Column-major matrix with basic arithmetic, transforms, and helpers. More...

#include <spk_matrix.hpp>

Collaboration diagram for spk::IMatrix< SizeX, SizeY >:

Classes
class	Column
	View of the values belonging to a single matrix column. More...

Public Member Functions
	IMatrix ()
	Builds an identity matrix.
	IMatrix (float *p_values)
	Builds a matrix from a contiguous column-major array.
	IMatrix (std::initializer_list< float > p_values)
	Builds from a flat initializer list (column-major).
Column &	operator[] (size_t p_index)
	Accesses a column.
const Column &	operator[] (size_t p_index) const
	Accesses a column.
template<size_t X = SizeX, size_t Y = SizeY, typename std::enable_if_t<(X==3 &&Y==3), int > = 0>
Vector3	operator* (const Vector3 &p_vec) const
	Transforms a 3D vector with a 3x3 matrix (homogeneous w=1).
template<size_t X = SizeX, size_t Y = SizeY, typename std::enable_if_t<(X==4 &&Y==4), int > = 0>
Vector3	operator* (const Vector3 &p_vec) const
	Transforms a 3D vector with a 4x4 matrix (homogeneous projection).
template<size_t X = SizeX, size_t Y = SizeY, typename std::enable_if_t<(X==3 &&Y==3), int > = 0>
Vector2	operator* (const Vector2 &p_vec) const
	Transforms a 2D vector with a 3x3 matrix (homogeneous).
template<size_t X = SizeX, size_t Y = SizeY, typename std::enable_if_t<(X==4 &&Y==4), int > = 0>
Vector4	operator* (const Vector4 &p_vec) const
	Transforms a 4D vector with a 4x4 matrix.
IMatrix< SizeX, SizeY >	operator* (const IMatrix< SizeX, SizeY > &p_other) const
	Multiplies two matrices of the same dimensions.
bool	operator== (const IMatrix &p_other) const
	Compares two matrices with tolerant float comparison.
bool	operator!= (const IMatrix &p_other) const
	Inequality helper.
std::wstring	toWstring () const
	Converts the matrix to a wide string representation.
std::string	toString () const
	Converts the matrix to a string representation.
template<size_t X = SizeX, size_t Y = SizeY, typename std::enable_if_t<(X==Y), int > = 0>
float	determinant () const
	Computes determinant for square matrices.
template<size_t X = SizeX, size_t Y = SizeY, typename std::enable_if_t<(X==Y), int > = 0>
bool	isInvertible () const
	Checks if the matrix is invertible (determinant non-zero).
template<size_t X = SizeX, size_t Y = SizeY, typename std::enable_if_t<(X==Y), int > = 0>
IMatrix< SizeX, SizeY >	inverse () const
	Returns the inverse of a square matrix.

