FrameScaled2 Class Reference

A transformation defined as the composition of a rotation, a translation and a scale. More...

#include <frame.h>

Inheritance diagram for FrameScaled2:

Public Member Functions
	FrameScaled2 (const Matrix2 &=Matrix2::Identity, const Vector2 &=Vector2::Null, const Vector2 &=Vector2(1.0))
	Creates a frame.
	FrameScaled2 (const Vector2 &, const Vector2 &)
	Creates a frame given the translation and scaling vectors.
	FrameScaled2 (const Vector2 &, const double &)
	Creates a frame given the translation and scale.
	FrameScaled2 (const Frame2 &, const Vector2 &=Vector2(1.0))
	Creates a frame.
	~FrameScaled2 ()
	Empty.
Matrix2	R () const
	Returns the rotation matrix of the frame.
Vector2	T () const
	Returns the translation vector of the frame.
Vector2	S () const
	Get scaling vector from transformation.
FrameScaled2	Inverse () const
	Compute and return the inverse transformation.
void	Rotate (const double &)
	Rotate the shape.
void	Scale (const Vector2 &)
	Scale the shape.
void	Scale (const double &)
	Scale the shape.
void	Translate (const Vector2 &)
	Translate the shape.
Vector2	Transform (const Vector2 &) const
	Transforms a given input point.
Vector2	InverseTransform (const Vector2 &) const
	Inverse transformation of a given input point.
Vector2	TransformDirection (const Vector2 &) const
	Transforms a given input normal.
Vector2	InverseTransformDirection (const Vector2 &) const
	Transforms a given input normal.
void	Compose (const FrameScaled2 &)
	Compose two frames.
FrameScaled2	Composed (const FrameScaled2 &) const
	Compose two frames.

Static Public Member Functions
static FrameScaled2	Scaling (const Vector2 &)
	Create a scaling frame.
static FrameScaled2	Scaling (const double &)
	Create a uniform scaling frame.

Static Public Attributes
static const FrameScaled2	Id
	Identity.

Protected Attributes
Vector2	s
	Scaling vector.
Protected Attributes inherited from Frame2
Matrix2	r
	Rotation matrix.
Vector2	t
	Translation vector.

Friends
std::ostream &	operator<< (std::ostream &s, const FrameScaled2 &frame)
	Overloaded.

Additional Inherited Members
Protected Member Functions inherited from Frame2
	Frame2 (const Matrix2 &=Matrix2::Identity, const Vector2 &=Vector2::Null)
	Creates a frame given a rotation matrix and a translation vector.
	Frame2 (const double &, const Vector2 &=Vector2::Null)
	Creates a frame given a rotation angle and a translation vector.
	Frame2 (const Vector2 &, const Vector2 &)
	Creates a frame given the origin and its orthogonal unit vectors.
	~Frame2 ()
	Empty.
Matrix2	R () const
	Returns the rotation matrix of the frame.
Vector2	T () const
	Returns the translation vector of the frame.
void	Compose (const Frame2 &)
	Compose the frame with another one.
Frame2	Composed (const Frame2 &) const
	Compose the frame with another one.
Frame2	Inverse () const
	Compute the inverse transformation.
Vector2	Transform (const Vector2 &) const
	Transform a point out of the frame coordinate system.
Vector2	InverseTransform (const Vector2 &) const
	Transform a point into the frame coordinate system.
Vector2	TransformDirection (const Vector2 &) const
	Transform a direction vector out of the frame coordinate system.
Vector2	InverseTransformDirection (const Vector2 &) const
	Transform a direction vector into the frame coordinate system.
void	Draw (QGraphicsScene &, const QPen &) const
	Draw a circle.
Static Protected Member Functions inherited from Frame2
static Frame2	Translation (const Vector2 &)
	Creates a translation transformation.
static Frame2	Rotation (const double &)
	Create a rotation frame.
Static Protected Attributes inherited from Frame2
static const Frame2	Id
	Identity.

Detailed Description

A transformation defined as the composition of a rotation, a translation and a scale.

The data-structure groups the rotation matrix, the translation and scaling vectors.

