#include <CUMat4.h>

Public Member Functions
	Mat4 ()

	Mat4 (float m11, float m12, float m13, float m14, float m21, float m22, float m23, float m24, float m31, float m32, float m33, float m34, float m41, float m42, float m43, float m44)

	Mat4 (const float *mat)

	Mat4 (const Mat4 &copy)

	Mat4 (Mat4 &&copy)

	Mat4 (const Quaternion &rotation)

	~Mat4 ()

Mat4 &	operator= (const Mat4 &mat)

Mat4 &	operator= (Mat4 &&mat)

Mat4 &	operator= (const float *array)

Mat4 &	operator= (const Quaternion &quat)

Mat4 &	set (float m11, float m12, float m13, float m14, float m21, float m22, float m23, float m24, float m31, float m32, float m33, float m34, float m41, float m42, float m43, float m44)

Mat4 &	set (const float *mat)

Mat4 &	set (const Quaternion &quat)

Mat4 &	set (const Mat4 &mat)

Mat4 &	setIdentity ()

Mat4 &	setZero ()

Mat4 &	add (float scalar)

Mat4 &	add (const Mat4 &mat)

Mat4 &	subtract (float scalar)

Mat4 &	subtract (const Mat4 &mat)

Mat4 &	multiply (float scalar)

Mat4 &	multiply (const Mat4 &mat)

Mat4 &	negate ()

Mat4	getNegation () const

Mat4 &	invert ()

Mat4	getInverse () const

Mat4 &	transpose ()

Mat4	getTranspose () const

Mat4 &	operator+= (const Mat4 &mat)

Mat4 &	operator-= (const Mat4 &mat)

Mat4 &	operator*= (const Mat4 &mat)

Mat4 &	operator*= (float scalar)

const Mat4	operator+ (const Mat4 &mat) const

const Mat4	operator- (const Mat4 &mat) const

const Mat4	operator- () const

const Mat4	operator* (const Mat4 &mat) const

const Mat4	operator* (float scalar) const

bool	isExactly (const Mat4 &mat) const

bool	equals (const Mat4 &mat, float epsilon=CU_MATH_EPSILON) const

bool	operator== (const Mat4 &mat) const

bool	operator!= (const Mat4 &mat) const

bool	isIdentity (float epsilon=CU_MATH_EPSILON) const

bool	isInvertible (float epsilon=CU_MATH_EPSILON) const

bool	isOrthogonal (float epsilon=CU_MATH_EPSILON) const

float	getDeterminant () const

Vec3	getScale () const

Quaternion	getRotation () const

Vec3	getTranslation () const

Vec3	getUpVector () const

Vec3	getDownVector () const

Vec3	getLeftVector () const

Vec3	getRightVector () const

Vec3	getForwardVector () const

Vec3	getBackVector () const

Vec2	transform (const Vec2 point) const

Rect	transform (const Rect rect) const

Vec2	transformVector (const Vec2 vec) const

Vec3	transform (const Vec3 point) const

Vec3	transformVector (const Vec3 vec) const

Vec4	transform (const Vec4 vec) const

Mat4 &	rotate (const Quaternion &q)

Mat4 &	rotate (const Vec3 axis, float angle)

Mat4 &	rotateX (float angle)

Mat4 &	rotateY (float angle)

Mat4 &	rotateZ (float angle)

Mat4 &	scale (float value)

Mat4 &	scale (const Vec3 s)

Mat4 &	scale (float sx, float sy, float sz)

Mat4 &	translate (const Vec3 t)

Mat4 &	translate (float tx, float ty, float tz)

std::string	toString (bool verbose=false) const

	operator std::string () const

	operator Affine2 () const

	Mat4 (const Affine2 &aff)

Mat4 &	operator= (const Affine2 &aff)

Mat4 &	set (const Affine2 &aff)

Static Public Member Functions
static Mat4	createLookAt (const Vec3 eye, const Vec3 target, const Vec3 up)

static Mat4 *	createLookAt (const Vec3 eye, const Vec3 target, const Vec3 up, Mat4 *dst)

static Mat4	createLookAt (float eyeX, float eyeY, float eyeZ, float targetX, float targetY, float targetZ, float upX, float upY, float upZ)

static Mat4 *	createLookAt (float eyeX, float eyeY, float eyeZ, float targetX, float targetY, float targetZ, float upX, float upY, float upZ, Mat4 *dst)

static Mat4	createPerspective (float fieldOfView, float aspectRatio, float zNearPlane, float zFarPlane)

static Mat4 *	createPerspective (float fieldOfView, float aspectRatio, float zNearPlane, float zFarPlane, Mat4 *dst)

static Mat4	createOrthographic (float width, float height, float zNearPlane, float zFarPlane)

static Mat4 *	createOrthographic (float width, float height, float zNearPlane, float zFarPlane, Mat4 *dst)

static Mat4	createOrthographicOffCenter (float left, float right, float bottom, float top, float zNearPlane, float zFarPlane)

static Mat4 *	createOrthographicOffCenter (float left, float right, float bottom, float top, float zNearPlane, float zFarPlane, Mat4 *dst)

static Mat4	createScale (float scale)

static Mat4 *	createScale (float scale, Mat4 *dst)

static Mat4	createScale (float sx, float sy, float sz)

static Mat4 *	createScale (float sx, float sy, float sz, Mat4 *dst)

static Mat4	createScale (const Vec3 scale)

static Mat4 *	createScale (const Vec3 scale, Mat4 *dst)

static Mat4	createRotation (const Quaternion &quat)

static Mat4 *	createRotation (const Quaternion &quat, Mat4 *dst)

static Mat4	createRotation (const Vec3 axis, float angle)

static Mat4 *	createRotation (const Vec3 axis, float angle, Mat4 *dst)

static Mat4	createRotationX (float angle)

static Mat4 *	createRotationX (float angle, Mat4 *dst)

static Mat4	createRotationY (float angle)

static Mat4 *	createRotationY (float angle, Mat4 *dst)

static Mat4	createRotationZ (float angle)

static Mat4 *	createRotationZ (float angle, Mat4 *dst)

static Mat4	createTranslation (const Vec3 trans)

static Mat4 *	createTranslation (const Vec3 trans, Mat4 *dst)

static Mat4	createTranslation (float tx, float ty, float tz)

static Mat4 *	createTranslation (float tx, float ty, float tz, Mat4 *dst)

static Mat4 *	add (const Mat4 &mat, float scalar, Mat4 *dst)

static float *	add (const float mat, float scalar, float dst)

static Mat4 *	add (const Mat4 &m1, const Mat4 &m2, Mat4 *dst)

static float *	add (const float m1, const float m2, float *dst)

static Mat4 *	subtract (const Mat4 &mat, float scalar, Mat4 *dst)

static float *	subtract (const float mat, float scalar, float dst)

static Mat4 *	subtract (const Mat4 &m1, const Mat4 &m2, Mat4 *dst)

static float *	subtract (const float m1, const float m2, float *dst)

static Mat4 *	multiply (const Mat4 &mat, float scalar, Mat4 *dst)

static float *	multiply (const float mat, float scalar, float dst)

static Mat4 *	multiply (const Mat4 &m1, const Mat4 &m2, Mat4 *dst)

static float *	multiply (const float m1, const float m2, float *dst)

static Mat4 *	negate (const Mat4 &m1, Mat4 *dst)

static float *	negate (const float m1, float dst)

static Mat4 *	invert (const Mat4 &m1, Mat4 *dst)

static float *	invert (const float m1, float dst)

static Mat4 *	transpose (const Mat4 &m1, Mat4 *dst)

static float *	transpose (const float m1, float dst)

static Vec2 *	transform (const Mat4 &mat, const Vec2 point, Vec2 *dst)

static float *	transform (const Mat4 &mat, const Vec2 point, float *dst)

static Rect *	transform (const Mat4 &mat, const Rect rect, Rect *dst)

static Vec2 *	transformVector (const Mat4 &mat, const Vec2 vec, Vec2 *dst)

static Vec3 *	transform (const Mat4 &mat, const Vec3 point, Vec3 *dst)

static Vec3 *	transformVector (const Mat4 &mat, const Vec3 vec, Vec3 *dst)

static Vec4 *	transform (const Mat4 &mat, const Vec4 vec, Vec4 *dst)

static float *	transform (const Mat4 &mat, float const input, float output, size_t size)

static float *	transform (const float mat, float const input, float *output, size_t size)

static Mat4 *	rotate (const Mat4 &mat, const Quaternion &quat, Mat4 *dst)

static Mat4 *	rotate (const Mat4 &mat, const Vec3 axis, float angle, Mat4 *dst)

static Mat4 *	rotateX (const Mat4 &mat, float angle, Mat4 *dst)

static Mat4 *	rotateY (const Mat4 &mat, float angle, Mat4 *dst)

static Mat4 *	rotateZ (const Mat4 &mat, float angle, Mat4 *dst)

static Mat4 *	scale (const Mat4 &mat, float value, Mat4 *dst)

static Mat4 *	scale (const Mat4 &mat, const Vec3 s, Mat4 *dst)

static Mat4 *	scale (const Mat4 &mat, float sx, float sy, float sz, Mat4 *dst)

static Mat4 *	translate (const Mat4 &mat, const Vec3 t, Mat4 *dst)

static Mat4 *	translate (const Mat4 &mat, float tx, float ty, float tz, Mat4 *dst)

static bool	decompose (const Mat4 &mat, Vec3 scale, Quaternion rot, Vec3 *trans)

Public Attributes
float	m [16]

Static Public Attributes
static const Mat4	ZERO

static const Mat4	ONE

static const Mat4	IDENTITY

Detailed Description

This class defines a 4 x 4 floating point matrix representing a 3D transformation.

