#include <Mat4.h>

Classes
struct	StereoMatrices
	Bundle of left/right view and projection matrices for stereo. More...

Public Member Functions
	Mat4t ()
	Construct identity matrix.
	Mat4t (T m11, T m12, T m13, T m14, T m21, T m22, T m23, T m24, T m31, T m32, T m33, T m34, T m41, T m42, T m43, T m44)
	Construct from 16 elements (column-major order).
	Mat4t (const std::array< T, 16 > &e)
	Construct from a raw array of 16 elements.
	Mat4t (const Vec3t< T > &e1, T e14, const Vec3t< T > &e2, T e24, const Vec3t< T > &e3, T e34, const Vec3t< T > &e4=Vec3(0, 0, 0), T e44=1)
	Construct from three Vec3 column vectors and their last column entries.
	Mat4t (const Mat4t &other)
	Copy-construct from another matrix.
const std::string	toString () const
	String representation (pretty-printed rows).
	operator T* (void)
	Implicit conversion to raw pointer (non-const).
	operator const T * (void) const
	Implicit conversion to raw pointer (const).
Mat4t	operator* (T scalar) const
	Component-wise multiplication by scalar.
Mat4t	operator+ (T scalar) const
	Component-wise addition of scalar.
Mat4t	operator- (T scalar) const
	Component-wise subtraction of scalar.
Mat4t	operator/ (T scalar) const
	Component-wise division by scalar.
Mat4t	operator* (const Mat4t &other) const
	Matrix–matrix product (column-major; standard linear algebra).
Vec2t< T >	operator* (const Vec2t< T > &other) const
	Transform a 2D vector (homogeneous with z=0,w=1) and drop back to 2D.
Vec3t< T >	operator* (const Vec3t< T > &other) const
	Transform a 3D point using homogeneous divide.
Vec4t< T >	operator* (const Vec4t< T > &other) const
	Transform a 4D homogeneous vector.

Static Public Member Functions
static Mat4t	scaling (T scale)
	Uniform scaling by `scale` on all axes.
static Mat4t	scaling (const Vec3t< T > &scale)
	Non-uniform scaling by components of `scale`.
static Mat4t	translation (const Vec3t< T > &trans)
	Translation by vector `trans`.
static Mat4t	translation (T x, T y, T z)
	Translation by components.
static Mat4t	scaling (T x, T y, T z)
	Non-uniform scaling by components.
static Mat4t	rotationX (T degree)
	Rotation about the X-axis by `degree` (degrees).
static Mat4t	rotationY (T degree)
	Rotation about the Y-axis by `degree` (degrees).
static Mat4t	rotationZ (T degree)
	Rotation about the Z-axis by `degree` (degrees).
static Mat4t	rotationAxis (const Vec3t< T > &axis, T degree)
	Rotation about an arbitrary axis by `degree` (degrees).
static Mat4t	transpose (const Mat4t &m)
	Matrix transpose.
static T	det (const Mat4t &m)
	Determinant of a 4×4 matrix.
static Mat4t	inverse (const Mat4t &m)
	Matrix inverse computed via adjugate and determinant.
static Mat4t	inverse (const Mat4t &m, T det)
	Matrix inverse with precomputed determinant.
static Mat4t	perspective (T fovy, T aspect, T znear, T zfar)
	Perspective projection from vertical FOV and aspect ratio.
static Mat4t	perspective (T left, T right, T bottom, T top, T znear, T zfar)
	Off-center perspective projection from frustum bounds.
static Mat4t	ortho (T left, T right, T bottom, T top, T znear, T zfar)
	Orthographic projection from axis-aligned view volume.
static Mat4t	lookAt (const Vec3t< T > &vEye, const Vec3t< T > &vAt, const Vec3t< T > &vUp)
	Right-handed view matrix that looks from `vEye` to `vAt` with up `vUp`.
static Mat4t	mirror (const Vec3t< T > &p, const Vec3t< T > &n)
	Reflection matrix for a plane through point `p` with normal `n`.
static StereoMatrices	stereoLookAtAndProjection (const Vec3t< T > &eye, const Vec3t< T > &at, const Vec3t< T > &up, T fovy, T aspect, T znear, T zfar, T focalLength, T eyeDist)
	Convenience builder for stereo view and projection matrices.

Friends
std::ostream &	operator<< (std::ostream &os, const Mat4t &m)
	Stream insertion using toString().

Constructor & Destructor Documentation

◆ Mat4t() [1/5]

template<typename T>

Mat4t< T >::Mat4t ( )

inline

Construct identity matrix.

◆ Mat4t() [2/5]

template<typename T>

Mat4t< T >::Mat4t	(	T	m11,
		T	m12,
		T	m13,
		T	m14,
		T	m21,
		T	m22,
		T	m23,
		T	m24,
		T	m31,
		T	m32,
		T	m33,
		T	m34,
		T	m41,
		T	m42,
		T	m43,
		T	m44 )

inline

Construct from 16 elements (column-major order).

Parameters

m11..m44 Elements of the matrix in column-major order.

