AtMatrix API

AtMatrix type creation and operation. More...

Data Structures
struct	AtMatrix

Functions
bool	AtMatrix::operator== (const AtMatrix &m) const
constexpr const float *	AtMatrix::operator[] (int t) const
float *	AtMatrix::operator[] (int t)
AI_API AI_DEVICE AtMatrix	AiM4Identity ()
	Create an identity matrix. More...
AI_API AtMatrix	AiM4Translation (const AtVector &t)
	Create a translation matrix from a translation vector. More...
AI_API AI_DEVICE AtMatrix	AiM4RotationX (float x)
	Create a X-axis rotation matrix. More...
AI_API AI_DEVICE AtMatrix	AiM4RotationY (float y)
	Create a Y-axis rotation matrix. More...
AI_API AI_DEVICE AtMatrix	AiM4RotationZ (float z)
	Create a Z-axis rotation matrix. More...
AI_API AtMatrix	AiM4Scaling (const AtVector &s)
	Create a scaling matrix from a scaling vector. More...
AI_API AI_DEVICE AtMatrix	AiM4Frame (const AtVector &o, const AtVector &u, const AtVector &v, const AtVector &w)
	Create a matrix that transforms into a new coordinate frame. More...
AI_API AI_DEVICE AtVector	AiM4PointByMatrixMult (const AtMatrix &m, const AtVector &pin)
	Left-multiply a point by a matrix. More...
AI_API AI_DEVICE AtHPoint	AiM4HPointByMatrixMult (const AtMatrix &m, const AtHPoint &pin)
	Left-multiply a 4D point by a matrix. More...
AI_API AI_DEVICE AtVector	AiM4VectorByMatrixMult (const AtMatrix &m, const AtVector &vin)
	Left-multiply a vector by a matrix. More...
AI_API AI_DEVICE AtVector	AiM4VectorByMatrixTMult (const AtMatrix &m, const AtVector &vin)
	Right-multiply a vector by a matrix. More...
AI_API AI_DEVICE AtMatrix	AiM4Mult (const AtMatrix &ma, const AtMatrix &mb)
	Multiply two matrices. More...
AI_API AI_DEVICE AtMatrix	AiM4Transpose (const AtMatrix &min)
	Calculate the transpose of a matrix. More...
AI_API AI_DEVICE AtMatrix	AiM4Invert (const AtMatrix &min)
	Calculate the inverse of a matrix. More...
AI_API AI_PURE float	AiM4Determinant (const AtMatrix &m)
	Determinant of a matrix. More...
AI_API AI_DEVICE AtMatrix	AiM4Lerp (float t, const AtMatrix &ma, const AtMatrix &mb)
	Linear interpolation of two matrices. More...
AI_API AI_PURE bool	AiM4IsIdentity (const AtMatrix &m)
	Is this an identity matrix? More...
AI_API AI_PURE bool	AiM4IsSingular (const AtMatrix &m)
	Is this a singular matrix? More...

Variables
float	AtMatrix::data [4][4]

Detailed Description

AtMatrix type creation and operation.

Function Documentation

AiM4Identity()

AI_API AI_DEVICE AtMatrix AiM4Identity

(

)

Create an identity matrix.

Parameters

[out]

mout

identity matrix result

AiM4Translation()

AI_API AtMatrix AiM4Translation

(

const AtVector &

t

)

Create a translation matrix from a translation vector.

Parameters

[out]	mout	matrix result
	t	translation vector

AiM4RotationX()

AI_API AI_DEVICE AtMatrix AiM4RotationX

(

float

x

)

Create a X-axis rotation matrix.

Parameters

[out]	mout	matrix result
	x	angle from the X axis (in degrees)

AiM4RotationY()

AI_API AI_DEVICE AtMatrix AiM4RotationY

(

float

y

)

Create a Y-axis rotation matrix.

Parameters

[out]	mout	matrix result
	y	angle from the Y axis (in degrees)

AiM4RotationZ()

AI_API AI_DEVICE AtMatrix AiM4RotationZ

(

float

z

)

Create a Z-axis rotation matrix.

