Vector math types and their related utilities. More...

Data Structures
struct	AtVector
	3D point (single precision) More...

struct	AtVector2
	2D point More...

struct	AtHPoint
	Homogeneous point. More...

struct	AtVectorDv
	Vector with differentials. More...

Functions
AI_DEVICE constexpr	AtVector::AtVector (float x, float y, float z)

AI_DEVICE constexpr AtVector	AtVector::operator+ (const AtVector &p) const

AI_DEVICE AtVector &	AtVector::operator+= (const AtVector &p)

AI_DEVICE constexpr AtVector	AtVector::operator+ (float f) const

AI_DEVICE AtVector &	AtVector::operator+= (float f)

AI_DEVICE constexpr AtVector	AtVector::operator- (const AtVector &p) const

AI_DEVICE AtVector &	AtVector::operator-= (const AtVector &p)

AI_DEVICE constexpr AtVector	AtVector::operator- (float f) const

AI_DEVICE AtVector &	AtVector::operator-= (float f)

AI_DEVICE constexpr AtVector	AtVector::operator- () const

AI_DEVICE constexpr AtVector	AtVector::operator* (const AtVector &p) const

AI_DEVICE AtVector	*AtVector::operator=** (const AtVector &p)

AI_DEVICE constexpr AtVector	AtVector::operator* (float f) const

AI_DEVICE AtVector	*AtVector::operator=** (float f)

AI_DEVICE constexpr AtVector	AtVector::operator/ (const AtVector &p) const

AI_DEVICE AtVector	AtVector::operator/= (const AtVector &p)

AI_DEVICE AtVector	AtVector::operator/ (float f) const

AI_DEVICE AtVector	AtVector::operator/= (float f)

AI_DEVICE constexpr bool	AtVector::operator== (const AtVector &p) const

AI_DEVICE constexpr bool	AtVector::operator!= (const AtVector &p) const

AI_DEVICE AtVector &	AtVector::operator= (float f)

AI_DEVICE float &	AtVector::operator[] (unsigned int i)

AI_DEVICE constexpr const float &	AtVector::operator[] (unsigned int i) const

AI_DEVICE constexpr AtVector	operator* (float f, const AtVector &p)

AI_DEVICE constexpr AtVector	operator+ (float f, const AtVector &p)

AI_DEVICE constexpr AtVector	operator- (float f, const AtVector &p)

AI_DEVICE AtBooleanMask< 3 >	operator< (const AtVector &lhs, float f)

AI_DEVICE AtBooleanMask< 3 >	operator<= (const AtVector &lhs, float f)

AI_DEVICE AtBooleanMask< 3 >	operator> (const AtVector &lhs, float f)

AI_DEVICE AtBooleanMask< 3 >	operator>= (const AtVector &lhs, float f)

AI_DEVICE AtBooleanMask< 3 >	operator< (const AtVector &lhs, const AtVector &rhs)

AI_DEVICE AtBooleanMask< 3 >	operator<= (const AtVector &lhs, const AtVector &rhs)

AI_DEVICE AtBooleanMask< 3 >	operator> (const AtVector &lhs, const AtVector &rhs)

AI_DEVICE AtBooleanMask< 3 >	operator>= (const AtVector &lhs, const AtVector &rhs)

AI_DEVICE constexpr	AtVector2::AtVector2 (float x, float y)

AI_DEVICE constexpr	AtVector2::AtVector2 (const AtVector &v)

AI_DEVICE constexpr AtVector2	AtVector2::operator+ (const AtVector2 &p) const

AI_DEVICE AtVector2 &	AtVector2::operator+= (const AtVector2 &p)

AI_DEVICE constexpr AtVector2	AtVector2::operator+ (float f) const

AI_DEVICE AtVector2 &	AtVector2::operator+= (float f)

AI_DEVICE constexpr AtVector2	AtVector2::operator- (const AtVector2 &p) const

AI_DEVICE AtVector2 &	AtVector2::operator-= (const AtVector2 &p)

