Frame Class Reference

Solid transformations. More...

#include <frame.h>

Inheritance diagram for Frame:

Public Member Functions
	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 Public Member Functions
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 Public Attributes
static const Frame	Id
	Identity.

Protected Attributes
Matrix	r
	Rotation matrix.
Vector	t
	Translation vector.

Friends
std::ostream &	operator<< (std::ostream &, const Frame &)
	Overloaded. More...

Detailed Description

Solid transformations.

The class groups the rotation matrix and the translation vector.

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

The inverse transformation is implicitly characterized as the transposed matrix and the opposite translation vector.

Constructor & Destructor Documentation

Frame() [1/2]

Frame::Frame ( const Matrix &  r = Matrix::Identity, const Vector &  t = Vector::Null  )

explicit

Creates a frame given a rotation matrix and a translation vector.

Parameters

r	Frame matrix.
t	Translation vector.

Frame() [2/2]

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

explicit

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

Parameters

c	Origin.
x,y,z	Orthonormal vectors.

Member Function Documentation

Canonical()

Frame Frame::Canonical ( const Vector &  p, const Vector &  axis  )

static

Given a point and a direction, compute the frame that brings these into a canonical coordinate system.

This is useful for computing the canonical coordinate system of revolution objects such as cylinders or cones.

Parameters

p	Origin of the frame.
axis	Vertical z-axis of the frame.

CircleNormal()

Vector Frame::CircleNormal	(	const double &	theta,
		int	i = 1,
		int	j = 2
	)		const

Compute the coordinates of the normal a point on a circle inside the frame;.

Parameters

theta	Euler angle.
i,j	Integers representing which column vector of the matrix will be used as basis.

CircleVertex()

Vector Frame::CircleVertex	(	const double &	theta,
		int	i = 1,
		int	j = 2
	)		const

Compute the coordinates of a point on a circle inside the frame;.

Parameters

theta	Euler angle.
i,j	Integers representing which column vector of the matrix will be used as basis.

Compose()

void Frame::Compose

(

const Frame &

frame

)

Compose the frame with another one.

Parameters

frame

The frame.

Composed()

Frame Frame::Composed

(

const Frame &

frame

)

const

Compose the frame with another one.

Parameters

frame

The frame.

GetVector()

Vector Frame::GetVector ( int  i ) const

inline

Returns the i-th basis vector of the frame.

This is a convenience function, which is the same as:

Frame frame;
Vector y=frame.R().C(1); // Get rotation matrix, and then column vector.

Parameters

i	Column index.

InverseTransform() [1/2]

Ray Frame::InverseTransform

(

const Ray &

ray

)

const

Transform a ray into the frame coordinate system.

Parameters

ray

The ray.

InverseTransform() [2/2]

Vector Frame::InverseTransform ( const Vector &  p ) const

inline

Transform a point into the frame coordinate system.

Parameters

p

Point.

Orthonormal()

Frame Frame::Orthonormal ( const Vector &  c, const Vector &  n  )

static

Compute a frame given an origin and direction vector.

See also

Vector::Orthonormal(Vector&,Vector&)

Parameters

c	Origin.
n	Direction.

Rotation() [1/3]

Frame Frame::Rotation ( const Vector &  a )

static

Creates a rotation frame.

Parameters

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

Rotation() [2/3]

Frame Frame::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]

Frame Frame::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 (which should be normalized).

SphereNormal()

Vector Frame::SphereNormal	(	const double &	theta,
		const double &	phi,
		int	i = 1,
		int	j = 2,
		int	k = 0
	)		const

Compute the coordinates of the normal of a point on a sphere inside the frame.

Parameters

theta,phi	Polar coordinates.
i,j,k	Integers representing which column vector of the matrix will be used as basis.

SphereVertex()

Vector Frame::SphereVertex	(	const double &	r,
		const double &	theta,
		const double &	phi,
		int	i = 1,
		int	j = 2,
		int	k = 0
	)		const

Compute the coordinates of a point on a sphere inside the frame.

Parameters

r	Radius.
theta,phi	Polar coordinates.
i,j,k	Integers representing which column vector of the matrix will be used as basis.

Transform() [1/2]

Ray Frame::Transform

(

const Ray &

ray

)

const

Transform a ray out of the frame coordinate system.

Parameters

ray

The ray.

Transform() [2/2]

Vector Frame::Transform ( const Vector &  p ) const

inline

Transform a point out of the frame coordinate system.

Parameters

p

Point.

TransformDirection()

Vector Frame::TransformDirection ( const Vector &  n ) const

inline

Transform a direction vector out of the frame coordinate system.

Parameters

n

Vector.

Translation()

Frame Frame::Translation ( const Vector &  t )

static

Creates a translation transformation.

Matrix is identity whereas the translation vector is computed from the argument vector.

Parameters

t	Translation vector.

Friends And Related Function Documentation

operator<<

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

friend

Overloaded.

Parameters

s	Stream.
frame	The frame.