G3D::Vector3::zxzx ( ) const

◆ zxzy()

Vector4 G3D::Vector3::zxzy ( ) const

◆ zxzz()

Vector4 G3D::Vector3::zxzz ( ) const

◆ zy()

Vector2 G3D::Vector3::zy ( ) const

◆ zyx()

Vector3 G3D::Vector3::zyx ( ) const

◆ zyxx()

Vector4 G3D::Vector3::zyxx ( ) const

◆ zyxy()

Vector4 G3D::Vector3::zyxy ( ) const

◆ zyxz()

Vector4 G3D::Vector3::zyxz ( ) const

◆ zyy()

Vector3 G3D::Vector3::zyy ( ) const

◆ zyyx()

Vector4 G3D::Vector3::zyyx ( ) const

◆ zyyy()

Vector4 G3D::Vector3::zyyy ( ) const

◆ zyyz()

Vector4 G3D::Vector3::zyyz ( ) const

◆ zyz()

Vector3 G3D::Vector3::zyz ( ) const

◆ zyzx()

Vector4 G3D::Vector3::zyzx ( ) const

◆ zyzy()

Vector4 G3D::Vector3::zyzy ( ) const

◆ zyzz()

Vector4 G3D::Vector3::zyzz ( ) const

◆ zz()

Vector2 G3D::Vector3::zz ( ) const

◆ zzx()

Vector3 G3D::Vector3::zzx ( ) const

◆ zzxx()

Vector4 G3D::Vector3::zzxx ( ) const

◆ zzxy()

Vector4 G3D::Vector3::zzxy ( ) const

◆ zzxz()

Vector4 G3D::Vector3::zzxz ( ) const

◆ zzy()

Vector3 G3D::Vector3::zzy ( ) const

◆ zzyx()

Vector4 G3D::Vector3::zzyx ( ) const

◆ zzyy()

Vector4 G3D::Vector3::zzyy ( ) const

◆ zzyz()

Vector4 G3D::Vector3::zzyz ( ) const

◆ zzz()

Vector3 G3D::Vector3::zzz ( ) const

◆ zzzx()

Vector4 G3D::Vector3::zzzx ( ) const

◆ zzzy()

Vector4 G3D::Vector3::zzzy ( ) const

◆ zzzz()

Vector4 G3D::Vector3::zzzz ( ) const

Member Data Documentation

◆ ignore

Vector3 G3D::Vector3::ignore

static

For use with default output arguments.

The value is always undefined.

Public Types

Public Member Functions

Static Public Member Functions

Public Attributes

Static Public Attributes

Detailed Description

Member Enumeration Documentation

◆ Axis

Constructor & Destructor Documentation

◆ Vector3() [1/14]

◆ Vector3() [2/14]

◆ Vector3() [3/14]

◆ Vector3() [4/14]

◆ Vector3() [5/14]

◆ Vector3() [6/14]

◆ Vector3() [7/14]

◆ Vector3() [8/14]

◆ Vector3() [9/14]

◆ Vector3() [10/14]

◆ Vector3() [11/14]

◆ Vector3() [12/14]

◆ Vector3() [13/14]

◆ Vector3() [14/14]

Member Function Documentation

◆ average()

◆ clamp() [1/2]

◆ clamp() [2/2]

◆ cosHemiPlusCosPowHemiHemiRandom()

◆ cosHemiRandom() [1/2]

◆ cosHemiRandom() [2/2]

◆ cosPowHemiHemiRandom()

◆ cosPowHemiRandom() [1/2]

◆ cosPowHemiRandom() [2/2]

◆ cosSphereRandom() [1/2]

◆ cosSphereRandom() [2/2]

◆ cross() [1/2]

◆ cross() [2/2]

◆ deserialize() [1/2]

◆ deserialize() [2/2]

◆ direction()

◆ directionOrZero()

◆ dot()

◆ fastDirection()

◆ fastUnit()

◆ floor()

◆ fuzzyEq()

◆ fuzzyNe()

◆ getTangents()

◆ hashCode()

◆ hemiRandom() [1/2]

◆ hemiRandom() [2/2]

◆ inf()

◆ isFinite()

◆ isNaN()

◆ isUnit()

◆ isZero()

◆ length()

◆ lerp()

◆ magnitude()

◆ max() [1/2]

◆ max() [2/2]

◆ maxFinite()

◆ min() [1/2]

◆ min() [2/2]

◆ minFinite()

◆ movedTowards()

◆ moveTowards()

◆ nan()

◆ nonZero()

◆ one()

◆ operator!=()

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ operator*=() [1/2]

◆ operator*=() [2/2]

◆ operator+()

◆ operator+=()

◆ operator-() [1/2]

◆ operator-() [2/2]

◆ operator-=()