Template structure representing a 3x3 matrix. More...

#include <Matrix3.hpp>

Public Member Functions
constexpr	t_Matrix3 ()
	Default constructor.

constexpr	t_Matrix3 (T v)
	Constructs a diagonal matrix with the same value on the diagonal.

constexpr	t_Matrix3 (T v0, T v1, T v2, T v3, T v4, T v5, T v6, T v7, T v8)
	Constructs a matrix from nine individual elements.

constexpr	t_Matrix3 (T v[9])
	Constructs a matrix from an array of nine elements.

constexpr	t_Matrix3 (const t_Vector3< T > &c0, const t_Vector3< T > &c1, const t_Vector3< T > &c2)
	Constructs a matrix from three column vectors.

template<typename R >
	t_Matrix3 (const t_Matrix3< R > &rhs)
	Type-converting constructor.

constexpr size_t	size () const
	Gets the total number of elements in the matrix.

constexpr size_t	columns () const
	Gets the number of columns in the matrix.

constexpr size_t	rows () const
	Gets the number of rows in the matrix.

t_Vector3< T > &	operator[] (size_t c)
	Column access operator (mutable).

const t_Vector3< T > &	operator[] (size_t c) const
	Column access operator (const).

T &	operator() (size_t c, size_t r)
	Element access operator (mutable).

T	operator() (size_t c, size_t r) const
	Element access operator (const).

template<typename R >
t_Matrix3 &	operator= (const t_Matrix3< R > &rhs)
	Type-converting assignment operator.

void	set (T v0, T v1, T v2, T v3, T v4, T v5, T v6, T v7, T v8)
	Sets all nine matrix elements.

template<typename R >
void	set (const t_Matrix3< R > &rhs)
	Sets this matrix equal to another matrix.

T *	data ()
	Gets a pointer to the underlying data.

const T *	data () const
	Gets a const pointer to the underlying data.

t_Matrix3	operator* (const t_Matrix3 &rhs) const
	Matrix multiplication operator.

t_Matrix3 &	operator*= (const t_Matrix3 &rhs)
	Matrix multiplication assignment operator.

t_Matrix3	operator* (T scalar) const
	Scalar multiplication operator.

t_Matrix3 &	operator*= (T scalar)
	Scalar multiplication assignment operator.

t_Vector3< T >	operator* (const t_Vector3< T > &v) const
	Matrix-vector multiplication operator.

t_Matrix3	operator+ (const t_Matrix3 &rhs) const
	Matrix addition operator.

t_Matrix3 &	operator+= (const t_Matrix3 &rhs)
	Matrix addition assignment operator.

t_Matrix3	operator- (const t_Matrix3 &rhs) const
	Matrix subtraction operator.

t_Matrix3 &	operator-= (const t_Matrix3 &rhs)
	Matrix subtraction assignment operator.

t_Matrix3	operator/ (T scalar) const
	Scalar division operator.

t_Matrix3 &	operator/= (T scalar)
	Scalar division assignment operator.

bool	operator== (const t_Matrix3 &rhs) const
	Equality comparison operator.

bool	operator!= (const t_Matrix3 &rhs) const
	Inequality comparison operator.

bool	operator< (const t_Matrix3 &rhs) const
	Less-than comparison operator for ordering.

t_Matrix3	transpose () const
	Computes the transpose of this matrix.

t_Matrix3	operator- () const
	Unary negation operator.

	operator bool () const noexcept
	Boolean conversion operator.

Public Attributes
t_Vector3< T >	value [3]
	Column vectors comprising the matrix.

Detailed Description

template<typename T>
struct Infinity::Types::Math::t_Matrix3< T >

Template structure representing a 3x3 matrix.

t_Matrix3 provides a column-major 3x3 matrix implementation suitable for representing 2D transformations in homogeneous coordinates and 3D rotations/scales. The matrix is stored as three column vectors, following the convention used by modern graphics APIs and mathematics libraries.

