ON_Xform2d Class Reference

#include <opennurbs_xform.h>

Public Member Functions
	ON_Xform2d ()
	ON_Xform2d (const ON_Xform2d &)=default
	ON_Xform2d (double m00, double m01, double m02, double m10, double m11, double m12)
	~ON_Xform2d ()=default
int	Compare (const ON_Xform2d &other) const
ON__UINT32	CRC32 (ON__UINT32 current_remainder) const
double	Determinant () const
void	GetAffineElements (double &a, double &b, double &c, double &d, double &tx, double &ty) const
	Get the six coefficients used by the traditional 2d drawing APIs. More...
void	GetAffineElements (double abcdtxty[6]) const
	Fills in an array of 6 doubles in (a,b,c,d,tx,ty) order. More...
void	GetAffineElements (float abcdtxty[6]) const
const ON_SHA1_Hash	Hash () const
ON_Xform2d	Inverse (double *determinant=nullptr) const
bool	Invert (double *determinant=nullptr)
bool	IsIdentity () const
bool	IsNan () const
bool	IsTranslation () const
bool	IsValid () const
bool	IsZeroTransformation () const
bool	operator!= (const ON_Xform2d &rhs) const
	Intentionally returns false if any coefficient is a nan. More...
ON_2dPoint	operator* (const ON_2dPoint &) const
	operators More...
ON_2dVector	operator* (const ON_2dVector &) const
ON_Xform2d	operator* (const ON_Xform2d &) const
ON_Xform2d &	operator= (const ON_Xform2d &)=default
bool	operator== (const ON_Xform2d &rhs) const
	Intentionally returns false if any coefficient is a nan. More...
double *	operator[] (int)
	Returns &m_xform[i][0] when 0 <= i < 2 and nullptr otherwise. More...
const double *	operator[] (int) const
const ON_Xform	ToXform () const

Static Public Member Functions
static const ON_Xform2d	FromAffineElements (const double abcdtxty[6])
	From an array of 6 doubles in (a,b,c,d,tx,ty) order. More...
static const ON_Xform2d	FromAffineElements (const float abcdtxty[6])
	From an array of 6 floats in (a,b,c,d,tx,ty) order. More...
static const ON_Xform2d	FromAffineElements (double a, double b, double c, double d, double tx, double ty)
static const ON_Xform2d	FromXform (const ON_Xform &xform, double zero_tolerance=0.0)
static const ON_Xform2d	RotationTransformation (const ON_2dVector &start_dir, const ON_2dVector &end_dir, const ON_2dPoint &rotation_center=ON_2dPoint::Origin)
static const ON_Xform2d	RotationTransformationFromAngleRadians (double angle_radians, const ON_2dPoint &rotation_center=ON_2dPoint::Origin)
static const ON_Xform2d	RotationTransformationFromSineAndCosine (double sin_angle, double cos_angle, const ON_2dPoint &rotation_center=ON_2dPoint::Origin)
static const ON_Xform2d	ScaleTransformation (const ON_2dPoint &fixed_point, double scale_factor)
static const ON_Xform2d	ScaleTransformation (const ON_2dPoint &fixed_point, double x_scale_factor, double y_scale_factor)
static const ON_Xform2d	TranslationTransformation (const ON_2dVector &delta)
	standard transformations More...
static const ON_Xform2d	TranslationTransformation (double dx, double dy)

Public Attributes
double	m_xform [2][3]

Static Public Attributes
static const ON_Xform2d	IdentityTransformation
static const ON_Xform2d	Nan
	ON_Xform2d::Nan - every stored coefficient is ON_DBL_QNAN. More...
static const ON_Xform2d	Unset
	ON_Xform2d::Unset - every stored coefficient is ON_UNSET_VALUE. More...
static const ON_Xform2d	ZeroTransformation

Detailed Description

Description: ON_Xform2d is a 2d affine transformation and is the 2d analog of ON_Xform. It is intended for use with the traditional 2d drawing APIs which represents a 2d transformation with six coefficients.

Constructor & Destructor Documentation

ON_Xform2d() [1/3]

ON_Xform2d::ON_Xform2d

(

)

Description: Like ON_Xform, the default constructor creates the ZERO transformation, not the identity transformation. Every coefficient is zero. Use ON_Xform2d::IdentityTransformation when you want the identity.

~ON_Xform2d()

ON_Xform2d::~ON_Xform2d ( )

default

ON_Xform2d() [2/3]

ON_Xform2d::ON_Xform2d ( const ON_Xform2d &  )

default

ON_Xform2d() [3/3]

ON_Xform2d::ON_Xform2d	(	double	m00,
		double	m01,
		double	m02,
		double	m10,
		double	m11,
		double	m12
	)

Member Function Documentation

Compare()

int ON_Xform2d::Compare

(

const ON_Xform2d &

other

)

const

Description: Well ordered dictionary compare that is nan aware.

CRC32()

ON__UINT32 ON_Xform2d::CRC32

(

ON__UINT32

current_remainder

)

const

Determinant()

double ON_Xform2d::Determinant

(

)

const

Returns: The determinant of the 2x2 linear part, m_xform[0][0]*m_xform[1][1] - m_xform[0][1]*m_xform[1][0]. Because the bottom row is (0,0,1), this is also the determinant of the full 3x3 matrix and the signed area scale factor of the transformation. A negative determinant means the transformation reverses orientation.

FromAffineElements() [1/3]

static const ON_Xform2d ON_Xform2d::FromAffineElements ( const double  abcdtxty[6] )

static

From an array of 6 doubles in (a,b,c,d,tx,ty) order.

FromAffineElements() [2/3]

static const ON_Xform2d ON_Xform2d::FromAffineElements ( const float  abcdtxty[6] )

static

From an array of 6 floats in (a,b,c,d,tx,ty) order.

FromAffineElements() [3/3]

static const ON_Xform2d ON_Xform2d::FromAffineElements ( double  a, double  b, double  c, double  d, double  tx, double  ty  )

static

Description: The traditional 2d drawing APIs store an affine transformation as six numbers (a,b,c,d,tx,ty) that map a point (x,y) to x1 = a*x + c*y + tx y1 = b*x + d*y + ty These are the six numbers, in this order, used by Eto.Drawing.Matrix, Windows GDI+, Direct2D (D2D1_MATRIX_3X2_F), Core Graphics (CGAffineTransform), Cairo (cairo_matrix_t), Java 2D, SVG and PDF. In terms of ON_Xform2d coefficients, a = m_xform[0][0] c = m_xform[0][1] tx = m_xform[0][2] b = m_xform[1][0] d = m_xform[1][1] ty = m_xform[1][2] Note well that (a,b,c,d,tx,ty) is the transpose of the ON_Xform2d coefficient order, because those APIs use the row vector convention. Composition order is reversed as well. If A2d and B2d are the ON_Xform2d equivalents of the platform transformations A and B, then A2d * B2d is the equivalent of B * A

FromXform()

static const ON_Xform2d ON_Xform2d::FromXform ( const ON_Xform &  xform, double  zero_tolerance = 0.0  )

static

Description: Get the 2d transformation defined by the x and y rows and columns of a 4x4 transformation. Parameters: xform - [in] zero_tolerance - [in] An element of xform is "zero" if fabs(x) <= zero_tolerance and is "one" if fabs(1.0-x) <= zero_tolerance. Returns: The 2d transformation xform[0][0] xform[0][1] xform[0][3] xform[1][0] xform[1][1] xform[1][3] if xform is affine and maps the world xy plane to itself, i.e. the z row and z column of the linear part are (0,0,1) and xform[2][3] is zero. Otherwise ON_Xform2d::Nan is returned.

GetAffineElements() [1/3]

void ON_Xform2d::GetAffineElements	(	double &	a,
		double &	b,
		double &	c,
		double &	d,
		double &	tx,
		double &	ty
	)		const

Get the six coefficients used by the traditional 2d drawing APIs.

GetAffineElements() [2/3]

void ON_Xform2d::GetAffineElements

(

double

abcdtxty[6]

)

const

Fills in an array of 6 doubles in (a,b,c,d,tx,ty) order.

GetAffineElements() [3/3]

void ON_Xform2d::GetAffineElements

(

float

abcdtxty[6]

)

const

Fills in an array of 6 floats in (a,b,c,d,tx,ty) order. This is the layout of D2D1_MATRIX_3X2_F.

Hash()

const ON_SHA1_Hash ON_Xform2d::Hash

(

)

const

Inverse()

ON_Xform2d ON_Xform2d::Inverse

(

double *

determinant = nullptr

)

const

Description: If the linear part of this transformation is non-singular, the inverse is returned. Otherwise the pseudo inverse is returned. Parameters: determinant - [out] If not nullptr, the determinant of this transformation is returned here.

Invert()

bool ON_Xform2d::Invert

(

double *

determinant = nullptr

)

Description: If the linear part of this transformation is non-singular, this is replaced with its inverse and true is returned. Otherwise this is replaced with the pseudo inverse and false is returned. Parameters: determinant - [out] If not nullptr, the determinant of the transformation before it was inverted is returned here. Returns: True if this transformation is invertible.

IsIdentity()

bool ON_Xform2d::IsIdentity

(

)

const

Returns: true if the matrix is the identity transformation

IsNan()

bool ON_Xform2d::IsNan

(

)

const

Returns: True if any coefficient in the transformation matrix is a nan.

IsTranslation()

bool ON_Xform2d::IsTranslation

(

)

const

Returns: true if the matrix is a pure translation

IsValid()

bool ON_Xform2d::IsValid

(

)

const

Returns: True if ON_IsValid() is true for every coefficient in the transformation matrix.

IsZeroTransformation()

bool ON_Xform2d::IsZeroTransformation

(

)

const

Returns: true if every stored coefficient is zero.

operator!=()

bool ON_Xform2d::operator!=

(

const ON_Xform2d &

rhs

)

const

Intentionally returns false if any coefficient is a nan.

operator*() [1/3]

ON_2dPoint ON_Xform2d::operator*

(

const ON_2dPoint &

)

const

operators

Note well: The right hand column is the translation. It has an important effect when transforming a Euclidean point and has no effect when transforming a vector.

operator*() [2/3]

ON_2dVector ON_Xform2d::operator*

(

const ON_2dVector &

)

const

Note well: The right hand column is the translation. It has an important effect when transforming a Euclidean point and has no effect when transforming a vector.

operator*() [3/3]

ON_Xform2d ON_Xform2d::operator*

(

const ON_Xform2d &

)

const

The returned transformation applies the right hand side first, i.e. (A*B)*P == A*(B*P).

operator=()

ON_Xform2d& ON_Xform2d::operator= ( const ON_Xform2d &  )

default

operator==()

bool ON_Xform2d::operator==

(

const ON_Xform2d &

rhs

)

const

Intentionally returns false if any coefficient is a nan.

operator[]() [1/2]

double* ON_Xform2d::operator[]

(

int

)

Returns &m_xform[i][0] when 0 <= i < 2 and nullptr otherwise.

operator[]() [2/2]

const double* ON_Xform2d::operator[]

(

int

)

const

RotationTransformation()

static const ON_Xform2d ON_Xform2d::RotationTransformation ( const ON_2dVector &  start_dir, const ON_2dVector &  end_dir, const ON_2dPoint &  rotation_center = ON_2dPoint::Origin  )

static

Description: Calculate the rotation that rotates start_dir to end_dir while fixing rotation_center. Parameters: start_dir - [in] nonzero vector end_dir - [in] nonzero vector rotation_center - [in] the fixed point of the rotation Returns: If the input is valid, a rotation transformation is returned. Otherwise ON_Xform2d::Nan is returned.

RotationTransformationFromAngleRadians()

static const ON_Xform2d ON_Xform2d::RotationTransformationFromAngleRadians ( double  angle_radians, const ON_2dPoint &  rotation_center = ON_2dPoint::Origin  )

static

Description Create a rotation transformation from an angle in radians and a rotation center. A positive angle rotates the x axis towards the y axis (counter-clockwise in a right handed coordinate system). Parameters: angle_radians [in] - An angle in radians rotation_center [in] - The fixed point of the rotation. Returns: If the input is valid, a rotation transformation is returned. Otherwise ON_Xform2d::Nan is returned.

RotationTransformationFromSineAndCosine()

static const ON_Xform2d ON_Xform2d::RotationTransformationFromSineAndCosine ( double  sin_angle, double  cos_angle, const ON_2dPoint &  rotation_center = ON_2dPoint::Origin  )

static

Description Create a rotation transformation from the sine and cosine of an angle and a rotation center. Returns: If the input is valid, a rotation transformation is returned. Otherwise ON_Xform2d::Nan is returned.

ScaleTransformation() [1/2]

static const ON_Xform2d ON_Xform2d::ScaleTransformation ( const ON_2dPoint &  fixed_point, double  scale_factor  )

static

Description: Create a uniform scale transformation with a specified fixed point.

ScaleTransformation() [2/2]

static const ON_Xform2d ON_Xform2d::ScaleTransformation ( const ON_2dPoint &  fixed_point, double  x_scale_factor, double  y_scale_factor  )

static

Description: Create a non-uniform scale transformation with a specified fixed point.

ToXform()

const ON_Xform ON_Xform2d::ToXform

(

)

const

Returns: The 4x4 transformation that applies this transformation to the x and y coordinates and leaves the z coordinate unchanged. m00 m01 0 m02 m10 m11 0 m12 0 0 1 0 0 0 0 1

TranslationTransformation() [1/2]

static const ON_Xform2d ON_Xform2d::TranslationTransformation ( const ON_2dVector &  delta )

static

standard transformations

Right column is (delta.x, delta.y).

TranslationTransformation() [2/2]

static const ON_Xform2d ON_Xform2d::TranslationTransformation ( double  dx, double  dy  )

static

Member Data Documentation

IdentityTransformation

const ON_Xform2d ON_Xform2d::IdentityTransformation

static

ON_Xform2d::IdentityTransformation The linear part is the 2x2 identity and the translation is zero. 1 0 0 0 1 0

m_xform

double ON_Xform2d::m_xform[2][3]

[i][j] = row i, column j. I.e., [0][0] [0][1] [0][2] [1][0] [1][1] [1][2]

Nan

const ON_Xform2d ON_Xform2d::Nan

static

ON_Xform2d::Nan - every stored coefficient is ON_DBL_QNAN.

Unset

const ON_Xform2d ON_Xform2d::Unset

static

ON_Xform2d::Unset - every stored coefficient is ON_UNSET_VALUE.

ZeroTransformation

const ON_Xform2d ON_Xform2d::ZeroTransformation

static

ON_Xform2d::ZeroTransformation Every stored coefficient is zero. 0 0 0 0 0 0