◆ Mat4t() [3/5]

template<typename T>

Mat4t< T >::Mat4t ( const std::array< T, 16 > & e )

inline

Construct from a raw array of 16 elements.

Parameters

e	Array in column-major order.

◆ Mat4t() [4/5]

template<typename T>

Mat4t< T >::Mat4t	(	const Vec3t< T > &	e1,
		T	e14,
		const Vec3t< T > &	e2,
		T	e24,
		const Vec3t< T > &	e3,
		T	e34,
		const Vec3t< T > &	e4 = Vec3(0,0,0),
		T	e44 = 1 )

inline

Construct from three Vec3 column vectors and their last column entries.

Parameters

e1,e2,e3	Columns 1–3 (x,y,z components).
e14,e24,e34	Elements of the 4th row for columns 1–3.
e4	Optional 4th column (xyz); defaults to (0,0,0).
e44	Optional (4,4) element; defaults to 1.

◆ Mat4t() [5/5]

template<typename T>

Mat4t< T >::Mat4t ( const Mat4t< T > & other )

inline

Copy-construct from another matrix.

Member Function Documentation

◆ det()

template<typename T>

T Mat4t< T >::det ( const Mat4t< T > & m )

inlinestatic

Determinant of a 4×4 matrix.

Here is the caller graph for this function:

◆ inverse() [1/2]

template<typename T>

Mat4t Mat4t< T >::inverse ( const Mat4t< T > & m )

inlinestatic

Matrix inverse computed via adjugate and determinant.

Parameters

m	Input matrix.

Returns: Inverse of m.

Note: This overload computes the determinant internally.

Here is the caller graph for this function:

◆ inverse() [2/2]

template<typename T>

Mat4t Mat4t< T >::inverse	(	const Mat4t< T > &	m,
		T	det )

inlinestatic

Matrix inverse with precomputed determinant.

Parameters

m	Input matrix.
det	Determinant of `m`.

Returns: Inverse of m.

Warning: No zero-check is performed; caller must ensure det ≠ 0.

2

3

4

◆ lookAt()

template<typename T>

Mat4t Mat4t< T >::lookAt	(	const Vec3t< T > &	vEye,
		const Vec3t< T > &	vAt,
		const Vec3t< T > &	vUp )

inlinestatic

Right-handed view matrix that looks from vEye to vAt with up vUp.

Equivalent to the common LookAt construction (OpenGL style).

Here is the caller graph for this function:

◆ mirror()

template<typename T>

Mat4t Mat4t< T >::mirror	(	const Vec3t< T > &	p,
		const Vec3t< T > &	n )

inlinestatic

Reflection matrix for a plane through point p with normal n.

◆ operator const T *()

template<typename T>

Mat4t< T >::operator const T * ( void ) const

inline

Implicit conversion to raw pointer (const).

Returns: Const pointer to the underlying e[0].

◆ operator T*()

template<typename T>

Mat4t< T >::operator T* ( void )

inline

Implicit conversion to raw pointer (non-const).

Returns: Pointer to the underlying e[0].

Warning: Exposes internal layout; use with care.

◆ operator*() [1/5]

template<typename T>

Mat4t Mat4t< T >::operator* ( const Mat4t< T > & other ) const

inline

Matrix–matrix product (column-major; standard linear algebra).

◆ operator*() [2/5]

template<typename T>

Vec2t< T > Mat4t< T >::operator* ( const Vec2t< T > & other ) const

inline

Transform a 2D vector (homogeneous with z=0,w=1) and drop back to 2D.

◆ operator*() [3/5]

template<typename T>

Vec3t< T > Mat4t< T >::operator* ( const Vec3t< T > & other ) const

inline

Transform a 3D point using homogeneous divide.

Uses w = M[3]*p + 1*e[15]. The result is divided by w.

◆ operator*() [4/5]

template<typename T>

Vec4t< T > Mat4t< T >::operator* ( const Vec4t< T > & other ) const

inline

Transform a 4D homogeneous vector.

◆ operator*() [5/5]

template<typename T>

Mat4t Mat4t< T >::operator* ( T scalar ) const

inline

Component-wise multiplication by scalar.

◆ operator+()

template<typename T>

Mat4t Mat4t< T >::operator+ ( T scalar ) const

inline

Component-wise addition of scalar.

◆ operator-()

template<typename T>

Mat4t Mat4t< T >::operator- ( T scalar ) const

inline

Component-wise subtraction of scalar.

◆ operator/()

template<typename T>

Mat4t Mat4t< T >::operator/ ( T scalar ) const

inline

Component-wise division by scalar.

◆ ortho()

template<typename T>

Mat4t Mat4t< T >::ortho	(	T	left,
		T	right,
		T	bottom,
		T	top,
		T	znear,
		T	zfar )

inlinestatic

Orthographic projection from axis-aligned view volume.

◆ perspective() [1/2]

template<typename T>

Mat4t Mat4t< T >::perspective	(	T	fovy,
		T	aspect,
		T	znear,
		T	zfar )

inlinestatic

Perspective projection from vertical FOV and aspect ratio.

