FrameScaled Class Reference

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

#include <frame.h>

Inheritance diagram for FrameScaled:

Public Member Functions
	FrameScaled (const Matrix &=Matrix::Identity, const Vector &=Vector::Null, const Vector &=Vector(1.0))
	Creates a frame.
	FrameScaled (const Vector &)
	Creates a translation frame.
	FrameScaled (const Vector &, const Vector &)
	Creates a frame given the translation and scaling vectors.
	FrameScaled (const Vector &, const double &)
	Creates a frame given the translation and scale.
	FrameScaled (const Vector &, const Vector &, const Vector &, const Vector &)
	Creates a frame given the origin of the frame and orthogonal unit vectors.
	FrameScaled (const Frame &, const Vector &=Vector(1.0))
	Creates a frame.
	FrameScaled (const Frame2 &, const Vector &=Vector(1.0))
	Creates a frame.
	~FrameScaled ()
	Empty.
Matrix	R () const
	Returns the rotation matrix of the frame.
Vector	T () const
	Returns the translation vector of the frame.
Vector	S () const
	Get scaling vector from transformation.
void	Rotate (const Vector &)
	Rotate the shape.
void	ObjectRotate (const Vector &)
	Rotate the shape in object coordinates (does not modify the translation vector).
void	Scale (const Vector &)
	Scale the shape.
void	Scale (const double &)
	Scale the shape.
void	Translate (const Vector &)
	Translate the shape.
FrameScaled	Inverse () const
	Compute and return the inverse transformation.
Matrix4	GetMatrix4 () const
	Get the homogeneous matrix out of the frame.
Vector	Transform (const Vector &) const
	Transforms a given input point.
Vector	InverseTransform (const Vector &) const
	Inverse transformation of a given input point.
Vector	TransformDirection (const Vector &) const
	Transforms a given input normal.
Vector	InverseTransformDirection (const Vector &) const
	Transforms a given input normal.
void	Compose (const FrameScaled &)
	Compose two frames.
FrameScaled	Composed (const FrameScaled &) const
	Compose two frames.
void	Lerp (const FrameScaled &, const FrameScaled &, const double &)
	Linear interpolation of two frames.

Static Public Member Functions
static FrameScaled	Translation (const Vector &)
	Creates a translation transformation.
static FrameScaled	Rotation (const Vector &)
	Creates a rotation frame.
static FrameScaled	Rotation (const Vector &, const double &)
	Create a rotation frame about an arbitrary axis.
static FrameScaled	Rotation (const Vector &, const Vector &)
	Create a frame that rotates a normalized vector into another one.
static FrameScaled	Scaling (const Vector &)
	Create a scaling frame.
static FrameScaled	Scaling (const double &)
	Create a uniform scaling frame.

Static Public Attributes
static const FrameScaled	Id
	Identity.

Protected Attributes
Vector	s
	Scaling vector.
Protected Attributes inherited from Frame
Matrix	r
	Rotation matrix.
Vector	t
	Translation vector.

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

Additional Inherited Members
Protected Member Functions inherited from Frame
	Frame (const Matrix &=Matrix::Identity, const Vector &=Vector::Null)
	Creates a frame given a rotation matrix and a translation vector.
	Frame (const Vector &, const Vector &, const Vector &, const Vector &)
	Creates a frame given the origin and its orthogonal unit vectors.
	Frame (const Frame2 &)
	Creates a frame from another planar frame.
	~Frame ()
	Empty.
Matrix	R () const
	Returns the rotation matrix of the frame.
Vector	T () const
	Returns the translation vector of the frame.
void	Compose (const Frame &)
	Compose the frame with another one.
Frame	Composed (const Frame &) const
	Compose the frame with another one.
Frame	Inverse () const
	Compute the inverse transformation.
Vector	Transform (const Vector &) const
	Transform a point out of the frame coordinate system.
Vector	InverseTransform (const Vector &) const
	Transform a point into the frame coordinate system.
Vector	TransformDirection (const Vector &) const
	Transform a direction vector out of the frame coordinate system.
Vector	InverseTransformDirection (const Vector &) const
	Transform a direction vector into the frame coordinate system.
Ray	Transform (const Ray &) const
	Transform a ray out of the frame coordinate system.
Ray	InverseTransform (const Ray &) const
	Transform a ray into the frame coordinate system.
Vector	CircleVertex (const double &, int=1, int=2) const
	Compute the coordinates of a point on a circle inside the frame;.
Vector	CircleNormal (const double &, int=1, int=2) const
	Compute the coordinates of the normal a point on a circle inside the frame;.
Vector	SphereVertex (const double &, const double &, const double &, int=1, int=2, int=0) const
	Compute the coordinates of a point on a sphere inside the frame.
Vector	SphereNormal (const double &, const double &, int=1, int=2, int=0) const
	Compute the coordinates of the normal of a point on a sphere inside the frame.
Static Protected Member Functions inherited from Frame
static Frame	Translation (const Vector &)
	Creates a translation transformation.
static Frame	Rotation (const Vector &)
	Creates a rotation frame.
static Frame	Rotation (const Vector &, const double &)
	Create a rotation frame about an arbitrary axis.
static Frame	Rotation (const Vector &, const Vector &)
	Create a frame that rotates a normalized vector into another one.
static Frame	Canonical (const Vector &, const Vector &)
	Given a point and a direction, compute the frame that brings these into a canonical coordinate system.
static Frame	Orthonormal (const Vector &, const Vector &)
	Compute a frame given an origin and direction vector.
Static Protected Attributes inherited from Frame
static const Frame	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 FrameScaled is defined by its rotation matrix, and a translation and scaling vector:

FrameScaled frame(Matrix::Rotation(Vector( Math::Pi/4.0,0.0, 0.0)),Vector(0.0),Vector(1.0,1.0,2.0));

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

FrameScaled frame(Matrix::Identity,Vector(-2.0,4.0,0.0),Vector(2.0,1.0,1.0));

It is also possible and simpler to use:

FrameScaled frame(Vector(-2.0,4.0,0.0),Vector(2.0,1.0,1.0));

Constructor & Destructor Documentation

FrameScaled() [1/7]

FrameScaled::FrameScaled ( const Matrix & r = Matrix::Identity, const Vector & t = Vector::Null, const Vector & s = Vector(1.0) )

explicit

Creates a frame.

Parameters

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

FrameScaled() [2/7]

FrameScaled::FrameScaled ( const Vector & t )

explicit

Creates a translation frame.

Parameters

t	Translation.

FrameScaled() [3/7]

FrameScaled::FrameScaled ( const Vector & t, const Vector & s )

explicit

Creates a frame given the translation and scaling vectors.

Parameters

t	Translation.
s	Scaling vector.

FrameScaled() [4/7]

FrameScaled::FrameScaled ( const Vector & t, const double & s )

explicit

Creates a frame given the translation and scale.

Parameters

t	Translation.
s	Uniform scaling factor.

FrameScaled() [5/7]

FrameScaled::FrameScaled ( const Vector & c, const Vector & x, const Vector & y, const Vector & z )

explicit

Creates a frame given the origin of the frame and orthogonal unit vectors.

Parameters

c	Origin.
x,y,z	Orthogonal unit vectors.

FrameScaled() [6/7]

FrameScaled::FrameScaled	(	const Frame &	frame,
		const Vector &	s = Vector(1.0) )

Creates a frame.

Parameters

frame	The frame.
s	Scaling.

FrameScaled() [7/7]

FrameScaled::FrameScaled	(	const Frame2 &	frame,
		const Vector &	s = Vector(1.0) )

Creates a frame.

Parameters

frame	The frame.
s	Scaling.

Member Function Documentation

Compose()

void FrameScaled::Compose

(

const FrameScaled &

frame

)

Compose two frames.

Parameters

frame

The frame.

Composed()

FrameScaled FrameScaled::Composed

(

const FrameScaled &

frame

)

const

Compose two frames.

Parameters

frame

The frame.

InverseTransform()

Vector FrameScaled::InverseTransform

(

const Vector &

p

)

const

Inverse transformation of a given input point.

Parameters

p

Point.

InverseTransformDirection()

Vector FrameScaled::InverseTransformDirection

(

const Vector &

n

)

const

Transforms a given input normal.

Parameters

n	Normal vector.

Lerp()

void FrameScaled::Lerp	(	const FrameScaled &	a,
		const FrameScaled &	b,
		const double &	alpha )

Linear interpolation of two frames.

Parameters

a,b	The two frames.
alpha	Interpolation parameter.

ObjectRotate()

void FrameScaled::ObjectRotate

(

const Vector &

r

)

Rotate the shape in object coordinates (does not modify the translation vector).

Parameters

r	Rotation vector representing the rotation angles around x, y and z axes.

Rotate()

void FrameScaled::Rotate

(

const Vector &

r

)

Rotate the shape.

Parameters

r	Rotation vector representing the rotation angles around x, y and z axes.

Rotation() [1/3]

FrameScaled FrameScaled::Rotation ( const Vector & a )

static

Creates a rotation frame.

Parameters

a	A vector of angles (expressed in radians) that defines the rotation around x-y-z axes.

Rotation() [2/3]

FrameScaled FrameScaled::Rotation ( const Vector & axis, const double & angle )

static

Create a rotation frame about an arbitrary axis.

Parameters

axis	Axis.
angle	Angle (should be in radian).

Rotation() [3/3]

FrameScaled FrameScaled::Rotation ( const Vector & a, const Vector & b )

static

Create a frame that rotates a normalized vector into another one.

Parameters

a,b	Initial and final vectors (should be normalized).

Scale() [1/2]

void FrameScaled::Scale

(

const double &

u

)

Scale the shape.

Parameters

u	Scaling factor.

Scale() [2/2]

void FrameScaled::Scale

(

const Vector &

u

)

Scale the shape.

Parameters

u	Scaling vector.

Scaling() [1/2]

FrameScaled FrameScaled::Scaling ( const double & s )

static

Create a uniform scaling frame.

Parameters

s

Scaling.

Scaling() [2/2]

FrameScaled FrameScaled::Scaling ( const Vector & s )

static

Create a scaling frame.

Parameters

s	Scaling vector.

Transform()

Vector FrameScaled::Transform

(

const Vector &

p

)

const

Transforms a given input point.

Parameters

p

Point.

TransformDirection()

Vector FrameScaled::TransformDirection

(

const Vector &

n

)

const

Transforms a given input normal.

Parameters

n	Normal vector.

Translate()

void FrameScaled::Translate

(

const Vector &

t

)

Translate the shape.

Parameters

t	Translation vector.

Translation()

FrameScaled FrameScaled::Translation ( const Vector & t )

static

Creates a translation transformation.

Parameters

t	Translation vector.

Friends And Related Symbol Documentation

operator<<

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

friend

Overloaded.

Parameters

s	Stream.
frame	The frame.