Matrix34< T > Class Template Reference

Detailed Description

template<typename T>
class cy::Matrix34< T >

3x4 matrix class.

Its data stores 12-value array of column-major matrix elements. I chose column-major format to be compatible with OpenGL You can use Matrix34 with Vec3<T> and Vec4<T> to transform 3D and 4D points.

#include <cyMatrix.h>

Public Member Functions
Constructors
	Matrix34 ()
	Default constructor.
template<typename S >
	Matrix34 (Matrix34< S > const &matrix)
	Copy constructor for different types.
	Matrix34 (T const *values)
	Initialize the matrix using an array of 9 values.
	Matrix34 (T v)
	Initialize the matrix as identity scaled by v.
	Matrix34 (Vec3< T > const &x, Vec3< T > const &y, Vec3< T > const &z, Vec3< T > const &pos)
	Initialize the matrix using x,y,z vectors and coordinate center.
	Matrix34 (Matrix3< T > const &m)
	Default constructor.
	Matrix34 (Matrix3< T > const &m, Vec3< T > const &pos)
	Default constructor.
	Matrix34 (Matrix2< T > const &m)
	Default constructor.
	Matrix34 (Matrix4< T > const &m)
	Default constructor.
	Matrix34 (T c00, T c01, T c02, T c03, T c10, T c11, T c12, T c13, T c20, T c21, T c22, T c23)
	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 12.
void	Set (T const *values)
	Set Matrix using an array of 12 values.
void	Set (Vec3< T > const &x, Vec3< T > const &y, Vec3< T > const &z, Vec3< T > const &pos)
	Set matrix using x,y,z vectors and coordinate center.
void	SetIdentity ()
	Converts the matrix to an identity matrix.
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	SetTranslation (Vec3< T > const &move)
	Sets a translation matrix with no rotation or scale.
void	AddTranslation (Vec3< T > const &move)
	Adds a translation to the matrix.
void	SetTranslationComponent (Vec3< T > const &move)
	Sets the translation component of the matrix.
void	SetNoTranslation ()
	Sets the translation component of the matrix to zero.
void	SetView (Vec3< T > const &pos, 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, Vec3< T > const &trans=Vec3< T >(T(0), T(0), T(0)))
	Sets a Cartesian coordinate frame using the given x direction, an approximate y direction, and a translation. x must be a unit vector.
void	SetCartesianFrameXZ (Vec3< T > const &x, Vec3< T > const &z_approx, Vec3< T > const &trans=Vec3< T >(T(0), T(0), T(0)))
	Sets a Cartesian coordinate frame using the given x direction, an approximate z direction, and a translation. x must be a unit vector.
void	SetCartesianFrameYX (Vec3< T > const &y, Vec3< T > const &x_approx, Vec3< T > const &trans=Vec3< T >(T(0), T(0), T(0)))
	Sets a Cartesian coordinate frame using the given y direction, an approximate x direction, and a translation. y must be a unit vector.
void	SetCartesianFrameYZ (Vec3< T > const &y, Vec3< T > const &z_approx, Vec3< T > const &trans=Vec3< T >(T(0), T(0), T(0)))
	Sets a Cartesian coordinate frame using the given y direction, an approximate z direction, and a translation. y must be a unit vector.
void	SetCartesianFrameZX (Vec3< T > const &z, Vec3< T > const &x_approx, Vec3< T > const &trans=Vec3< T >(T(0), T(0), T(0)))
	Sets a Cartesian coordinate frame using the given z direction, an approximate x direction, and a translation. z must be a unit vector.
void	SetCartesianFrameZY (Vec3< T > const &z, Vec3< T > const &y_approx, Vec3< T > const &trans=Vec3< T >(T(0), T(0), T(0)))
	Sets a Cartesian coordinate frame using the given z direction, an approximate y direction, and a translation. z must be a unit vector.
Set Row, Column, or Diagonal
void	SetRow (int ri, T x, T y, T z, T w)
	Sets a row of the matrix.
void	SetRow (int ri, Vec4< 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.
Vec4< T >	GetRow (int ri) const
	Returns a row of the matrix.
Vec3< T >	GetDiagonal () const
	Returns the diagonal of the matrix.
Get Sub-matrix cell
Matrix3< T > &	GetSubMatrix3 ()
	Returns the 3x3 portion of the matrix.
Matrix3< T > const &	GetSubMatrix3 () const
	Returns the 3x3 portion of the matrix.
Matrix2< T >	GetSubMatrix2 () const
	Returns the 2x2 portion of the matrix.
Vec3< T >	GetTranslation () const
	Returns the translation component of the matrix.
Matrix3< T >	GetRotation () const
	Returns the rotation portion of the transformation.
Matrix3< T >	GetScale () const
	Returns the scale portion of the transformation.
T	GetAvrgScale () const
	Returns the average scale factor of the 3 by 3 sub-matrix.
void	GetComponents (Matrix3< T > &scale, Matrix3< T > &rotation, Vec3< T > &translation) const
	Returns separate transformation components.
Comparison Operators
bool	operator== (Matrix34 const &right) const
	compare equal
bool	operator!= (Matrix34 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
Matrix34	operator- () const
	negative matrix
Matrix34	operator* (T const value) const
	multiply matrix by a value
Matrix34	operator/ (T const value) const
	divide matrix by a value
Matrix34	operator+ (Matrix34 const &right) const
	add two Matrices
Matrix34	operator- (Matrix34 const &right) const
	subtract one Matrix4 from another
Matrix34	operator* (Matrix34 const &right) const
	< multiply a matrix with another
Matrix34	operator* (Matrix3< T > const &right) const
	< multiply a matrix with another
Vec3< T >	operator* (Vec3< T > const &p) const
	negative matrix
Vec4< T >	operator* (Vec4< T > const &p) const
	negative matrix
Matrix34	operator+ (T value) const
	add a value times identity matrix
Matrix34	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.
Vec3< T >	VectorTransform (Vec3< T > const &p) const
	Transforms the vector by multiplying it with the matrix, ignoring the translation component.
Assignment Operators
Matrix34 const &	operator+= (Matrix34 const &right)
	add two Matrices modify this
Matrix34 const &	operator-= (Matrix34 const &right)
	subtract one Matrix4 from another matrix and modify this matrix
Matrix34 const &	operator*= (Matrix34 const &right)
	multiply a matrix with another matrix and modify this matrix
Matrix34 const &	operator*= (Matrix3< T > const &right)
	multiply a matrix with another matrix and modify this matrix
Matrix34 const &	operator*= (T const value)
	multiply a matrix with a value modify this matrix
Matrix34 const &	operator/= (T const value)
	divide the matrix by a value modify the this matrix
Matrix34 const &	operator+= (T const value)
	add a value times identity matrix
Matrix34 const &	operator-= (T const value)
	subtract a value times identity matrix
Other Methods
void	Transpose ()
	Transpose this matrix.
Matrix4< T >	GetTranspose () const
	Returns the transpose of this matrix.
Vec4< T >	TransposeMult (Vec3< T > const &p) const
	Multiply the give vector with the transpose of the matrix.
Vec4< T >	TransposeMult (Vec4< T > const &p) const
	Multiply the give vector with the transpose of the matrix.
T	GetDeterminant () const
	< Get the determinant of this matrix
void	Invert ()
	Invert this matrix.
Matrix34	GetInverse () const
	< Get the inverse of this matrix
void	Normalize ()
	Removes the scale component of the matrix by normalizing the first three columns. 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.