Vectors are treated as columns, resulting in a matrix that is represented as follows, where x, y and z are the translation components of the matrix:

This matrix class is directly compatible with OpenGL since its elements are laid out in memory exactly as they are expected by OpenGL.

The matrix uses column-major format such that array indices increase down column first. However, this is only a data representation format, and it should not have any affect on issues such as multiplication order.

With that said, the convention in OpenGL (and respected by this class) is that transforms are applied by multiplying a vector on the right. For example, suppose we have a translation matrix T and a rotation matrix R. To first rotate an object around the origin and then translate it, you would multiply the two matrices as RT, with T on the right.

Constructor & Destructor Documentation

◆ Mat4() [1/7]

cugl::Mat4::Mat4 ( )

Creates the identity matrix.

◆ Mat4() [2/7]

cugl::Mat4::Mat4	(	float	m11,
		float	m12,
		float	m13,
		float	m14,
		float	m21,
		float	m22,
		float	m23,
		float	m24,
		float	m31,
		float	m32,
		float	m33,
		float	m34,
		float	m41,
		float	m42,
		float	m43,
		float	m44
	)

Constructs a matrix initialized to the specified values.

Parameters

m11	The first element of the first row.
m12	The second element of the first row.
m13	The third element of the first row.
m14	The fourth element of the first row.
m21	The first element of the second row.
m22	The second element of the second row.
m23	The third element of the second row.
m24	The fourth element of the second row.
m31	The first element of the third row.
m32	The second element of the third row.
m33	The third element of the third row.
m34	The fourth element of the third row.
m41	The first element of the fourth row.
m42	The second element of the fourth row.
m43	The third element of the fourth row.
m44	The fourth element of the fourth row.

◆ Mat4() [3/7]

cugl::Mat4::Mat4 ( const float * mat )

Creates a matrix initialized to the specified column-major array.

The passed-in array is in column-major order, so the memory layout of the array is as follows:

0   4   8   12
1   5   9   13
2   6   10  14
3   7   11  15

Parameters

mat	An array containing 16 elements in column-major order.

◆ Mat4() [4/7]

cugl::Mat4::Mat4 ( const Mat4 & copy )

Constructs a new matrix that is the copy of the specified one.

Parameters

copy	The matrix to copy.

◆ Mat4() [5/7]

cugl::Mat4::Mat4 ( Mat4 && copy )

Constructs a new matrix that contains the resources of the specified one.

Parameters

copy	The matrix contributing resources.

◆ Mat4() [6/7]

cugl::Mat4::Mat4 ( const Quaternion & rotation )

inline

Constructs a new matrix that is specified by the given quaternion.

Parameters

rotation The quaternion specifying a rotation.

◆ ~Mat4()

cugl::Mat4::~Mat4 ( )

inline

Destroys this matrix, releasing all resources.

◆ Mat4() [7/7]

cugl::Mat4::Mat4 ( const Affine2 & aff )

explicit

Creates a matrix from the given affine transform.

The z values are set to the identity.

Parameters

aff	The transform to convert

Member Function Documentation

◆ add() [1/6]

static float * cugl::Mat4::add	(	const float *	m1,
		const float *	m2,
		float *	dst
	)

static

Adds the specified matrices and stores the result in dst.

This method assumes the float arrays are in column major order.

Parameters

m1	The first matrix in column-major order
m2	The second matrix in column-major order
dst	The destination matrix in column-major order

Returns: A reference to dst for chaining

◆ add() [2/6]

static float * cugl::Mat4::add	(	const float *	mat,
		float	scalar,
		float *	dst
	)

static

Adds a scalar to each component of mat and stores the result in dst.

This method assumes the float arrays are in column major order.

Parameters

mat	The matrix to add to in column-major order
scalar	The scalar value to add.
dst	A matrix to store the result in column-major order

Returns: A reference to dst for chaining

◆ add() [3/6]

static Mat4 * cugl::Mat4::add	(	const Mat4 &	m1,
		const Mat4 &	m2,
		Mat4 *	dst
	)

static

Adds the specified matrices and stores the result in dst.

Parameters

m1	The first matrix.
m2	The second matrix.
dst	The destination matrix to add to.

Returns: A reference to dst for chaining

◆ add() [4/6]

Mat4 & cugl::Mat4::add ( const Mat4 & mat )

inline

Adds the specified matrix to this matrix.

Parameters

mat	The matrix to add.

Returns: A reference to the Mat4 after addition.

◆ add() [5/6]

static Mat4 * cugl::Mat4::add	(	const Mat4 &	mat,
		float	scalar,
		Mat4 *	dst
	)

static

Adds a scalar to each component of mat and stores the result in dst.

Parameters

mat	The matrix to add to.
scalar	The scalar value to add.
dst	A matrix to store the result in.

Returns: A reference to dst for chaining

◆ add() [6/6]

Mat4 & cugl::Mat4::add ( float scalar )

inline

Adds a scalar value to each component of this matrix.

Parameters

scalar The scalar to add.

Returns: A reference to the Mat4 after addition.

◆ createLookAt() [1/4]

static Mat4 cugl::Mat4::createLookAt	(	const Vec3	eye,
		const Vec3	target,
		const Vec3	up
	)

inlinestatic

Creates a view matrix based on the specified input vectors.

Parameters

eye	The eye position.
target	The target's center position.
up	The up vector.

Returns: a view matrix based on the specified input vectors.

◆ createLookAt() [2/4]

static Mat4 * cugl::Mat4::createLookAt	(	const Vec3	eye,
		const Vec3	target,
		const Vec3	up,
		Mat4 *	dst
	)

static

Creates a view matrix based on the specified input vectors, putting it in dst.

Parameters

eye	The eye position.
target	The target's center position.
up	The up vector.
dst	A matrix to store the result in.

Returns: A reference to dst for chaining

◆ createLookAt() [3/4]

static Mat4 cugl::Mat4::createLookAt	(	float	eyeX,
		float	eyeY,
		float	eyeZ,
		float	targetX,
		float	targetY,
		float	targetZ,
		float	upX,
		float	upY,
		float	upZ
	)

inlinestatic

Returns a view matrix based on the specified input parameters.

Parameters

eyeX	The eye x-coordinate position.
eyeY	The eye y-coordinate position.
eyeZ	The eye z-coordinate position.
targetX	The target's center x-coordinate position.
targetY	The target's center y-coordinate position.
targetZ	The target's center z-coordinate position.
upX	The up vector x-coordinate value.
upY	The up vector y-coordinate value.
upZ	The up vector z-coordinate value.

Returns: a view matrix based on the specified input parameters.

◆ createLookAt() [4/4]

static Mat4 * cugl::Mat4::createLookAt	(	float	eyeX,
		float	eyeY,
		float	eyeZ,
		float	targetX,
		float	targetY,
		float	targetZ,
		float	upX,
		float	upY,
		float	upZ,
		Mat4 *	dst
	)

static

Creates a view matrix based on the specified input parameters, putting it in dst.

Parameters

eyeX	The eye x-coordinate position.
eyeY	The eye y-coordinate position.
eyeZ	The eye z-coordinate position.
targetX	The target's center x-coordinate position.
targetY	The target's center y-coordinate position.
targetZ	The target's center z-coordinate position.
upX	The up vector x-coordinate value.
upY	The up vector y-coordinate value.
upZ	The up vector z-coordinate value.
dst	A matrix to store the result in.

Returns: A reference to dst for chaining

◆ createOrthographic() [1/2]

static Mat4 cugl::Mat4::createOrthographic	(	float	width,
		float	height,
		float	zNearPlane,
		float	zFarPlane
	)

inlinestatic

Returns an orthographic projection matrix anchored at the origin.

Projection space refers to the space after applying projection transformation from view space. After the projection transformation, visible content has x and y coordinates ranging from -1 to 1, and z coordinates ranging from 0 to 1. Unlike perspective projection, there is no perspective foreshortening in orthographic projection.

The viewable area of this orthographic projection places the origin at the center, with the given width and height.. The z-axis is bound between zNearPlane and zFarPlane. These values are relative to the position and x, y, and z-axes of the view.

