Isis::Affine Class Reference

Affine basis function. More...

#include <Affine.h>

Collaboration diagram for Isis::Affine:

Public Types
typedef TNT::Array2D< double >	AMatrix
	Affine Matrix.

Public Member Functions
	Affine ()
	Constructs an Affine transform.
	Affine (const AMatrix &a)
	Create Affine transform from matrix.
	~Affine ()
	Destroys the Affine object.
void	Solve (const double x[], const double y[], const double xp[], const double yp[], int n)
	Given a set of coordinate pairs (n >= 3), compute the affine transform that best fits the points.
void	Identity ()
	Set the forward and inverse affine transform to the identity.
void	Translate (double tx, double ty)
	Apply a translation to the current affine transform.
void	Rotate (double rot)
	Apply a translation to the current affine transform.
void	Scale (double scaleFactor)
	Apply a scale to the current affine transform.
void	Compute (double x, double y)
	Compute (xp,yp) given (x,y).
double	xp () const
	Returns the computed x'.
double	yp () const
	Returns the computed y'.
void	ComputeInverse (double xp, double yp)
	Compute (x,y) given (xp,yp).
double	x () const
	Returns the computed x.
double	y () const
	Returns the computed y.
std::vector< double >	Coefficients (int var)
	Return the affine coeffients for the entered variable (1 or 2).
std::vector< double >	InverseCoefficients (int var)
	Return the inverse affine coeffients for the entered variable (1 or 2).
AMatrix	Forward () const
	Returns the forward Affine matrix.
AMatrix	Inverse () const
	Returns the inverse Affine matrix.

Static Public Member Functions
static AMatrix	getIdentity ()
	Return an Affine identity matrix.

Detailed Description

Affine basis function.

An affine transform in two-dimensional space is defined as

x' = Ax + By + C
y' = Dx + Ey + F

This routine allows the programmer to define three or more mappings from (x,y) to (x',y') and will solve for A,B,C,D,E,F.

If the above coefficients can be computed then the inverse of the affine transform exists and will be computed such that

x = A'x' + B'y' + C'
y = D'x' + E'y' + F'

Alternatively (or in combination), translations and rotations can be applied to create a transform.

See also

http://www.gnome.org/~mathieu/libart/libart-affine-transformation-matrices.html

Author

2005-03-24 Jeff Anderson

Member Typedef Documentation

AMatrix

typedef TNT::Array2D<double> Isis::Affine::AMatrix

Affine Matrix.

Constructor & Destructor Documentation

Affine() [1/2]

Isis::Affine::Affine

(

)

Constructs an Affine transform.

The default transform is the identity.

References Identity().

Affine() [2/2]

Isis::Affine::Affine

(

const AMatrix &

a

)

Create Affine transform from matrix.

This constructor creates the affine transform from a forward matrix. The input matrix is checked for the proper dimensions (3x3) and is then inverted to complete the inverse functionality.

The input matrix must be invertable or an exception will be thrown!

Parameters

a	Forward affine matrix

~Affine()

Isis::Affine::~Affine

(

)

Destroys the Affine object.

Member Function Documentation

Coefficients()

vector< double > Isis::Affine::Coefficients

(

int

var

)

Return the affine coeffients for the entered variable (1 or 2).

The coefficients are returned in a 3-dimensional vector

Parameters

var	The coefficient vector index (1 or 2)

Returns

vector<double> Vector of coefficients

Compute()

void Isis::Affine::Compute	(	double	x,
		double	y )

Compute (xp,yp) given (x,y).

Use the methods xp() and yp() to obtain the results.

Parameters

x	The transformation x factor
y	The transformation y factor

References x(), and y().

Referenced by Isis::Chip::Load(), and Isis::Chip::SetChipPosition().

ComputeInverse()

void Isis::Affine::ComputeInverse	(	double	xp,
		double	yp )

Compute (x,y) given (xp,yp).

Use the methods x() and y() to obtain the results.

