#include <Matrix3x3.h>

Public Member Functions
	Matrix3x3 ()

	Matrix3x3 (const Matrix3x3 &M)

	Matrix3x3 (double m11, double m12, double m13, double m21, double m22, double m23, double m31, double m32, double m33)

virtual	~Matrix3x3 ()

Matrix3x3	operator= (const Matrix3x3 &rhs)

Matrix3x3	operator*= (const Matrix3x3 &rhs)

Matrix3x3	operator*= (double f)

Matrix3x3	operator+= (const Matrix3x3 &rhs)

AffPoint	operator* (const AffPoint &p) const

AffVector	operator* (const AffVector &v) const

Matrix3x3	operator* (const Matrix3x3 &m2) const

Matrix3x3	operator+ (const Matrix3x3 &m2) const

Matrix3x3	operator- (const Matrix3x3 &m2) const

double	determinant () const

double	elementAt (int i, int j) const

float *	extractColMajor (float m[9]) const

double *	extractColMajor (double m[9]) const

float *	extractRowMajor (float m[9]) const

double *	extractRowMajor (double m[9]) const

int	extractAxisAngle (AffVector &w, double &theta) const

void	extractRows (AffVector &row1, AffVector &row2, AffVector &row3) const

bool	inverse (Matrix3x3 &mInv) const

bool	isOrthogonal () const

bool	isRightHanded () const

double	largestDiagonalElement (int &pos) const

void	multiply (const double a[], double b[]) const

void	setElementAt (int i, int j, double newValue)

double	trace () const

void	transpose ()

Static Public Member Functions
static Matrix3x3	xRotationDegrees (double angle)

static Matrix3x3	xRotationRadians (double angle)

static Matrix3x3	yRotationDegrees (double angle)

static Matrix3x3	yRotationRadians (double angle)

static Matrix3x3	zRotationDegrees (double angle)

static Matrix3x3	zRotationRadians (double angle)

static Matrix3x3	generalRotationRadians (const AffVector &rotationAxis, double angle)

static Matrix3x3	alignVectors (const AffVector &uFrom, const AffVector &uTo)

static Matrix3x3	alignVectors (const AffVector &uFrom, const AffVector &vFrom, const AffVector &uTo, const AffVector &vTo)

static Matrix3x3	scale (double sx, double sy, double sz)

static Matrix3x3	shear (const AffVector &n, const AffVector &u, double f)

static Matrix3x3	crossProductMatrix (const AffVector &u)

static Matrix3x3	mirrorMatrix (const AffVector &mirrorPlaneNormal)

static Matrix3x3	tensorProductMatrix (const AffVector &u, const AffVector &v)

Static Public Attributes
static const Matrix3x3	IdentityMatrix

static const Matrix3x3	ZeroMatrix

static const int	ImMDeterminantNotZero = -20

static const int	CannotDetermineUnitAxisVector = -19

static const int	CosTermsNotEqual = -18

static const int	SinTermsNotEqual = -17

static const int	NotOrthogonal = -5

static const int	NotRightHanded = -4

static const int	Extracted_wTheta = 0

Protected Attributes
double	mElem [3][3]

Friends
class	Matrix4x4

Matrix3x3	operator* (double f, const Matrix3x3 &m)

std::ostream &	operator<< (std::ostream &os, const Matrix3x3 &m)

std::istream &	operator>> (std::istream &is, Matrix3x3 &m)

Detailed Description

This class is designed for the specification and manipulation of 3x3 matrices as a part of Affine transformations specified on 3D vectors As such, it provides facilities to create 3x3 matrices that rotate and mirror vectors, form tensor products of vectors, and provide other support required by Matrix4x4 in its role of representing transformations of 3D geometry. This interface is NOT intended to provide facilities for representing 2D transformations in homogeneous form.

Constructor & Destructor Documentation

cryph::Matrix3x3::Matrix3x3 ( )

Default constructor creates a 3x3 identity matrix

cryph::Matrix3x3::Matrix3x3 ( const Matrix3x3 & M )

The copy constructor

Parameters

M	the matrix whose elements are copied

cryph::Matrix3x3::Matrix3x3	(	double	m11,
		double	m12,
		double	m13,
		double	m21,
		double	m22,
		double	m23,
		double	m31,
		double	m32,
		double	m33
	)

Construct a 3x3 matrix directly from 9 values given in row-major order

Parameters

mrc	The element for row r, column c

cryph::Matrix3x3::~Matrix3x3 ( )

virtual

The destructor

Member Function Documentation

Matrix3x3 cryph::Matrix3x3::alignVectors	(	const AffVector &	uFrom,
		const AffVector &	uTo
	)

static

Factory method to create a 3x3 matrix that can be used to rotate one 3D vector onto another 3D vector.