To obtain the viewable area (in world space) of a scene, create a bounding frustum and pass the combined view and projection matrix to the constructor.

Parameters

width	The width of the view.
height	The height of the view.
zNearPlane	The minimum z-value of the view volume.
zFarPlane	The maximum z-value of the view volume.

Returns: an orthographic projection matrix anchored at the origin.

◆ createOrthographic() [2/2]

static Mat4 * cugl::Mat4::createOrthographic	(	float	width,
		float	height,
		float	zNearPlane,
		float	zFarPlane,
		Mat4 *	dst
	)

inlinestatic

Creates an orthographic projection matrix anchored at the origin, putting it in dst.

Projection space refers to the space after applying projection transformation from view space. After the projection transformation, visible content has x and y coordinates ranging from -1 to 1, and z coordinates ranging from 0 to 1. Unlike perspective projection, there is no perspective foreshortening in orthographic projection.

The viewable area of this orthographic projection places the origin at the center, with the given width and height.. The z-axis is bound between zNearPlane and zFarPlane. These values are relative to the position and x, y, and z-axes of the view.

To obtain the viewable area (in world space) of a scene, create a bounding frustum and pass the combined view and projection matrix to the constructor.

Parameters

width	The width of the view.
height	The height of the view.
zNearPlane	The minimum z-value of the view volume.
zFarPlane	The maximum z-value of the view volume.
dst	A matrix to store the result in.

Returns: A reference to dst for chaining

◆ createOrthographicOffCenter() [1/2]

static Mat4 cugl::Mat4::createOrthographicOffCenter	(	float	left,
		float	right,
		float	bottom,
		float	top,
		float	zNearPlane,
		float	zFarPlane
	)

inlinestatic

Returns an orthographic projection matrix.

Projection space refers to the space after applying projection transformation from view space. After the projection transformation, visible content has x and y coordinates ranging from -1 to 1, and z coordinates ranging from 0 to 1. Unlike perspective projection, there is no perspective foreshortening in orthographic projection.

The viewable area of this orthographic projection extends from left to right on the x-axis and bottom to top on the y-axis. The z-axis is bound between zNearPlane and zFarPlane. These values are relative to the position and x, y, and z-axes of the view.

To obtain the viewable area (in world space) of a scene, create a bounding frustum and pass the combined view and projection matrix to the constructor.

Parameters

left	The minimum x-value of the view volume.
right	The maximum x-value of the view volume.
bottom	The minimum y-value of the view volume.
top	The maximum y-value of the view volume.
zNearPlane	The minimum z-value of the view volume.
zFarPlane	The maximum z-value of the view volume.

Returns: an orthographic projection matrix.

◆ createOrthographicOffCenter() [2/2]

static Mat4 * cugl::Mat4::createOrthographicOffCenter	(	float	left,
		float	right,
		float	bottom,
		float	top,
		float	zNearPlane,
		float	zFarPlane,
		Mat4 *	dst
	)

static

Creates an orthographic projection matrix, putting it in dst.

Projection space refers to the space after applying projection transformation from view space. After the projection transformation, visible content has x and y coordinates ranging from -1 to 1, and z coordinates ranging from 0 to 1. Unlike perspective projection, there is no perspective foreshortening in orthographic projection.

The viewable area of this orthographic projection extends from left to right on the x-axis and bottom to top on the y-axis. The z-axis is bound between zNearPlane and zFarPlane. These values are relative to the position and x, y, and z-axes of the view.

To obtain the viewable area (in world space) of a scene, create a bounding frustum and pass the combined view and projection matrix to the constructor.

Parameters

left	The minimum x-value of the view volume.
right	The maximum x-value of the view volume.
bottom	The minimum y-value of the view volume.
top	The maximum y-value of the view volume.
zNearPlane	The minimum z-value of the view volume.
zFarPlane	The maximum z-value of the view volume.
dst	A matrix to store the result in.

Returns: A reference to dst for chaining

◆ createPerspective() [1/2]

static Mat4 cugl::Mat4::createPerspective	(	float	fieldOfView,
		float	aspectRatio,
		float	zNearPlane,
		float	zFarPlane
	)

inlinestatic

Returns a perspective projection matrix based on a field of view.

Projection space refers to the space after applying projection transformation from view space. After the projection transformation, visible content has x- and y-coordinates ranging from -1 to 1, and a z-coordinate ranging from 0 to 1. To obtain the viewable area (in world space) of a scene, create a bounding frustum and pass the combined view and projection matrix to the constructor.

Parameters

fieldOfView	The field of view in the y direction (in degrees).
aspectRatio	The aspect ratio, defined as view space width divided by height.
zNearPlane	The distance to the near view plane.
zFarPlane	The distance to the far view plane.

Returns: a perspective projection matrix based on a field of view.

◆ createPerspective() [2/2]

static Mat4 * cugl::Mat4::createPerspective	(	float	fieldOfView,
		float	aspectRatio,
		float	zNearPlane,
		float	zFarPlane,
		Mat4 *	dst
	)

static

Creates a perspective projection matrix based on a field of view, putting it in dst.

Projection space refers to the space after applying projection transformation from view space. After the projection transformation, visible content has x- and y-coordinates ranging from -1 to 1, and a z-coordinate ranging from 0 to 1. To obtain the viewable area (in world space) of a scene, create a bounding frustum and pass the combined view and projection matrix to the constructor.

Parameters

fieldOfView	The field of view in the y direction (in degrees).
aspectRatio	The aspect ratio, defined as view space width divided by height.
zNearPlane	The distance to the near view plane.
zFarPlane	The distance to the far view plane.
dst	A matrix to store the result in.

Returns: A reference to dst for chaining

◆ createRotation() [1/4]

static Mat4 cugl::Mat4::createRotation ( const Quaternion & quat )

inlinestatic

Returns a rotation matrix from the specified quaternion.

Parameters

quat	A quaternion describing a 3D orientation.

Returns: a rotation matrix from the specified quaternion.

◆ createRotation() [2/4]

static Mat4 * cugl::Mat4::createRotation	(	const Quaternion &	quat,
		Mat4 *	dst
	)

static

Creates a rotation matrix from the specified quaternion, putting it in dst.

Parameters

quat	A quaternion describing a 3D orientation.
dst	A matrix to store the result in.

Returns: A reference to dst for chaining

◆ createRotation() [3/4]

static Mat4 cugl::Mat4::createRotation	(	const Vec3	axis,
		float	angle
	)

inlinestatic

Returns a rotation matrix from the specified axis and angle.

The angle measurement is in radians. The rotation is counter clockwise about the axis.

Parameters

axis	A vector describing the axis to rotate about.
angle	The angle (in radians).

Returns: a rotation matrix from the specified axis and angle.

◆ createRotation() [4/4]

static Mat4 * cugl::Mat4::createRotation	(	const Vec3	axis,
		float	angle,
		Mat4 *	dst
	)

static

Creates a rotation matrix from the specified axis and angle, putting it in dst.

The angle measurement is in radians. The rotation is counter clockwise about the axis.

Parameters

axis	A vector describing the axis to rotate about.
angle	The angle (in radians).
dst	A matrix to store the result in.

Returns: A reference to dst for chaining

◆ createRotationX() [1/2]

static Mat4 cugl::Mat4::createRotationX ( float angle )

inlinestatic

Returns a matrix specifying a rotation around the x-axis.

The angle measurement is in radians. The rotation is counter clockwise about the axis.

Parameters

angle The angle of rotation (in radians).

Returns: a matrix specifying a rotation around the x-axis.

◆ createRotationX() [2/2]

static Mat4 * cugl::Mat4::createRotationX	(	float	angle,
		Mat4 *	dst
	)

static

Creates a matrix specifying a rotation around the x-axis, putting it in dst.

The angle measurement is in radians. The rotation is counter clockwise about the axis.

Parameters

angle	The angle of rotation (in radians).
dst	A matrix to store the result in.

Returns: A reference to dst for chaining

◆ createRotationY() [1/2]

static Mat4 cugl::Mat4::createRotationY ( float angle )

inlinestatic

Returns a matrix specifying a rotation around the y-axis.

The angle measurement is in radians. The rotation is counter clockwise about the axis.

Parameters

angle The angle of rotation (in radians).

Returns: a matrix specifying a rotation around the y-axis.

◆ createRotationY() [2/2]

static Mat4 * cugl::Mat4::createRotationY	(	float	angle,
		Mat4 *	dst
	)

static

Creates a matrix specifying a rotation around the y-axis, putting it in dst.

The angle measurement is in radians. The rotation is counter clockwise about the axis.

Parameters

angle	The angle of rotation (in radians).
dst	A matrix to store the result in.

Returns: A reference to dst for chaining

◆ createRotationZ() [1/2]

static Mat4 cugl::Mat4::createRotationZ ( float angle )

inlinestatic

Returns a matrix specifying a rotation around the z-axis.

