2D transform, which can be up to a projective transformation. More...

#include <vimt_transform_2d.h>

Public Types
enum	Form { Identity, Translation, ZoomOnly, RigidBody, Similarity, Affine, Projective, Reflection }
	Defines form of transformation. More...
Public Member Functions
	vimt_transform_2d ()
bool	is_identity () const
Form	form () const
vnl_matrix< double >	matrix () const
void	matrix (vnl_matrix< double > &) const
vimt_transform_2d &	set_matrix (const vnl_matrix< double > &M)
	Define the transform in terms of a 3x3 homogeneous matrix.
void	params (vnl_vector< double > &v) const
	Fills v with parameters.
void	params_of (vnl_vector< double > &v, Form) const
	Fills v with parameters of transform of type Form.
vimt_transform_2d &	set (const vnl_vector< double > &v, Form)
	Sets transform using v (converse of params(v)).
vimt_transform_2d &	set_identity ()
	Set to identity transformation.
vimt_transform_2d &	set_zoom_only (double s_x, double s_y, double t_x, double t_y)
	Sets the transformation to be separable affine.
vimt_transform_2d &	set_zoom_only (double s, double t_x, double t_y)
	Sets the transformation to be a zoom.
vimt_transform_2d &	set_zoom_only (double s_x, double s_y)
	Sets the transformation to be separable affine.
vimt_transform_2d &	set_zoom_only (double s)
	Sets the transformation to be a zoom.
vimt_transform_2d &	set_translation (double t_x, double t_y)
	Sets the transformation to be a translation.
vimt_transform_2d &	set_rigid_body (double theta, double t_x, double t_y)
	Sets the transformation to rotation then translation.
vimt_transform_2d &	set_similarity (double s, double theta, double t_x, double t_y)
	Sets the transformation to apply scaling, rotation then translation.
vimt_transform_2d &	set_similarity (const vgl_point_2d< double > &dx, const vgl_point_2d< double > &t)
	Sets Euclidean transformation.
vimt_transform_2d &	set_similarity (const vgl_vector_2d< double > &dx, const vgl_point_2d< double > &t)
	Sets Euclidean transformation.
vimt_transform_2d &	set_reflection (const vgl_point_2d< double > &m1, const vgl_point_2d< double > &m2)
	reflect about a line though the points m1, and m2.
vimt_transform_2d &	set_affine (const vnl_matrix< double > &)
	Sets to be 2D affine transformation using 2x3 matrix.
vimt_transform_2d &	set_affine (const vgl_point_2d< double > &p, const vgl_vector_2d< double > &u, const vgl_vector_2d< double > &v)
	Sets to be 2D affine transformation T(x,y)=p+x.u+y.v.
vimt_transform_2d &	set_projective (const vnl_matrix< double > &)
	Sets to be 2D projective transformation.
vgl_point_2d< double >	origin () const
	Returns the coordinates of the origin.
vimt_transform_2d &	set_origin (const vgl_point_2d< double > &)
	Modifies the transformation so that operator()(vgl_point_2d<double> (0,0)) == p.
vgl_point_2d< double >	operator() (double x, double y) const
	Applies transformation to (x,y).
vgl_point_2d< double >	operator() (const vgl_point_2d< double > &p) const
	Returns transformation applied to point p.
vimt_transform_2d	inverse () const
	Calculates inverse of this transformation.
vgl_vector_2d< double >	delta (const vgl_point_2d< double > &p, const vgl_vector_2d< double > &dp) const
	Returns change in transformed point when original point moved by dp.
short	version_no () const
void	print_summary (vcl_ostream &) const
void	b_write (vsl_b_ostream &bfs) const
void	b_read (vsl_b_istream &bfs)
bool	operator== (const vimt_transform_2d &t) const
	True if t is the same as this.
vimt_transform_2d &	simplify (double tol=1e-10)
	Reduce to the simplest form possible.
Private Member Functions
void	calcInverse () const
void	setCheck (int n1, int n2, const char *str) const
Private Attributes
double	xx_
double	xy_
double	xt_
double	yx_
double	yy_
double	yt_
double	tx_
double	ty_
double	tt_
Form	form_
double	xx2_
double	xy2_
double	xt2_
double	yx2_
double	yy2_
double	yt2_
double	tx2_
double	ty2_
double	tt2_
bool	inv_uptodate_
Friends
vimt_transform_2d	operator* (const vimt_transform_2d &, const vimt_transform_2d &)
	Transform composition (L*R)(x) = L(R(x)).

