Axis Class Reference

A core axis class. More...

#include <axis.h>

Inheritance diagram for Axis:

Public Member Functions
	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...

Static Public Member Functions
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...

Protected Member Functions
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
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 Axis &)
	Overloaded. More...

Detailed Description

A core axis class.

The class includes the two end vertices Axis::a and Axis::b, the normalized direction Axis::axis and the length Axis::length. It is used in several geometric classes such as Cylinder, Capsule, Cone and deformations such as Taper or Twist.

Constructor & Destructor Documentation

Axis()

Axis::Axis ( const Vector &  a, const Vector &  b  )

explicit

Creates an axis given end vertices.

Parameters

a,b	End vertices of the axis.

Member Function Documentation

BoxVector()

Vector Axis::BoxVector ( const Vector &  axis )

inlinestatic

Compute the box vector extent of a unit circle with a given axis.

Parameters

axis	Axis (should be unit).

This function is used in particular in Cylinder::GetBox(), Cone::GetBox(), Capsule::GetBox().

Equation()

Quadric Axis::Equation

(

const Ray &

ray

)

const

Compute the polynomial equation of the Euclidean distance between a ray and the axis.

Parameters

ray

The ray.

GetFrame() [1/2]

Matrix Axis::GetFrame

(

)

const

Compute an orthonormal frame attached to the axis.

See also

Axis::GetFrame(const Vector&)

GetFrame() [2/2]

Matrix Axis::GetFrame ( const Vector &  z )

static

Compute an orthonormal frame attached to the axis.

The axes of the frame are defined as the column vectors of the returned matrix.

Matrix m = Axis::GetFrame(Vector(1.0,2.0,-1.0));
for (int i=0;i<16;i++)
{
Vector p=m*Vector(cos(i/16.0),sin(i/16.0),0.0);
}

Parameters

z	Vector, which should be unit.

See also

Axis::GetFrame()

Normal()

Vector Axis::Normal

(

const Vector &

p

)

const

Compute the normal vector between a point and its projection onto the edge.

Parameters

p

Point.

R() [1/3]

double Axis::R

(

const Axis &

axis

)

const

Compute the squared distance between two axes.

Parameters

axis	The other axis.

R() [2/3]

double Axis::R

(

const Vector &

p

)

const

Compute the squared distance to the segment.

This function is more efficient than Segment::R(const Vector&) const as Axis stores the unit vector.

Parameters

p

Point.

R() [3/3]

double Axis::R	(	const Vector &	p,
		double &	s
	)		const

Compute the squared distance to the axis.

Parameters

p	Point.
s	Signed distance of the projection of argument point p onto the edge.

Radial() [1/2]

Vector2 Axis::Radial ( const Vector &  p ) const

inlineprotected

Compute the radial coordinates of a point.

Parameters

p

Point.

Returns

A vector (x,y) where x is the radial coordinate and y the axial coordinate.

Radial() [2/2]

double Axis::Radial ( const Vector &  p, Vector &  av, Vector &  rv  ) const

inlineprotected

Compute the radial coordinates of a point.

Parameters

p	Point.
av	Returned axis vector.
rv	Returned radial vector.

Returns

Axial coordinate.

Rotate()

void Axis::Rotate

(

const Matrix &

r

)

Rotates an axis.

Only the vertices and the axis vector are modified, whereas the length is perserved.

Parameters

r	Rotation matrix.

Scale() [1/2]

void Axis::Scale

(

const double &

s

)

Uniformly scales an axis.

Parameters

s	Scaling factor.

Scale() [2/2]

void Axis::Scale

(

const Vector &

s

)

Scales an axis.

Parameters

s	Scaling vector.

Symmetric() [1/2]

Sphere Axis::Symmetric

(

const Sphere &

sphere

)

const

Symmetric sphere.

Parameters

sphere

The sphere.

Symmetric() [2/2]

Vector Axis::Symmetric

(

const Vector &

p

)

const

Symmetric point.

Parameters

p	The point.

Translate()

void Axis::Translate

(

const Vector &

t

)

Translates an axis.

Parameters

t	Translation vector.

Friends And Related Function Documentation

operator<<

std::ostream & operator<< ( std::ostream &  s, const Axis &  axis  )

friend

Overloaded.

Parameters

s	Stream.
axis	The axis.