The angle measurement is in radians. The rotation is counter clockwise about the axis.

Parameters

angle The angle of rotation (in radians).

Returns: a matrix specifying a rotation around the z-axis.

◆ createRotationZ() [2/2]

static Mat4 * cugl::Mat4::createRotationZ	(	float	angle,
		Mat4 *	dst
	)

static

Creates a matrix specifying a rotation around the z-axis, putting it in dst.

The angle measurement is in radians. The rotation is counter clockwise about the axis.

Parameters

angle	The angle of rotation (in radians).
dst	A matrix to store the result in.

Returns: A reference to dst for chaining

◆ createScale() [1/6]

static Mat4 cugl::Mat4::createScale ( const Vec3 scale )

inlinestatic

Returns a nonuniform scale matrix from the given vector.

Parameters

scale The nonuniform scale value.

Returns: a nonuniform scale matrix from the given vector.

◆ createScale() [2/6]

static Mat4 * cugl::Mat4::createScale	(	const Vec3	scale,
		Mat4 *	dst
	)

static

Creates a nonuniform scale matrix from the given vector, putting it in dst.

Parameters

scale	The nonuniform scale value.
dst	A matrix to store the result in.

Returns: A reference to dst for chaining

◆ createScale() [3/6]

static Mat4 cugl::Mat4::createScale ( float scale )

inlinestatic

Returns a uniform scale matrix.

Parameters

scale The amount to scale.

Returns: a uniform scale matrix.

◆ createScale() [4/6]

static Mat4 * cugl::Mat4::createScale	(	float	scale,
		Mat4 *	dst
	)

static

Creates a uniform scale matrix, putting it in dst.

Parameters

scale	The amount to scale.
dst	A matrix to store the result in.

Returns: A reference to dst for chaining

◆ createScale() [5/6]

static Mat4 cugl::Mat4::createScale	(	float	sx,
		float	sy,
		float	sz
	)

inlinestatic

Returns a nonuniform scale matrix.

Parameters

sx	The amount to scale along the x-axis.
sy	The amount to scale along the y-axis.
sz	The amount to scale along the z-axis.

Returns: a nonuniform scale matrix.

◆ createScale() [6/6]

static Mat4 * cugl::Mat4::createScale	(	float	sx,
		float	sy,
		float	sz,
		Mat4 *	dst
	)

static

Creates a nonuniform scale matrix, putting it in dst.

Parameters

sx	The amount to scale along the x-axis.
sy	The amount to scale along the y-axis.
sz	The amount to scale along the z-axis.
dst	A matrix to store the result in.

Returns: A reference to dst for chaining

◆ createTranslation() [1/4]

static Mat4 cugl::Mat4::createTranslation ( const Vec3 trans )

inlinestatic

Returns a translation matrix from the given offset.

Parameters

trans The translation offset.

Returns: a translation matrix from the given offset.

◆ createTranslation() [2/4]

static Mat4 * cugl::Mat4::createTranslation	(	const Vec3	trans,
		Mat4 *	dst
	)

static

Creates a translation matrix from the given offset, putting it in dst.

Parameters

trans	The translation offset.
dst	A matrix to store the result in.

Returns: A reference to dst for chaining

◆ createTranslation() [3/4]

static Mat4 cugl::Mat4::createTranslation	(	float	tx,
		float	ty,
		float	tz
	)

inlinestatic

Returns a translation matrix from the given parameters.

Parameters

tx	The translation on the x-axis.
ty	The translation on the y-axis.
tz	The translation on the z-axis.

Returns: A reference to dst for chaining

◆ createTranslation() [4/4]

static Mat4 * cugl::Mat4::createTranslation	(	float	tx,
		float	ty,
		float	tz,
		Mat4 *	dst
	)

static

Creates a translation matrix from the given parameters, putting it in dst.

Parameters

tx	The translation on the x-axis.
ty	The translation on the y-axis.
tz	The translation on the z-axis.
dst	A matrix to store the result in.

Returns: A reference to dst for chaining

◆ decompose()

static bool cugl::Mat4::decompose	(	const Mat4 &	mat,
		Vec3 *	scale,
		Quaternion *	rot,
		Vec3 *	trans
	)

static

Decomposes the scale, rotation and translation components of the given matrix.

To work properly, the matrix must have been constructed in the following order: scale, then rotate, then translation. While the rotation matrix will always be correct, the scale and translation are not guaranteed to be correct if this is violated.

If any pointer is null, the method simply does not assign that result. However, it will still continue to compute the component with non-null vectors to store the result.

If the scale component is too small, then it may be impossible to extract the rotation. In that case, if the rotation pointer is not null, this method will return false.

Parameters

mat	The matrix to decompose.
scale	The scale component.
rot	The rotation component.
trans	The translation component.

Returns: true if all requested components were properly extracted

◆ equals()

bool cugl::Mat4::equals	(	const Mat4 &	mat,
		float	epsilon = `CU_MATH_EPSILON`
	)		const

Returns true if the matrices are within tolerance of each other.

The tolerance is applied to each element of the matrix individually.

Parameters

mat	The matrix to compare against.
epsilon	The comparison tolerance.

Returns: true if the matrices are within tolerance of each other.

◆ getBackVector()

Vec3 cugl::Mat4::getBackVector ( ) const

Returns the backward vector of this matrix, when treated as a camera.

Returns: the backward vector of this matrix, when treated as a camera.

◆ getDeterminant()

float cugl::Mat4::getDeterminant ( ) const

Returns the determinant of this matrix.

Returns: the determinant of this matrix.

◆ getDownVector()

Vec3 cugl::Mat4::getDownVector ( ) const

Returns the down vector of this matrix, when treated as a camera.

Returns: the down vector of this matrix, when treated as a camera.

◆ getForwardVector()

Vec3 cugl::Mat4::getForwardVector ( ) const

Returns the forward vector of this matrix, when treated as a camera.

Returns: the forward vector of this matrix, when treated as a camera.

◆ getInverse()

Mat4 cugl::Mat4::getInverse ( ) const

inline

Returns a copy of the inverse of this matrix.

If the matrix cannot be inverted, this method returns the zero matrix.

Note: This does not modify the matrix.

Returns: a copy of the inverse of this matrix.

◆ getLeftVector()

Vec3 cugl::Mat4::getLeftVector ( ) const

Returns the left vector of this matrix, when treated as a camera.

Returns: the left vector of this matrix, when treated as a camera.

◆ getNegation()

Mat4 cugl::Mat4::getNegation ( ) const

inline

Returns a copy of this matrix with all elements negated.

Note: This does not modify the matrix.

Returns: a copy of this matrix with all elements negated.

◆ getRightVector()

Vec3 cugl::Mat4::getRightVector ( ) const

Returns the right vector of this matrix, when treated as a camera.

Returns: the right vector of this matrix, when treated as a camera.

◆ getRotation()

Quaternion cugl::Mat4::getRotation ( ) const

Returns the rotational component of this matrix.

If the scale component is too close to zero, we cannot extract the rotation. In that case, we return the zero quaternion. (

Returns: the rotational component of this matrix.

◆ getScale()

Vec3 cugl::Mat4::getScale ( ) const

Returns the scale component of this matrix.

If the scale component of this matrix has negative parts, it is not possible to always extract the exact scale component. In that case, a scale vector that is mathematically equivalent to the original scale vector is extracted and returned.

To work properly, the matrix must have been constructed in the following order: scale, then rotate, then translation. In any other order, the scale is not guaranteed to be correct.

Returns: the scale component of this matrix.

◆ getTranslation()

Vec3 cugl::Mat4::getTranslation ( ) const

Returns the translational component of this matrix.

To work properly, the matrix must have been constructed in the following order: scale, then rotate, then translation. In any other order, the translation is not guaranteed to be correct.

Returns: the translational component of this matrix.

◆ getTranspose()

Mat4 cugl::Mat4::getTranspose ( ) const

inline

Returns a copy of the transpose of this matrix.

Transposing a matrix swaps columns and rows. This allows to transform a vector by multiplying it on the left. If the matrix is orthonormal, this is also the inverse.

Note: This does not modify the matrix.

Returns: a copy of the transpose of this matrix.

◆ getUpVector()

Vec3 cugl::Mat4::getUpVector ( ) const

Returns the up vector of this matrix, when treated as a camera.

Returns: the up vector of this matrix, when treated as a camera.

◆ invert() [1/3]

Mat4 & cugl::Mat4::invert ( )

inline

Inverts this matrix in place.

If the matrix cannot be inverted, this method sets it to the zero matrix.

Returns: A reference to the Mat4 after the inversion.

◆ invert() [2/3]

static float * cugl::Mat4::invert	(	const float *	m1,
		float *	dst
	)

static

Inverts m1 and stores the result in dst.

If the matrix cannot be inverted, this method stores the zero matrix in dst.

This method assumes the float arrays are in column major order.

Parameters

m1	The matrix to invert in column major order
dst	A matrix to store the result in column major order

Returns: A reference to dst for chaining

◆ invert() [3/3]

static Mat4 * cugl::Mat4::invert	(	const Mat4 &	m1,
		Mat4 *	dst
	)

static

Inverts m1 and stores the result in dst.

If the matrix cannot be inverted, this method stores the zero matrix in dst.

Parameters

m1	The matrix to invert.
dst	A matrix to store the result in.

Returns: A reference to dst for chaining

◆ isExactly()

bool cugl::Mat4::isExactly ( const Mat4 & mat ) const

Returns true if the matrices are exactly equal to each other.

This method may be unreliable given that the elements are floats. It should only be used to compared matrices that have not undergone a lot of transformations.

Parameters

mat	The matrix to compare against.

Returns: true if the matrices are exactly equal to each other.

◆ isIdentity()

bool cugl::Mat4::isIdentity ( float epsilon = CU_MATH_EPSILON ) const

Returns true if this matrix is equal to the identity matrix.

The optional comparison tolerance takes into accout that elements are floats and this may not be exact. The tolerance is applied to each element individually. By default, the match must be exact.

Parameters

epsilon The comparison tolerance

Returns: true if this matrix is equal to the identity matrix.

◆ isInvertible()

bool cugl::Mat4::isInvertible ( float epsilon = CU_MATH_EPSILON ) const

inline

Returns true if this matrix is invertible.

The optional comparison tolerance takes into accout that elements are floats and this may not be exact. The tolerance is applied to the matrix determinant.

Parameters

epsilon The comparison tolerance

Returns: true if this matrix is invertible.

◆ isOrthogonal()

bool cugl::Mat4::isOrthogonal ( float epsilon = CU_MATH_EPSILON ) const

Returns true if this matrix is orthogonal.

The optional comparison tolerance takes into accout that elements are floats and this may not be exact. The tolerance is applied to BOTH the normality test and the dot-product test for each pair.

Parameters

epsilon The comparison tolerance

Returns: true if this matrix is orthogonal.

◆ multiply() [1/6]

static float * cugl::Mat4::multiply	(	const float *	m1,
		const float *	m2,
		float *	dst
	)

static

Multiplies m1 by the matrix m2 and stores the result in dst.

The matrix m2 is on the right. This means that it corresponds to an subsequent transform, when looking at a sequence of transforms.

This method assumes the float arrays are in column major order.

Parameters

m1	The first matrix to multiply in column-major order
m2	The second matrix to multiply in column-major order
dst	A matrix to store the result in column-major order

Returns: A reference to dst for chaining

◆ multiply() [2/6]

static float * cugl::Mat4::multiply	(	const float *	mat,
		float	scalar,
		float *	dst
	)

static

Multiplies the specified matrix by a scalar and stores the result in dst.

This method assumes the float arrays are in column major order.

Parameters

mat	The matrix in column-major order
scalar	The scalar value.
dst	A matrix to store the result in column-major order

Returns: A reference to dst for chaining

◆ multiply() [3/6]

static Mat4 * cugl::Mat4::multiply	(	const Mat4 &	m1,
		const Mat4 &	m2,
		Mat4 *	dst
	)

static

Multiplies m1 by the matrix m2 and stores the result in dst.

The matrix m2 is on the right. This means that it corresponds to an subsequent transform, when looking at a sequence of transforms.

Parameters

m1	The first matrix to multiply.
m2	The second matrix to multiply.
dst	A matrix to store the result in.

Returns: A reference to dst for chaining

◆ multiply() [4/6]

Mat4 & cugl::Mat4::multiply ( const Mat4 & mat )

inline

Multiplies this matrix by the specified one.

The matrix mat is on the right. This means that it corresponds to a subsequent transform, when looking at the order of transforms.

Parameters

mat	The matrix to multiply.

Returns: A reference to the Mat4 after multiplication.

◆ multiply() [5/6]

static Mat4 * cugl::Mat4::multiply	(	const Mat4 &	mat,
		float	scalar,
		Mat4 *	dst
	)

static

Multiplies the specified matrix by a scalar and stores the result in dst.

Parameters

mat	The matrix.
scalar	The scalar value.
dst	A matrix to store the result in.

Returns: A reference to dst for chaining

◆ multiply() [6/6]

Mat4 & cugl::Mat4::multiply ( float scalar )

inline

Multiplies the components of this matrix by the specified scalar.

Parameters

scalar The scalar value.

Returns: A reference to the Mat4 after multiplication.

◆ negate() [1/3]

Mat4 & cugl::Mat4::negate ( )

inline

Negates this matrix in place.

Returns: A reference to the Mat4 after negation.

◆ negate() [2/3]

static float * cugl::Mat4::negate	(	const float *	m1,
		float *	dst
	)

static

Negates m1 and stores the result in dst.

This method assumes the float arrays are in column major order.

Parameters

m1	The matrix to negate in column major order
dst	A matrix to store the result in column major order

Returns: A reference to dst for chaining

◆ negate() [3/3]

static Mat4 * cugl::Mat4::negate	(	const Mat4 &	m1,
		Mat4 *	dst
	)

static

Negates m1 and stores the result in dst.

Parameters

m1	The matrix to negate.
dst	A matrix to store the result in.

Returns: A reference to dst for chaining

◆ operator Affine2()

cugl::Mat4::operator Affine2 ( ) const

Cast from Mat4 to a Affine2.

The z values are all uniformly ignored. However, it the final element of the matrix is not 1 (e.g. the translation has a w value of 1), then it divides the entire matrix before creating the affine transform.

◆ operator std::string()

cugl::Mat4::operator std::string ( ) const

inline

Cast from Vec4 to a string.

◆ operator!=()

bool cugl::Mat4::operator!= ( const Mat4 & mat ) const

inline

Returns true if this matrix is not equal to the given matrix.

Comparison is exact, which may be unreliable given that the elements are floats.

Parameters

mat	The matrix to compare against.

Returns: true if this matrix is not equal to the given matrix.

◆ operator*() [1/2]

const Mat4 cugl::Mat4::operator* ( const Mat4 & mat ) const

inline

Returns the matrix product of this matrix with the given matrix.

The matrix mat is on the right. This means that it corresponds to an subsequent transform, when looking at a sequence of transforms.

Note: This does not modify the matrix.

Parameters

mat	The matrix to multiply by.

Returns: the matrix product of this matrix with the given matrix.

◆ operator*() [2/2]

const Mat4 cugl::Mat4::operator* ( float scalar ) const

inline

Returns a copy of this matrix with all elements multiplied by the scalar.

Note: This does not modify the matrix.

Parameters

scalar The scalar value.

Returns: the matrix product of this matrix with the given matrix.

◆ operator*=() [1/2]

Mat4 & cugl::Mat4::operator*= ( const Mat4 & mat )

inline

Right-multiplies this matrix by the given matrix.

The matrix mat is on the right. This means that it corresponds to a subsequent transform, when looking at the order of transforms.

Parameters

mat	The matrix to multiply by.

Returns: A reference to this (modified) Mat4 for chaining.

◆ operator*=() [2/2]

Mat4 & cugl::Mat4::operator*= ( float scalar )

inline

Multiplies the components of this matrix by the specified scalar.

Parameters

scalar The scalar value.

Returns: A reference to this (modified) Mat4 for chaining.

◆ operator+()

const Mat4 cugl::Mat4::operator+ ( const Mat4 & mat ) const

inline

Returns the sum of this matrix with the given matrix.

Note: This does not modify the matrix.

Parameters

mat	The matrix to add.

Returns: the sum of this matrix with the given matrix.

◆ operator+=()

Mat4 & cugl::Mat4::operator+= ( const Mat4 & mat )

inline

Adds the given matrix to this one in place.

Parameters

mat	The matrix to add

Returns: A reference to this (modified) Mat4 for chaining.

◆ operator-() [1/2]

const Mat4 cugl::Mat4::operator- ( ) const

inline

Returns the negation of this matrix.

Note: This does not modify the matrix.

Returns: the negation of this matrix.

◆ operator-() [2/2]

const Mat4 cugl::Mat4::operator- ( const Mat4 & mat ) const

inline

Returns the difference of this matrix with the given matrix.

Note: This does not modify the matrix.

Parameters

mat	The matrix to subtract.

Returns: the difference of this matrix with the given matrix.

◆ operator-=()

Mat4 & cugl::Mat4::operator-= ( const Mat4 & mat )

inline

Subtracts the given matrix from this one in place.

Parameters

mat	The matrix to subtract

Returns: A reference to this (modified) Mat4 for chaining.

◆ operator=() [1/5]

Mat4 & cugl::Mat4::operator= ( const Affine2 & aff )

Sets the elements of this matrix to those of the given transform.

The z values are set to the identity.

Parameters

aff	The transform to convert

Returns: A reference to this (modified) Mat4 for chaining.

◆ operator=() [2/5]

Mat4 & cugl::Mat4::operator= ( const float * array )

inline

Sets the values of this matrix to those in the specified column-major array.

The passed-in array is in column-major order, so the memory layout of the array is as follows:

0   4   8   12
1   5   9   13
2   6   10  14
3   7   11  15

Parameters

array An array containing 16 elements in column-major order.

Returns: A reference to this (modified) Mat4 for chaining.

◆ operator=() [3/5]

Mat4 & cugl::Mat4::operator= ( const Mat4 & mat )

inline

Sets the elements of this matrix to those in the specified matrix.

Parameters

mat	The matrix to copy.

Returns: A reference to this (modified) Mat4 for chaining.

◆ operator=() [4/5]

Mat4 & cugl::Mat4::operator= ( const Quaternion & quat )

inline

Sets this matrix as a rotation matrix from the specified quaternion.

Parameters

quat	A quaternion describing a 3D orientation.

Returns: A reference to this (modified) Mat4 for chaining.

◆ operator=() [5/5]

Mat4 & cugl::Mat4::operator= ( Mat4 && mat )

inline

Sets the elements of this matrix to those in the specified one.

Parameters

mat	The matrix to take resources from.

Returns: A reference to this (modified) Mat4 for chaining.

◆ operator==()

bool cugl::Mat4::operator== ( const Mat4 & mat ) const

inline

Returns true if this matrix is equal to the given matrix.

Comparison is exact, which may be unreliable given that the elements are floats. It should only be used to compared matrices that have not undergone a lot of transformations.

Parameters

mat	The matrix to compare against.

Returns: true if this matrix is equal to the given matrix.

◆ rotate() [1/4]

static Mat4 * cugl::Mat4::rotate	(	const Mat4 &	mat,
		const Quaternion &	quat,
		Mat4 *	dst
	)

inlinestatic

Applies a quaternion rotation to the given matrix and stores the result in dst.

The rotation is applied on the right. Given our convention, that means that it takes place AFTER any previously applied transforms.

Parameters

mat	The matrix to rotate.
quat	The quaternion to rotate by.
dst	A matrix to store the result in.

Returns: A reference to dst for chaining

◆ rotate() [2/4]

static Mat4 * cugl::Mat4::rotate	(	const Mat4 &	mat,
		const Vec3	axis,
		float	angle,
		Mat4 *	dst
	)

inlinestatic

Applies an axis rotation to the given matrix and stores the result in dst.

The rotation is in radians, counter-clockwise about the given axis.

The rotation is applied on the right. Given our convention, that means that it takes place AFTER any previously applied transforms.

Parameters

mat	The matrix to rotate.
axis	The axis to rotate about.
angle	The angle (in radians).
dst	A matrix to store the result in.

Returns: A reference to dst for chaining

◆ rotate() [3/4]

Mat4 & cugl::Mat4::rotate ( const Quaternion & q )

inline

Applies a quaternion rotation to this matrix.

The rotation is applied on the right. Given our convention, that means that it takes place AFTER any previously applied transforms.

Parameters

q	The quaternion to rotate by.

Returns: This matrix, after rotation.

◆ rotate() [4/4]

Mat4 & cugl::Mat4::rotate	(	const Vec3	axis,
		float	angle
	)

inline

Applies an axis rotation to the this matrix.

The rotation is in radians, counter-clockwise about the given axis.

The rotation is applied on the right. Given our convention, that means that it takes place AFTER any previously applied transforms.

Parameters

axis	The axis to rotate about.
angle	The angle (in radians).

Returns: This matrix, after rotation.

◆ rotateX() [1/2]

static Mat4 * cugl::Mat4::rotateX	(	const Mat4 &	mat,
		float	angle,
		Mat4 *	dst
	)

inlinestatic

Applies an x-axis rotation to the given matrix and stores the result in dst.

The rotation is in radians, counter-clockwise about the x-axis.

The rotation is applied on the right. Given our convention, that means that it takes place AFTER any previously applied transforms.

Parameters

mat	The matrix to rotate.
angle	The angle (in radians).
dst	A matrix to store the result in.

Returns: A reference to dst for chaining

◆ rotateX() [2/2]

Mat4 & cugl::Mat4::rotateX ( float angle )

inline

Applies an x-axis rotation to this matrix.

The rotation is in radians, counter-clockwise about the x-axis.

The rotation is applied on the right. Given our convention, that means that it takes place AFTER any previously applied transforms.

Parameters

angle The angle (in radians).

Returns: This matrix, after rotation.

◆ rotateY() [1/2]

static Mat4 * cugl::Mat4::rotateY	(	const Mat4 &	mat,
		float	angle,
		Mat4 *	dst
	)

inlinestatic

Applies an y-axis rotation to the given matrix and stores the result in dst.

The rotation is in radians, counter-clockwise about the y-axis.

The rotation is applied on the right. Given our convention, that means that it takes place AFTER any previously applied transforms.

Parameters

mat	The matrix to rotate.
angle	The angle (in radians).
dst	A matrix to store the result in.

Returns: A reference to dst for chaining

◆ rotateY() [2/2]

Mat4 & cugl::Mat4::rotateY ( float angle )

inline

Applies a y-axis rotation to this matrix.

The rotation is in radians, counter-clockwise about the y-axis.

The rotation is applied on the right. Given our convention, that means that it takes place AFTER any previously applied transforms.

Parameters

angle The angle (in radians).

Returns: This matrix, after rotation.

◆ rotateZ() [1/2]

static Mat4 * cugl::Mat4::rotateZ	(	const Mat4 &	mat,
		float	angle,
		Mat4 *	dst
	)

inlinestatic

Applies an z-axis rotation to the given matrix and stores the result in dst.

The rotation is in radians, counter-clockwise about the z-axis.

The rotation is applied on the right. Given our convention, that means that it takes place AFTER any previously applied transforms.

Parameters

mat	The matrix to rotate.
angle	The angle (in radians).
dst	A matrix to store the result in.

Returns: A reference to dst for chaining

◆ rotateZ() [2/2]

Mat4 & cugl::Mat4::rotateZ ( float angle )

inline

Applies a z-axis rotation to this matrix.

The rotation is in radians, counter-clockwise about the z-axis.

The rotation is applied on the right. Given our convention, that means that it takes place AFTER any previously applied transforms.

Parameters

angle The angle (in radians).

Returns: This matrix, after rotation.

◆ scale() [1/6]

static Mat4 * cugl::Mat4::scale	(	const Mat4 &	mat,
		const Vec3	s,
		Mat4 *	dst
	)

inlinestatic

Applies a non-uniform scale to the given matrix and stores the result in dst.

The scaling operation is applied on the right. Given our convention, that means that it takes place AFTER any previously applied transforms.

Parameters

mat	The matrix to scale.
s	The vector storing the individual scaling factors
dst	A matrix to store the result in.

Returns: A reference to dst for chaining

◆ scale() [2/6]

static Mat4 * cugl::Mat4::scale	(	const Mat4 &	mat,
		float	sx,
		float	sy,
		float	sz,
		Mat4 *	dst
	)

inlinestatic

Applies a non-uniform scale to the given matrix and stores the result in dst.

The scaling operation is applied on the right. Given our convention, that means that it takes place AFTER any previously applied transforms.

Parameters

mat	The matrix to scale.
sx	The amount to scale along the x-axis.
sy	The amount to scale along the y-axis.
sz	The amount to scale along the z-axis.
dst	A matrix to store the result in.

Returns: A reference to dst for chaining

◆ scale() [3/6]

static Mat4 * cugl::Mat4::scale	(	const Mat4 &	mat,
		float	value,
		Mat4 *	dst
	)

inlinestatic

Applies a uniform scale to the given matrix and stores the result in dst.

The scaling operation is applied on the right. Given our convention, that means that it takes place AFTER any previously applied transforms.

Parameters

mat	The matrix to scale.
value	The scalar to multiply by.
dst	A matrix to store the result in.

Returns: A reference to dst for chaining

◆ scale() [4/6]

Mat4 & cugl::Mat4::scale ( const Vec3 s )

inline

Applies a non-uniform scale to this matrix.

The scaling operation is applied on the right. Given our convention, that means that it takes place AFTER any previously applied transforms.

Parameters

s	The vector storing the individual scaling factors

Returns: This matrix, after scaling.

◆ scale() [5/6]

Mat4 & cugl::Mat4::scale	(	float	sx,
		float	sy,
		float	sz
	)

inline

Applies a non-uniform scale to this matrix.

The scaling operation is applied on the right. Given our convention, that means that it takes place AFTER any previously applied transforms.

Parameters

sx	The amount to scale along the x-axis.
sy	The amount to scale along the y-axis.
sz	The amount to scale along the z-axis.

Returns: This matrix, after scaling.

◆ scale() [6/6]

Mat4 & cugl::Mat4::scale ( float value )

inline

Applies a uniform scale to this matrix.

