Generic 4x4 matrix [specializations fMat4, dMat4]. More...

#include <Mat4.h>

Public Member Functions
	Mat4 ()
	Default constructor. More...

constexpr	Mat4 (T x1, T y1, T z1, T t1, T x2, T y2, T z2, T t2, T x3, T y3, T z3, T t3, T x4, T y4, T z4, T t4)
	Constructor from explicit values.

	Mat4 (const T *mat)
	Constructor from an array (with column major ordering same as `M`).

	Mat4 (const Mat4 &mat)=default
	Copy constructor.

Mat4 &	operator= (const Mat4 &mat)=default
	Assignement operator.

	operator T* ()
	Implicit conversion to an array T[16].

void	setZero ()
	Set as the null matrix (all coefficients equal 0).

void	setIdentity ()
	Set as the identity matrix.

void	setOrtho (T left, T right, T bottom, T top, T zNear, T zFar)
	Set as an orthographic projection matrix. More...

void	setFrustum (T left, T right, T bottom, T top, T zNear, T zFar)
	Set as a perspective projection matrix. More...

void	setPerspective (T fovy, T aspect, T zNear, T zFar)
	Set as a perspective projection matrix. More...

void	setRotate (T angle, T x, T y, T z)
	Set as a rotation matrix. More...

void	setRotate (T angle, const Vec3< T > v)
	Set as a rotation matrix. More...

void	multRotate (T angle, T x, T y, T z)
	Pre-multiply this matrix by a rotation matrix. More...

void	multRotate (T angle, const Vec3< T > v)
	Pre-multiply this matrix by a rotation matrix. More...

void	setTranslate (T x, T y, T z)
	Set as a translation matrix. More...

void	setTranslate (const Vec3< T > v)
	Set as a translation matrix. More...

void	multTranslate (T x, T y, T z)
	Pre-multiply this matrix by a translation matrix. More...

void	multTranslate (const Vec3< T > v)
	Pre-multiply this matrix by a translation matrix. More...

void	setScale (T x, T y, T z)
	Set as a dilatation matrix. More...

void	setScale (const Vec3< T > v)
	Set as a dilatation matrix. More...

void	multScale (T x, T y, T z)
	Pre-multiply this matrix by a dilatation matrix. More...

void	multScale (const Vec3< T > v)
	Pre-multiply this matrix by a dilatation matrix. More...

void	invertYaxis ()
	invert the y axis, same as multScale({1,-1,1})

void	setLookAt (T eyeX, T eyeY, T eyeZ, T centerX, T centerY, T centerZ, T upX, T upY, T upZ)
	Set the matrix for a camera looking at a given direction. More...

void	setLookAt (const Vec3< T > eye, const Vec3< T > center, const Vec3< T > up)
	Set the matrix for a camera looking at a given direction. More...

TGX_INLINE Vec4< T >	mult (const Vec4< T > V) const
	Matrix-vector multiplication.

TGX_INLINE Vec4< T >	mult (const Vec3< T > &V, float w) const
	Matrix-vector multiplication.

TGX_INLINE Vec4< T >	mult0 (const Vec3< T > &V) const
	Matrix-vector multiplication (last component of vector set to w = 0).

TGX_INLINE Vec4< T >	mult1 (const Vec3< T > &V) const
	Matrix-vector multiplication (last component of vector set to w = 1)

void	*operator=** (T a)
	Scalar multiplication.

void	transpose ()
	Transpose the matrix (in place)

void	print (Stream &outputStream=Serial) const
	Output a representation of the matrix using a given Stream. More...

Public Attributes
T	M [16]
	The matrix array in column major ordering: More...

Detailed Description

template<typename T>
struct tgx::Mat4< T >

Generic 4x4 matrix [specializations fMat4, dMat4].

The class encapsulate a 4x4 matrix with element of type T which must be a floating point type (either float or double). Such a matrix is used in 3D grpahics to represent a transformation (translation, rotation, dilatation...).

The matrix is internally represented by an public array M[16] in column major ordering:

+-----------------------------+
| M[0] | M[4] | M[8]  | M[12] |
|------+------+-------+-------|
| M[1] | M[5] | M[9]  | M[13] |
|------+------+-------+-------|
| M[2] | M[6] | M[10] | M[14] |
|------+------+-------+-------|
| M[3] | M[7] | M[11] | M[15] |
+-----------------------------+

See also: Vec2, Vec3, Vec4

Constructor & Destructor Documentation

◆ Mat4()

template<typename T >

tgx::Mat4< T >::Mat4 ( )

inline

Default constructor.

the matrix content is undefined.

