Matrix3< T > Class Template Reference

Detailed Description

template<typename T>
class cy::Matrix3< T >

3x3 matrix class.

Its data stores 9-value array of column-major matrix elements. You can use Matrix3 with Vec3<T> to transform 3D points.

#include <cyMatrix.h>

Public Member Functions
Constructors
	Matrix3 ()
	Default constructor.
template<typename TT >
	Matrix3 (Matrix3< TT > const &matrix)
	Copy constructor for different types.
	Matrix3 (T const *values)
	Initialize the matrix using an array of 9 values.
	Matrix3 (T v)
	Initialize the matrix as identity scaled by v.
	Matrix3 (Vec3< T > const &x, Vec3< T > const &y, Vec3< T > const &z)
	Initialize the matrix using x,y,z vectors as columns.
	Matrix3 (Matrix2< T > const &m)
	Default constructor.
	Matrix3 (Matrix34< T > const &m)
	Default constructor.
	Matrix3 (Matrix4< T > const &m)
	Default constructor.
	Matrix3 (T c00, T c01, T c02, T c10, T c11, T c12, T c20, T c21, T c22)
	Constructor using row-major order for initialization.
Set & Get Methods
void	Zero ()
	Set all the values as zero.
bool	IsZero () const
	Returns true if the matrix is exactly zero.
bool	IsFinite () const
	Returns true if all components are finite real numbers.
void	Get (T *values)
	Copies the matrix cell to the given values array of size 9.
void	Set (T const *values)
	Set matrix using an array of 9 values.
void	Set (Vec3< T > const &x, Vec3< T > const &y, Vec3< T > const &z)
	Set matrix using x,y,z vectors as columns.
void	SetIdentity ()
	Converts the matrix to an identity matrix.
void	SetTensorProduct (Vec3< T > const &v0, Vec3< T > const &v1)
	Set all the values as zero.
void	SetCrossProd (Vec3< T > const &p)
	Matrix representation of the cross product ( a x b)
Affine transformations
void	SetScale (T uniformScale)
	Sets a uniform scale matrix.
void	SetScale (T scaleX, T scaleY, T scaleZ)
	Sets a scale matrix.
void	SetScale (Vec3< T > const &scale)
	Sets a scale matrix.
void	SetRotationX (T angle)
	Set as rotation matrix around x axis.
void	SetRotationX (T sinAngle, T cosAngle)
	Set as rotation matrix around x axis by cos and sin of angle.
void	SetRotationY (T angle)
	Set as rotation matrix around y axis.
void	SetRotationY (T sinAngle, T cosAngle)
	Set as rotation matrix around y axis by cos and sin of angle.
void	SetRotationZ (T angle)
	Set as rotation matrix around z axis.
void	SetRotationZ (T sinAngle, T cosAngle)
	Set as rotation matrix around z axis by cos and sin of angle.
void	SetRotationXYZ (T angleX, T angleY, T angleZ)
	Set as rotation matrix around x, y, and then z axes ( Rz * Ry * Rx )
void	SetRotationZYX (T angleX, T angleY, T angleZ)
	Set as rotation matrix around z, y, and then x axes ( Rx * Ry * Rz )
void	SetRotation (Vec3< T > const &axis, T angle)
	Set a rotation matrix about the given axis by angle.
void	SetRotation (Vec3< T > const &axis, T sinAngle, T cosAngle)
	Set a rotation matrix about the given axis by cos and sin of angle.
void	SetRotation (Vec3< T > const &from, Vec3< T > const &to)
	Set a rotation matrix that sets [from] unit vector to [to] unit vector.
void	SetView (Vec3< T > const &target, Vec3< T > const &up)
	Set view matrix using position, target and approximate up vector.
void	SetCartesianFrameXY (Vec3< T > const &x, Vec3< T > const &y_approx)
	Sets a Cartesian coordinate frame using the given x direction and an approximate y direction. x must be a unit vector.
void	SetCartesianFrameXZ (Vec3< T > const &x, Vec3< T > const &z_approx)
	Sets a Cartesian coordinate frame using the given x direction and an approximate z direction. x must be a unit vector.
void	SetCartesianFrameYX (Vec3< T > const &y, Vec3< T > const &x_approx)
	Sets a Cartesian coordinate frame using the given y direction and an approximate x direction. y must be a unit vector.
void	SetCartesianFrameYZ (Vec3< T > const &y, Vec3< T > const &z_approx)
	Sets a Cartesian coordinate frame using the given y direction and an approximate z direction. y must be a unit vector.
void	SetCartesianFrameZX (Vec3< T > const &z, Vec3< T > const &x_approx)
	Sets a Cartesian coordinate frame using the given z direction and an approximate x direction. z must be a unit vector.
void	SetCartesianFrameZY (Vec3< T > const &z, Vec3< T > const &y_approx)
	Sets a Cartesian coordinate frame using the given z direction and an approximate y direction. z must be a unit vector.
Set Row, Column, or Diagonal
void	SetRow (int ri, T x, T y, T z)
	Sets a row of the matrix.
void	SetRow (int ri, Vec3< T > const &v)
	Sets a row of the matrix.
void	SetColumn (int ci, T x, T y, T z)
	Sets a column of the matrix.
void	SetColumn (int ci, Vec3< T > const &v)
	Sets a column of the matrix.
void	SetDiagonal (T xx, T yy, T zz)
	Sets the diagonal values of the matrix.
void	SetDiagonal (Vec3< T > const &p)
	Sets the diagonal values of the matrix.
void	SetDiagonal (T const *values)
	Sets the diagonal values of the matrix.
Get Row, Column, or Diagonal
Vec3< T > *	Columns ()
	Returns a row of the matrix.
Vec3< T > const *	Columns () const
	Returns a row of the matrix.
Vec3< T > &	Column (int ci)
	Returns a row of the matrix.
Vec3< T > const &	Column (int ci) const
	Returns a row of the matrix.
Vec3< T >	GetRow (int ri) const
	Returns a row of the matrix.
Vec3< T >	GetDiagonal () const
	Returns the diagonal of the matrix.
Matrix3	GetRotation () const
	Returns the rotation portion of the transformation.
Matrix3	GetScale () const
	Returns the scale portion of the transformation. The returned matrix is symmetric, but not necessarily diagonal, and it can include non-uniform scale.
T	GetAvrgScale () const
	Returns the average scale factor.
void	GetComponents (Matrix3< T > &scale, Matrix3< T > &rotation) const
	Returns separate transformation components.
Get Sub-matrix cell
Matrix2< T >	GetSubMatrix2 () const
	Returns the 2x2 portion of the matrix.
Comparison Operators
bool	operator== (Matrix3 const &right) const
	compare equal
bool	operator!= (Matrix3 const &right) const
	compare not equal
Access Operators
T &	operator() (int ri, int ci)
	subscript operator
T const &	operator() (int ri, int ci) const
	constant subscript operator
T &	operator[] (int i)
	subscript operator
T const &	operator[] (int i) const
	constant subscript operator
Unary and Binary Operators
Matrix3	operator- () const
	negative matrix
Matrix3	operator* (T const value) const
	multiply matrix by a value
Matrix3	operator/ (T const value) const
	divide matrix by a value
Matrix3	operator+ (Matrix3 const &right) const
	add two Matrices
Matrix3	operator- (Matrix3 const &right) const
	subtract one Matrix3 from another
Matrix3	operator* (Matrix3 const &right) const
	< multiply a matrix with another
Vec3< T >	operator* (Vec3< T > const &p) const
	negative matrix
Matrix3	operator+ (T value) const
	add a value times identity matrix
Matrix3	operator- (T value) const
	subtract a value times identity matrix
3D Transform Methods
void	Transform (Vec3< T > &p) const
	Transforms the given vector by multiplying it with the matrix.
Assignment Operators
Matrix3 const &	operator*= (Matrix3 const &right)
	multiply a matrix with another matrix and modify this matrix
Matrix3 const &	operator+= (Matrix3 const &right)
	add two Matrices modify this
Matrix3 const &	operator-= (Matrix3 const &right)
	subtract one Matrix3 from another matrix and modify this matrix
Matrix3 const &	operator*= (T const value)
	multiply a matrix with a value modify this matrix
Matrix3 const &	operator/= (T const value)
	divide the matrix by a value modify the this matrix
Matrix3 const &	operator+= (T const value)
	add a value times identity matrix
Matrix3 const &	operator-= (T const value)
	subtract a value times identity matrix
Other Methods
Matrix3	AddDiagonal (T xx, T yy, T zz) const
	Adds a diagonal matrix to this matrix and returns the result.
Matrix3	AddDiagonal (Vec3< T > const &diag) const
	Adds a diagonal matrix to this matrix and returns the result.
Matrix3	AddIdentity (T scale=T(1)) const
	Adds a scaled identity matrix to this matrix and returns the result.
void	Transpose ()
	Adds a diagonal matrix to this matrix and returns the result.
Matrix3	GetTranspose () const
	< Return the transpose of this matrix
Vec3< T >	TransposeMult (Vec3< T > const &p) const
	Multiply the give vector with the transpose of the matrix.
Matrix3	TransposeMult (Matrix3 const &right) const
	< Multiply a matrix by the transpose of this one (i.e. this^T * right).
Matrix3	MultTranspose (Matrix3 const &right) const
	< Multiply the transpose of a matrix by this one (i.e. this * right^T).
Matrix3	TransposeMultSelf () const
	Multiply the transpose of this matrix with itself (i.e. this^T * this).
Matrix3	MultSelfTranspose () const
	Multiply the matrix with its transpose (i.e. this * this^T).
T	GetTrace () const
	Adds a diagonal matrix to this matrix and returns the result.
T	GetDeterminant () const
void	Invert ()
	Invert this matrix.
Matrix3	GetInverse () const
	< Get the inverse of this matrix
void	Normalize ()
	Removes the scale component of the matrix by normalizing each column. The resulting matrix can contain shear, if it originally contained non-uniform scale and rotation.
void	OrthogonalizeX ()
	Orthogonalizes the matrix and removes the scale component, preserving the x direction.
void	OrthogonalizeY ()
	Orthogonalizes the matrix and removes the scale component, preserving the y direction.
void	OrthogonalizeZ ()
	Orthogonalizes the matrix and removes the scale component, preserving the z direction.
bool	IsIdentity (T tollerance=T(0.0001)) const
	Returns if the matrix is identity within the given error tollerance.
bool	IsSymmetric (T tollerance=T(0.0001)) const
	Returns if the matrix is symmetric within the given error tollerance.
bool	IsDiagonal (T tollerance=T(0.0001)) const
	Returns if the matrix is diagonal.
Vec3< T >	GetEigenvalues (T tollerance=T(0.0001)) const
	Returns the eigenvalues of the matrix. The eigenvalues are ordered, such that the first one is the largest. The given tollerance value is used for checking whether the matrix is diagonal.
Vec3< T >	GetEigenvectors (Vec3< T > &evec0, Vec3< T > &evec1, Vec3< T > &evec2, T tollerance=T(0.0001)) const
	Returns the eigenvalues and sets the given vector as the eigenvectors of the matrix. The eigenvalues are ordered, such that the first one is the largest. The given tollerance is used for checking whether the eigenvalues are the same.
void	SingularValueDecomposition (Matrix3< T > &U, Vec3< T > &S, Matrix3< T > &V, T tollerance=T(0.0001))
	Singular value decomposition (SVD) Returns the SVD of the matrix, where U and V are orthogonal matrices and S is the diagonal elements of a diagonal matrix (including zeros), such that this matrix A = U S V^T. The given tollerance is used for checking whether the eigenvalues are the same.

Static Public Member Functions
Static Methods
static Matrix3	Identity ()
	Returns an identity matrix.
static Matrix3	View (Vec3< T > const &target, Vec3< T > const &up)
	Returns a view matrix using position, target and approximate up vector.
static Matrix3	RotationX (T angle)
	Returns a rotation matrix around x axis by angle in radians.
static Matrix3	RotationY (T angle)
	Returns a rotation matrix around y axis by angle in radians.
static Matrix3	RotationZ (T angle)
	Returns a rotation matrix around z axis by angle in radians.
static Matrix3	RotationXYZ (T angleX, T angleY, T angleZ)
	Returns a rotation matrix around x, y, and then z axes by angle in radians (Rz * Ry * Rx)
static Matrix3	RotationZYX (T angleX, T angleY, T angleZ)
	Returns a rotation matrix around z, y, and then x axes by angle in radians (Rx * Ry * Rz)
static Matrix3	Rotation (Vec3< T > const &axis, T angle)
	Returns a rotation matrix about the given axis by angle in radians.
static Matrix3	Rotation (Vec3< T > const &axis, T cosAngle, T sinAngle)
	Returns a rotation matrix about the given axis by cos and sin of the rotation angle.
static Matrix3	Rotation (Vec3< T > const &from, Vec3< T > const &to)
	Returns a rotation matrix that sets [from] unit vector to [to] unit vector.
static Matrix3	Scale (T uniformScale)
	Returns a uniform scale matrix.
static Matrix3	Scale (T scaleX, T scaleY, T scaleZ)
	Returns a scale matrix.
static Matrix3	Scale (Vec3< T > const &scale)
	Returns a scale matrix.
static Matrix3	TensorProduct (Vec3< T > const &v0, Vec3< T > const &v1)
	Returns the tensor product (outer product) matrix of two vectors.
static Matrix3	MatrixCrossProd (Vec3< T > const &a)
	Returns the matrix representation of cross product ( a x b )

Public Attributes
T	cell [9]
	Elements of the matrix are column-major: | 0 3 6 | | 1 4 7 | | 2 5 8 | .

Friends
Matrix3	operator* (T value, Matrix3 const &right)
	multiply matrix by a value
Matrix3	operator+ (T value, Matrix3 const &right)
	add a value times identity matrix to a matrix
Matrix3	operator- (T value, Matrix3 const &right)
	subtract a matrix from a value times identity matrix
Matrix3	Inverse (Matrix3 const &m)
	return the inverse of the matrix

Member Function Documentation

SetTensorProduct()

template<typename T >

void SetTensorProduct	(	Vec3< T > const &	v0,
		Vec3< T > const &	v1 )

Set all the values as zero.

Parameters

v1	Sets the matrix as the tensor product (outer product) of two vectors

GetDeterminant()

template<typename T >

T GetDeterminant

(

)

const

< Get the determinant of this matrix