Parameters

uFrom	the 3D vector to be aligned with uTo
uTo	the 3D vector onto which we want the created matrix to rotate uFrom

Returns: the 3x3 matrix encoding the rotation

See also: extractAxisAngle

Matrix3x3 cryph::Matrix3x3::alignVectors	(	const AffVector &	uFrom,
		const AffVector &	vFrom,
		const AffVector &	uTo,
		const AffVector &	vTo
	)

static

Factory method to create a 3x3 matrix that can be used to rotate a pair of 3D vectors onto another pair of 3D vectors. Since a rigid rotation to perform this cannot always be created, the matrix created will align uFrom with uTo, and it will encode one additional rotation that will rotate vFrom into the plane of (uTo, vTo) such that the dot product of vTo with the transformed vFrom is non-negative.

Parameters

uFrom	the 3D vector to be aligned with uTo
vFrom	the 3D vector to be aligned with vTo
uTo	the 3D vector onto which we want the created matrix to rotate uFrom
vTo	the 3D vector onto which we want the created matrix to rotate vFrom, subject to the constraint explained above.

Returns: the 3x3 matrix encoding the rotation

Matrix3x3 cryph::Matrix3x3::crossProductMatrix ( const AffVector & u )

static

Factory method to create a 3x3 matrix that can be used to encode a cross product with the given vector. That is, if U is the 3x3 matrix returned by this method, then for an arbitrary vector v: U*v = u x v.

Parameters

u	the desired vector

Returns: the 3x3 matrix encoding the cross product

double cryph::Matrix3x3::determinant ( ) const

Return the determinantof "this" 3x3 matrix

Returns: the determinant

double cryph::Matrix3x3::elementAt	(	int	i,
		int	j
	)		const

Return "this" matrix element at row i and column j.

Parameters

i	the desired row
j	the desired column

Returns: the matrix element at row i and column j

int cryph::Matrix3x3::extractAxisAngle	(	AffVector &	w,
		double &	theta
	)		const

If "this" matrix is orthogonal and right-handed, then this method will determine the rotation axis and angle which, if passed to generalRotationRadians, would exactly reproduce "this" matrix.

Parameters

w	on exit, this vector will have the rotation axis
theta	on exit, this will hold the rotation angle in radians

Returns

an integer code indicating whether the extraction succeeded:

Matrix3x3::NotOrthogonal - if "this" matrix is not orthogonal
Matrix3x3::NotRightHanded - if "this" matrix is not right-handed
Matrix3x3::Extracted_wTheta - if w and theta were successfully computed

See also: isOrthogonal; isRightHanded; generalRotationRadians

float * cryph::Matrix3x3::extractColMajor ( float m[9] ) const

Extract the components of the matrix into the given single-precision array in column-major order.

Parameters

m	[OUTPUT ONLY] an array of float of length 9

Returns: the base address of "m" so that the method call can be used as a parameter to an OpenGL function expecting an array of float.

double * cryph::Matrix3x3::extractColMajor ( double m[9] ) const

Extract the components of the matrix into the given double-precision array in column-major order.

Parameters

m	[OUTPUT ONLY] an array of double of length 9

Returns: the base address of "m" so that the method call can be used as a parameter to an OpenGL function expecting an array of double.

float * cryph::Matrix3x3::extractRowMajor ( float m[9] ) const

Extract the components of the matrix into the given single-precision array in row-major order.

Parameters

m	[OUTPUT ONLY] an array of float of length 9

Returns: the base address of "m" so that the method call can be used as a parameter to an OpenGL function expecting an array of float.

double * cryph::Matrix3x3::extractRowMajor ( double m[9] ) const

Extract the components of the matrix into the given double-precision array in row-major order.

Parameters

m	[OUTPUT ONLY] an array of double of length 9

Returns: the base address of "m" so that the method call can be used as a parameter to an OpenGL function expecting an array of double.

void cryph::Matrix3x3::extractRows	(	AffVector &	row1,
		AffVector &	row2,
		AffVector &	row3
	)		const

Extract the rows of "this" matrix, writing them into the given output parameters

Parameters

row1	on exit, this will hold the first row of "this" matrix
row2	on exit, this will hold the second row of "this" matrix
row3	on exit, this will hold the third row of "this" matrix

Matrix3x3 cryph::Matrix3x3::generalRotationRadians	(	const AffVector &	rotationAxis,
		double	angle
	)

static

Factory method to create a 3x3 matrix that can be used to rotate a vector by a given angle about the given axis vector.

Parameters

rotationAxis	a 3D vector about which the rotation is to be performed
angle	the desired rotation angle in radians

Returns: the 3x3 matrix encoding the rotation

bool cryph::Matrix3x3::inverse ( Matrix3x3 & mInv ) const

Compute and return the inverse of "this" matrix.

