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.
	~Axis ()
	Empty.
void	Rotate (const Matrix &)
	Rotates an axis.
void	Translate (const Vector &)
	Translates an axis.
void	Scale (const double &)
	Uniformly scales an axis.
void	Scale (const Vector &)
	Scales an axis.
Quadric	Equation (const Ray &) const
	Compute the polynomial equation of the Euclidean distance between a ray and the axis.
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.
Sphere	Symmetric (const Sphere &) const
	Symmetric sphere.
Vector	Normal (const Vector &) const
	Compute the normal vector between a point and its projection onto the edge.
double	R (const Vector &) const
	Compute the squared distance to the segment.
double	R (const Axis &) const
	Compute the squared distance between two axes.
double	R (const Vector &, double &) const
	Compute the squared distance to the axis.
Matrix	GetFrame () const
	Compute an orthonormal frame attached to the axis.
Vector2	Radial (const Vector &) const
	Compute the radial coordinates of a point.

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

Static Public Attributes
static const Axis	Z
	Axes from origin, identical to Axis(Vector::Null,Vector::X) ...

Protected Member Functions
double	Radial (const Vector &, Vector &, Vector &) const
	Compute the radial coordinates of a point.

Protected Attributes
Vector	b = Vector::Z
	End vertexes of the axis.
Vector	axis = Vector::Z
	Normalized axis vector.
double	length = 1.0
	Length of the axis.

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

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

inline

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 Symbol Documentation

operator<<

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

friend

Overloaded.

Parameters

s	Stream.
axis	The axis.