Twist Class Reference

The twist deformation. More...

#include <twist.h>

Inheritance diagram for Twist:

Public Member Functions
	Twist (const double &, const double &)
	Creates a twisting operator. More...
	Twist (const Vector &, const Vector &, const double &)
	Creates a twisting operator. More...
	~Twist ()
	Empty.
Cylinder	GetCylinder (const Box &) const
	Compute the bounding cylinder of a box that would be deformed by the twist. More...
Box	GetBox (const Box &) const
	Compute the bounding box of a box that would be deformed by the twist. More...
Vector	Transform (const Vector &) const
	Transforms a point. More...
Vector	InverseTransform (const Vector &) const
	Transforms a point. More...
Matrix	Jacobian (const Vector &) const
	Compute the Jacobian of the transformation. More...
double	K (const double &) const
	Compute the Lipschitz constant using the maximum distance to the axis.
Public Member Functions inherited from Axis
	Axis ()
	Empty.
	Axis (const Vector &, const Vector &)
	Creates an axis given end vertices. More...
	~Axis ()
	Empty.
void	Rotate (const Matrix &)
	Rotates an axis. More...
void	Translate (const Vector &)
	Translates an axis. More...
void	Scale (const double &)
	Uniformly scales an axis. More...
void	Scale (const Vector &)
	Scales an axis. More...
Quadric	Equation (const Ray &) const
	Compute the polynomial equation of the Euclidean distance between a ray and the axis. More...
Vector	Vertex (int) const
	Return one of the end vertexes of the axis.
Vector	Point (const double &) const
	Compute a point on the axis.
Vector	GetAxis () const
	Returns the normalized axis vector.
double	Length () const
	Return the axis length.
Vector	Symmetric (const Vector &) const
	Symmetric point. More...
Sphere	Symmetric (const Sphere &) const
	Symmetric sphere. More...
Vector	Normal (const Vector &) const
	Compute the normal vector between a point and its projection onto the edge. More...
double	R (const Vector &) const
	Compute the squared distance to the segment. More...
double	R (const Axis &) const
	Compute the squared distance between two axes. More...
double	R (const Vector &, double &) const
	Compute the squared distance to the axis. More...
Matrix	GetFrame () const
	Compute an orthonormal frame attached to the axis. More...

Protected Member Functions
Circle	GetCircle (const Vector &) const
	Compute the circle obtained by rotating the point around the axis. More...
Protected Member Functions inherited from Axis
double	Radial (const Vector &, Vector &, Vector &) const
	Compute the radial coordinates of a point. More...
Vector2	Radial (const Vector &) const
	Compute the radial coordinates of a point. More...

Protected Attributes
double	omega
	Angular velocity.
double	angle
	Twisting angle between end vertices.
Vector	y
	Orthonormal vectors.
Protected Attributes inherited from Axis
Vector	b = Vector::Z
	End vertices of the axis.
Vector	axis = Vector::Z
	Normalized axis vector.
double	length = 1.0
	Length of the axis.

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

Additional Inherited Members
Static Public Member Functions inherited from Axis
static Matrix	GetFrame (const Vector &)
	Compute an orthonormal frame attached to the axis. More...
static Vector	BoxVector (const Vector &)
	Compute the box vector extent of a unit circle with a given axis. More...

Detailed Description

The twist deformation.

Example of how to code a twist:

Twist twist(Vector(0,0,0),Vector(1,1,1),Math::Pi);

Constructor & Destructor Documentation

Twist() [1/2]

Twist::Twist ( const double &  length, const double &  angle  )

explicit

Creates a twisting operator.

Parameters

length	Length of the vertial twisting axis.
angle	The twisting angle.

Twist() [2/2]

Twist::Twist ( const Vector &  a, const Vector &  b, const double &  angle  )

explicit

Creates a twisting operator.

Parameters

a,b	End vertices of the twisting axis.
angle	The twisting angle between end vertices.

Member Function Documentation

GetBox()

Box Twist::GetBox

(

const Box &

box

)

const

Compute the bounding box of a box that would be deformed by the twist.

This function is slightly more accurate than computing the bounding cylinder, and then taking its bouding box.

Twist t;
Box b = t.GetBox(Box::Unit); 
Box c = t.GetCylinder().GetBox(Box::Unit); // %Box c should be embedding box a

See also

GetCylinder(const Box&) const

Parameters

box

The box.

GetCircle()

Circle Twist::GetCircle ( const Vector &  p ) const

protected

Compute the circle obtained by rotating the point around the axis.

Parameters

p

Point.

GetCylinder()

Cylinder Twist::GetCylinder

(

const Box &

box

)

const

Compute the bounding cylinder of a box that would be deformed by the twist.

Parameters

box

The box.

InverseTransform()

Vector Twist::InverseTransform

(

const Vector &

p

)

const

Transforms a point.

Parameters

p	Argument point.

Jacobian()

Matrix Twist::Jacobian

(

const Vector &

p

)

const

Compute the Jacobian of the transformation.

This function is needed to implement the computation of the gradient of the field function. The argument point is assumed to be in the frame of the twist.

Parameters

p	Point (in the twisting coordinate system).

Transform()

Vector Twist::Transform

(

const Vector &

p

)

const

Transforms a point.

Parameters

p	Argument point.