Infinity::Types::Math::t_Matrix4< T > Struct Template Reference

Template structure representing a 4x4 matrix. More...

#include <Matrix4.hpp>

Public Member Functions
constexpr	t_Matrix4 ()
	Default constructor.
constexpr	t_Matrix4 (T v)
	Constructs a diagonal matrix with the same value on the diagonal.
constexpr	t_Matrix4 (T v0, T v1, T v2, T v3, T v4, T v5, T v6, T v7, T v8, T v9, T v10, T v11, T v12, T v13, T v14, T v15)
	Constructs a matrix from sixteen individual elements.
constexpr	t_Matrix4 (T v[16])
	Constructs a matrix from an array of sixteen elements.
constexpr	t_Matrix4 (const t_Vector4< T > &c0, const t_Vector4< T > &c1, const t_Vector4< T > &c2, const t_Vector4< T > &c3)
	Constructs a matrix from four column vectors.
template<typename R >
	t_Matrix4 (const t_Matrix4< 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_Vector4< T > &	operator[] (size_t c)
	Column access operator (mutable).
const t_Vector4< 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_Matrix4 &	operator= (const t_Matrix4< 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, T v9, T v10, T v11, T v12, T v13, T v14, T v15)
	Sets all sixteen matrix elements.
template<typename R >
void	set (const t_Matrix4< 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_Matrix4	operator* (T scalar) const
	Scalar multiplication operator.
t_Matrix4 &	operator*= (T scalar)
	Scalar multiplication assignment operator.
t_Matrix4	operator* (const t_Matrix4 &rhs) const
	Matrix multiplication operator.
t_Matrix4 &	operator*= (const t_Matrix4 &rhs)
	Matrix multiplication assignment operator.
t_Vector4< T >	operator* (const t_Vector4< T > &v) const
	Matrix-vector multiplication operator.
t_Matrix4	operator+ (const t_Matrix4 &rhs) const
	Matrix addition operator.
t_Matrix4 &	operator+= (const t_Matrix4 &rhs)
	Matrix addition assignment operator.
t_Matrix4	operator- (const t_Matrix4 &rhs) const
	Matrix subtraction operator.
t_Matrix4 &	operator-= (const t_Matrix4 &rhs)
	Matrix subtraction assignment operator.
t_Matrix4	operator/ (T scalar) const
	Scalar division operator.
t_Matrix4 &	operator/= (T scalar)
	Scalar division assignment operator.
bool	operator== (const t_Matrix4 &rhs) const
	Equality comparison operator.
bool	operator!= (const t_Matrix4 &rhs) const
	Inequality comparison operator.
bool	operator< (const t_Matrix4 &rhs) const
	Less-than comparison operator for ordering.
t_Matrix4	transpose () const
	Computes the transpose of this matrix.
t_Matrix4	operator- () const
	Unary negation operator.
	operator bool () const noexcept
	Boolean conversion operator.

Public Attributes
t_Vector4< T >	value [4]
	Column vectors comprising the matrix.

Detailed Description

template<typename T>
struct Infinity::Types::Math::t_Matrix4< T >

Template structure representing a 4x4 matrix.

t_Matrix4 provides a column-major 4x4 matrix implementation for 3D transformations in homogeneous coordinates. This is the standard matrix for representing complete 3D transformations including translation, rotation, scale, and perspective projection. The matrix is stored as four column vectors, following the convention used by modern graphics APIs like OpenGL and Vulkan.

Common applications in procedural generation and 3D graphics:

• Complete 3D transformations (translation, rotation, scale combined)
• Model-view-projection matrices for rendering
• Camera transformations (view and projection matrices)
• Skeletal animation transformations (bone matrices)
• Coordinate space conversions (object to world, world to view, etc.)
• Perspective and orthographic projections
• Instance transformations for procedurally placed objects

Matrix layout (column-major):

[ m00  m01  m02  m03 ]   [ value[0].x  value[1].x  value[2].x  value[3].x ]
[ m10  m11  m12  m13 ] = [ value[0].y  value[1].y  value[2].y  value[3].y ]
[ m20  m21  m22  m23 ]   [ value[0].z  value[1].z  value[2].z  value[3].z ]
[ m30  m31  m32  m33 ]   [ value[0].w  value[1].w  value[2].w  value[3].w ]

For typical 3D transformations, the upper-left 3x3 submatrix represents rotation and scale, the fourth column (value[3].xyz) represents translation, and the bottom row is typically [0, 0, 0, 1] for affine transformations.

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

Example usage:

// Identity matrix (default constructor)
Matrix4 identity;
 
// Translation matrix
Matrix4 translation(
    1, 0, 0, 0,
    0, 1, 0, 0,
    0, 0, 1, 0,
    5, 10, 3, 1  // Translate by (5, 10, 3)
);
 
// Scale matrix
Matrix4 scale(
    2, 0, 0, 0,
    0, 2, 0, 0,
    0, 0, 2, 0,
    0, 0, 0, 1  // Uniform scale by 2
);
 
// Combine transformations (scale then translate)
Matrix4 transform = translation * scale;
 
// Transform a point in homogeneous coordinates
Vector4 point(1, 2, 3, 1);  // w=1 for position
Vector4 transformed = transform * point;
 
// Transpose for converting between APIs
Matrix4 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, Vulkan, and other modern graphics APIs.

Matrix-vector multiplication treats vectors as column vectors.

For affine transformations (translation, rotation, scale), the bottom row is typically [0, 0, 0, 1].

See also

Matrix4, Matrix4d

t_Vector4, t_Matrix3

Constructor & Destructor Documentation

t_Matrix4() [1/6]

template<typename T >

constexpr Infinity::Types::Math::t_Matrix4< T >::t_Matrix4 ( )

inlineconstexpr

Default constructor.

Constructs an identity matrix:

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

t_Matrix4() [2/6]

template<typename T >

constexpr Infinity::Types::Math::t_Matrix4< T >::t_Matrix4 ( 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 ]
[ 0  v  0  0 ]
[ 0  0  v  0 ]
[ 0  0  0  v ]

Parameters

v	The value for all diagonal elements.

Matrix4 scaleMatrix(2.0f);  // Uniform scale by 2 (including w)

t_Matrix4() [3/6]

template<typename T >

constexpr Infinity::Types::Math::t_Matrix4< T >::t_Matrix4 ( T  v0, T  v1, T  v2, T  v3, T  v4, T  v5, T  v6, T  v7, T  v8, T  v9, T  v10, T  v11, T  v12, T  v13, T  v14, T  v15  )

inlineconstexpr

Constructs a matrix from sixteen individual elements.

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

Parameters

v0	through v15 Matrix elements in row-major order.

// Translation matrix: translate by (5, 10, 3)
Matrix4 translation(
    1, 0, 0, 0,
    0, 1, 0, 0,
    0, 0, 1, 0,
    5, 10, 3, 1
);

t_Matrix4() [4/6]

template<typename T >

constexpr Infinity::Types::Math::t_Matrix4< T >::t_Matrix4 ( T  v[16] )

inlineexplicitconstexpr

Constructs a matrix from an array of sixteen elements.

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

Parameters

v	Array of 16 elements in row-major order.

float data[16] = {1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1};
Matrix4 mat(data);

t_Matrix4() [5/6]

template<typename T >

constexpr Infinity::Types::Math::t_Matrix4< T >::t_Matrix4 ( const t_Vector4< T > &  c0, const t_Vector4< T > &  c1, const t_Vector4< T > &  c2, const t_Vector4< T > &  c3  )

inlineconstexpr

Constructs a matrix from four column vectors.

Directly specifies the four columns of the matrix.

Parameters

c0	First column vector.
c1	Second column vector.
c2	Third column vector.
c3	Fourth column vector (typically translation for affine transforms).

Vector4 xAxis(1, 0, 0, 0);
Vector4 yAxis(0, 1, 0, 0);
Vector4 zAxis(0, 0, 1, 0);
Vector4 translation(5, 10, 3, 1);
Matrix4 transform(xAxis, yAxis, zAxis, translation);

t_Matrix4() [6/6]

template<typename T >

template<typename R >

Infinity::Types::Math::t_Matrix4< T >::t_Matrix4 ( const t_Matrix4< 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_Matrix4< T >::columns ( ) const

inlineconstexpr

Gets the number of columns in the matrix.

Returns

4 (always 4 columns).

data() [1/2]

template<typename T >

T * Infinity::Types::Math::t_Matrix4< 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, suitable for passing directly to graphics APIs like OpenGL.

Returns

Pointer to the first matrix element.

data() [2/2]

template<typename T >

const T * Infinity::Types::Math::t_Matrix4< 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_Matrix4< 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_Matrix4< T >::operator!= ( const t_Matrix4< 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_Matrix4< 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, 2, or 3).
r	Row index (0, 1, 2, or 3).

Returns

Reference to the matrix element.

Matrix4 m;
m(3, 0) = 5.0f;  // Set translation X (column 3, row 0)

operator()() [2/2]

template<typename T >

T Infinity::Types::Math::t_Matrix4< 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, 2, or 3).
r	Row index (0, 1, 2, or 3).

Returns

Value of the matrix element.

operator*() [1/3]

template<typename T >

t_Matrix4 Infinity::Types::Math::t_Matrix4< T >::operator* ( const t_Matrix4< T > &  rhs ) const

inline

Matrix multiplication operator.

Performs standard matrix multiplication (this * rhs). This composes transformations: the result applies rhs first, then this.

Parameters

rhs	Right-hand side matrix.

Returns

Result of matrix multiplication.

Matrix4 scale = ...;
Matrix4 rotation = ...;
Matrix4 translation = ...;
 
// Apply scale, then rotation, then translation
Matrix4 transform = translation * rotation * scale;

operator*() [2/3]

template<typename T >

t_Vector4< T > Infinity::Types::Math::t_Matrix4< T >::operator* ( const t_Vector4< T > &  v ) const

inline

Matrix-vector multiplication operator.

Transforms a vector by this matrix, treating the vector as a column vector. This is used to transform points and directions in homogeneous coordinates.

Parameters

v	Vector to transform.

Returns

Transformed vector.

Matrix4 transform = ...;
Vector4 point(1, 2, 3, 1);  // Position (w=1)
Vector4 transformed = transform * point;
 
// For perspective projection, don't forget to divide by w
if (transformed.w != 0) {
    transformed.x /= transformed.w;
    transformed.y /= transformed.w;
    transformed.z /= transformed.w;
}

operator*() [3/3]

template<typename T >

t_Matrix4 Infinity::Types::Math::t_Matrix4< 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.

Matrix4 m;
Matrix4 scaled = m * 2.0f;  // Double all elements

operator*=() [1/2]

template<typename T >

t_Matrix4 & Infinity::Types::Math::t_Matrix4< T >::operator*= ( const t_Matrix4< 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_Matrix4 & Infinity::Types::Math::t_Matrix4< 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_Matrix4 Infinity::Types::Math::t_Matrix4< T >::operator+ ( const t_Matrix4< 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_Matrix4 & Infinity::Types::Math::t_Matrix4< T >::operator+= ( const t_Matrix4< 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_Matrix4 Infinity::Types::Math::t_Matrix4< T >::operator- ( ) const

inline

Unary negation operator.

Returns a matrix with all elements negated.

Returns

Negated matrix.

operator-() [2/2]

template<typename T >

t_Matrix4 Infinity::Types::Math::t_Matrix4< T >::operator- ( const t_Matrix4< 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_Matrix4 & Infinity::Types::Math::t_Matrix4< T >::operator-= ( const t_Matrix4< 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_Matrix4 Infinity::Types::Math::t_Matrix4< 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_Matrix4 & Infinity::Types::Math::t_Matrix4< 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_Matrix4< T >::operator< ( const t_Matrix4< 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_Matrix4 & Infinity::Types::Math::t_Matrix4< T >::operator= ( const t_Matrix4< 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_Matrix4< T >::operator== ( const t_Matrix4< 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_Vector4< T > & Infinity::Types::Math::t_Matrix4< T >::operator[] ( size_t  c )

inline

Column access operator (mutable).

Returns a reference to the specified column vector.

Parameters

c	Column index (0, 1, 2, or 3).

Returns

Reference to the column vector.

Matrix4 m;
m[3] = Vector4(5, 10, 3, 1);  // Set translation column

operator[]() [2/2]

template<typename T >

const t_Vector4< T > & Infinity::Types::Math::t_Matrix4< 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, 2, or 3).

Returns

Const reference to the column vector.

rows()

template<typename T >

constexpr size_t Infinity::Types::Math::t_Matrix4< T >::rows ( ) const

inlineconstexpr

Gets the number of rows in the matrix.

Returns

4 (always 4 rows).

set() [1/2]

template<typename T >

template<typename R >

void Infinity::Types::Math::t_Matrix4< T >::set ( const t_Matrix4< 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_Matrix4< T >::set ( T  v0, T  v1, T  v2, T  v3, T  v4, T  v5, T  v6, T  v7, T  v8, T  v9, T  v10, T  v11, T  v12, T  v13, T  v14, T  v15  )

inline

Sets all sixteen matrix elements.

Elements are specified in row-major order for readability.

Parameters

v0	through v15 Matrix elements in row-major order.

size()

template<typename T >

constexpr size_t Infinity::Types::Math::t_Matrix4< T >::size ( ) const

inlineconstexpr

Gets the total number of elements in the matrix.

Returns

16 (always 4x4 = 16 elements).

transpose()

template<typename T >

t_Matrix4 Infinity::Types::Math::t_Matrix4< T >::transpose ( ) const

inline

Computes the transpose of this matrix.

Returns a new matrix with rows and columns swapped. For orthogonal matrices (like pure rotation matrices), the transpose equals the inverse.

Returns

Transposed matrix.

Matrix4 m = ...;
Matrix4 mT = m.transpose();
// mT[i][j] == m[j][i]
 
// For rotation matrices: M^T = M^-1
Matrix4 rotation = ...;
Matrix4 inverse = rotation.transpose();

Member Data Documentation

value

template<typename T >

t_Vector4<T> Infinity::Types::Math::t_Matrix4< T >::value[4]

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, value[3] is the fourth column (typically translation for affine transforms).