Member Function Documentation

◆ setOrtho()

template<typename T >

void tgx::Mat4< T >::setOrtho	(	T	left,
		T	right,
		T	bottom,
		T	top,
		T	zNear,
		T	zFar
	)

inline

Set as an orthographic projection matrix.

https://www.khronos.org/registry/OpenGL-Refpages/gl2.1/xhtml/glOrtho.xml

Parameters

left,right	coordinates for the left and right vertical clipping planes
bottom,top	coordinates for the bottom and top horizontal clipping planes.
zNear,zFar	distances to the nearer and farther depth clipping planes.

◆ setFrustum()

template<typename T >

void tgx::Mat4< T >::setFrustum	(	T	left,
		T	right,
		T	bottom,
		T	top,
		T	zNear,
		T	zFar
	)

inline

Set as a perspective projection matrix.

https://www.khronos.org/registry/OpenGL-Refpages/gl2.1/xhtml/glFrustum.xml

Parameters

left,right	coordinates for the left and right vertical clipping planes
bottom,top	coordinates for the bottom and top horizontal clipping planes.
zNear,zFar	distances to the nearer and farther depth clipping planes.

◆ setPerspective()

template<typename T >

void tgx::Mat4< T >::setPerspective	(	T	fovy,
		T	aspect,
		T	zNear,
		T	zFar
	)

inline

Set as a perspective projection matrix.

https://www.khronos.org/registry/OpenGL-Refpages/gl2.1/xhtml/gluPerspective.xml

Parameters

fovy	field of view angle, in degrees, in the y direction.
aspect	aspect ratio that determines the field of view in the x direction. The aspect ratio is the ratio of x (width) to y (height).
zNear	distance from the viewer to the near clipping plane.
zFar	distance from the viewer to the far clipping plane.

◆ setRotate() [1/2]

template<typename T >

void tgx::Mat4< T >::setRotate	(	T	angle,
		T	x,
		T	y,
		T	z
	)

inline

Set as a rotation matrix.

https://www.khronos.org/registry/OpenGL-Refpages/gl2.1/xhtml/glRotate.xml

Parameters

angle	rotation angle in degrees.
x,y,z	coordinates of the direction vector for the rotation.

◆ setRotate() [2/2]

template<typename T >

void tgx::Mat4< T >::setRotate	(	T	angle,
		const Vec3< T >	v
	)

inline

Set as a rotation matrix.

https://www.khronos.org/registry/OpenGL-Refpages/gl2.1/xhtml/glRotate.xml

Parameters

angle	rotation angle in degrees.
v	direction vector for the rotation.

◆ multRotate() [1/2]

template<typename T >

void tgx::Mat4< T >::multRotate	(	T	angle,
		T	x,
		T	y,
		T	z
	)

inline

Pre-multiply this matrix by a rotation matrix.

https://www.khronos.org/registry/OpenGL-Refpages/gl2.1/xhtml/glRotate.xml

Parameters

angle	rotation angle in degrees.
x,y,z	coordinates of the direction vector for the rotation.

◆ multRotate() [2/2]

template<typename T >

void tgx::Mat4< T >::multRotate	(	T	angle,
		const Vec3< T >	v
	)

inline

Pre-multiply this matrix by a rotation matrix.

https://www.khronos.org/registry/OpenGL-Refpages/gl2.1/xhtml/glRotate.xml

Parameters

angle	rotation angle in degrees.
v	direction vector for the rotation.

◆ setTranslate() [1/2]

template<typename T >

void tgx::Mat4< T >::setTranslate	(	T	x,
		T	y,
		T	z
	)

inline

Set as a translation matrix.

https://www.khronos.org/registry/OpenGL-Refpages/gl2.1/xhtml/glTranslate.xml

Parameters

x,y,z coordinates of the translation vector.

◆ setTranslate() [2/2]

template<typename T >

void tgx::Mat4< T >::setTranslate ( const Vec3< T > v )

inline

Set as a translation matrix.

https://www.khronos.org/registry/OpenGL-Refpages/gl2.1/xhtml/glTranslate.xml

Parameters

v	the translation vector.

◆ multTranslate() [1/2]

template<typename T >

void tgx::Mat4< T >::multTranslate	(	T	x,
		T	y,
		T	z
	)

inline

Pre-multiply this matrix by a translation matrix.

https://www.khronos.org/registry/OpenGL-Refpages/gl2.1/xhtml/glTranslate.xml

Parameters

x,y,z coordinates of the translation vector.

◆ multTranslate() [2/2]

template<typename T >

void tgx::Mat4< T >::multTranslate ( const Vec3< T > v )

inline

Pre-multiply this matrix by a translation matrix.

https://www.khronos.org/registry/OpenGL-Refpages/gl2.1/xhtml/glTranslate.xml

Parameters

v	the translation vector.

◆ setScale() [1/2]

template<typename T >

void tgx::Mat4< T >::setScale	(	T	x,
		T	y,
		T	z
	)

inline

Set as a dilatation matrix.

https://www.khronos.org/registry/OpenGL-Refpages/gl2.1/xhtml/glScale.xml

Parameters

x,y,z scale factors along the x, y, and z axes respectively.

◆ setScale() [2/2]

template<typename T >

void tgx::Mat4< T >::setScale ( const Vec3< T > v )

inline

Set as a dilatation matrix.

https://www.khronos.org/registry/OpenGL-Refpages/gl2.1/xhtml/glScale.xml

Parameters

v	vector representing the scale factors along each axis.

◆ multScale() [1/2]

template<typename T >

void tgx::Mat4< T >::multScale	(	T	x,
		T	y,
		T	z
	)

inline

Pre-multiply this matrix by a dilatation matrix.

https://www.khronos.org/registry/OpenGL-Refpages/gl2.1/xhtml/glScale.xml

Parameters

x,y,z scale factors along the x, y, and z axes respectively.

◆ multScale() [2/2]

template<typename T >

void tgx::Mat4< T >::multScale ( const Vec3< T > v )

inline

Pre-multiply this matrix by a dilatation matrix.

https://www.khronos.org/registry/OpenGL-Refpages/gl2.1/xhtml/glScale.xml

Parameters

v	vector representing the scale factors along each axis.

◆ setLookAt() [1/2]

template<typename T >

void tgx::Mat4< T >::setLookAt	(	T	eyeX,
		T	eyeY,
		T	eyeZ,
		T	centerX,
		T	centerY,
		T	centerZ,
		T	upX,
		T	upY,
		T	upZ
	)

inline

Set the matrix for a camera looking at a given direction.

https://www.khronos.org/registry/OpenGL-Refpages/gl2.1/xhtml/gluLookAt.xml

The formula given by khronos is wrong ! The cross-product of two unit vectors is not normalized.

See https://stackoverflow.com/questions/30409318/lookat-matrix-distorts-when-looking-up-or-down

Parameters

eyeX,eyeY,eyeZ	position of the eye point.
centerX,centerY,centerZ	position of the reference point (the camera points toward this point).
upX,upY,upZ	direction of the up vector.

◆ setLookAt() [2/2]

template<typename T >

void tgx::Mat4< T >::setLookAt	(	const Vec3< T >	eye,
		const Vec3< T >	center,
		const Vec3< T >	up
	)

inline

Set the matrix for a camera looking at a given direction.

https://www.khronos.org/registry/OpenGL-Refpages/gl2.1/xhtml/gluLookAt.xml

The formula given by khronos is wrong ! The cross-product of two unit vectors is not normalized.

See https://stackoverflow.com/questions/30409318/lookat-matrix-distorts-when-looking-up-or-down

Parameters

eye	eye position.
center	reference point (the camera points toward this point).
up	up vector.

◆ print()

template<typename T >

void tgx::Mat4< T >::print ( Stream & outputStream = Serial ) const

inline

Output a representation of the matrix using a given Stream.

Attention: Defined only in the Arduino environment.

Member Data Documentation

◆ M

template<typename T >

T tgx::Mat4< T >::M[16]

The matrix array in column major ordering:

+-----------------------------+
| M[0] | M[4] | M[8]  | M[12] |
|------+------+-------+-------|
| M[1] | M[5] | M[9]  | M[13] |
|------+------+-------+-------|
| M[2] | M[6] | M[10] | M[14] |
|------+------+-------+-------|
| M[3] | M[7] | M[11] | M[15] |
+-----------------------------+

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

src/Mat4.h

Public Member Functions

Public Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Mat4()

Member Function Documentation

◆ setOrtho()

◆ setFrustum()

◆ setPerspective()

◆ setRotate() [1/2]

◆ setRotate() [2/2]

◆ multRotate() [1/2]

◆ multRotate() [2/2]

◆ setTranslate() [1/2]

◆ setTranslate() [2/2]

◆ multTranslate() [1/2]

◆ multTranslate() [2/2]

◆ setScale() [1/2]

◆ setScale() [2/2]

◆ multScale() [1/2]

◆ multScale() [2/2]

◆ setLookAt() [1/2]

◆ setLookAt() [2/2]

◆ print()

Member Data Documentation

◆ M