Parameters

[out]	mout	matrix result
	z	angle from the Z axis (in degrees)

AiM4Scaling()

AI_API AtMatrix AiM4Scaling

(

const AtVector &

s

)

Create a scaling matrix from a scaling vector.

Parameters

[out]	mout	matrix result
	s	scaling vector

AiM4Frame()

AI_API AI_DEVICE AtMatrix AiM4Frame	(	const AtVector &	o,
		const AtVector &	u,
		const AtVector &	v,
		const AtVector &	w
	)

Create a matrix that transforms into a new coordinate frame.

The new coordinate frame is formed from an origin and a set of orthonormal vectors {U,V,W}, all expressed in world coordinates.

Parameters

[out]	mout	matrix result
	o	origin vector
	u	U basis vector
	v	V basis vector
	w	W basis vector

AiM4PointByMatrixMult()

AI_API AI_DEVICE AtVector AiM4PointByMatrixMult	(	const AtMatrix &	m,
		const AtVector &	pin
	)

Left-multiply a point by a matrix.

Parameters

[out]	pout	multiplied point pout = m pin
	m	input matrix
	pin	input point

AiM4HPointByMatrixMult()

AI_API AI_DEVICE AtHPoint AiM4HPointByMatrixMult	(	const AtMatrix &	m,
		const AtHPoint &	pin
	)

Left-multiply a 4D point by a matrix.

Parameters

[out]	pout	multiplied 4D point, pout = m pin
	m	input matrix
	pin	input 4D point

AiM4VectorByMatrixMult()

AI_API AI_DEVICE AtVector AiM4VectorByMatrixMult	(	const AtMatrix &	m,
		const AtVector &	vin
	)

Left-multiply a vector by a matrix.

Note that multiplying a vector by a matrix is different than multiplying a point by a matrix.

Parameters

[out]	vout	multiplied vector, vout = m vin
	m	input matrix
	vin	input vector

AiM4VectorByMatrixTMult()

AI_API AI_DEVICE AtVector AiM4VectorByMatrixTMult	(	const AtMatrix &	m,
		const AtVector &	vin
	)

Right-multiply a vector by a matrix.

This is equivalent to left-multiply vector by transpose of a matrix: vout = (m^T) vin

Parameters

[out]	vout	multiplied vector, vout = vin m
	m	input matrix
	vin	input vector

AiM4Mult()

AI_API AI_DEVICE AtMatrix AiM4Mult	(	const AtMatrix &	ma,
		const AtMatrix &	mb
	)

Multiply two matrices.

Parameters

[out]	mout	multiplied matrix result, mout = ma mb
	ma	input matrix
	mb	input matrix

AiM4Transpose()

AI_API AI_DEVICE AtMatrix AiM4Transpose

(

const AtMatrix &

min

)

Calculate the transpose of a matrix.

Parameters

	min	input matrix
[out]	mout	transpose matrix: mout = min^T

AiM4Invert()

AI_API AI_DEVICE AtMatrix AiM4Invert

(

const AtMatrix &

min

)

Calculate the inverse of a matrix.

Parameters

	min	input matrix to be inverted
[out]	mout	inverted matrix: mout = min^-1

AiM4Determinant()

AI_API AI_PURE float AiM4Determinant

(

const AtMatrix &

m

)

Determinant of a matrix.

Parameters

m	input matrix

Returns

determinant of m

AiM4Lerp()

AI_API AI_DEVICE AtMatrix AiM4Lerp	(	float	t,
		const AtMatrix &	ma,
		const AtMatrix &	mb
	)

Linear interpolation of two matrices.

Parameters

[out]	mout	interpolated matrix: mout = (1-t)*ma + t*mb
	t	interpolation parameter, in [0,1]
	ma	input matrix at t=0
	mb	input matrix at t=1

AiM4IsIdentity()

AI_API AI_PURE bool AiM4IsIdentity

(

const AtMatrix &

m

)

Is this an identity matrix?

Parameters

m	input matrix

Returns

true if m is the identity

AiM4IsSingular()

AI_API AI_PURE bool AiM4IsSingular

(

const AtMatrix &

m

)

Is this a singular matrix?

Parameters

m	input matrix

Returns

true if m is singular (its determinant is zero or almost zero)