Detailed Description

2D transform, which can be up to a projective transformation.

In order of complexity the transform can be

   Identity     x->x, y->y
   Translation  x->x + tx, y->y + ty
   ZoomOnly     x->sx.x + tx, y->sy.y + ty
   RigidBody    (Translate + rotation)
   Euclidean    (Translation + rotation + scale)
   Affine
   Projective

NOTES: The transformation can be represented by a 3x3 matrix mapping homogeneous co-ordinates about.

   ( xx xy xt )
   ( yx yy yt )
   ( tx ty tt )

For efficiency the elements are stored explicitly, rather than in a vnl_matrix<double>, to avoid lots of copying of matrices with all the attendant memory allocation.

Example:

 vimt_transform_2d T1;
 vimt_transform_2d T2;
 T1.set_zoom(scale,translation.x(),translation.y());
 T2.set_similarity(scale2,theta,translation2.x(),translation2.y());

 vimt_transform_2d T3 = T2 * T1; // T1 followed by T2

 vgl_point_2d<double>  p(10,10);
 vgl_point_2d<double>  p_new = T3(p);

 vimt_transform_2d T_inverse = T3.inverse();

Definition at line 59 of file vimt_transform_2d.h.

Member Enumeration Documentation

enum vimt_transform_2d::Form

Defines form of transformation.

Enumerator:

Identity
Translation
ZoomOnly
RigidBody
Similarity
Affine
Projective
Reflection

Definition at line 63 of file vimt_transform_2d.h.

Constructor & Destructor Documentation

vimt_transform_2d::vimt_transform_2d ( ) [inline]

Definition at line 72 of file vimt_transform_2d.h.

Member Function Documentation

void vimt_transform_2d::b_read ( vsl_b_istream & bfs )

Definition at line 806 of file vimt_transform_2d.cxx.

void vimt_transform_2d::b_write ( vsl_b_ostream & bfs ) const

Definition at line 797 of file vimt_transform_2d.cxx.

void vimt_transform_2d::calcInverse ( ) const [private]

Definition at line 518 of file vimt_transform_2d.cxx.

vgl_vector_2d< double > vimt_transform_2d::delta	(	const vgl_point_2d< double > &	p,
		const vgl_vector_2d< double > &	dp
	)		const

Returns change in transformed point when original point moved by dp.

Point dp: Movement from point Returns: T(p+dp)-T(p)

Definition at line 473 of file vimt_transform_2d.cxx.

Form vimt_transform_2d::form ( ) const [inline]

Definition at line 80 of file vimt_transform_2d.h.

vimt_transform_2d vimt_transform_2d::inverse ( ) const

Calculates inverse of this transformation.

Definition at line 498 of file vimt_transform_2d.cxx.

bool vimt_transform_2d::is_identity ( ) const [inline]

Definition at line 79 of file vimt_transform_2d.h.

vnl_matrix< double > vimt_transform_2d::matrix ( ) const

Definition at line 19 of file vimt_transform_2d.cxx.

void vimt_transform_2d::matrix ( vnl_matrix< double > & M ) const

Definition at line 26 of file vimt_transform_2d.cxx.

vgl_point_2d< double > vimt_transform_2d::operator()	(	double	x,
		double	y
	)		const

Applies transformation to (x,y).

Definition at line 445 of file vimt_transform_2d.cxx.

vgl_point_2d<double> vimt_transform_2d::operator() ( const vgl_point_2d< double > & p ) const [inline]

Returns transformation applied to point p.

Definition at line 172 of file vimt_transform_2d.h.

bool vimt_transform_2d::operator== ( const vimt_transform_2d & t ) const

True if t is the same as this.

Definition at line 578 of file vimt_transform_2d.cxx.

vgl_point_2d<double> vimt_transform_2d::origin ( ) const [inline]

Returns the coordinates of the origin.

I.e. operator()(vgl_point_2d<double> (0,0))

Definition at line 161 of file vimt_transform_2d.h.

void vimt_transform_2d::params ( vnl_vector< double > & v ) const [inline]

Fills v with parameters.

Definition at line 91 of file vimt_transform_2d.h.

void vimt_transform_2d::params_of	(	vnl_vector< double > &	v,
		Form	form
	)		const

Fills v with parameters of transform of type Form.