Static Public Member Functions
static spk::IMatrix< SizeX, SizeY >	identity ()
	Returns an identity matrix of the same dimension.
static IMatrix< 4, 4 >	rotation (float p_angleX, float p_angleY, float p_angleZ)
	Builds a 4x4 rotation matrix from Euler angles in degrees.
static IMatrix< 4, 4 >	rotation (spk::Vector3 p_angle)
	Builds a 4x4 rotation matrix from Euler components in degrees.
template<size_t X = SizeX, size_t Y = SizeY, typename std::enable_if_t<(X==4 &&Y==4), int > = 0>
static IMatrix< 4, 4 >	rotation (const spk::Quaternion &p_q)
	Converts a quaternion to a 4x4 rotation matrix.
static IMatrix< 4, 4 >	translation (float p_translateX, float p_translateY, float p_translateZ)
	Builds a translation matrix.
static IMatrix< 4, 4 >	translation (spk::Vector3 p_translation)
	Builds a translation matrix from a vector.
static IMatrix< 4, 4 >	scale (float p_scaleX, float p_scaleY, float p_scaleZ)
	Builds a scale matrix.
static IMatrix< 4, 4 >	scale (spk::Vector3 p_scale)
	Builds a scale matrix from a vector.
template<size_t X = SizeX, size_t Y = SizeY, typename std::enable_if_t<(X==4 &&Y==4), int > = 0>
static IMatrix	lookAt (const spk::Vector3 &p_from, const spk::Vector3 &p_to, const spk::Vector3 &p_up)
	Builds a view matrix looking from one point to another.
template<size_t X = SizeX, size_t Y = SizeY, typename std::enable_if_t<(X==4 &&Y==4), int > = 0>
static IMatrix	rotateAroundAxis (const spk::Vector3 &p_axis, const float &p_rotationAngle)
	Builds a rotation matrix around an arbitrary axis.
template<size_t X = SizeX, size_t Y = SizeY, typename std::enable_if_t<(X==4 &&Y==4), int > = 0>
static IMatrix	perspective (float p_fov, float p_aspectRatio, float p_nearPlane, float p_farPlane)
	Builds a perspective projection matrix.
template<size_t X = SizeX, size_t Y = SizeY, typename std::enable_if_t<(X==4 &&Y==4), int > = 0>
static IMatrix	ortho (float p_left, float p_right, float p_bottom, float p_top, float p_nearPlane, float p_farPlane)
	Builds an orthographic projection matrix.
template<size_t X = SizeX, size_t Y = SizeY, typename std::enable_if_t<(X==3 &&Y==3), int > = 0>
static IMatrix< 3, 3 >	translation (float p_translateX, float p_translateY)
	Creates a 2D translation matrix.
template<size_t X = SizeX, size_t Y = SizeY, typename std::enable_if_t<(X==3 &&Y==3), int > = 0>
static IMatrix< 3, 3 >	translation (const spk::Vector2 &p_translation)
	Creates a 2D translation matrix from a vector.
template<size_t X = SizeX, size_t Y = SizeY, typename std::enable_if_t<(X==3 &&Y==3), int > = 0>
static IMatrix< 3, 3 >	scale (float p_scaleX, float p_scaleY)
	Creates a 2D scale matrix.
template<size_t X = SizeX, size_t Y = SizeY, typename std::enable_if_t<(X==3 &&Y==3), int > = 0>
static IMatrix< 3, 3 >	scale (const spk::Vector2 &p_scale)
	Creates a 2D scale matrix from a vector.
template<size_t X = SizeX, size_t Y = SizeY, typename std::enable_if_t<(X==3 &&Y==3), int > = 0>
static IMatrix< 3, 3 >	rotationZ (float p_angleDegrees)
	Creates a 2D rotation matrix around Z axis.

Friends
std::wostream &	operator<< (std::wostream &p_os, const IMatrix &p_mat)
	Streams the matrix to a wide output stream.
std::ostream &	operator<< (std::ostream &p_os, const IMatrix &p_mat)
	Streams the matrix to a narrow output stream.

Detailed Description

template<size_t SizeX, size_t SizeY>
class spk::IMatrix< SizeX, SizeY >

Column-major matrix with basic arithmetic, transforms, and helpers.

Template Parameters

SizeX	Number of columns.
SizeY	Number of rows.

See also: Matrix2x2, Matrix3x3, Matrix4x4

spk::Matrix4x4 proj = spk::IMatrix<4,4>::perspective(60.f, 16.f/9.f, 0.1f, 100.f);

spk::Vector3 world = proj * spk::Vector3{1,2,3};

spk::IMatrix::perspective

static IMatrix perspective(float p_fov, float p_aspectRatio, float p_nearPlane, float p_farPlane)

Builds a perspective projection matrix.

Definition spk_matrix.hpp:592

Constructor & Destructor Documentation

◆ IMatrix() [1/2]

template<size_t SizeX, size_t SizeY>

spk::IMatrix< SizeX, SizeY >::IMatrix ( float * p_values )

inline

Builds a matrix from a contiguous column-major array.

Parameters

p_values Pointer to SizeX*SizeY float values ordered by column.

◆ IMatrix() [2/2]

template<size_t SizeX, size_t SizeY>

spk::IMatrix< SizeX, SizeY >::IMatrix ( std::initializer_list< float > p_values )

inline

Builds from a flat initializer list (column-major).

Parameters

p_values Values of size SizeX*SizeY.