Common applications in procedural generation:

2D transformations (rotation, scale, translation in homogeneous coordinates)
3D rotation matrices (without translation)
Normal matrix transformations (inverse transpose of model matrix)
Texture coordinate transformations
Basis transformations and coordinate system changes
Tensor operations in procedural algorithms

Matrix layout (column-major):

[ m00  m01  m02 ]   [ value[0].x  value[1].x  value[2].x ]
[ m10  m11  m12 ] = [ value[0].y  value[1].y  value[2].y ]
[ m20  m21  m22 ]   [ value[0].z  value[1].z  value[2].z ]

The template parameter allows instantiation with different numeric types (float, double) to match precision requirements.

Example usage:

// Identity matrix (default constructor)
Matrix3 identity;
 
// Rotation matrix (2D rotation by 45 degrees)
float angle = M_PI / 4.0f;
Matrix3 rotation(
    std::cos(angle), std::sin(angle), 0,
    -std::sin(angle), std::cos(angle), 0,
    0, 0, 1
);
 
// Scale matrix
Matrix3 scale(
    2.0f, 0, 0,
    0, 3.0f, 0,
    0, 0, 1.0f
);
 
// Matrix multiplication
Matrix3 transform = scale * rotation;
 
// Transform a vector
Vector3 point(1, 0, 1);
Vector3 transformed = transform * point;
 
// Transpose for converting between row/column major
Matrix3 transposed = transform.transpose();

Template Parameters

T	The numeric type for matrix elements (float, double).

Note: Matrices are stored in column-major order for compatibility with OpenGL and modern graphics APIs.; Matrix-vector multiplication treats vectors as column vectors.

See also: Matrix3, Matrix3d; t_Vector3

Constructor & Destructor Documentation

◆ t_Matrix3() [1/6]

template<typename T >

constexpr Infinity::Types::Math::t_Matrix3< T >::t_Matrix3 ( )

inlineconstexpr

Default constructor.

Constructs an identity matrix:

[ 1  0  0 ]
[ 0  1  0 ]
[ 0  0  1 ]

◆ t_Matrix3() [2/6]

template<typename T >

constexpr Infinity::Types::Math::t_Matrix3< T >::t_Matrix3 ( T v )

inlineexplicitconstexpr

Constructs a diagonal matrix with the same value on the diagonal.

Creates a matrix with v on the diagonal and zeros elsewhere:

[ v  0  0 ]
[ 0  v  0 ]
[ 0  0  v ]

Parameters

v	The value for all diagonal elements.

Matrix3 scaleMatrix(2.0f); // Uniform scale by 2

◆ t_Matrix3() [3/6]

template<typename T >

constexpr Infinity::Types::Math::t_Matrix3< T >::t_Matrix3	(	T	v0,
		T	v1,
		T	v2,
		T	v3,
		T	v4,
		T	v5,
		T	v6,
		T	v7,
		T	v8
	)

inlineconstexpr

Constructs a matrix from nine individual elements.

Elements are specified in row-major order for readability, but stored in column-major order internally.

Parameters

v0	Element at row 0, column 0.
v1	Element at row 0, column 1.
v2	Element at row 0, column 2.
v3	Element at row 1, column 0.
v4	Element at row 1, column 1.
v5	Element at row 1, column 2.
v6	Element at row 2, column 0.
v7	Element at row 2, column 1.
v8	Element at row 2, column 2.

// Identity matrix
Matrix3 identity(
    1, 0, 0,
    0, 1, 0,
    0, 0, 1
);

◆ t_Matrix3() [4/6]

template<typename T >

constexpr Infinity::Types::Math::t_Matrix3< T >::t_Matrix3 ( T v[9] )

inlineexplicitconstexpr

Constructs a matrix from an array of nine elements.

Elements are read in row-major order from the array.

Parameters

v	Array of 9 elements in row-major order.

float data[9] = {1, 0, 0, 0, 1, 0, 0, 0, 1};

Matrix3 mat(data);

Infinity::Types::Math::t_Matrix3::data

T * data()

Gets a pointer to the underlying data.

Definition Matrix3.hpp:348

◆ t_Matrix3() [5/6]

template<typename T >

constexpr Infinity::Types::Math::t_Matrix3< T >::t_Matrix3	(	const t_Vector3< T > &	c0,
		const t_Vector3< T > &	c1,
		const t_Vector3< T > &	c2
	)

inlineconstexpr

Constructs a matrix from three column vectors.

