This class implements 4² matrix. More...

#include <matrix.h>

Public Member Functions
	Matrix4 ()
	Empty.

	Matrix4 (const double &)
	Create an scaling matrix with the same diagonal terms. More...

	Matrix4 (const Vector &)
	Create a homogeneous diagonal matrix with diagonal terms set to the vector entries. More...

	Matrix4 (const Matrix &)
	Create an homogeneous matrix from a simple Matrix. More...

	Matrix4 (const Matrix &, const Vector &)
	Create an homogeneous matrix from a simple Matrix and a translation vector. More...

	Matrix4 (const Matrix &, const Vector &, const Vector &)
	Constructor from a Matrix, a translation and a shear vector. More...

	Matrix4 (const double &, const double &, const double &, const double &, const double &, const double &, const double &, const double &, const double &, const double &, const double &, const double &, const double &, const double &, const double &, const double &)
	Create a matrix given its coefficients.

Matrix4	operator- () const
	Returns the opposite of a matrix -A.

Matrix4 &	operator+= (const Matrix4 &)
	Destructive addition.

Matrix4 &	operator-= (const Matrix4 &)
	Destructive subtraction.

Matrix4 &	operator*= (const Matrix4 &)
	Destructive multiplication. More...

Matrix4 &	*operator=** (double)
	Destructive scalar multiply.

Matrix4 &	operator/= (double)
	Destructive scalar divide.

Vector	operator* (const Vector &) const
	Right multiply by a vector. More...

double	Determinant () const
	Compute the determinant of the matrix. More...

double	Trace () const
	Compute the trace (sum of diagonal terms).

Matrix4	T () const
	Transpose a matrix.

void	Float (float[16]) const
	Convert to a generic 4×4 float matrix. More...

Matrix	Rotation () const
	Return the rotation matrix.

Static Public Member Functions
static Matrix4	LookAt (const Vector &, const Vector &, const double &)
	Create a viewing transformation matrix. More...

static Matrix4	Rotation (const Vector &, const double &)
	Create a rotation matrix about an arbitrary axis. More...

static Matrix4	Rotation (const Vector &)
	Create a rotation matrix about the orthogonal axes. More...

static Matrix4	Scale (const Vector &)
	Creates a scaling matrix. More...

static Matrix4	Translate (const Vector &)
	Creates a translation matrix. More...

static Matrix4	Shear (const Vector &)
	Creates a shear matrix. More...

Static Public Attributes
static const Matrix4	Null
	Null matrix.

static const Matrix4	Identity
	Identity matrix.

static const Matrix4	Hermite
	Hermite matrix, usefull for bi-cubic Hermite interpolation.

Protected Attributes
double	r [16] = { 1.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,1.0 }
	Coefficients.

Static Protected Attributes
static const double	epsilon = 1.0e-18
	Epsilon value used to check if the determinant of a matrix is null (used in Inverse(const Matrix4&)).

Friends
Matrix4	operator+ (const Matrix4 &, const Matrix4 &)
	Overloaded. More...

Matrix4	operator- (const Matrix4 &, const Matrix4 &)
	Overloaded. More...

Matrix4	operator* (const Matrix4 &, const Matrix4 &)
	Multiplication. More...

Matrix4	Inverse (const Matrix4 &)
	Computes the inverse of a matrix A^-1. More...

std::ostream &	operator<< (std::ostream &, const Matrix4 &)
	Overloaded. More...

Detailed Description

This class implements 4² matrix.

Components are stored in a single dimension array, starting from element a₀₀ and sorting components by column.

The diagonal elements of a matrix A are A₀₀=A[0], A₁₁=A[5], A₂₂=A[10], A₃₃=A[15]. The terms corresponding to the translation vector are A[12], A[13], A[14].

Constructor & Destructor Documentation

◆ Matrix4() [1/5]

Matrix4::Matrix4 ( const double & a )

explicit

Create an scaling matrix with the same diagonal terms.

The last term of the matrix is set to 1.0.

Parameters

a	Value of diagonal entries.

◆ Matrix4() [2/5]

Matrix4::Matrix4 ( const Vector & a )

explicit

Create a homogeneous diagonal matrix with diagonal terms set to the vector entries.

Last diagonal entry is set to 1.0.

Parameters

a	Vector of diagonal entries.

◆ Matrix4() [3/5]

Matrix4::Matrix4 ( const Matrix & a )

explicit

Create an homogeneous matrix from a simple Matrix.

The translation and shear coefficients are set to 0.0.

Parameters

a Matrix.

◆ Matrix4() [4/5]

Matrix4::Matrix4	(	const Matrix &	a,
		const Vector &	t
	)

explicit

Create an homogeneous matrix from a simple Matrix and a translation vector.

The shear coefficients are set to 0.0.

Parameters

a	Matrix.
t	Translation vector.

◆ Matrix4() [5/5]

Matrix4::Matrix4	(	const Matrix &	a,
		const Vector &	t,
		const Vector &	s
	)

explicit

Constructor from a Matrix, a translation and a shear vector.

Parameters

a	Matrix.
t	Translation vector.
s	Shear vector.

Member Function Documentation

◆ Determinant()

double Matrix4::Determinant ( ) const

Compute the determinant of the matrix.

See also: Matrix::Determinant().

◆ Float()

void Matrix4::Float ( float a[16] ) const

Convert to a generic 4×4 float matrix.

Parameters

a	Returned matrix.

◆ LookAt()

Matrix4 Matrix4::LookAt	(	const Vector &	eye,
		const Vector &	look,
		const double &	twist
	)

static

Create a viewing transformation matrix.

Parameters

eye	Eye location.
look	Look at position.
twist	Twisting angle from vertical.

◆ operator*()

Vector Matrix4::operator* ( const Vector & v ) const

Right multiply by a vector.

Parameters

v Vector.

◆ operator*=()

Matrix4 & Matrix4::operator*= ( const Matrix4 & v )

Destructive multiplication.

Parameters

v Matrix.

◆ Rotation() [1/2]

Matrix4 Matrix4::Rotation ( const Vector & u )

static

Create a rotation matrix about the orthogonal axes.

Parameters

u	Vector of angles in radian.

◆ Rotation() [2/2]

Matrix4 Matrix4::Rotation	(	const Vector &	v,
		const double &	a
	)

static

Create a rotation matrix about an arbitrary axis.

Parameters

v	Axis (should be normalized).
a	Angle.

◆ Scale()

Matrix4 Matrix4::Scale ( const Vector & u )

static

Creates a scaling matrix.

Parameters

u	Scaling vector.

◆ Shear()

Matrix4 Matrix4::Shear ( const Vector & s )

static

Creates a shear matrix.

Parameters

s	Shear vector.

◆ Translate()

Matrix4 Matrix4::Translate ( const Vector & t )

static

Creates a translation matrix.

Parameters

t	Translation vector.

Friends And Related Function Documentation

◆ Inverse

Matrix4 Inverse ( const Matrix4 & m )

friend

Computes the inverse of a matrix A^-1.

This function returns the null matrix if A cannot be inverted. The threshold value involved in the singular matrix detection is set to 10^-18.

Parameters

m	Argument matrix.

◆ operator*

Matrix4 operator*	(	const Matrix4 &	u,
		const Matrix4 &	v
	)

friend

Multiplication.

Parameters

u,v	Argument matrix.

◆ operator+

Matrix4 operator+	(	const Matrix4 &	u,
		const Matrix4 &	v
	)

friend

Overloaded.

Parameters

u,v	Argument matrixes.

◆ operator-

Matrix4 operator-	(	const Matrix4 &	u,
		const Matrix4 &	v
	)

friend

Overloaded.

Parameters

u,v	Argument matrixes.

◆ operator<<

std::ostream & operator<<	(	std::ostream &	s,
		const Matrix4 &	matrix
	)

friend

Overloaded.

Parameters

s	Stream.
matrix	The matrix.

Public Member Functions

Static Public Member Functions

Static Public Attributes

Protected Attributes

Static Protected Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ Matrix4() [1/5]

◆ Matrix4() [2/5]

◆ Matrix4() [3/5]

◆ Matrix4() [4/5]

◆ Matrix4() [5/5]

Member Function Documentation

◆ Determinant()

◆ Float()

◆ LookAt()

◆ operator*()

◆ operator*=()

◆ Rotation() [1/2]

◆ Rotation() [2/2]

◆ Scale()

◆ Shear()

◆ Translate()

Friends And Related Function Documentation

◆ Inverse

◆ operator*

◆ operator+

◆ operator-

◆ operator<<