4x4 matrix. Extends Mat with 4D-specific functionality and constructors. More...

#include <easy3d/core/mat.h>

Inheritance diagram for Mat4< T >:

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

	Mat4 (T s)
	Initialized with diagonal as s and others zeros.

	Mat4 (const Mat< 4, 4, T > &rhs)
	Copy constructor. This provides compatibility with generic operations implemented by Mat.

	Mat4 (T s00, T s01, T s02, T s03, T s10, T s11, T s12, T s13, T s20, T s21, T s22, T s23, T s30, T s31, T s32, T s33)
	Initialize elements from individual scalars. The digits following s in the parameter names indicate the row/column of the element being set.

	Mat4 (const T *m)
	Initialize elements from an array of type T.

	Mat4 (const Vec< 4, T > &x, const Vec< 4, T > &y, const Vec< 4, T > &z, const Vec< 4, T > &w)
	Initialize elements from four vectors. If MATRIX_ROW_MAJOR is defined, x, y, z and w specify rows of the matrix, else columns.

	Mat4 (const Mat< 3, 3, T > &rhs)
	Initialize from a 3D matrix. rhs forms the upper-left 3x3 sub-matrix, other elements are initialized as the identity.

	Mat4 (const Vec< 3, T > &s, const Quat< T > &r, const Vec< 3, T > &t)
	Initialize from scale/rotation/translation.

Mat3< T >	sub () const

Public Member Functions inherited from Mat< 4, 4, T >
	Mat ()=default
	Default constructor. More...

	Mat (T s)
	Initialized with diagonal as s and others zeros.

	Mat (const Mat< rN, rM, T > &rhs)
	Copy constructor for rN >= N, rM >= M. For smaller incoming matrices (i.e, rN < N, rM < M ) specialization is required in order to fill the remaining elements with appropriate values (usually 0 or 1). rN: Number of rows in rhs. rM: Number of columns in rhs. rhs: rN by rM matrix of type T to copy. NOTE: This is explicit to prevent 'accidental' assignment of differently-sized matrices. TODO: Can this ever actually get called? A templated constructor for a templated class seems dodgy!

	Mat (const T *m)
	Initialize elements from an array of type T.

size_t	num_rows () const
	Return the number of rows.

size_t	num_columns () const
	Return the number of columns.

Vec< M, T >	row (size_t r) const
	Return row r as a vector.

Vec< N, T >	col (size_t c) const
	Return col c as a vector.

const T &	operator() (size_t r, size_t c) const
	Const row/column access to elements.

T &	operator() (size_t r, size_t c)
	Non-const row/column access to elements.

	operator const T * () const
	const array/low-level access to elements.

	operator T* ()
	Non-const array/low-level access to elements.

void	load_zero ()
	Set all elements 0.

void	load_identity (T s=T(1))
	Set diagonal elements s and others 0.

void	set_row (size_t r, const Vec< vN, T > &v)
	Set row r from vector v. This copies the first M components from v, so vN must be >= M. vN: Dimension (number of components) of v.

void	set_col (size_t c, const Vec< vN, T > &v)
	Set col c from vector v. This copies the first N components from v, so vN must be >= N. vN: Dimension (number of components) in v.

void	swap_rows (size_t a, size_t b)
	Swaps row a with row b.

void	swap_cols (size_t a, size_t b)
	Swaps col a with col b.

bool	operator== (const Mat< N, M, T > &rhs) const
	Equality test.

bool	operator!= (const Mat< N, M, T > &rhs) const
	Inequality test.

Mat< N, rM, T >	operator* (const Mat< M, rM, T > &rhs) const
	Matrix-matrix multiplication. rhs must have the same number of rows as this matrix has columns. rM: Columns in rhs. return Matrix of dimensions N x rM.

Vec< N, T >	operator* (const Vec< M, T > &rhs) const
	Matrix-vector multiplication. rhs must have the same number of elements as this matrix has columns. return vec of size N.

Mat< N, M, T >	operator* (T rhs) const
	Component-wise matrix-scalar multiplication.

Mat< N, M, T >	operator+ (const Mat< N, M, T > &rhs) const
	Component-wise matrix-matrix addition.

Mat< N, M, T >	operator- (const Mat< N, M, T > &rhs) const
	Component-wise matrix-matrix subtraction.

Mat< N, M, T >	operator- () const
	Component-wise matrix negation.

Mat< N, M, T >	operator/ (T rhs) const
	Component-wise matrix-scalar division.

Mat< N, M, T > &	*operator=** (const Mat< N, M, T > &rhs)
	Matrix-matrix multiplication/assignment.

Mat< N, M, T > &	*operator=** (T rhs)
	Component-wise matrix-scalar multiplication/assignment.

Mat< N, M, T > &	operator+= (const Mat< N, M, T > &rhs)
	Component-wise matrix-matrix addition/assignment.

Mat< N, M, T > &	operator+= (T rhs)
	Component-wise matrix-scalar addition/assignment.

Mat< N, M, T > &	operator-= (const Mat< N, M, T > &rhs)
	Component-wise matrix-matrix subtraction/assignment.

Mat< N, M, T > &	operator-= (T rhs)
	Component-wise matrix-scalar subtraction/assignment.

Mat< N, M, T > &	operator/= (T rhs)
	Component-wise matrix-scalar division/assignment.

Static Public Member Functions
static Mat4< T >	scale (T s)
	Static constructor returning a 4D uniform scale matrix. More...

static Mat4< T >	scale (const Vec< 4, T > &s)
	Static constructor returning a 4D non-uniform scale matrix,. More...

static Mat4< T >	scale (T x, T y, T z, T w)

static Mat4< T >	rotation (const Vec< 3, T > &axis, T angle)
	Static constructor returning a 3D rotation matrix defined by its axis and angle. More...

static Mat4< T >	rotation (const Vec< 3, T > &axis_angle)
	Static constructor returning a 3D rotation matrix defined by the axis–angle representation. Both the axis and the angle are represented by a vector codirectional with the rotation axis whose length is the rotation angle. More...

static Mat4< T >	rotation (const Quat< T > &q)
	Static constructor returning a 3D rotation matrix defined by a quaternion. More...

static Mat4< T >	rotation (T x, T y, T z, int order=312)
	Static constructor returning a 3D rotation matrix defined by Euler angles. The three rotations are applied successively. More...

static Mat4< T >	translation (const Vec< 3, T > &t)
	Static constructor return a 3D translation matrix (as a 4D affine transformation). More...

static Mat4< T >	translation (T x, T y, T z)

Static Public Member Functions inherited from Mat< 4, 4, T >
static Mat< N, M, T >	identity ()
	Static constructor return an N x M identity matrix. see also load_identity()

Detailed Description

template<typename T>
class easy3d::Mat4< T >

4x4 matrix. Extends Mat with 4D-specific functionality and constructors.

Template Parameters

T	The scalar type for vector elements.

See also: Mat.

Constructor & Destructor Documentation

◆ Mat4()

Mat4 ( )

default

Default constructor.

Note: The matrix elements are intentionally not initialized. This is efficient if the user assigns their values from subsequent computations. Use Mat4(T s) to initialize the elements during construction.

Member Function Documentation

◆ rotation() [1/4]

Mat4< T > rotation ( const Quat< T > & q )

inlinestatic

Static constructor returning a 3D rotation matrix defined by a quaternion.

Note: q is a unit quaternion representing a rotation.

◆ rotation() [2/4]

Mat4< T > rotation	(	const Vec< 3, T > &	axis,
		T	angle
	)

inlinestatic

Static constructor returning a 3D rotation matrix defined by its axis and angle.

Parameters

axis	Axis of rotation. This MUST be normalized.
angle	Angle of rotation in radians. Positive values of angle rotate counter-clockwise about axis as per the right-hand rule.

Note: The axis defines only the direction of the rotation axis, i.e., the rotation is about the axis passing through the origin.

◆ rotation() [3/4]

Mat4< T > rotation ( const Vec< 3, T > & axis_angle )

inlinestatic

Static constructor returning a 3D rotation matrix defined by the axis–angle representation. Both the axis and the angle are represented by a vector codirectional with the rotation axis whose length is the rotation angle.

Parameters

axis_angle direction is the axis and length is the angle (in radian)

Note: The axis defines only the direction of the rotation axis, i.e., the rotation is about the axis passing through the origin.

◆ rotation() [4/4]

Mat4< T > rotation	(	T	x,
		T	y,
		T	z,
		int	order = `312`
	)

inlinestatic

Static constructor returning a 3D rotation matrix defined by Euler angles. The three rotations are applied successively.

Parameters

x,y,z	the rotation angles (in radians) around X, Y, and Z axes respectively.
order	the order of the rotations to be applied. 1 first and 3 for last.

Note: Using a different order yields different results. The default order is first Y, then Z, then X. See http://www.opengl-tutorial.org/intermediate-tutorials/tutorial-17-quaternions/

◆ scale() [1/2]

Mat4< T > scale ( const Vec< 4, T > & s )

inlinestatic

Static constructor returning a 4D non-uniform scale matrix,.

Parameters

x	x scale.
y	y scale.
z	z scale.
w	w scale.

◆ scale() [2/2]

Mat4< T > scale ( T s )

inlinestatic

Static constructor returning a 4D uniform scale matrix.

Parameters

s	x, y, z, w scale (uniform).

◆ translation()

Mat4< T > translation ( const Vec< 3, T > & t )

inlinestatic

Static constructor return a 3D translation matrix (as a 4D affine transformation).

Parameters

t	Translation vector.

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

/Users/lnan/Documents/Projects/Easy3D/easy3d/core/mat.h

Public Member Functions

Static Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ Mat4()

Member Function Documentation

◆ rotation() [1/4]

◆ rotation() [2/4]

◆ rotation() [3/4]

◆ rotation() [4/4]

◆ scale() [1/2]

◆ scale() [2/2]

◆ translation()