Segment Class Reference

A segment defined by its end vertices. More...

#include <segment.h>

Inheritance diagram for Segment:

Public Member Functions
	Segment ()
	Empty.
	Segment (const Vector &, const Vector &)
	Creates a segment given its end vertices. More...
	~Segment ()
	Empty.
void	Rotate (const Matrix &)
	Rotates a segment. More...
void	Translate (const Vector &)
	Translates a segment. More...
void	Scale (const double &)
	Uniformly scales a segment. More...
Segment	Translated (const Vector &) const
	Translates a segment. More...
Segment	Scaled (const Vector &) const
	Scales a segment. More...
Segment	Scaled (const double &) const
	Uniformly scales a segment. More...
Segment	Rotated (const Matrix &) const
	Rotates a segment. More...
Segment	InverseTransformed (const Frame &) const
	Inverse transformation. More...
Quadric	Equation (const Ray &) const
	Computes the polynomial equation of the Euclidean distance between a ray and the line corresponding to the segment. More...
Vector	Vertex (int) const
	Return one of the end vertex of the axis.
Vector &	Vertex (int)
	Return one of the end vertex of the axis.
Vector	VertexAt (const double &) const
	Compute a point on the segment. More...
Vector	Center () const
	Compute the center of the segment.
bool	Intersect (const Box &) const
	Check if a segment intersects a box. More...
Vector	GetAxis () const
	Returns the normalized axis vector.
Box	GetBox () const
	Compute the bounding box of the segment.
double	Length () const
	Return axis length.
double	R (const Vector &) const
	Compute the squared distance to the segment. More...
double	R (const Vector &, double &) const
	Compute the squared distance to the segment. More...
double	R (const Segment &) const
	Compute the squared distance between two segments. More...
Vector	Normal (const Vector &) const
	Compute the normal vector between a point and its projection onto the segment. More...
bool	Equal (const Segment &, const double &) const
	Test if two segments are almost equal. More...

Static Public Member Functions
static Quadric	EdgeEquation (const Ray &, const Vector &, const Vector &, const Vector &)
	Compute the polynomial equation of the distance function along the ray. More...
static Vector	Intersect (const Vector &, const Vector &, const double, const double, double=0.0)
	Compute the intersection between the line f(x)=y and a line such that f(a)=va and f(b)=vb, on the segment ab. More...

Protected Attributes
Vector	b = Vector::Z
	End vertices of the segment.

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

Detailed Description

A segment defined by its end vertices.

Axis inherits Segment and extends the structure by storing the normalized axis vector and its length. Lines are implemented by the class Line.

How do I compute the intersection of two segments?
In general, segments do not intersect, use the distance function.

Segment a(Vector(0,1,-1),Vector(-1,0,3));
Segment b(Vector(0,1,-1),Vector(-1,0,3));
double r=a.R(b);

Alternatively, it is possible to compute the intersection between two segments in the plane, using Segment2::Intersect(const Segment2&).

Constructor & Destructor Documentation

Segment()

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

inlineexplicit

Creates a segment given its end vertices.

Parameters

a,b	End vertices of the segment.

Member Function Documentation

EdgeEquation()

Quadric Segment::EdgeEquation ( const Ray &  ray, const Vector &  a, const Vector &  , const Vector &  axis  )

static

Compute the polynomial equation of the distance function along the ray.

Parameters

ray	The ray.
a	First vertex of the segment.
axis	Axis.

Equal()

bool Segment::Equal	(	const Segment &	s,
		const double &	epsilon
	)		const

Test if two segments are almost equal.

This function computes the distance between the end vertices of the two argument segments. If the norm infinity of this difference is greater than the epsilon threshold value, then the segments are different.

Parameters

s	Other segment.
epsilon	Precision. This is a convenience function which is the same as: Segment a,b; // Two segments double e; // Epsilon value bool t=Vector::Equal(a.Vertex(0), b.Vertex(0), e) && Vector::Equal(a.Vertex(1), b.Vertex(1), e);

Equation()

Quadric Segment::Equation

(

const Ray &

ray

)

const

Computes the polynomial equation of the Euclidean distance between a ray and the line corresponding to the segment.

Parameters

ray

The ray.

Intersect() [1/2]

bool Segment::Intersect

(

const Box &

box

)

const

Check if a segment intersects a box.

Parameters

box

The box.

Intersect() [2/2]

Vector Segment::Intersect ( const Vector &  a, const Vector &  b, const double  va, const double  vb, double  y = 0.0  )

static

Compute the intersection between the line f(x)=y and a line such that f(a)=va and f(b)=vb, on the segment ab.

Parameters

a,b	Points.
va,vb	Values.
y	Threshold.

InverseTransformed()

Segment Segment::InverseTransformed

(

const Frame &

f

)

const

Inverse transformation.

Parameters

f	The frame.

Normal()

Vector Segment::Normal

(

const Vector &

p

)

const

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

Parameters

p

Point.

R() [1/3]

double Segment::R

(

const Segment &

segment

)

const

Compute the squared distance between two segments.

Parameters

segment

The segment.

R() [2/3]

double Segment::R

(

const Vector &

p

)

const

Compute the squared distance to the segment.

Parameters

p

Point.

R() [3/3]

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

Compute the squared distance to the segment.

Parameters

p	Point.
s	Linear coefficient corresponding to the projection of argument point p onto the segment.

Rotate()

void Segment::Rotate

(

const Matrix &

r

)

Rotates a segment.

Only the vertices and the axis are modified, the length is preserved.

Parameters

r	Rotation matrix.

Rotated()

Segment Segment::Rotated

(

const Matrix &

r

)

const

Rotates a segment.

Parameters

r	Rotation matrix.

Scale()

void Segment::Scale

(

const double &

s

)

Uniformly scales a segment.

Parameters

s	Scaling factor.

Scaled() [1/2]

Segment Segment::Scaled

(

const double &

s

)

const

Uniformly scales a segment.

Parameters

s	Scaling factor.

Scaled() [2/2]

Segment Segment::Scaled

(

const Vector &

s

)

const

Scales a segment.

Parameters

s	Scaling vector.

Translate()

void Segment::Translate

(

const Vector &

t

)

Translates a segment.

Parameters

t	Translation vector.

Translated()

Segment Segment::Translated

(

const Vector &

t

)

const

Translates a segment.

Parameters

t	Translation vector.

VertexAt()

Vector Segment::VertexAt ( const double &  t ) const

inline

Compute a point on the segment.

Parameters

t	Interpolation parameter.

Friends And Related Function Documentation

operator<<

std::ostream & operator<< ( std::ostream &  s, const Segment &  segment  )

friend

Overloaded.

Parameters

s	Stream.
segment	The segment.