Directly specifies the three columns of the matrix.

Parameters

c0	First column vector.
c1	Second column vector.
c2	Third column vector.

Vector3 xAxis(1, 0, 0);
Vector3 yAxis(0, 1, 0);
Vector3 zAxis(0, 0, 1);
Matrix3 basis(xAxis, yAxis, zAxis);

◆ t_Matrix3() [6/6]

template<typename T >

template<typename R >

Infinity::Types::Math::t_Matrix3< T >::t_Matrix3 ( const t_Matrix3< R > & rhs )

inlineexplicit

Type-converting constructor.

Constructs a matrix from another matrix with a different element type.

Template Parameters

R	The source element type.

Parameters

rhs	Matrix to convert from.

Member Function Documentation

◆ columns()

template<typename T >

constexpr size_t Infinity::Types::Math::t_Matrix3< T >::columns ( ) const

inlineconstexpr

Gets the number of columns in the matrix.

Returns: 3 (always 3 columns).

◆ data() [1/2]

template<typename T >

T * Infinity::Types::Math::t_Matrix3< T >::data ( )

inline

Gets a pointer to the underlying data.

Returns a pointer to the first element, allowing direct memory access. Elements are stored in column-major order.

Returns: Pointer to the first matrix element.

◆ data() [2/2]

template<typename T >

const T * Infinity::Types::Math::t_Matrix3< T >::data ( ) const

inline

Gets a const pointer to the underlying data.

Returns: Const pointer to the first matrix element.

◆ operator bool()

template<typename T >

Infinity::Types::Math::t_Matrix3< T >::operator bool ( ) const

inlineexplicitnoexcept

Boolean conversion operator.

Returns true if the matrix is non-zero (at least one column is non-zero).

Returns: true if matrix is non-zero, false if zero matrix.

◆ operator!=()

template<typename T >

bool Infinity::Types::Math::t_Matrix3< T >::operator!= ( const t_Matrix3< T > & rhs ) const

inline

Inequality comparison operator.

Parameters

rhs	Matrix to compare against.

Returns: true if any element differs.

◆ operator()() [1/2]

template<typename T >

T & Infinity::Types::Math::t_Matrix3< T >::operator()	(	size_t	c,
		size_t	r
	)

inline

Element access operator (mutable).

Returns a reference to the element at the specified column and row.

Parameters

c	Column index (0, 1, or 2).
r	Row index (0, 1, or 2).

Returns: Reference to the matrix element.

Matrix3 m;

m(1, 2) = 5.0f; // Set element at column 1, row 2

◆ operator()() [2/2]

template<typename T >

T Infinity::Types::Math::t_Matrix3< T >::operator()	(	size_t	c,
		size_t	r
	)		const

inline

Element access operator (const).

Returns the value of the element at the specified column and row.

Parameters

c	Column index (0, 1, or 2).
r	Row index (0, 1, or 2).

Returns: Value of the matrix element.

◆ operator*() [1/3]

template<typename T >

t_Matrix3 Infinity::Types::Math::t_Matrix3< T >::operator* ( const t_Matrix3< T > & rhs ) const

inline

Matrix multiplication operator.

Performs standard matrix multiplication (this * rhs).

Parameters

rhs	Right-hand side matrix.

Returns: Result of matrix multiplication.

Matrix3 a, b;

Matrix3 c = a * b; // Compose transformations

◆ operator*() [2/3]

template<typename T >

t_Vector3< T > Infinity::Types::Math::t_Matrix3< T >::operator* ( const t_Vector3< T > & v ) const

inline

Matrix-vector multiplication operator.

Transforms a vector by this matrix, treating the vector as a column vector.

Parameters

v	Vector to transform.

Returns: Transformed vector.

Matrix3 rotation = ...;
Vector3 point(1, 0, 0);
Vector3 rotated = rotation * point;

◆ operator*() [3/3]

template<typename T >

t_Matrix3 Infinity::Types::Math::t_Matrix3< T >::operator* ( T scalar ) const

inline

Scalar multiplication operator.