Parameters

xp	The inverse transformation xp factor
yp	The inverse transformation yp factor

References xp(), and yp().

Referenced by Isis::Chip::SetCubePosition().

Forward()

AMatrix Isis::Affine::Forward ( ) const

inline

Returns the forward Affine matrix.

Returns

AMatrix Forward Affine matrix

Referenced by Isis::Chip::Extract().

getIdentity()

Affine::AMatrix Isis::Affine::getIdentity ( )

static

Return an Affine identity matrix.

Returns

Affine::AMatrix The identity matrix

Referenced by Isis::Threshold::hasConverged(), Identity(), Isis::AffineRadio::operator+=(), Rotate(), Scale(), Isis::AffineRadio::Translate(), and Translate().

Identity()

void Isis::Affine::Identity

(

)

Set the forward and inverse affine transform to the identity.

That is, xp = x and yp = y for all (x,y).

References getIdentity().

Referenced by Affine(), Isis::Chip::Load(), Isis::Chip::SetSize(), and Isis::Chip::TackCube().

Inverse()

AMatrix Isis::Affine::Inverse ( ) const

inline

Returns the inverse Affine matrix.

Returns

AMatrix Inverse Affine matrix

InverseCoefficients()

vector< double > Isis::Affine::InverseCoefficients

(

int

var

)

Return the inverse affine coeffients for the entered variable (1 or 2).

The coefficients are returned in a 3-dimensional vector

Parameters

var	The inverse coefficient vector index

Returns

vector<double> Vector of inverse coefficients

Rotate()

void Isis::Affine::Rotate

(

double

angle

)

Apply a translation to the current affine transform.

Parameters

angle

degrees of counterclockwise rotation

References getIdentity(), and Isis::PI.

Referenced by Isis::Chip::Load().

Scale()

void Isis::Affine::Scale

(

double

scaleFactor

)

Apply a scale to the current affine transform.

Parameters

scaleFactor

The scale factor

References getIdentity().

Referenced by Isis::Chip::Load(), and Isis::Chip::Load().

Solve()

void Isis::Affine::Solve	(	const double	x[],
		const double	y[],
		const double	xp[],
		const double	yp[],
		int	n )

Given a set of coordinate pairs (n >= 3), compute the affine transform that best fits the points.

If given exactly three coordinates that are not colinear, the fit will be guarenteed to be exact through the points.

Parameters

x	The transformation x coordinates
y	The transformation y coordinates
xp	The transformation xp coordinates
yp	The transformation yp coordinates
n	The number of coordiante pairs

Exceptions

Isis::iException::Math

- Affine transform not invertible

References x(), xp(), y(), and yp().

Referenced by Isis::Chip::Load().

Translate()

void Isis::Affine::Translate	(	double	tx,
		double	ty )

Apply a translation to the current affine transform.

Parameters

tx	translatation to add to x'
ty	translation to add to y'

References getIdentity().

Referenced by Isis::Chip::Load(), Isis::Chip::Load(), and Isis::Chip::TackCube().

x()

double Isis::Affine::x ( ) const

inline

Returns the computed x.

Returns

double Computed x

Referenced by Compute(), Isis::Chip::SetCubePosition(), and Solve().

xp()

double Isis::Affine::xp ( ) const

inline

Returns the computed x'.

Returns

double Computed x'

Referenced by ComputeInverse(), Isis::Chip::Load(), Isis::Chip::SetChipPosition(), and Solve().

y()

double Isis::Affine::y ( ) const

inline

Returns the computed y.

Returns

double Computed y

Referenced by Compute(), Isis::Chip::SetCubePosition(), and Solve().

yp()

double Isis::Affine::yp ( ) const

inline

Returns the computed y'.

Returns

double Computed y'

Referenced by ComputeInverse(), Isis::Chip::Load(), Isis::Chip::SetChipPosition(), and Solve().

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

• /Users/astamile/ISIS3/isis/src/base/objs/Affine/Affine.h
• /Users/astamile/ISIS3/isis/src/base/objs/Affine/Affine.cpp