AI_DEVICE constexpr AtVector2	AtVector2::operator- (float f) const

AI_DEVICE AtVector2 &	AtVector2::operator-= (float f)

AI_DEVICE constexpr AtVector2	AtVector2::operator- () const

AI_DEVICE constexpr AtVector2	AtVector2::operator* (const AtVector2 &p) const

AI_DEVICE AtVector2	*AtVector2::operator=** (const AtVector2 &p)

AI_DEVICE constexpr AtVector2	AtVector2::operator* (float f) const

AI_DEVICE AtVector2	*AtVector2::operator=** (float f)

AI_DEVICE constexpr AtVector2	AtVector2::operator/ (const AtVector2 &p) const

AI_DEVICE AtVector2	AtVector2::operator/= (const AtVector2 &p)

AI_DEVICE AtVector2	AtVector2::operator/ (float f) const

AI_DEVICE AtVector2	AtVector2::operator/= (float f)

AI_DEVICE constexpr bool	AtVector2::operator== (const AtVector2 &p) const

AI_DEVICE constexpr bool	AtVector2::operator!= (const AtVector2 &p) const

AI_DEVICE AtVector2 &	AtVector2::operator= (float f)

AI_DEVICE float &	AtVector2::operator[] (unsigned int i)

AI_DEVICE constexpr const float &	AtVector2::operator[] (unsigned int i) const

AI_DEVICE constexpr AtVector2	operator* (float f, const AtVector2 &p)

AI_DEVICE constexpr AtVector2	operator+ (float f, const AtVector2 &p)

AI_DEVICE constexpr AtVector2	operator- (float f, const AtVector2 &p)

AI_DEVICE AtBooleanMask< 2 >	operator< (const AtVector2 &lhs, float f)

AI_DEVICE AtBooleanMask< 2 >	operator<= (const AtVector2 &lhs, float f)

AI_DEVICE AtBooleanMask< 2 >	operator> (const AtVector2 &lhs, float f)

AI_DEVICE AtBooleanMask< 2 >	operator>= (const AtVector2 &lhs, float f)

AI_DEVICE AtBooleanMask< 2 >	operator< (const AtVector2 &lhs, const AtVector2 &rhs)

AI_DEVICE AtBooleanMask< 2 >	operator<= (const AtVector2 &lhs, const AtVector2 &rhs)

AI_DEVICE AtBooleanMask< 2 >	operator> (const AtVector2 &lhs, const AtVector2 &rhs)

AI_DEVICE AtBooleanMask< 2 >	operator>= (const AtVector2 &lhs, const AtVector2 &rhs)

AI_DEVICE constexpr	AtHPoint::AtHPoint (float x, float y, float z, float w)

AI_DEVICE constexpr	AtHPoint::AtHPoint (const AtVector &v, float w)

AI_DEVICE constexpr AtHPoint	AtHPoint::operator+ (const AtHPoint &p) const

AI_DEVICE constexpr AtHPoint	AtHPoint::operator- (const AtHPoint &p) const

AI_DEVICE constexpr AtHPoint	AtHPoint::operator* (float k) const

AI_DEVICE constexpr AtHPoint	AtHPoint::operator- () const

AI_DEVICE AtVector	AtHPoint::project () const
	Project a homogeneous vector back into 3d: vout = vin.w != 0 ? vin * (1 / vin.w) : (0,0,0)

AI_DEVICE constexpr	AtVectorDv::AtVectorDv (AtVector val, AtVector dx, AtVector dy)

AI_DEVICE constexpr	AtVectorDv::AtVectorDv (AtVector val)

AI_DEVICE constexpr AtVectorDv	AtVectorDv::operator- () const

Variables
float	AtVector::x

float	AtVector::y

float	AtVector::z

float	AtVector2::x

float	AtVector2::y

float	AtHPoint::x

float	AtHPoint::y

float	AtHPoint::z

float	AtHPoint::w

AtVector	AtVectorDv::val

AtVector	AtVectorDv::dx

AtVector	AtVectorDv::dy

Friends
AI_DEVICE friend constexpr AtVector	AtVector::operator* (float f, const AtVector &p)

AI_DEVICE friend constexpr AtVector	AtVector::operator+ (float f, const AtVector &p)

AI_DEVICE friend constexpr AtVector	AtVector::operator- (float f, const AtVector &p)

AI_DEVICE friend constexpr AtVector2	AtVector2::operator* (float f, const AtVector2 &p)

AI_DEVICE friend constexpr AtVector2	AtVector2::operator+ (float f, const AtVector2 &p)

AI_DEVICE friend constexpr AtVector2	AtVector2::operator- (float f, const AtVector2 &p)

2D Vector Operations
AI_DEVICE constexpr float	AiV2Dot (const AtVector2 &v1, const AtVector2 &v2)
	Dot product: <v1, v2>

AI_DEVICE float	AiV2Length (const AtVector2 &v1)
	Vector Length: \|\|v1\|\|.

float	AiV2Dist (const AtVector2 &p1, const AtVector2 &p2)
	Distance between two points: \|\|p1-p2\|\|.

constexpr AtVector2	AiV2Lerp (float t, const AtVector2 &lo, const AtVector2 &hi)
	2D vector linear interpolation (t=0 -> result=lo, t=1 -> result=hi)

constexpr AtVector2	AiV2Clamp (const AtVector2 &in, float lo, float hi)
	Clamp each vector coordinate to the range [lo,hi].

AI_DEVICE AtVector2	ABS (const AtVector2 &a)
	Absolute value of each component.

AI_DEVICE float	AiMaxElement (const AtVector2 &a)
	Element-wise max.

float	AiMinElement (const AtVector2 &a)
	Element-wise min.

3D Vector Operations
AI_DEVICE float	AiV3Length (const AtVector &a)
	Vector Length: \|\|a\|\|.

AI_DEVICE constexpr float	AiV3Dot (const AtVector &a, const AtVector &b)
	Dot product: <a, b>

AI_DEVICE float	AiV3Dist (const AtVector &a, const AtVector &b)
	Distance between two points: \|\|a-b\|\|.

AI_DEVICE constexpr float	AiV3Dist2 (const AtVector &a, const AtVector &b)
	Squared distance between two points: \|\|a-b\|\|^2.

AI_DEVICE constexpr float	AiV3DistPlane (const AtVector &x, const AtVector &p, const AtVector &n)
	Signed distance between point x and a plane defined by point p and normalized vector n.

AI_DEVICE constexpr AtVector	AiV3Cross (const AtVector &a, const AtVector &b)
	Cross product: a x b.

AI_DEVICE AtVector	AiV3Normalize (const AtVector &a)
	Normalize a vector: a / \|\|a\|\|.

AI_DEVICE constexpr AtVector	AiV3Lerp (float t, const AtVector &lo, const AtVector &hi)
	3D vector linear interpolation (t=0 -> result=lo, t=1 -> result=hi)

AI_DEVICE constexpr AtVector	AiV3Clamp (const AtVector &in, float lo, float hi)
	Clamp each vector coordinate to the range [lo,hi].

AI_DEVICE constexpr AtVector	AiV3Min (const AtVector &a, const AtVector &b)
	Minimum of two vectors, component-wise.

AI_DEVICE constexpr AtVector	AiV3Max (const AtVector &a, const AtVector &b)
	Maximum of two vectors, component-wise.

AI_DEVICE AtVector	ABS (const AtVector &a)
	Absolute value of each component.

AI_DEVICE float	AiMaxElement (const AtVector &a)
	Element-wise max.

AI_DEVICE float	AiMinElement (const AtVector &a)
	Element-wise min.

AI_DEVICE AtVector	AiBerpXYZ (float a, float b, const AtVector &p0, const AtVector &p1, const AtVector &p2)
	Barycentric interpolation of a point inside a triangle.

AI_API AI_DEVICE AI_PURE bool	AiV3IsFinite (const AtVector &a)
	Check whether a vector has all valid components (not NaN and not infinite)

AI_DEVICE bool	AiV3IsSmall (const AtVector &a, float epsilon=AI_EPSILON)
	Check for a zero vector, within a small tolerance: \|\|a\|\| < epsilon.

AI_DEVICE void	AiV3RotateToFrame (AtVector &a, const AtVector &u, const AtVector &v, const AtVector &w)
	Rotate vector a so that it aligns with frame {u,v,w}.

AI_DEVICE void	AiBerpUV (float a, float b, float u0, float v0, float u1, float v1, float u2, float v2, float u, float v)
	Barycentric interpolation of UV coordinates inside a 3D triangle.

4D Vector Operations
AI_DEVICE AtHPoint	AiV4CreatePoint (const AtVector &v)
	Create a 4D point: pout = (v.x, v.y, v.z, 1)

AI_DEVICE AtHPoint	AiV4CreateVector (const AtVector &v)
	Create a 4D vector: vout = (v.x, v.y, v.z, 0)

AI_DEVICE void	AiV4CreatePoint (AtHPoint &pout, const AtVector &v)

void	AiV4CreateVector (AtHPoint &vout, const AtVector &v)
	Create a 4D vector: vout = (v.x, v.y, v.z, 0)

void	AiV4Add (AtHPoint &vout, const AtHPoint &v1, const AtHPoint &v2)
	Add two vectors: vout = v1 + v2.

void	AiV4Sub (AtHPoint &vout, const AtHPoint &v1, const AtHPoint &v2)
	Substract two vectors: vout = v1 - v2.

void	AiV4Scale (AtHPoint &vout, const AtHPoint &vin, float k)
	Scale a vector by a constant: vout = vin * k.

void	AiV4Neg (AtHPoint &vout, const AtHPoint &vin)
	Negate a vector: vout = -vin.

void	AiV4Project (AtVector &vout, const AtHPoint &vin)
	Project a homogeneous vector back into 3d: vout = vin.w != 0 ? vin * (1 / vin.w) : (0,0,0)

AI_API AI_DEVICE void	AiV3BuildLocalFrame (AtVector &u, AtVector &v, const AtVector &N)
	Build an orthonormal basis aligned with vector N (Frisvad's method). More...

AI_API AI_DEVICE void	AiV3BuildLocalFramePolar (AtVector &u, AtVector &v, const AtVector &N)
	Build an orthonormal basis aligned with vector N (polar method). More...

Vector Components
#define	AI_X 0
	X component.

#define	AI_Y 1
	Y component.

#define	AI_Z 2
	Z component.

Detailed Description

Vector math types and their related utilities.

Function Documentation

◆ AiV3BuildLocalFrame()

AI_API AI_DEVICE void AiV3BuildLocalFrame	(	AtVector &	U,
		AtVector &	V,
		const AtVector &	N
	)

Build an orthonormal basis aligned with vector N (Frisvad's method).

This is Frisvad's method of building a local reference frame (U,V,W), where W = N. This method is discontinuous at the Z = 0 plane.

Parameters

[out]	U	normalized U basis vector
[out]	V	normalized V basis vector
	N	normalized vector that will serve as our W basis vector (usually this is a surface normal)

◆ AiV3BuildLocalFramePolar()

AI_API AI_DEVICE void AiV3BuildLocalFramePolar	(	AtVector &	U,
		AtVector &	V,
		const AtVector &	N
	)

Build an orthonormal basis aligned with vector N (polar method).

Builds local reference frame (U,V,W), where W = N. Uses the parametric tangent vectors in polar coordinates. This is continuous all across the sphere but at the poles.

Parameters

[out]	U	normalized U basis vector
[out]	V	normalized V basis vector
	N	normalized vector that will serve as our W basis vector (usually this is a surface normal)

Data Structures

Functions

Variables

Friends

2D Vector Operations

3D Vector Operations

4D Vector Operations

Vector Components

Detailed Description

Function Documentation

◆ AiV3BuildLocalFrame()

◆ AiV3BuildLocalFramePolar()