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. More...

	FrameScaled (const Vector &)
	Creates a translation frame. More...

	FrameScaled (const Vector &, const Vector &)
	Creates a frame given the translation and scaling vectors. More...

	FrameScaled (const Vector &, const double &)
	Creates a frame given the translation and scale. More...

	FrameScaled (const Vector &, const Vector &, const Vector &, const Vector &)
	Creates a frame given the origin of the frame and orthogonal unit vectors. More...

	FrameScaled (const Frame &, const Vector &=Vector(1.0))
	Creates a frame. More...

	~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. More...

void	ObjectRotate (const Vector &)
	Rotate the shape in object coordinates (does not modify the translation vector). More...

void	Scale (const Vector &)
	Scale the shape. More...

void	Scale (const double &)
	Scale the shape. More...

void	Translate (const Vector &)
	Translate the shape. More...

Matrix4	GetMatrix () const
	Get the homogeneous matrix out of the frame.

Vector	Transform (const Vector &) const
	Transforms a given input point. More...

Vector	InverseTransform (const Vector &) const
	Inverse transformation of a given input point. More...

Vector	TransformDirection (const Vector &) const
	Transforms a given input normal. More...

Vector	InverseTransformDirection (const Vector &) const
	Transforms a given input normal. More...

void	Compose (const FrameScaled &)
	Compose two frames. More...

FrameScaled	Composed (const FrameScaled &) const
	Compose two frames. More...

void	Lerp (const FrameScaled &, const FrameScaled &, const double &)
	Linear interpolation of two frames. More...

Static Public Member Functions
static FrameScaled	Translation (const Vector &)
	Creates a translation transformation. More...

static FrameScaled	Rotation (const Vector &)
	Creates a rotation frame. More...

static FrameScaled	Rotation (const Vector &, const double &)
	Create a rotation frame about an arbitrary axis. More...

static FrameScaled	Rotation (const Vector &, const Vector &)
	Create a frame that rotates a normalized vector into another one. More...

static FrameScaled	Scaling (const Vector &)
	Create a scaling frame. More...

static FrameScaled	Scaling (const double &)
	Create a uniform scaling frame. More...

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 &, const FrameScaled &)
	Overloaded. More...

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. More...

	Frame (const Vector &, const Vector &, const Vector &, const Vector &)
	Creates a frame given the origin and its orthogonal unit vectors. More...

	~Frame ()
	Empty.

Matrix	R () const
	Returns the rotation matrix of the frame.

Vector	T () const
	Returns the translation vector of the frame.

Vector	GetVector (int) const
	Returns the i-th basis vector of the frame. More...

void	Compose (const Frame &)
	Compose the frame with another one. More...

Frame	Composed (const Frame &) const
	Compose the frame with another one. More...

Frame	Inverse () const
	Compute the inverse transformation.

Vector	Transform (const Vector &) const
	Transform a point out of the frame coordinate system. More...

Vector	InverseTransform (const Vector &) const
	Transform a point into the frame coordinate system. More...

Vector	TransformDirection (const Vector &) const
	Transform a direction vector out of the frame coordinate system. More...

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. More...

Ray	InverseTransform (const Ray &) const
	Transform a ray into the frame coordinate system. More...

Vector	CircleVertex (const double &, int=1, int=2) const
	Compute the coordinates of a point on a circle inside the frame;. More...

Vector	CircleNormal (const double &, int=1, int=2) const
	Compute the coordinates of the normal a point on a circle inside the frame;. More...

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. More...

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. More...

Static Protected Member Functions inherited from Frame
static Frame	Translation (const Vector &)
	Creates a translation transformation. More...

static Frame	Rotation (const Vector &)
	Creates a rotation frame. More...

static Frame	Rotation (const Vector &, const double &)
	Create a rotation frame about an arbitrary axis. More...

static Frame	Rotation (const Vector &, const Vector &)
	Create a frame that rotates a normalized vector into another one. More...

static Frame	Canonical (const Vector &, const Vector &)
	Given a point and a direction, compute the frame that brings these into a canonical coordinate system. More...

static Frame	Orthonormal (const Vector &, const Vector &)
	Compute a frame given an origin and direction vector. More...

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));

FrameScaled

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

Definition: frame.h:131

Math::Pi

static const double Pi

π.

Definition: mathematics.h:174

Matrix::Rotation

static Matrix Rotation(const Vector &)

Create a rotation matrix given a vector of angles that specifies the rotation around each world coord...

Definition: matrix.cpp:117

Vector

Vectors in three dimensions.

Definition: evector.h:21

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));

Matrix::Identity

static const Matrix Identity

Identity matrix.

Definition: matrix.h:26

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() [1/6]

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() [2/6]

FrameScaled::FrameScaled ( const Vector & t )

explicit

Creates a translation frame.

Parameters

t	Translation.

◆ FrameScaled() [3/6]

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() [4/6]

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() [5/6]

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() [6/6]

FrameScaled::FrameScaled	(	const Frame &	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.

Returns: Interpolated frame.

◆ 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 Function Documentation

◆ operator<<

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

friend

Overloaded.

Parameters

s	Stream.
frame	The frame.

Public Member Functions

Static Public Member Functions

Static Public Attributes

Protected Attributes

Friends

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ FrameScaled() [1/6]

◆ FrameScaled() [2/6]

◆ FrameScaled() [3/6]

◆ FrameScaled() [4/6]

◆ FrameScaled() [5/6]

◆ FrameScaled() [6/6]

Member Function Documentation

◆ Compose()

◆ Composed()

◆ InverseTransform()

◆ InverseTransformDirection()

◆ Lerp()

◆ ObjectRotate()

◆ Rotate()

◆ Rotation() [1/3]

◆ Rotation() [2/3]

◆ Rotation() [3/3]

◆ Scale() [1/2]

◆ Scale() [2/2]

◆ Scaling() [1/2]

◆ Scaling() [2/2]

◆ Transform()

◆ TransformDirection()

◆ Translate()

◆ Translation()

Friends And Related Function Documentation

◆ operator<<