Multiplies all matrix elements by a scalar value.

Parameters

scalar Scalar value to multiply by.

Returns: Scaled matrix.

Matrix3 m;

Matrix3 scaled = m * 2.0f; // Double all elements

◆ operator*=() [1/2]

template<typename T >

t_Matrix3 & Infinity::Types::Math::t_Matrix3< T >::operator*= ( const t_Matrix3< T > & rhs )

inline

Matrix multiplication assignment operator.

Multiplies this matrix by another matrix and stores the result.

Parameters

rhs	Right-hand side matrix.

Returns: Reference to this matrix.

◆ operator*=() [2/2]

template<typename T >

t_Matrix3 & Infinity::Types::Math::t_Matrix3< T >::operator*= ( T scalar )

inline

Scalar multiplication assignment operator.

Multiplies all elements of this matrix by a scalar.

Parameters

scalar Scalar value to multiply by.

Returns: Reference to this matrix.

◆ operator+()

template<typename T >

t_Matrix3 Infinity::Types::Math::t_Matrix3< T >::operator+ ( const t_Matrix3< T > & rhs ) const

inline

Matrix addition operator.

Adds two matrices element-wise.

Parameters

rhs	Matrix to add.

Returns: Sum of the matrices.

◆ operator+=()

template<typename T >

t_Matrix3 & Infinity::Types::Math::t_Matrix3< T >::operator+= ( const t_Matrix3< T > & rhs )

inline

Matrix addition assignment operator.

Adds another matrix to this matrix element-wise.

Parameters

rhs	Matrix to add.

Returns: Reference to this matrix.

◆ operator-() [1/2]

template<typename T >

t_Matrix3 Infinity::Types::Math::t_Matrix3< T >::operator- ( ) const

inline

Unary negation operator.

Returns a matrix with all elements negated.

Returns: Negated matrix.

◆ operator-() [2/2]

template<typename T >

t_Matrix3 Infinity::Types::Math::t_Matrix3< T >::operator- ( const t_Matrix3< T > & rhs ) const

inline

Matrix subtraction operator.

Subtracts one matrix from another element-wise.

Parameters

rhs	Matrix to subtract.

Returns: Difference of the matrices.

◆ operator-=()

template<typename T >

t_Matrix3 & Infinity::Types::Math::t_Matrix3< T >::operator-= ( const t_Matrix3< T > & rhs )

inline

Matrix subtraction assignment operator.

Subtracts another matrix from this matrix element-wise.

Parameters

rhs	Matrix to subtract.

Returns: Reference to this matrix.

◆ operator/()

template<typename T >

t_Matrix3 Infinity::Types::Math::t_Matrix3< T >::operator/ ( T scalar ) const

inline

Scalar division operator.

Divides all matrix elements by a scalar value. For floating-point types, uses reciprocal multiplication for better performance.

Parameters

scalar Scalar value to divide by.

Returns: Scaled matrix.

Warning: Division by zero is undefined behavior.

◆ operator/=()

template<typename T >

t_Matrix3 & Infinity::Types::Math::t_Matrix3< T >::operator/= ( T scalar )

inline

Scalar division assignment operator.

Divides all elements of this matrix by a scalar.

Parameters

scalar Scalar value to divide by.

Returns: Reference to this matrix.

Warning: Division by zero is undefined behavior.

◆ operator<()

template<typename T >

bool Infinity::Types::Math::t_Matrix3< T >::operator< ( const t_Matrix3< T > & rhs ) const

inline

Less-than comparison operator for ordering.

Performs lexicographic comparison of columns. Useful for using matrices as keys in ordered containers like std::map.

Parameters

rhs	Matrix to compare against.

Returns: true if this matrix is lexicographically less than rhs.

◆ operator=()

template<typename T >

template<typename R >

t_Matrix3 & Infinity::Types::Math::t_Matrix3< T >::operator= ( const t_Matrix3< R > & rhs )

inline

Type-converting assignment operator.

Assigns from a matrix with a different element type.

Template Parameters

R	The source element type.

Parameters

rhs	Matrix to assign from.

Returns: Reference to this matrix.

◆ operator==()

template<typename T >

bool Infinity::Types::Math::t_Matrix3< T >::operator== ( const t_Matrix3< T > & rhs ) const

inline

Equality comparison operator.

Two matrices are equal if all their elements are equal.

Parameters

rhs	Matrix to compare against.

Returns: true if all elements are equal.

◆ operator[]() [1/2]

template<typename T >

t_Vector3< T > & Infinity::Types::Math::t_Matrix3< T >::operator[] ( size_t c )

inline

Column access operator (mutable).

Returns a reference to the specified column vector.

Parameters

c	Column index (0, 1, or 2).

Returns: Reference to the column vector.

Matrix3 m;

m[0] = Vector3(1, 2, 3); // Set first column

Infinity::Types::Math::Vector3

t_Vector3< float > Vector3

Alias for t_Vector3<float>, the default 3D vector type.

Definition Vector3.hpp:580

◆ operator[]() [2/2]

template<typename T >

const t_Vector3< T > & Infinity::Types::Math::t_Matrix3< T >::operator[] ( size_t c ) const

inline

Column access operator (const).

Returns a const reference to the specified column vector.

Parameters

c	Column index (0, 1, or 2).

Returns: Const reference to the column vector.

◆ rows()

template<typename T >

constexpr size_t Infinity::Types::Math::t_Matrix3< T >::rows ( ) const

inlineconstexpr

Gets the number of rows in the matrix.

Returns: 3 (always 3 rows).

◆ set() [1/2]

template<typename T >

template<typename R >

void Infinity::Types::Math::t_Matrix3< T >::set ( const t_Matrix3< R > & rhs )

inline

Sets this matrix equal to another matrix.

Template Parameters

R	The source element type.

Parameters

rhs	Matrix to copy from.

◆ set() [2/2]

template<typename T >

void Infinity::Types::Math::t_Matrix3< T >::set	(	T	v0,
		T	v1,
		T	v2,
		T	v3,
		T	v4,
		T	v5,
		T	v6,
		T	v7,
		T	v8
	)

inline

Sets all nine matrix elements.

Elements are specified in row-major order for readability.

Parameters

v0	through v8 Matrix elements in row-major order.

◆ size()

template<typename T >

constexpr size_t Infinity::Types::Math::t_Matrix3< T >::size ( ) const

inlineconstexpr

Gets the total number of elements in the matrix.

Returns: 9 (always 3x3 = 9 elements).

◆ transpose()

template<typename T >

t_Matrix3 Infinity::Types::Math::t_Matrix3< T >::transpose ( ) const

inline

Computes the transpose of this matrix.

Returns a new matrix with rows and columns swapped. For rotation matrices, the transpose equals the inverse.

Returns: Transposed matrix.

Matrix3 m = ...;
Matrix3 mT = m.transpose();
// mT[i][j] == m[j][i]

Member Data Documentation

◆ value

template<typename T >

t_Vector3<T> Infinity::Types::Math::t_Matrix3< T >::value[3]

Column vectors comprising the matrix.

Stored in column-major order: value[0] is the first column, value[1] is the second column, value[2] is the third column.

Public Member Functions

Public Attributes

Detailed Description

Constructor & Destructor Documentation

◆ t_Matrix3() [1/6]

◆ t_Matrix3() [2/6]

◆ t_Matrix3() [3/6]

◆ t_Matrix3() [4/6]

◆ t_Matrix3() [5/6]

◆ t_Matrix3() [6/6]

Member Function Documentation

◆ columns()

◆ data() [1/2]

◆ data() [2/2]

◆ operator bool()

◆ operator!=()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator*() [1/3]

◆ operator*() [2/3]

◆ operator*() [3/3]

◆ operator*=() [1/2]

◆ operator*=() [2/2]

◆ operator+()

◆ operator+=()

◆ operator-() [1/2]

◆ operator-() [2/2]

◆ operator-=()

◆ operator/()

◆ operator/=()

◆ operator<()

◆ operator=()

◆ operator==()

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ rows()

◆ set() [1/2]

◆ set() [2/2]

◆ size()

◆ transpose()

Member Data Documentation

◆ value