Parameters

fovy	Vertical field of view in degrees.
aspect	Aspect ratio (width / height).
znear	Near plane distance (> 0).
zfar	Far plane distance (> znear).

Here is the caller graph for this function:

◆ perspective() [2/2]

template<typename T>

Mat4t Mat4t< T >::perspective	(	T	left,
		T	right,
		T	bottom,
		T	top,
		T	znear,
		T	zfar )

inlinestatic

Off-center perspective projection from frustum bounds.

Parameters

left,right,bottom,top	Frustum bounds at the near plane.
znear,zfar	Near and far plane distances.

◆ rotationAxis()

template<typename T>

Mat4t Mat4t< T >::rotationAxis	(	const Vec3t< T > &	axis,
		T	degree )

inlinestatic

Rotation about an arbitrary axis by degree (degrees).

Parameters

axis	Unit rotation axis (not normalized internally).
degree	Rotation angle in degrees (right-handed).

◆ rotationX()

template<typename T>

Mat4t Mat4t< T >::rotationX ( T degree )

inlinestatic

Rotation about the X-axis by degree (degrees).

◆ rotationY()

template<typename T>

Mat4t Mat4t< T >::rotationY ( T degree )

inlinestatic

Rotation about the Y-axis by degree (degrees).

◆ rotationZ()

template<typename T>

Mat4t Mat4t< T >::rotationZ ( T degree )

inlinestatic

Rotation about the Z-axis by degree (degrees).

◆ scaling() [1/3]

template<typename T>

Mat4t Mat4t< T >::scaling ( const Vec3t< T > & scale )

inlinestatic

Non-uniform scaling by components of scale.

◆ scaling() [2/3]

template<typename T>

Mat4t Mat4t< T >::scaling ( T scale )

inlinestatic

Uniform scaling by scale on all axes.

Here is the caller graph for this function:

◆ scaling() [3/3]

template<typename T>

Mat4t Mat4t< T >::scaling	(	T	x,
		T	y,
		T	z )

inlinestatic

Non-uniform scaling by components.

◆ stereoLookAtAndProjection()

template<typename T>

StereoMatrices Mat4t< T >::stereoLookAtAndProjection	(	const Vec3t< T > &	eye,
		const Vec3t< T > &	at,
		const Vec3t< T > &	up,
		T	fovy,
		T	aspect,
		T	znear,
		T	zfar,
		T	focalLength,
		T	eyeDist )

inlinestatic

Convenience builder for stereo view and projection matrices.

Parameters

eye	Camera position.
at	Look-at target point.
up	Up direction.
fovy	Vertical field of view in degrees.
aspect	Aspect ratio (width/height).
znear,zfar	Near/Far plane distances.
focalLength	Distance from eye to focus plane used for frustum shift.
eyeDist	Inter-pupillary distance (eye separation).

◆ toString()

template<typename T>

const std::string Mat4t< T >::toString ( ) const

inline

String representation (pretty-printed rows).

Returns: New string describing the matrix.

Here is the caller graph for this function:

◆ translation() [1/2]

template<typename T>

Mat4t Mat4t< T >::translation ( const Vec3t< T > & trans )

inlinestatic

Translation by vector trans.

Here is the caller graph for this function:

◆ translation() [2/2]

template<typename T>

Mat4t Mat4t< T >::translation	(	T	x,
		T	y,
		T	z )

inlinestatic

Translation by components.

◆ transpose()

template<typename T>

Mat4t Mat4t< T >::transpose ( const Mat4t< T > & m )

inlinestatic

Matrix transpose.

◆ operator<<

template<typename T>

std::ostream & operator<<	(	std::ostream &	os,
		const Mat4t< T > &	m )

friend

Stream insertion using toString().

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

Mat4.h

Classes

Public Member Functions

Static Public Member Functions

Friends

Constructor & Destructor Documentation

◆ Mat4t() [1/5]

◆ Mat4t() [2/5]

◆ Mat4t() [3/5]

◆ Mat4t() [4/5]

◆ Mat4t() [5/5]

Member Function Documentation

◆ det()

◆ inverse() [1/2]

◆ inverse() [2/2]

◆ lookAt()

◆ mirror()

◆ operator const T *()

◆ operator T*()

◆ operator*() [1/5]

◆ operator*() [2/5]

◆ operator*() [3/5]

◆ operator*() [4/5]

◆ operator*() [5/5]

◆ operator+()

◆ operator-()

◆ operator/()

◆ ortho()

◆ perspective() [1/2]

◆ perspective() [2/2]

◆ rotationAxis()

◆ rotationX()

◆ rotationY()

◆ rotationZ()

◆ scaling() [1/3]

◆ scaling() [2/3]

◆ scaling() [3/3]

◆ stereoLookAtAndProjection()

◆ toString()

◆ translation() [1/2]

◆ translation() [2/2]

◆ transpose()

Friends And Related Symbol Documentation

◆ operator<<