Definition at line 54 of file vimt_transform_2d.cxx.

void vimt_transform_2d::print_summary ( vcl_ostream & o ) const

Definition at line 726 of file vimt_transform_2d.cxx.

vimt_transform_2d & vimt_transform_2d::set	(	const vnl_vector< double > &	v,
		Form	form
	)

Sets transform using v (converse of params(v)).

Definition at line 189 of file vimt_transform_2d.cxx.

vimt_transform_2d & vimt_transform_2d::set_affine ( const vnl_matrix< double > & M23 )

Sets to be 2D affine transformation using 2x3 matrix.

Definition at line 387 of file vimt_transform_2d.cxx.

vimt_transform_2d & vimt_transform_2d::set_affine	(	const vgl_point_2d< double > &	p,
		const vgl_vector_2d< double > &	u,
		const vgl_vector_2d< double > &	v
	)

Sets to be 2D affine transformation T(x,y)=p+x.u+y.v.

Definition at line 413 of file vimt_transform_2d.cxx.

vimt_transform_2d & vimt_transform_2d::set_identity ( )

Set to identity transformation.

Definition at line 246 of file vimt_transform_2d.cxx.

vimt_transform_2d & vimt_transform_2d::set_matrix ( const vnl_matrix< double > & M )

Define the transform in terms of a 3x3 homogeneous matrix.

Parameters:

M	3x3 homogeneous matrix defining the transform.

Note:: Client must ensure that M is a valid representation of an affine (or simpler) transform.; The form will be set to Affine - call simplify() if you need the simplest form.

Definition at line 37 of file vimt_transform_2d.cxx.

vimt_transform_2d & vimt_transform_2d::set_origin ( const vgl_point_2d< double > & p )

Modifies the transformation so that operator()(vgl_point_2d<double> (0,0)) == p.

The rest of the transformation is unaffected. If the transformation was previously the identity, it becomes a translation.

Definition at line 274 of file vimt_transform_2d.cxx.

vimt_transform_2d & vimt_transform_2d::set_projective ( const vnl_matrix< double > & M33 )

Sets to be 2D projective transformation.

Definition at line 428 of file vimt_transform_2d.cxx.

vimt_transform_2d & vimt_transform_2d::set_reflection	(	const vgl_point_2d< double > &	m1,
		const vgl_point_2d< double > &	m2
	)

reflect about a line though the points m1, and m2.

Definition at line 294 of file vimt_transform_2d.cxx.

vimt_transform_2d & vimt_transform_2d::set_rigid_body	(	double	theta,
		double	t_x,
		double	t_y
	)

Sets the transformation to rotation then translation.

theta: rotation t_x: Translation in x t_y: Translation in y

Definition at line 328 of file vimt_transform_2d.cxx.

vimt_transform_2d & vimt_transform_2d::set_similarity	(	double	s,
		double	theta,
		double	t_x,
		double	t_y
	)

Sets the transformation to apply scaling, rotation then translation.

s: Scaling theta: rotation t_x: Translation in x t_y: Translation in y

Definition at line 345 of file vimt_transform_2d.cxx.

vimt_transform_2d & vimt_transform_2d::set_similarity	(	const vgl_point_2d< double > &	dx,
		const vgl_point_2d< double > &	t
	)

Sets Euclidean transformation.

Parameters:

dx	Rotation and scaling of x axis
t	Translation

Definition at line 363 of file vimt_transform_2d.cxx.

vimt_transform_2d & vimt_transform_2d::set_similarity	(	const vgl_vector_2d< double > &	dx,
		const vgl_point_2d< double > &	t
	)

Sets Euclidean transformation.

Parameters:

dx	Rotation and scaling of x axis
t	Translation

Definition at line 375 of file vimt_transform_2d.cxx.

vimt_transform_2d & vimt_transform_2d::set_translation	(	double	t_x,
		double	t_y
	)

Sets the transformation to be a translation.

t_x: Translation in x t_y: Translation in y

Definition at line 256 of file vimt_transform_2d.cxx.

vimt_transform_2d & vimt_transform_2d::set_zoom_only	(	double	s_x,
		double	s_y,
		double	t_x,
		double	t_y
	)

Sets the transformation to be separable affine.

x' = s_x.x + t_x, y' = s_y.y + t_y s_x: Scaling in x s_y: Scaling in y t_x: Translation in x t_y: Translation in y