The orientation of the frame should be defined by the appropriate rotation matrix.

In general, a FrameScaled2 is defined by its rotation matrix, and a translation and scaling vector:

FrameScaled2 frame(Matrix2::Rotation(Math::Pi/4.0),Vector2(0.0),Vector2(1.0,1.0));

When there is no rotation, the rotation matrix can be defined using the identity matrix:

FrameScaled2 frame(Matrix2::Identity,Vecto2r(-2.0,4.0),Vector2(2.0,1.0));

It is also possible and simpler to use:

FrameScaled2 frame(Vector2(-2.0,4.0),Vector2(2.0,1.0));

Some static member functions are not implemented and benefit on the conversion constructor. As an example, a translation can be coded as:

FrameScaled2 frame = Frame2::Translation(Vector2(-1.0, 2.0));

Constructor & Destructor Documentation

FrameScaled2() [1/4]

FrameScaled2::FrameScaled2 ( const Matrix2 & r = Matrix2::Identity, const Vector2 & t = Vector2::Null, const Vector2 & s = Vector2(1.0) )

explicit

Creates a frame.

Parameters

r	Rotation matrix.
t	Translation vector.
s	Scaling vector.

FrameScaled2() [2/4]

FrameScaled2::FrameScaled2 ( const Vector2 & t, const Vector2 & s )

explicit

Creates a frame given the translation and scaling vectors.

Parameters

t	Translation.
s	Scaling vector.

FrameScaled2() [3/4]

FrameScaled2::FrameScaled2 ( const Vector2 & t, const double & s )

explicit

Creates a frame given the translation and scale.

Parameters

t	Translation.
s	Uniform scaling factor.

FrameScaled2() [4/4]

FrameScaled2::FrameScaled2	(	const Frame2 &	frame,
		const Vector2 &	s = Vector2(1.0) )

Creates a frame.

Parameters

frame	The frame.
s	Scaling.

Member Function Documentation

Compose()

void FrameScaled2::Compose

(

const FrameScaled2 &

frame

)

Compose two frames.

Parameters

frame

The frame.

Composed()

FrameScaled2 FrameScaled2::Composed

(

const FrameScaled2 &

frame

)

const

Compose two frames.

Parameters

frame

The frame.

InverseTransform()

Vector2 FrameScaled2::InverseTransform

(

const Vector2 &

p

)

const

Inverse transformation of a given input point.

Parameters

p

Point.

InverseTransformDirection()

Vector2 FrameScaled2::InverseTransformDirection

(

const Vector2 &

n

)

const

Transforms a given input normal.

Parameters

n	Normal vector.

Rotate()

void FrameScaled2::Rotate

(

const double &

a

)

Rotate the shape.

Parameters

a	Rotation angle.

Scale() [1/2]

void FrameScaled2::Scale

(

const double &

u

)

Scale the shape.

Parameters

u	Scaling factor.

Scale() [2/2]

void FrameScaled2::Scale

(

const Vector2 &

u

)

Scale the shape.

Parameters

u	Scaling vector.

Scaling() [1/2]

FrameScaled2 FrameScaled2::Scaling ( const double & s )

static

Create a uniform scaling frame.

Parameters

s

Scaling.

Scaling() [2/2]

FrameScaled2 FrameScaled2::Scaling ( const Vector2 & s )

static

Create a scaling frame.

Parameters

s	Scaling vector.

Transform()

Vector2 FrameScaled2::Transform

(

const Vector2 &

p

)

const

Transforms a given input point.

Parameters

p

Point.

TransformDirection()

Vector2 FrameScaled2::TransformDirection

(

const Vector2 &

n

)

const

Transforms a given input normal.

Parameters

n	Normal vector.

Translate()

void FrameScaled2::Translate

(

const Vector2 &

t

)

Translate the shape.

Parameters

t	Translation vector.

Friends And Related Symbol Documentation

operator<<

std::ostream & operator<< ( std::ostream & s, const FrameScaled2 & frame )

friend

Overloaded.

Parameters

s	Stream.
frame	The frame.