Static Public Member Functions
Static Methods
static Matrix34	Identity ()
	Returns an identity matrix.
static Matrix34	View (Vec3< T > const &pos, Vec3< T > const &target, Vec3< T > const &up)
	Returns a view matrix using position, target and approximate up vector.
static Matrix34	RotationX (T angle)
	Returns a rotation matrix around x axis by angle in radians.
static Matrix34	RotationY (T angle)
	Returns a rotation matrix around y axis by angle in radians.
static Matrix34	RotationZ (T angle)
	Returns a rotation matrix around z axis by angle in radians.
static Matrix34	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 Matrix34	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 Matrix34	Rotation (Vec3< T > const &axis, T angle)
	Returns a rotation matrix about the given axis by angle in radians.
static Matrix34	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 Matrix34	Rotation (Vec3< T > const &from, Vec3< T > const &to)
	Returns a rotation matrix that sets [from] unit vector to [to] unit vector.
static Matrix34	Scale (T uniformScale)
	Returns a uniform scale matrix.
static Matrix34	Scale (T scaleX, T scaleY, T scaleZ)
	Returns a scale matrix.
static Matrix34	Scale (Vec3< T > const &scale)
	Returns a scale matrix.
static Matrix34	Translation (Vec3< T > const &move)
	Returns a translation matrix with no rotation or scale.

Public Attributes
T	cell [12]
	Elements of the matrix are column-major: | 0 3 6 9 | | 1 4 7 10 | | 2 5 8 11 | .

Friends
Matrix34	operator* (T value, Matrix34 const &right)
	multiply matrix by a value
Matrix34	operator+ (T value, Matrix34 const &right)
	add a value times identity matrix to a matrix
Matrix34	operator- (T value, Matrix34 const &right)
	subtract a matrix from a value times identity matrix
Matrix34	Inverse (Matrix34 const &m)
	return the inverse of the matrix