3x3 matrix. Extends Mat with 3D-specific functionality and constructors. More...

#include <easy3d/core/mat.h>

Inheritance diagram for Mat3< T >:

Public Member Functions
	Mat3 ()=default
	Default constructor. More...

	Mat3 (T s)
	Initialized with diagonal as s and others zeros.

	Mat3 (const Mat< 3, 3, T > &rhs)
	Copy constructor. This provides compatibility with generic operations implemented by Mat.

	Mat3 (const Mat< 4, 4, T > &rhs)
	Copies the top-left corner of rhs. This provides compatibility with generic operations implemented by Mat.

	Mat3 (T s00, T s01, T s02, T s10, T s11, T s12, T s20, T s21, T s22)
	Initialize elements from individual scalars. The digits following s in the parameter names indicate the row/column of the element being set.

	Mat3 (const T *m)

	Mat3 (const Vec< 3, T > &x, const Vec< 3, T > &y, const Vec< 3, T > &z)
	Initialize elements from three vectors. If MATRIX_ROW_MAJOR is defined, x, y and z specify rows of the matrix, else columns.

	Mat3 (const Mat< 2, 2, T > &rhs)

Mat2< T >	sub () const
	the upper-left 2x2 sub-matrix.

Public Member Functions inherited from Mat< 3, 3, 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 Mat3< T >	scale (T s)
	Static constructor returning a 3D uniform scale matrix. More...

static Mat3< T >	scale (T x, T y, T z)
	Static constructor returning a 3D non-uniform scale matrix. More...

static Mat3< T >	rotation (const Vec< 3, T > &axis, T angle)
	Static constructor returning a 3D rotation matrix defined by its axis and angle. More...

static Mat3< 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 Mat3< T >	rotation (const Quat< T > &q)
	Static constructor return a 3D rotation matrix defined by a quaternion. More...

static Mat3< 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 Public Member Functions inherited from Mat< 3, 3, 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::Mat3< T >

3x3 matrix. Extends Mat with 3D-specific functionality and constructors.

Template Parameters

T	The scalar type for vector elements.

See also: Mat.

Examples: Tutorial_207_RealCamera.

Constructor & Destructor Documentation

◆ Mat3() [1/3]

Mat3 ( )

default

Default constructor.

Note: The matrix elements are intentionally not initialized. This is efficient if the user assigns their values from subsequent computations. Use Mat3(T s) to initialize the elements during construction.

◆ Mat3() [2/3]

Mat3 ( const T * m )

inlineexplicit

Initialize elements from an array of type T.

◆ Mat3() [3/3]

Mat3 ( const Mat< 2, 2, T > & rhs )

inlineexplicit

Initialize from a 2D matrix. rhs forms the upper-left 2x2 sub-matrix, other elements are initialized as the identity.

Member Function Documentation

◆ rotation() [1/4]

Mat3< T > rotation ( const Quat< T > & q )

inlinestatic

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

Note: q is a unit quaternion representing a rotation.

◆ rotation() [2/4]

Mat3< 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]

Mat3< 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]

Mat3< 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.

◆ scale() [1/2]

Mat3< T > scale ( T s )

inlinestatic

Static constructor returning a 3D uniform scale matrix.

Parameters

s	x, y, z scale (uniform).

◆ scale() [2/2]

Mat3< T > scale	(	T	x,
		T	y,
		T	z
	)

inlinestatic

Static constructor returning a 3D non-uniform scale matrix.

Parameters

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

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

◆ Mat3() [1/3]

◆ Mat3() [2/3]

◆ Mat3() [3/3]

Member Function Documentation

◆ rotation() [1/4]

◆ rotation() [2/4]

◆ rotation() [3/4]

◆ rotation() [4/4]

◆ scale() [1/2]

◆ scale() [2/2]