The scaling operation is applied on the right. Given our convention, that means that it takes place AFTER any previously applied transforms.

Parameters

value The scalar to multiply by.

Returns: This matrix, after scaling.

◆ set() [1/5]

Mat4 & cugl::Mat4::set ( const Affine2 & aff )

Sets the elements of this matrix to those of the given transform.

The z values are set to the identity.

Parameters

aff	The transform to convert

Returns: A reference to this (modified) Mat4 for chaining.

◆ set() [2/5]

Mat4 & cugl::Mat4::set ( const float * mat )

Sets the values of this matrix to those in the specified column-major array.

The passed-in array is in column-major order, so the memory layout of the array is as follows:

0   4   8   12
1   5   9   13
2   6   10  14
3   7   11  15

Parameters

mat	An array containing 16 elements in column-major order.

Returns: A reference to this (modified) Mat4 for chaining.

◆ set() [3/5]

Mat4 & cugl::Mat4::set ( const Mat4 & mat )

Sets the elements of this matrix to those in the specified matrix.

Parameters

mat	The matrix to copy.

Returns: A reference to this (modified) Mat4 for chaining.

◆ set() [4/5]

Mat4 & cugl::Mat4::set ( const Quaternion & quat )

Sets this matrix as a rotation matrix from the specified quaternion.

Parameters

quat	A quaternion describing a 3D orientation.

Returns: A reference to this (modified) Mat4 for chaining.

◆ set() [5/5]

Mat4 & cugl::Mat4::set	(	float	m11,
		float	m12,
		float	m13,
		float	m14,
		float	m21,
		float	m22,
		float	m23,
		float	m24,
		float	m31,
		float	m32,
		float	m33,
		float	m34,
		float	m41,
		float	m42,
		float	m43,
		float	m44
	)

Sets the individal values of this matrix.

Parameters

m11	The first element of the first row.
m12	The second element of the first row.
m13	The third element of the first row.
m14	The fourth element of the first row.
m21	The first element of the second row.
m22	The second element of the second row.
m23	The third element of the second row.
m24	The fourth element of the second row.
m31	The first element of the third row.
m32	The second element of the third row.
m33	The third element of the third row.
m34	The fourth element of the third row.
m41	The first element of the fourth row.
m42	The second element of the fourth row.
m43	The third element of the fourth row.
m44	The fourth element of the fourth row.

Returns: A reference to this (modified) Mat4 for chaining.

◆ setIdentity()

Mat4 & cugl::Mat4::setIdentity ( )

Sets this matrix to the identity matrix.

Returns: A reference to this (modified) Mat4 for chaining.

◆ setZero()

Mat4 & cugl::Mat4::setZero ( )

Sets all elements of the current matrix to zero.

Returns: A reference to this (modified) Mat4 for chaining.

◆ subtract() [1/6]

static float * cugl::Mat4::subtract	(	const float *	m1,
		const float *	m2,
		float *	dst
	)

static

Subtracts the matrix m2 from m1 and stores the result in dst.

This method assumes the float arrays are in column major order.

Parameters

m1	The first matrix in column-major order
m2	The second matrix in column-major order
dst	The destination matrix in column-major order

Returns: A reference to dst for chaining

◆ subtract() [2/6]

static float * cugl::Mat4::subtract	(	const float *	mat,
		float	scalar,
		float *	dst
	)

static

Subtracts a scalar from each component of mat and stores the result in dst.

This method assumes the float arrays are in column major order.

Parameters

mat	The matrix to subtract from in column major order
scalar	The scalar value to subtract in column major order
dst	A matrix to store the result in column major order

Returns: A reference to dst for chaining

◆ subtract() [3/6]

static Mat4 * cugl::Mat4::subtract	(	const Mat4 &	m1,
		const Mat4 &	m2,
		Mat4 *	dst
	)

static

Subtracts the matrix m2 from m1 and stores the result in dst.

Parameters

m1	The first matrix.
m2	The second matrix.
dst	A matrix to store the result in.

Returns: A reference to dst for chaining

◆ subtract() [4/6]

Mat4 & cugl::Mat4::subtract ( const Mat4 & mat )

inline

Subtracts the specified matrix from the current matrix.

Parameters

mat	The matrix to subtract.

Returns: A reference to the Mat4 after subtraction.

◆ subtract() [5/6]

static Mat4 * cugl::Mat4::subtract	(	const Mat4 &	mat,
		float	scalar,
		Mat4 *	dst
	)

static

Subtracts a scalar from each component of mat and stores the result in dst.

Parameters

mat	The matrix to subtract from.
scalar	The scalar value to subtract.
dst	A matrix to store the result in.

Returns: A reference to dst for chaining

◆ subtract() [6/6]

Mat4 & cugl::Mat4::subtract ( float scalar )

inline

Subtracts a scalar value from each component of this matrix.

Parameters

scalar The scalar to subtract.

Returns: A reference to the Mat4 after subtraction.

◆ toString()

std::string cugl::Mat4::toString ( bool verbose = false ) const

Returns a string representation of this matrix for debugging purposes.

If verbose is true, the string will include class information. This allows us to unambiguously identify the class.

Parameters

verbose Whether to include class information

Returns: a string representation of this matrix for debugging purposes.

◆ transform() [1/11]

static float * cugl::Mat4::transform	(	const float *	mat,
		float const *	input,
		float *	output,
		size_t	size
	)

static

Transforms the vector array by the given matrix, and stores the result in dst.

The vector is array is treated as a list of 4 element vectors (

See also: Vec4). The transform is applied in order and written to the output array. The float array for the matrix should be in column major order

Parameters

mat	The transform matrix in column major order
input	The array of vectors to transform.
output	The array to store the transformed vectors.
size	The size of the two arrays.

Returns: A reference to dst for chaining

◆ transform() [2/11]

static Rect * cugl::Mat4::transform	(	const Mat4 &	mat,
		const Rect	rect,
		Rect *	dst
	)

static

Transforms the rectangle by the given matrix, and stores the result in dst.

This method transforms the four defining points of the rectangle. It then computes the minimal bounding box storing these four points.

Parameters

mat	The transform matrix.
rect	The rect to transform.
dst	A rect to store the transformed rectangle in.

Returns: A reference to dst for chaining

◆ transform() [3/11]

static float * cugl::Mat4::transform	(	const Mat4 &	mat,
		const Vec2	point,
		float *	dst
	)

static

Transforms the point by the given matrix, and stores the result in dst.

The vector is treated as a point, which means that translation is applied to the result. The destination array will be assigned only 2 elements.

Parameters

mat	The transform matrix.
point	The point to transform.
dst	An array to store the transformed point.

Returns: A reference to dst for chaining

◆ transform() [4/11]

static Vec2 * cugl::Mat4::transform	(	const Mat4 &	mat,
		const Vec2	point,
		Vec2 *	dst
	)

static

Transforms the point by the given matrix, and stores the result in dst.

The vector is treated as a point, which means that translation is applied to the result.

Parameters

mat	The transform matrix.
point	The point to transform.
dst	A vector to store the transformed point in.

Returns: A reference to dst for chaining

◆ transform() [5/11]

static Vec3 * cugl::Mat4::transform	(	const Mat4 &	mat,
		const Vec3	point,
		Vec3 *	dst
	)

static

Transforms the point by the given matrix, and stores the result in dst.

The vector is treated as a point, which means that translation is applied to the result.

Parameters

mat	The transform matrix.
point	The point to transform.
dst	A vector to store the transformed point in.

Returns: A reference to dst for chaining

◆ transform() [6/11]

static Vec4 * cugl::Mat4::transform	(	const Mat4 &	mat,
		const Vec4	vec,
		Vec4 *	dst
	)

static

Transforms the vector by the given matrix, and stores the result in dst.

The vector is treated as is. Hence whether or not translation is applied depends on the value of w.

Parameters

mat	The transform matrix.
vec	The vector to transform.
dst	A vector to store the transformed point in.

Returns: A reference to dst for chaining

◆ transform() [7/11]

static float * cugl::Mat4::transform	(	const Mat4 &	mat,
		float const *	input,
		float *	output,
		size_t	size
	)

static

Transforms the vector array by the given matrix, and stores the result in dst.

The vector is array is treated as a list of 4 element vectors (

See also: Vec4). The transform is applied in order and written to the output array.

Parameters

mat	The transform matrix.
input	The array of vectors to transform.
output	The array to store the transformed vectors.
size	The size of the two arrays.

Returns: A reference to dst for chaining

◆ transform() [8/11]

Rect cugl::Mat4::transform ( const Rect rect ) const

Returns a copy of the given rectangle transformed.

This method transforms the four defining points of the rectangle. It then computes the minimal bounding box storing these four points

Note: This does not modify the original rectangle. To transform a point in place, use the static method.

Parameters

rect	The rect to transform.

Returns: A reference to dst for chaining

◆ transform() [9/11]

Vec2 cugl::Mat4::transform ( const Vec2 point ) const

Returns a copy of this point transformed by the matrix.

The vector is treated as a point, which means that translation is applied to the result.

Note: This does not modify the original point. To transform a point in place, use the static method (or the appropriate operator).

Parameters

point The point to transform.

Returns: a copy of this point transformed by the matrix.

◆ transform() [10/11]

Vec3 cugl::Mat4::transform ( const Vec3 point ) const

Returns a copy of this point transformed by the matrix.

The vector is treated as a point, which means that translation is applied to the result.

Note: This does not modify the original point. To transform a point in place, use the static method (or the appropriate operator).

Parameters

point The point to transform.

Returns: a copy of this point transformed by the matrix.

◆ transform() [11/11]

Vec4 cugl::Mat4::transform ( const Vec4 vec ) const

Returns a copy of this vector transformed by the matrix.

The vector is treated as is. Hence whether or not translation is applied depends on the value of w.

Note: This does not modify the original vector. To transform a vector in place, use the static method (or the appropriate operator).

Parameters

vec	The vector to transform.

Returns: a copy of this point transformed by the matrix.

◆ transformVector() [1/4]

static Vec2 * cugl::Mat4::transformVector	(	const Mat4 &	mat,
		const Vec2	vec,
		Vec2 *	dst
	)

static

Transforms the vector by the given matrix, and stores the result in dst.

The vector is treated as a direction, which means that translation is not applied to the result.

Parameters

mat	The transform matrix.
vec	The vector to transform.
dst	A vector to store the transformed point in.

Returns: A reference to dst for chaining

◆ transformVector() [2/4]

static Vec3 * cugl::Mat4::transformVector	(	const Mat4 &	mat,
		const Vec3	vec,
		Vec3 *	dst
	)

static

Transforms the vector by the given matrix, and stores the result in dst.

The vector is treated as a direction, which means that translation is not applied to the result.

Parameters

mat	The transform matrix.
vec	The vector to transform.
dst	A vector to store the transformed point in.

Returns: A reference to dst for chaining

◆ transformVector() [3/4]

Vec2 cugl::Mat4::transformVector ( const Vec2 vec ) const

Returns a copy of this vector transformed by the matrix.

The vector is treated as a direction, which means that translation is not applied to the result.

Note: This does not modify the original vector. To transform a vector in place, use the static method (or the appropriate operator).

Parameters

vec	The vector to transform.

Returns: a copy of this point transformed by the matrix.

◆ transformVector() [4/4]

Vec3 cugl::Mat4::transformVector ( const Vec3 vec ) const

Returns a copy of this vector transformed by the matrix.

The vector is treated as a direction, which means that translation is not applied to the result.

Note: This does not modify the original vector. To transform a vector in place, use the static method (or the appropriate operator).

Parameters

vec	The vector to transform.

Returns: a copy of this point transformed by the matrix.

◆ translate() [1/4]

static Mat4 * cugl::Mat4::translate	(	const Mat4 &	mat,
		const Vec3	t,
		Mat4 *	dst
	)

inlinestatic

Applies a translation to the given matrix and stores the result in dst.

The translation operation is applied on the right. Given our convention, that means that it takes place AFTER any previously applied transforms.

Parameters

mat	The matrix to translate.
t	The vector storing the individual translation offsets
dst	A matrix to store the result in.

Returns: A reference to dst for chaining

◆ translate() [2/4]

static Mat4 * cugl::Mat4::translate	(	const Mat4 &	mat,
		float	tx,
		float	ty,
		float	tz,
		Mat4 *	dst
	)

inlinestatic

Applies a translation to the given matrix and stores the result in dst.

The translation operation is applied on the right. Given our convention, that means that it takes place AFTER any previously applied transforms.

Parameters

mat	The matrix to translate.
tx	The translation offset for the x-axis.
ty	The translation offset for the y-axis.
tz	The translation offset for the z-axis.
dst	A matrix to store the result in.

Returns: A reference to dst for chaining

◆ translate() [3/4]

Mat4 & cugl::Mat4::translate ( const Vec3 t )

inline

Applies a translation to this matrix.

The translation operation is applied on the right. Given our convention, that means that it takes place AFTER any previously applied transforms.

Parameters

t	The vector storing the individual translation offsets

Returns: This matrix, after translation.

◆ translate() [4/4]

Mat4 & cugl::Mat4::translate	(	float	tx,
		float	ty,
		float	tz
	)

inline

Applies a translation to this matrix.

The translation operation is applied on the right. Given our convention, that means that it takes place AFTER any previously applied transforms.

Parameters

tx	The translation offset for the x-axis.
ty	The translation offset for the y-axis.
tz	The translation offset for the z-axis.

Returns: This matrix, after translation.

◆ transpose() [1/3]

Mat4 & cugl::Mat4::transpose ( )

inline

Transposes this matrix in place.

Transposing a matrix swaps columns and rows. This allows to transform a vector by multiplying it on the left. If the matrix is orthonormal, this is also the inverse.

Returns: A reference to the Mat4 after the transposition.

◆ transpose() [2/3]

static float * cugl::Mat4::transpose	(	const float *	m1,
		float *	dst
	)

static

Transposes m1 and stores the result in dst.

Transposing a matrix swaps columns and rows. This allows to transform a vector by multiplying it on the left. If the matrix is orthonormal, this is also the inverse.

This method assumes the float arrays are in column major order.

Parameters

m1	The matrix to transpose in column major order
dst	A matrix to store the result in column major order

Returns: A reference to dst for chaining

◆ transpose() [3/3]

static Mat4 * cugl::Mat4::transpose	(	const Mat4 &	m1,
		Mat4 *	dst
	)

static

Transposes m1 and stores the result in dst.

Transposing a matrix swaps columns and rows. This allows to transform a vector by multiplying it on the left. If the matrix is orthonormal, this is also the inverse.

Parameters

m1	The matrix to transpose.
dst	A matrix to store the result in.

Returns: A reference to dst for chaining

Member Data Documentation

◆ IDENTITY

const Mat4 cugl::Mat4::IDENTITY

static

The identity matrix (ones on the diagonal)

◆ m

float cugl::Mat4::m[16]

The underlying matrix elements

◆ ONE

const Mat4 cugl::Mat4::ONE

static

The matrix with all ones

◆ ZERO

const Mat4 cugl::Mat4::ZERO

static

The matrix with all zeroes

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

cugl/include/cugl/math/CUMat4.h

Public Member Functions

Static Public Member Functions

Public Attributes

Static Public Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Mat4() [1/7]

◆ Mat4() [2/7]

◆ Mat4() [3/7]

◆ Mat4() [4/7]

◆ Mat4() [5/7]

◆ Mat4() [6/7]

◆ ~Mat4()

◆ Mat4() [7/7]

Member Function Documentation

◆ add() [1/6]

◆ add() [2/6]

◆ add() [3/6]

◆ add() [4/6]

◆ add() [5/6]

◆ add() [6/6]

◆ createLookAt() [1/4]

◆ createLookAt() [2/4]

◆ createLookAt() [3/4]

◆ createLookAt() [4/4]

◆ createOrthographic() [1/2]

◆ createOrthographic() [2/2]

◆ createOrthographicOffCenter() [1/2]

◆ createOrthographicOffCenter() [2/2]

◆ createPerspective() [1/2]

◆ createPerspective() [2/2]

◆ createRotation() [1/4]

◆ createRotation() [2/4]

◆ createRotation() [3/4]

◆ createRotation() [4/4]

◆ createRotationX() [1/2]

◆ createRotationX() [2/2]

◆ createRotationY() [1/2]

◆ createRotationY() [2/2]

◆ createRotationZ() [1/2]

◆ createRotationZ() [2/2]

◆ createScale() [1/6]

◆ createScale() [2/6]

◆ createScale() [3/6]

◆ createScale() [4/6]

◆ createScale() [5/6]

◆ createScale() [6/6]

◆ createTranslation() [1/4]

◆ createTranslation() [2/4]

◆ createTranslation() [3/4]

◆ createTranslation() [4/4]

◆ decompose()

◆ equals()

◆ getBackVector()

◆ getDeterminant()

◆ getDownVector()

◆ getForwardVector()

◆ getInverse()

◆ getLeftVector()

◆ getNegation()

◆ getRightVector()

◆ getRotation()

◆ getScale()

◆ getTranslation()

◆ getTranspose()

◆ getUpVector()

◆ invert() [1/3]

◆ invert() [2/3]

◆ invert() [3/3]

◆ isExactly()

◆ isIdentity()

◆ isInvertible()

◆ isOrthogonal()

◆ multiply() [1/6]

◆ multiply() [2/6]

◆ multiply() [3/6]

◆ multiply() [4/6]

◆ multiply() [5/6]

◆ multiply() [6/6]

◆ negate() [1/3]