Parameters

mInv	the matrix into which the inverse will be written

Returns: true if the inverse was successfully computed

bool cryph::Matrix3x3::isOrthogonal ( ) const

Report whether "this" matrix is orthogonal. A matrix is orthogonal if its inverse is the same as its transpose.

Returns: true if the matrix is orthogonal

See also: extractAxisAngle

bool cryph::Matrix3x3::isRightHanded ( ) const

Report whether "this" matrix is right-handed. A matrix is right-handed if the dot product of (row1 x row2) with row3 is positive.

Returns: true if the matrix is right-handed

See also: extractAxisAngle

double cryph::Matrix3x3::largestDiagonalElement ( int & pos ) const

Determine the diagonal element with the largest value. Return the position in "pos" and the value itself as the method return.

Parameters

pos	on exit, the row that contains the largest diagonal element

Returns: the value of the element with the largest value.

Matrix3x3 cryph::Matrix3x3::mirrorMatrix ( const AffVector & mirrorPlaneNormal )

static

Factory method to create a 3x3 matrix that can be used to mirror a vector about the plane whose normal is specified by the given vector.

Parameters

mirrorPlaneNormal the normal vector to the desired mirror plane

Returns: the 3x3 matrix encoding the mirror

void cryph::Matrix3x3::multiply	(	const double	a[],
		double	b[]
	)		const

Multiply "a" on the left by "this" matrix, placing the result in "b": b = "this" * a.

Parameters

a	an array of length 3 to be multiplied
b	an array of length 3 that recieves the product "this" * a.

AffPoint cryph::Matrix3x3::operator* ( const AffPoint & p ) const

Multiply the point p on the left by "this" matrix.

Parameters

p	the point to be multiplied

Returns: the transformed point

AffVector cryph::Matrix3x3::operator* ( const AffVector & v ) const

Multiply the vector v on the left by "this" matrix.

Parameters

v	the vector to be multiplied

Returns: the transformed vector

Matrix3x3 cryph::Matrix3x3::operator* ( const Matrix3x3 & m2 ) const

Multiply the matrix m2 on the left by "this" matrix.

Parameters

m2	the matrix to be multiplied

Returns: the 3x3 matrix that is the product: "this" * m2

Matrix3x3 cryph::Matrix3x3::operator*= ( const Matrix3x3 & rhs )

Assign to "this" matrix the product of "this" matrix and rhs

Parameters

rhs	the matrix to be concatenated onto the right-hand side of "this" matrix

Returns: the updated "this" matrix

Matrix3x3 cryph::Matrix3x3::operator*= ( double f )

Assign to "this" matrix the product of "this" matrix with the given scalar. That is, each element of "this" matrix is multiplied by f.

Parameters

f	the scale factor

Returns: the updated "this" matrix

Matrix3x3 cryph::Matrix3x3::operator+ ( const Matrix3x3 & m2 ) const

Add the matrix m2 to "this" matrix.

Parameters

m2	the matrix to be added

Returns: the 3x3 matrix that is the sum: "this" + m2

Matrix3x3 cryph::Matrix3x3::operator+= ( const Matrix3x3 & rhs )

Assign to "this" matrix the sum of "this" matrix and rhs

Parameters

rhs	the matrix to be added to "this" matrix

Returns: the updated "this" matrix

Matrix3x3 cryph::Matrix3x3::operator- ( const Matrix3x3 & m2 ) const

Subtract the matrix m2 from "this" matrix.

Parameters

m2	the matrix to be subtracted

Returns: the 3x3 matrix that is the difference: "this" - m2

Matrix3x3 cryph::Matrix3x3::operator= ( const Matrix3x3 & rhs )

The assignment operator

Parameters

rhs	the 3x3 matrix to be assigned to "this" matrix

Returns: the assigned matrix

Matrix3x3 cryph::Matrix3x3::scale	(	double	sx,
		double	sy,
		double	sz
	)

static

Factory method to create a 3x3 matrix that can be used to scale a vector by the given scale factors along the x-, y-, and z-axes.

Parameters

sx	the desired scale factor in the x direction
sy	the desired scale factor in the y direction
sz	the desired scale factor in the z direction

Returns: the 3x3 matrix encoding the scale

void cryph::Matrix3x3::setElementAt	(	int	i,
		int	j,
		double	newValue
	)

Set this[i][j] = newValue.

Parameters

i	the row containing the element to be set
j	the column containing the element to be set
newValue	the value to be copied into row i and column j

Matrix3x3 cryph::Matrix3x3::shear	(	const AffVector &	n,
		const AffVector &	u,
		double	f
	)

static

Factory method to create a 3x3 matrix that can be used to shear a vector. The matrix created will shear an arbitrary vector, v, by adding to v: f*v.dot(nHat)uHat where nHat is a unit vector perpendicular to the shear plane; uHat is a unit vector in the direction of the component of the given u vector perpendicular to the given normal vector, n; and f is a constant.

Parameters

n	the vector perpendicular to the shear plane
u	a vector in the shear plane that specifies the shear direction (only the component of u perpendicular to n will be used when creating uHat)
f	a constant adjusting the amount of shear per length of v in the direction of nHat.

Returns: the 3x3 matrix encoding the shear

Matrix3x3 cryph::Matrix3x3::tensorProductMatrix	(	const AffVector &	u,
		const AffVector &	v
	)

static

Factory method to create a 3x3 matrix that is the tensor product of the two given vectors. That is, matrix[i][j] will be u[i]*v[j]

Parameters

u	the first vector
v	the second vector

Returns: the matrix that holds the tensor product of u and v.

double cryph::Matrix3x3::trace ( ) const

Compute and return the trace of "this" matrix. The trace is the sum of the diagonal elements.

Returns: the trace = this[0][0]+this[1][1]+this[2][2]

void cryph::Matrix3x3::transpose ( )

Transpose "this" matrix in place. On exit, "this" matrix will have been transposed.

Matrix3x3 cryph::Matrix3x3::xRotationDegrees ( double angle )

static

Factory method to create a 3x3 matrix that can be used to rotate a vector by a given angle about the x-axis.

Parameters

angle the desired rotation angle in degrees

Returns: the 3x3 matrix encoding the rotation

Matrix3x3 cryph::Matrix3x3::xRotationRadians ( double angle )

static

Factory method to create a 3x3 matrix that can be used to rotate a vector by a given angle about the x-axis.

Parameters

angle the desired rotation angle in radians

Returns: the 3x3 matrix encoding the rotation

Matrix3x3 cryph::Matrix3x3::yRotationDegrees ( double angle )

static

Factory method to create a 3x3 matrix that can be used to rotate a vector by a given angle about the y-axis.

Parameters

angle the desired rotation angle in degrees

Returns: the 3x3 matrix encoding the rotation

Matrix3x3 cryph::Matrix3x3::yRotationRadians ( double angle )

static

Factory method to create a 3x3 matrix that can be used to rotate a vector by a given angle about the y-axis.

Parameters

angle the desired rotation angle in radians

Returns: the 3x3 matrix encoding the rotation

Matrix3x3 cryph::Matrix3x3::zRotationDegrees ( double angle )

static

Factory method to create a 3x3 matrix that can be used to rotate a vector by a given angle about the z-axis.

Parameters

angle the desired rotation angle in degrees

Returns: the 3x3 matrix encoding the rotation

Matrix3x3 cryph::Matrix3x3::zRotationRadians ( double angle )

static

Factory method to create a 3x3 matrix that can be used to rotate a vector by a given angle about the z-axis.

Parameters

angle the desired rotation angle in radians

Returns: the 3x3 matrix encoding the rotation

Friends And Related Function Documentation

Matrix3x3 operator*	(	double	f,
		const Matrix3x3 &	m
	)

friend

Return a matrix that is the product f*m where f is a scale factor used to multiply each element of the matrix, m.

Parameters

f	the scale factor
m	the matrix to be scaled (m is unchanged)

Returns: the product f*m

std::ostream& operator<<	(	std::ostream &	os,
		const Matrix3x3 &	m
	)

friend

Output the matrix m to the given output stream. Elements are output in row-major order, all on one line, with a single space between each element.

Parameters

os	the stream to which the matrix is written
m	the matrix to be written

Returns: the updated output stream

std::istream& operator>>	(	std::istream &	is,
		Matrix3x3 &	m
	)

friend

Read 9 elements into the matrix m from the given input stream. Elements are read in row-major order and assumed to be whitespace-delimited.

Parameters

is	the stream from which the matrix is read
m	the matrix into which the values read are placed

Returns: the updated input stream

Member Data Documentation

const Matrix3x3 cryph::Matrix3x3::IdentityMatrix

static

Initial value:

=
    Matrix3x3(
        1.0 , 0.0 , 0.0 ,
        0.0 , 1.0 , 0.0 ,
        0.0 , 0.0 , 1.0
        )

the 3x3 identity matrix

const Matrix3x3 cryph::Matrix3x3::ZeroMatrix

static

Initial value:

=
    Matrix3x3(
        0.0 , 0.0 , 0.0 ,
        0.0 , 0.0 , 0.0 ,
        0.0 , 0.0 , 0.0
        )

the 3x3 zero matrix

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

Matrix3x3.h
Matrix3x3.c++

Public Member Functions

Static Public Member Functions

Static Public Attributes

Protected Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation