Matrix4 Class Reference

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.
	Matrix4 (const Vector &)
	Create a homogeneous diagonal matrix with diagonal terms set to the vector entries.
	Matrix4 (const Matrix &)
	Create an homogeneous matrix from a simple Matrix.
	Matrix4 (const Matrix &, const Vector &)
	Create an homogeneous matrix from a simple Matrix and a translation vector.
	Matrix4 (const Matrix &, const Vector &, const Vector &)
	Constructor from a Matrix, a translation and a shear vector.
	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.
Matrix4 &	operator*= (double)
	Destructive scalar multiply.
Matrix4 &	operator/= (double)
	Destructive scalar divide.
Vector	operator* (const Vector &) const
	Right multiply by a vector.
QString	ToGLSL () const
	Return a string expression.
double	Determinant () const
	Compute the determinant of the matrix.
double	Trace () const
	Compute the trace (sum of diagonal terms).
Matrix4	T () const
	Transpose a matrix.
Matrix4	Inverse () const
	Computes the inverse of a matrix A-1.
void	Float (float[16]) const
	Convert to a generic 4×4 float matrix.
Matrix	Sub () const
	Return the sub-matrix obtained by removing the last column and row.

Static Public Member Functions
static Matrix4	LookAt (const Vector &, const Vector &, const double &)
	Create a viewing transformation matrix.
static Matrix4	Perspective (const double &, const double &, const double &, const double &, const double &)
	Perspective projection matrix.
static Matrix4	Rotation (const Vector &, const double &)
	Create a rotation matrix about an arbitrary axis.
static Matrix4	Rotation (const Vector &)
	Create a rotation matrix about the orthogonal axes.
static Matrix4	Scale (const Vector &)
	Creates a scaling matrix.
static Matrix4	Translate (const Vector &)
	Creates a translation matrix.
static Matrix4	Shear (const Vector &)
	Creates a shear matrix.

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 Matrix4::Inverse()).

Friends
Matrix4	operator+ (const Matrix4 &u, const Matrix4 &v)
	Overloaded.
Matrix4	operator- (const Matrix4 &u, const Matrix4 &v)
	Overloaded.
Matrix4	operator* (const Matrix4 &u, const Matrix4 &v)
	Multiplication.
Matrix4	operator* (const Matrix4 &A, const double &r)
	Multiplication by a real.
std::ostream &	operator<< (std::ostream &s, const Matrix4 &matrix)
	Overloaded.

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.

Inverse()

Matrix4 Matrix4::Inverse

(

)

const

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.

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.

Perspective()

Matrix4 Matrix4::Perspective ( const double & fovy, const double & zNear, const double & zFar, const double & width, const double & height )

static

Perspective projection matrix.

Parameters

fovy	Vertical field of view.
zNear,zFar	Near and far distance.
width,height	Screen width and heigh.

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.

ToGLSL()

QString Matrix4::ToGLSL

(

)

const

Return a string expression.

Author

Hubert-Brierre Pierre

Yields a QString of the form 'mat4(m(0, 0), ..., m(3, 3))' that write the matrix in GLSL.

Translate()

Matrix4 Matrix4::Translate ( const Vector & t )

static

Creates a translation matrix.

Parameters

t	Translation vector.

Friends And Related Symbol Documentation

operator* [1/2]

Matrix4 operator* ( const Matrix4 & A, const double & r )

friend

Multiplication by a real.

Parameters

A	matrix.
r	Real.

operator* [2/2]

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.