Definition at line 283 of file vimt_transform_2d.cxx.

vimt_transform_2d& vimt_transform_2d::set_zoom_only	(	double	s,
		double	t_x,
		double	t_y
	)		`[inline]`

Sets the transformation to be a zoom.

x' = s.x + t_x, y' = s.y + t_y s: Scaling t_x: Translation in x t_y: Translation in y

Definition at line 110 of file vimt_transform_2d.h.

vimt_transform_2d& vimt_transform_2d::set_zoom_only	(	double	s_x,
		double	s_y
	)		`[inline]`

Sets the transformation to be separable affine.

x' = s_x.x + xt_, y' = s_y.y + yt_ s_x: Scaling in x s_y: Scaling in y Translation in x and y kept as it was

Definition at line 116 of file vimt_transform_2d.h.

vimt_transform_2d& vimt_transform_2d::set_zoom_only ( double s ) [inline]

Sets the transformation to be a zoom.

x' = s.x + xt_, y' = s.y + yt_ s: Scaling Translation in x and y kept as it was

Definition at line 121 of file vimt_transform_2d.h.

void vimt_transform_2d::setCheck	(	int	n1,
		int	n2,
		const char *	str
	)		const `[private]`

Definition at line 181 of file vimt_transform_2d.cxx.

vimt_transform_2d & vimt_transform_2d::simplify ( double tol = 1e-10 )

Reduce to the simplest form possible.

Definition at line 108 of file vimt_transform_2d.cxx.

short vimt_transform_2d::version_no ( ) const

Definition at line 794 of file vimt_transform_2d.cxx.

Friends And Related Function Documentation

vimt_transform_2d operator*	(	const vimt_transform_2d &	L,
		const vimt_transform_2d &	R
	)		`[friend]`

Transform composition (L*R)(x) = L(R(x)).

Definition at line 593 of file vimt_transform_2d.cxx.

Member Data Documentation

Form vimt_transform_2d::form_ [private]

Definition at line 198 of file vimt_transform_2d.h.

bool vimt_transform_2d::inv_uptodate_ [mutable, private]

Definition at line 202 of file vimt_transform_2d.h.

double vimt_transform_2d::tt2_ [mutable, private]

Definition at line 201 of file vimt_transform_2d.h.

double vimt_transform_2d::tt_ [private]

Definition at line 197 of file vimt_transform_2d.h.

double vimt_transform_2d::tx2_ [mutable, private]

Definition at line 201 of file vimt_transform_2d.h.

double vimt_transform_2d::tx_ [private]

Definition at line 197 of file vimt_transform_2d.h.

double vimt_transform_2d::ty2_ [mutable, private]

Definition at line 201 of file vimt_transform_2d.h.

double vimt_transform_2d::ty_ [private]

Definition at line 197 of file vimt_transform_2d.h.

double vimt_transform_2d::xt2_ [mutable, private]

Definition at line 201 of file vimt_transform_2d.h.

double vimt_transform_2d::xt_ [private]

Definition at line 197 of file vimt_transform_2d.h.

double vimt_transform_2d::xx2_ [mutable, private]

Definition at line 201 of file vimt_transform_2d.h.

double vimt_transform_2d::xx_ [private]

Definition at line 197 of file vimt_transform_2d.h.

double vimt_transform_2d::xy2_ [mutable, private]

Definition at line 201 of file vimt_transform_2d.h.

double vimt_transform_2d::xy_ [private]

Definition at line 197 of file vimt_transform_2d.h.

double vimt_transform_2d::yt2_ [mutable, private]

Definition at line 201 of file vimt_transform_2d.h.

double vimt_transform_2d::yt_ [private]

Definition at line 197 of file vimt_transform_2d.h.

double vimt_transform_2d::yx2_ [mutable, private]

Definition at line 201 of file vimt_transform_2d.h.

double vimt_transform_2d::yx_ [private]

Definition at line 197 of file vimt_transform_2d.h.

double vimt_transform_2d::yy2_ [mutable, private]

Definition at line 201 of file vimt_transform_2d.h.

double vimt_transform_2d::yy_ [private]

Definition at line 197 of file vimt_transform_2d.h.

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

contrib/mul/vimt/vimt_transform_2d.h
contrib/mul/vimt/vimt_transform_2d.cxx

Public Types

Public Member Functions

Private Member Functions

Private Attributes

Friends

Detailed Description

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation