ON_2x2Matrix Class Reference

#include <opennurbs_matrix.h>

Public Member Functions
	ON_2x2Matrix ()=default
	ON_2x2Matrix (const class ON_Matrix &M)
	ON_2x2Matrix (const double M[2][2])
	ON_2x2Matrix (const ON_2x2Matrix &)=default
	ON_2x2Matrix (double a, double b, double c, double d)
	ON_2x2Matrix (double d)
	ON_2x2Matrix (double d0, double d1)
	ON_2x2Matrix (double M[2][2])
	~ON_2x2Matrix ()=default
double	Coefficient (int i, int j) const
double	Determinant () const
const ON_2x2Matrix	Inverse () const
bool	IsDiagonal () const
bool	IsDiagonal (double relative_tolerance) const
bool	IsIdentity () const
bool	IsIdentity (double tolerance) const
bool	IsNotZero () const
bool	IsNotZero (double zero_tolerance) const
bool	IsOrthoganal () const
bool	IsOrthoganal (double tolerance) const
	M is an orthoganal matrix if M * Transpose(M) = Identity. More...
bool	IsValid () const
bool	IsZero () const
bool	IsZero (double zero_tolerance) const
double	MaximumCoefficientAbsoluteValue () const
double	MaximumDigonalAbsoluteValue () const
double	MaximumOffDigonalAbsoluteValue () const
double	MinimumCoefficientAbsoluteValue () const
double	MinimumDigonalAbsoluteValue () const
double	MinimumOffDigonalAbsoluteValue () const
ON_2x2Matrix &	operator= (const ON_2x2Matrix &)=default
double *	operator[] (int i)
const double *	operator[] (int i) const
const ON_2x2Matrix	PseudoInverse () const
	Use the singular value decomposition to get the pseudo inverse. More...
int	Rank () const
int	Rank (double zero_tolerance) const
bool	SVD (ON_2x2Matrix &U, double singular_values[2], ON_2x2Matrix &V) const
	Get the singular vaue decomposition of this matrix = U * Diagonal(singular_values[0], singular_values[1]) * Transpose(V). More...
const ON_2x2Matrix	SwapColumns () const
const ON_2x2Matrix	SwapRows () const
const ON_2x2Matrix	SwapRowsAndColumns () const
double	Trace () const
const ON_2x2Matrix	Transpose () const

Static Public Member Functions
static const ON_2x2Matrix	CombineSVD (const ON_2x2Matrix &U, double s0, double s1, const ON_2x2Matrix &V)
static const ON_2x2Matrix	ProcrustesRotation (const ON_2dPoint &P0, const ON_2dPoint &P1, const ON_2dPoint &P2, const ON_2dPoint &Q0, const ON_2dPoint &Q1, const ON_2dPoint &Q2)
	Use theKabsch-Umeyama algorithm to calculate the rotation matrix R that minimizes |R*P0 - Q0|^2 + |R*P1 - Q1|^2 + |R*P2 - Q2|^2. The input must satisfy P0 + P1 + P2 = (0,0) and Q0 + Q1 + Q2 = (0,0). Typically, by the time you are calculating this rotation, the P and Q triangles have the same orientation. If you want a rotation matrix that acts on the right, take the transpose of the returned value. If you have more than 3 points, use the version of ProcrustesRotation() that takes a 2x2 matrix H = P * Transpose(Q). More...
static const ON_2x2Matrix	ProcrustesRotation (const ON_2x2Matrix &H)
	If P[] and Q[] are sets of N 2d points, N gt;= 3, P[0] + ... + P[N-1] = (0,0) and Q[0] + ... + Q[N-1] = (0,0), then the Procrustes left rotation R is the rotation matrix that minimizes |R*P[0] - Q[0]|^2 + ... + |R*P[N-1] - Q[N-1]|^2. More...
static const ON_2x2Matrix	Rotation (double cos_angle, double sin_angle)
	Get a rotation matrix that acts on the left (rotated point = R * point). If you want a rotation matrix that acts on the right, then use the transpose of the returned matrix. More...
static const ON_2x2Matrix	Rotation (ON_2dVector V)
	Get a rotation matrix that acts on the left (rotated point = R * point). If you want a rotation matrix that acts on the right, then use the transpose of the returned matrix. More...
static const ON_2x2Matrix	RotationDegrees (double angle_degrees)
	Get a rotation matrix that acts on the left (rotated point = R * point). If you want a rotation matrix that acts on the right, then use the transpose of the returned matrix. More...
static const ON_2x2Matrix	RotationRadians (double angle_radians)
	Get a rotation matrix that acts on the left (rotated point = R * point). If you want a rotation matrix that acts on the right, then use the transpose of the returned matrix. More...
static bool	Test (ON_TextLog &text_log)
	Test a ON_2x2Matrix::SVD(), ON_2x2Matrix::Determinant(), ON_2x2Matrix::Rank() and ON_2x2Matrix::Inverse() on every matrix returned by the version of TestList() with a callback parameter More...
static unsigned	TestList (ON__UINT_PTR context, bool(*Callback)(ON__UINT_PTR context, int A_rank, const ON_2x2Matrix A))
	Iterates through a sequence of test matrices. More...

Public Attributes
double	m [2][2]

Static Public Attributes
static const ON_2x2Matrix	Identity
	The diagonal coefficients are 1 and the off diagonal coefficients are 0. More...
static const ON_2x2Matrix	Nan
	Every coefficient is ON_DBL_QNAN. More...
static const ON_2x2Matrix	Zero
	All coefficients are 0. More...
static const double	ZeroTolerance
	Default zero tolerance that can be used when a nonzero tolerance is needed and you don't know what to pass. 1.0e-12. More...

Constructor & Destructor Documentation

ON_2x2Matrix() [1/8]

ON_2x2Matrix::ON_2x2Matrix ( )

default

~ON_2x2Matrix()

ON_2x2Matrix::~ON_2x2Matrix ( )

default

ON_2x2Matrix() [2/8]

ON_2x2Matrix::ON_2x2Matrix ( const ON_2x2Matrix &  )

default

ON_2x2Matrix() [3/8]

ON_2x2Matrix::ON_2x2Matrix

(

double

M[2][2]

)

ON_2x2Matrix() [4/8]

ON_2x2Matrix::ON_2x2Matrix

(

const double

M[2][2]

)

ON_2x2Matrix() [5/8]

ON_2x2Matrix::ON_2x2Matrix

(

double

d

)

ON_2x2Matrix() [6/8]

ON_2x2Matrix::ON_2x2Matrix	(	double	d0,
		double	d1
	)

ON_2x2Matrix() [7/8]

ON_2x2Matrix::ON_2x2Matrix	(	double	a,
		double	b,
		double	c,
		double	d
	)

ON_2x2Matrix() [8/8]

ON_2x2Matrix::ON_2x2Matrix

(

const class ON_Matrix &

M

)

Member Function Documentation

Coefficient()

double ON_2x2Matrix::Coefficient	(	int	i,
		int	j
	)		const

CombineSVD()

static const ON_2x2Matrix ON_2x2Matrix::CombineSVD ( const ON_2x2Matrix &  U, double  s0, double  s1, const ON_2x2Matrix &  V  )

static

Determinant()

double ON_2x2Matrix::Determinant

(

)

const

Inverse()

const ON_2x2Matrix ON_2x2Matrix::Inverse

(

)

const

IsDiagonal() [1/2]

bool ON_2x2Matrix::IsDiagonal

(

)

const

IsDiagonal() [2/2]

bool ON_2x2Matrix::IsDiagonal

(

double

relative_tolerance

)

const

IsIdentity() [1/2]

bool ON_2x2Matrix::IsIdentity

(

)

const

Returns

True if the diagonal coefficients are 1 and the off diagonal coefficients are 0.

IsIdentity() [2/2]

bool ON_2x2Matrix::IsIdentity

(

double

tolerance

)

const

Parameters

tolerance

Returns

True if fabs(x - 1.0) <= tolerance for both diagonal coefficients and fabs(x) <= tolerance for both off diagonal coefficients.

IsNotZero() [1/2]

bool ON_2x2Matrix::IsNotZero

(

)

const

Parameters

zero_tolerance

Returns

True if at least one coefficient is not zero and all coefficients are valid.

IsNotZero() [2/2]

bool ON_2x2Matrix::IsNotZero

(

double

zero_tolerance

)

const

Parameters

zero_tolerance

Returns

True if the absolute value of at least one coefficient is > zero_tolerance and coefficients are valid.

IsOrthoganal() [1/2]

bool ON_2x2Matrix::IsOrthoganal

(

)

const

IsOrthoganal() [2/2]

bool ON_2x2Matrix::IsOrthoganal

(

double

tolerance

)

const

M is an orthoganal matrix if M * Transpose(M) = Identity.

Parameters

tolerance

If every coefficient of (M * Transpose(M) - Idenity) has absolute value <= tolerance, then true is returned.

Returns

True if this matrix is orthoganal.

IsValid()

bool ON_2x2Matrix::IsValid

(

)

const

IsZero() [1/2]

bool ON_2x2Matrix::IsZero

(

)

const

Returns

True if the absolute values of all four coefficients are 0.

IsZero() [2/2]

bool ON_2x2Matrix::IsZero

(

double

zero_tolerance

)

const

Parameters

zero_tolerance

Returns

True if the absolute values of all four coefficients are <= zero_tolerance.

MaximumCoefficientAbsoluteValue()

double ON_2x2Matrix::MaximumCoefficientAbsoluteValue

(

)

const

MaximumDigonalAbsoluteValue()

double ON_2x2Matrix::MaximumDigonalAbsoluteValue

(

)

const

MaximumOffDigonalAbsoluteValue()

double ON_2x2Matrix::MaximumOffDigonalAbsoluteValue

(

)

const

MinimumCoefficientAbsoluteValue()

double ON_2x2Matrix::MinimumCoefficientAbsoluteValue

(

)

const

MinimumDigonalAbsoluteValue()

double ON_2x2Matrix::MinimumDigonalAbsoluteValue

(

)

const

MinimumOffDigonalAbsoluteValue()

double ON_2x2Matrix::MinimumOffDigonalAbsoluteValue

(

)

const

operator=()

ON_2x2Matrix& ON_2x2Matrix::operator= ( const ON_2x2Matrix &  )

default

operator[]() [1/2]

double* ON_2x2Matrix::operator[]

(

int

i

)

Parameters

i	0 <= i < 1

Returns

If i is 0 or 1, the pointer to the i-th row is returned. Otherwise nullptr is returned.

operator[]() [2/2]

const double* ON_2x2Matrix::operator[]

(

int

i

)

const

Parameters

i	0 <= i < 1

Returns

If i is 0 or 1, the pointer to the i-th row is returned. Otherwise nullptr is returned.

ProcrustesRotation() [1/2]

static const ON_2x2Matrix ON_2x2Matrix::ProcrustesRotation ( const ON_2dPoint &  P0, const ON_2dPoint &  P1, const ON_2dPoint &  P2, const ON_2dPoint &  Q0, const ON_2dPoint &  Q1, const ON_2dPoint &  Q2  )

static

Use theKabsch-Umeyama algorithm to calculate the rotation matrix R that minimizes |R*P0 - Q0|^2 + |R*P1 - Q1|^2 + |R*P2 - Q2|^2.
The input must satisfy P0 + P1 + P2 = (0,0) and Q0 + Q1 + Q2 = (0,0). Typically, by the time you are calculating this rotation, the P and Q triangles have the same orientation. If you want a rotation matrix that acts on the right, take the transpose of the returned value. If you have more than 3 points, use the version of ProcrustesRotation() that takes a 2x2 matrix H = P * Transpose(Q).

Parameters

P0
P1
P2
Q0
Q1
Q2

Returns

The Procrustes rotation matrix that acts on the left of points.

ProcrustesRotation() [2/2]

static const ON_2x2Matrix ON_2x2Matrix::ProcrustesRotation ( const ON_2x2Matrix &  H )

static

If P[] and Q[] are sets of N 2d points, N gt;= 3, P[0] + ... + P[N-1] = (0,0) and Q[0] + ... + Q[N-1] = (0,0), then the Procrustes left rotation R is the rotation matrix that minimizes |R*P[0] - Q[0]|^2 + ... + |R*P[N-1] - Q[N-1]|^2.

Parameters

H	H = P * Transpose(Q), where P is the 2xN matrix whose columns are P[0], ..., P[N-1] and Q is the 2xN matrix whose columns are Q[0], ..., Q[N-1].

Returns

The Procrustes rotation matrix that acts on the left of points.

PseudoInverse()

const ON_2x2Matrix ON_2x2Matrix::PseudoInverse

(

)

const

Use the singular value decomposition to get the pseudo inverse.

Returns

V*Diagonal(1/sigma0, 1/sigma1)*Transpose(U) where U * Diagonal(sigma0, sigma1) * Transpose(V) is the singular value decomposistion.

Rank() [1/2]

int ON_2x2Matrix::Rank

(

)

const

Returns

Rank(0.0).

Rank() [2/2]

int ON_2x2Matrix::Rank

(

double

zero_tolerance

)

const

Parameters

zero_tolerance

Coefficients and determinants with absolute value <= zero_tolerance are treated as 0. ///

Returns

If this matrix is valid, the rank is returned. Otherwise -1 is returned.

Rotation() [1/2]

static const ON_2x2Matrix ON_2x2Matrix::Rotation ( double  cos_angle, double  sin_angle  )

static

Get a rotation matrix that acts on the left (rotated point = R * point). If you want a rotation matrix that acts on the right, then use the transpose of the returned matrix.

Parameters

cos_angle
sin_angle

Returns

The matrix R such that ON_2dVector(cos_angle, sin_angle) = R * ON_2dVector::XAxis.

Rotation() [2/2]

static const ON_2x2Matrix ON_2x2Matrix::Rotation ( ON_2dVector  V )

static

Get a rotation matrix that acts on the left (rotated point = R * point). If you want a rotation matrix that acts on the right, then use the transpose of the returned matrix.

Parameters

V

Returns

The matrix R such that V = R * ON_2dVector::XAxis.

RotationDegrees()

static const ON_2x2Matrix ON_2x2Matrix::RotationDegrees ( double  angle_degrees )

static

Get a rotation matrix that acts on the left (rotated point = R * point). If you want a rotation matrix that acts on the right, then use the transpose of the returned matrix.

Parameters

angle_degrees

Returns

The matrix R such that R * P rotates P counterclockwise by angle_degrees.

RotationRadians()

static const ON_2x2Matrix ON_2x2Matrix::RotationRadians ( double  angle_radians )

static

Get a rotation matrix that acts on the left (rotated point = R * point). If you want a rotation matrix that acts on the right, then use the transpose of the returned matrix.

Parameters

angle_radians

Returns

The matrix R such that R * P rotates P counterclockwise by angle_radians.

SVD()

bool ON_2x2Matrix::SVD	(	ON_2x2Matrix &	U,
		double	singular_values[2],
		ON_2x2Matrix &	V
	)		const

Get the singular vaue decomposition of this matrix = U * Diagonal(singular_values[0], singular_values[1]) * Transpose(V).

Parameters

U	The returned U will be an orthoganal matrix.
singular_values	The singular values are returned in increasing order 0 <= singular_values[0] <= singular_values[1].
V	The returned V will be an orthoganal matrix.

Returns

SwapColumns()

const ON_2x2Matrix ON_2x2Matrix::SwapColumns

(

)

const

SwapRows()

const ON_2x2Matrix ON_2x2Matrix::SwapRows

(

)

const

SwapRowsAndColumns()

const ON_2x2Matrix ON_2x2Matrix::SwapRowsAndColumns

(

)

const

Test()

static bool ON_2x2Matrix::Test ( ON_TextLog &  text_log )

static

Test a ON_2x2Matrix::SVD(), ON_2x2Matrix::Determinant(), ON_2x2Matrix::Rank() and ON_2x2Matrix::Inverse() on every matrix returned by the version of TestList() with a callback parameter

Parameters

text_log

A description of any failure and the number of successful tests is sent to text_log.

Returns

True if every test passes.

TestList()

static unsigned ON_2x2Matrix::TestList ( ON__UINT_PTR  context, bool(*)(ON__UINT_PTR context, int A_rank, const ON_2x2Matrix A)  Callback  )

static

Iterates through a sequence of test matrices.

Parameters

context	Value passed as the first parameter to Callback()
Callback	This function is called for each test matrix. A is the matrix being tested. If the A_rank paratmer is >=0, then A was computed in a way that if arithmetic was perfect, then A.rank() would be A_rank. Otherwise A_rank = -1 and the rank of A is unknown. Return true to continue testing

Returns

Number of times Callback() returned true.

Trace()

double ON_2x2Matrix::Trace

(

)

const

Transpose()

const ON_2x2Matrix ON_2x2Matrix::Transpose

(

)

const

Member Data Documentation

Identity

const ON_2x2Matrix ON_2x2Matrix::Identity

static

The diagonal coefficients are 1 and the off diagonal coefficients are 0.

m

double ON_2x2Matrix::m[2][2]

Nan

const ON_2x2Matrix ON_2x2Matrix::Nan

static

Every coefficient is ON_DBL_QNAN.

Zero

const ON_2x2Matrix ON_2x2Matrix::Zero

static

All coefficients are 0.

ZeroTolerance

const double ON_2x2Matrix::ZeroTolerance

static

Default zero tolerance that can be used when a nonzero tolerance is needed and you don't know what to pass. 1.0e-12.