Member Function Documentation

◆ determinant()

template<size_t SizeX, size_t SizeY>

template<size_t X = SizeX, size_t Y = SizeY, typename std::enable_if_t<(X==Y), int > = 0>

float spk::IMatrix< SizeX, SizeY >::determinant ( ) const

inline

Computes determinant for square matrices.

Returns: Determinant value.

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◆ identity()

template<size_t SizeX, size_t SizeY>

spk::IMatrix< SizeX, SizeY > spk::IMatrix< SizeX, SizeY >::identity ( )

inlinestatic

Returns an identity matrix of the same dimension.

Returns: Matrix with ones on the diagonal and zeros elsewhere.

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◆ inverse()

template<size_t SizeX, size_t SizeY>

template<size_t X = SizeX, size_t Y = SizeY, typename std::enable_if_t<(X==Y), int > = 0>

IMatrix< SizeX, SizeY > spk::IMatrix< SizeX, SizeY >::inverse ( ) const

inline

Returns the inverse of a square matrix.

Returns: Inverted matrix.

Exceptions

spk::Exception when singular.

◆ isInvertible()

template<size_t SizeX, size_t SizeY>

template<size_t X = SizeX, size_t Y = SizeY, typename std::enable_if_t<(X==Y), int > = 0>

bool spk::IMatrix< SizeX, SizeY >::isInvertible ( ) const

inline

Checks if the matrix is invertible (determinant non-zero).

Returns: true when invertible.

◆ lookAt()

template<size_t SizeX, size_t SizeY>

template<size_t X = SizeX, size_t Y = SizeY, typename std::enable_if_t<(X==4 &&Y==4), int > = 0>

IMatrix spk::IMatrix< SizeX, SizeY >::lookAt	(	const spk::Vector3 &	p_from,
		const spk::Vector3 &	p_to,
		const spk::Vector3 &	p_up )

inlinestatic

Builds a view matrix looking from one point to another.

Template Parameters

X	Compile-time column count (requires 4).
Y	Compile-time row count (requires 4).

Parameters

p_from	Eye position.
p_to	Target position.
p_up	Up direction (not parallel to view direction).

Returns: View transform aligning the forward axis toward the target.

◆ operator!=()

template<size_t SizeX, size_t SizeY>

bool spk::IMatrix< SizeX, SizeY >::operator!= ( const IMatrix< SizeX, SizeY > & p_other ) const

inline

Inequality helper.

Parameters

p_other Matrix to compare against.

Returns: true when at least one coefficient differs.

See also: operator==

◆ operator*() [1/5]

template<size_t SizeX, size_t SizeY>

IMatrix< SizeX, SizeY > spk::IMatrix< SizeX, SizeY >::operator* ( const IMatrix< SizeX, SizeY > & p_other ) const

inline

Multiplies two matrices of the same dimensions.

Parameters

p_other Right-hand matrix.

Returns: Product matrix.

◆ operator*() [2/5]

template<size_t SizeX, size_t SizeY>

template<size_t X = SizeX, size_t Y = SizeY, typename std::enable_if_t<(X==3 &&Y==3), int > = 0>

Vector2 spk::IMatrix< SizeX, SizeY >::operator* ( const Vector2 & p_vec ) const

inline

Transforms a 2D vector with a 3x3 matrix (homogeneous).

Template Parameters

X	compile-time column count (requires 3x3).
Y	compile-time row count (requires 3x3).

Parameters

p_vec 2D vector (z assumed 1).

Returns: Transformed vector.

◆ operator*() [3/5]

template<size_t SizeX, size_t SizeY>

template<size_t X = SizeX, size_t Y = SizeY, typename std::enable_if_t<(X==3 &&Y==3), int > = 0>

Vector3 spk::IMatrix< SizeX, SizeY >::operator* ( const Vector3 & p_vec ) const

inline

Transforms a 3D vector with a 3x3 matrix (homogeneous w=1).

Parameters

p_vec Input vector.

Returns: Transformed vector.

◆ operator*() [4/5]

template<size_t SizeX, size_t SizeY>

template<size_t X = SizeX, size_t Y = SizeY, typename std::enable_if_t<(X==4 &&Y==4), int > = 0>

Vector3 spk::IMatrix< SizeX, SizeY >::operator* ( const Vector3 & p_vec ) const

inline

Transforms a 3D vector with a 4x4 matrix (homogeneous projection).

Parameters

p_vec Input vector.

Returns: Transformed vector after perspective divide.

◆ operator*() [5/5]

template<size_t SizeX, size_t SizeY>

template<size_t X = SizeX, size_t Y = SizeY, typename std::enable_if_t<(X==4 &&Y==4), int > = 0>

Vector4 spk::IMatrix< SizeX, SizeY >::operator* ( const Vector4 & p_vec ) const

inline

Transforms a 4D vector with a 4x4 matrix.

Parameters

p_vec Input vector.

Returns: Transformed vector.

◆ operator==()

template<size_t SizeX, size_t SizeY>

bool spk::IMatrix< SizeX, SizeY >::operator== ( const IMatrix< SizeX, SizeY > & p_other ) const

inline

Compares two matrices with tolerant float comparison.

Parameters

p_other Matrix to compare against.

Returns: true when every coefficient matches within SafeComparand tolerance.

◆ operator[]() [1/2]

template<size_t SizeX, size_t SizeY>

Column & spk::IMatrix< SizeX, SizeY >::operator[] ( size_t p_index )

inline

Accesses a column.

Parameters

p_index Column index.

Returns: Mutable column.

◆ operator[]() [2/2]

template<size_t SizeX, size_t SizeY>

const Column & spk::IMatrix< SizeX, SizeY >::operator[] ( size_t p_index ) const

inline

Accesses a column.

Parameters

p_index Column index.

Returns: Const column.

◆ ortho()

template<size_t SizeX, size_t SizeY>

template<size_t X = SizeX, size_t Y = SizeY, typename std::enable_if_t<(X==4 &&Y==4), int > = 0>

IMatrix spk::IMatrix< SizeX, SizeY >::ortho	(	float	p_left,
		float	p_right,
		float	p_bottom,
		float	p_top,
		float	p_nearPlane,
		float	p_farPlane )

inlinestatic

Builds an orthographic projection matrix.

Template Parameters

X	Compile-time column count (requires 4).
Y	Compile-time row count (requires 4).

Parameters

p_left	Left view plane.
p_right	Right view plane.
p_bottom	Bottom view plane.
p_top	Top view plane.
p_nearPlane	Near clipping plane distance.
p_farPlane	Far clipping plane distance.

Returns: Orthographic projection matrix.

◆ perspective()

template<size_t SizeX, size_t SizeY>

template<size_t X = SizeX, size_t Y = SizeY, typename std::enable_if_t<(X==4 &&Y==4), int > = 0>

IMatrix spk::IMatrix< SizeX, SizeY >::perspective	(	float	p_fov,
		float	p_aspectRatio,
		float	p_nearPlane,
		float	p_farPlane )

inlinestatic

Builds a perspective projection matrix.

Template Parameters

X	Compile-time column count (requires 4).
Y	Compile-time row count (requires 4).

Parameters

p_fov	Field of view in degrees.
p_aspectRatio	Viewport aspect ratio (width/height).
p_nearPlane	Near clipping plane distance.
p_farPlane	Far clipping plane distance.

Returns: 4x4 projection matrix suitable for homogeneous coordinates.

◆ rotateAroundAxis()

template<size_t SizeX, size_t SizeY>

template<size_t X = SizeX, size_t Y = SizeY, typename std::enable_if_t<(X==4 &&Y==4), int > = 0>

IMatrix spk::IMatrix< SizeX, SizeY >::rotateAroundAxis	(	const spk::Vector3 &	p_axis,
		const float &	p_rotationAngle )

inlinestatic

Builds a rotation matrix around an arbitrary axis.

Template Parameters

X	Compile-time column count (requires 4).
Y	Compile-time row count (requires 4).

Parameters

p_axis	Axis to rotate around (normalized internally).
p_rotationAngle	Rotation angle in degrees.

Returns: 4x4 matrix representing the axis/angle rotation.

◆ rotation() [1/3]

template<size_t SizeX, size_t SizeY>

template<size_t X = SizeX, size_t Y = SizeY, typename std::enable_if_t<(X==4 &&Y==4), int > = 0>

IMatrix< 4, 4 > spk::IMatrix< SizeX, SizeY >::rotation ( const spk::Quaternion & p_q )

inlinestatic

Converts a quaternion to a 4x4 rotation matrix.

Template Parameters

X	Compile-time column count (requires 4).
Y	Compile-time row count (requires 4).

Parameters

p_q	Unit quaternion describing the rotation.

Returns: Rotation matrix equivalent to the quaternion.

See also: spk::Quaternion

◆ rotation() [2/3]

template<size_t SizeX, size_t SizeY>

IMatrix< 4, 4 > spk::IMatrix< SizeX, SizeY >::rotation	(	float	p_angleX,
		float	p_angleY,
		float	p_angleZ )

inlinestatic

Builds a 4x4 rotation matrix from Euler angles in degrees.

Parameters

p_angleX	Rotation around X axis in degrees.
p_angleY	Rotation around Y axis in degrees.
p_angleZ	Rotation around Z axis in degrees.

Returns: Composition of Z * Y * X rotations.

See also: rotation(spk::Vector3), rotation(const spk::Quaternion &)

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◆ rotation() [3/3]

template<size_t SizeX, size_t SizeY>

IMatrix< 4, 4 > spk::IMatrix< SizeX, SizeY >::rotation ( spk::Vector3 p_angle )

inlinestatic

Builds a 4x4 rotation matrix from Euler components in degrees.

Parameters

p_angle Vector containing (x, y, z) Euler rotations in degrees.

Returns: Rotation matrix matching the provided angles.

See also: rotation(float, float, float)

◆ rotationZ()

template<size_t SizeX, size_t SizeY>

template<size_t X = SizeX, size_t Y = SizeY, typename std::enable_if_t<(X==3 &&Y==3), int > = 0>

IMatrix< 3, 3 > spk::IMatrix< SizeX, SizeY >::rotationZ ( float p_angleDegrees )

inlinestatic

Creates a 2D rotation matrix around Z axis.

Parameters

p_angleDegrees Rotation angle in degrees.

Returns: 3x3 rotation matrix.

◆ scale() [1/4]

template<size_t SizeX, size_t SizeY>

template<size_t X = SizeX, size_t Y = SizeY, typename std::enable_if_t<(X==3 &&Y==3), int > = 0>

IMatrix< 3, 3 > spk::IMatrix< SizeX, SizeY >::scale ( const spk::Vector2 & p_scale )

inlinestatic

Creates a 2D scale matrix from a vector.

Parameters

p_scale Scale vector.

Returns: 3x3 scale matrix.

◆ scale() [2/4]

template<size_t SizeX, size_t SizeY>

template<size_t X = SizeX, size_t Y = SizeY, typename std::enable_if_t<(X==3 &&Y==3), int > = 0>

IMatrix< 3, 3 > spk::IMatrix< SizeX, SizeY >::scale	(	float	p_scaleX,
		float	p_scaleY )

inlinestatic

Creates a 2D scale matrix.

Parameters

p_scaleX	Scale factor on X axis.
p_scaleY	Scale factor on Y axis.

Returns: 3x3 scale matrix.

◆ scale() [3/4]

template<size_t SizeX, size_t SizeY>

IMatrix< 4, 4 > spk::IMatrix< SizeX, SizeY >::scale	(	float	p_scaleX,
		float	p_scaleY,
		float	p_scaleZ )

inlinestatic

Builds a scale matrix.

Parameters

p_scaleX	Scale factor along X axis.
p_scaleY	Scale factor along Y axis.
p_scaleZ	Scale factor along Z axis.

Returns: 4x4 matrix scaling coordinates by the provided factors.

See also: scale(spk::Vector3)

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◆ scale() [4/4]

template<size_t SizeX, size_t SizeY>

IMatrix< 4, 4 > spk::IMatrix< SizeX, SizeY >::scale ( spk::Vector3 p_scale )

inlinestatic

Builds a scale matrix from a vector.

Parameters

p_scale Scale factors along each axis.

Returns: Scale matrix.

See also: scale(float, float, float)

◆ toString()

template<size_t SizeX, size_t SizeY>

std::string spk::IMatrix< SizeX, SizeY >::toString ( ) const

inline

Converts the matrix to a string representation.

Returns: Human-readable matrix layout.

◆ toWstring()

template<size_t SizeX, size_t SizeY>

std::wstring spk::IMatrix< SizeX, SizeY >::toWstring ( ) const

inline

Converts the matrix to a wide string representation.

Returns: Human-readable matrix layout using wide characters.

◆ translation() [1/4]

template<size_t SizeX, size_t SizeY>

template<size_t X = SizeX, size_t Y = SizeY, typename std::enable_if_t<(X==3 &&Y==3), int > = 0>

IMatrix< 3, 3 > spk::IMatrix< SizeX, SizeY >::translation ( const spk::Vector2 & p_translation )

inlinestatic

Creates a 2D translation matrix from a vector.

Parameters

p_translation Translation vector.

Returns: 3x3 translation matrix.

◆ translation() [2/4]

template<size_t SizeX, size_t SizeY>

template<size_t X = SizeX, size_t Y = SizeY, typename std::enable_if_t<(X==3 &&Y==3), int > = 0>

IMatrix< 3, 3 > spk::IMatrix< SizeX, SizeY >::translation	(	float	p_translateX,
		float	p_translateY )

inlinestatic

Creates a 2D translation matrix.

Parameters

p_translateX	Translation on X axis.
p_translateY	Translation on Y axis.

Returns: 3x3 translation matrix.

◆ translation() [3/4]

template<size_t SizeX, size_t SizeY>

IMatrix< 4, 4 > spk::IMatrix< SizeX, SizeY >::translation	(	float	p_translateX,
		float	p_translateY,
		float	p_translateZ )

inlinestatic

Builds a translation matrix.

Parameters

p_translateX	Offset along X axis.
p_translateY	Offset along Y axis.
p_translateZ	Offset along Z axis.

Returns: 4x4 matrix translating coordinates by the provided offsets.

See also: translation(spk::Vector3)

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◆ translation() [4/4]

template<size_t SizeX, size_t SizeY>

IMatrix< 4, 4 > spk::IMatrix< SizeX, SizeY >::translation ( spk::Vector3 p_translation )

inlinestatic

Builds a translation matrix from a vector.

Parameters

p_translation Offsets along each axis.

Returns: Translation matrix.

See also: translation(float, float, float)

◆ operator<< [1/2]

template<size_t SizeX, size_t SizeY>

std::ostream & operator<<	(	std::ostream &	p_os,
		const IMatrix< SizeX, SizeY > &	p_mat )

friend

Streams the matrix to a narrow output stream.

Parameters

p_os	Destination stream.
p_mat	Matrix to print.

Returns: Stream reference after write.

◆ operator<< [2/2]

template<size_t SizeX, size_t SizeY>

std::wostream & operator<<	(	std::wostream &	p_os,
		const IMatrix< SizeX, SizeY > &	p_mat )

friend

Streams the matrix to a wide output stream.

Parameters

p_os	Destination stream.
p_mat	Matrix to print.

Returns: Stream reference after write.

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

includes/structure/math/spk_matrix.hpp

Classes

Public Member Functions

Static Public Member Functions

Friends

Detailed Description

Constructor & Destructor Documentation

◆ IMatrix() [1/2]

◆ IMatrix() [2/2]

Member Function Documentation

◆ determinant()

◆ identity()

◆ inverse()

◆ isInvertible()

◆ lookAt()

◆ operator!=()

◆ operator*() [1/5]

◆ operator*() [2/5]

◆ operator*() [3/5]

◆ operator*() [4/5]

◆ operator*() [5/5]

◆ operator==()

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ ortho()

◆ perspective()

◆ rotateAroundAxis()

◆ rotation() [1/3]

◆ rotation() [2/3]

◆ rotation() [3/3]

◆ rotationZ()

◆ scale() [1/4]

◆ scale() [2/4]

◆ scale() [3/4]

◆ scale() [4/4]

◆ toString()

◆ toWstring()

◆ translation() [1/4]

◆ translation() [2/4]

◆ translation() [3/4]

◆ translation() [4/4]

Friends And Related Symbol Documentation

◆ operator<< [1/2]

◆ operator<< [2/2]