Triangle2 Class Reference

Base minimum storage triangle class in the plane. More...

#include <triangle.h>

Public Member Functions
	Triangle2 ()
	Empty.
	Triangle2 (const Vector2 &, const Vector2 &, const Vector2 &)
	Create a triangle given three points. More...
	Triangle2 (const Triangle &)
	Create a triangle. More...
	~Triangle2 ()
	Empty.
Vector2	operator[] (int) const
	Return the i-th vertex.
Vector2	Center () const
	Compute the barycenter of the triangle.
Circle2	Inscribed () const
	Compute the circle inscribed in the triangle. More...
Circle2	Circumscribed () const
	Compute the circle circumscribing the triangle. More...
double	R (const Vector2 &) const
	Computes the squared distance between a point and a triangle. More...
Vector2	Normal (const Vector2 &) const
	Computes the normal vector to a triangle. More...
bool	Intersect (const Circle2 &) const
	Check the intersection with a circle. More...
bool	Intersect (const Ray2 &, double &, double &) const
	Compute the intersection with a ray. More...
double	Area () const
	Compute the area of the triangle.
double	Perimeter () const
	Compute the perimeter of the triangle.
Box2	GetBox () const
	Computes the axis aligned box enclosing the triangle.
Vector	BarycentricCoordinates (const Vector2 &) const
	Compute the barycentric coordinates of an argument vector with respect to the triangle. More...
double	InscribedRadius () const
	Compute the radius of the circle inscribed in the triangle. More...
double	CircumscribedRadius () const
	Compute the radius of the circumscribed circle of the triangle.
double	Aspect () const
	Computes the aspect ratio of the triangle. More...
bool	Inside (const Box2 &) const
	Test if a box lies inside the triangle. More...
bool	Inside (const Circle2 &) const
	Test if a circle lies inside the triangle. More...
bool	Inside (const Vector2 &) const
	Test if a point lies inside the triangle. More...
bool	Inside (const Vector2 &, double &, double &) const
	Test if a point lies inside the triangle and computes its uv-coordinates. More...
Vector2	RandomInside (Random &=Random::R239) const
	Generate a random vector inside the triangle. More...
void	Rotate (const Matrix2 &)
	Rotate the triangle. More...
void	Translate (const Vector2 &)
	Translate the triangle. More...
void	Scale (const double &)
	Scale the triangle. More...
void	Scale (const Vector2 &)
	Scale the triangle. More...
void	Shrink (const double &)
	Shrinks a triangle. More...
bool	Overlap (const Triangle2 &) const
	Test if two triangles overlap. More...
bool	Intersect (const Triangle2 &) const
	Test if two triangles intersect. More...
void	Draw (QGraphicsScene &, const QPen &=QPen(), const QBrush &=QBrush()) const
	Draw a triangle. More...

Protected Member Functions
bool	IntersectEdge (const Triangle2 &) const
	Test if the edges of two triangles intersect. More...
bool	IntersectVertex (const Triangle2 &) const
	Test if two triangles are intersecting by performing a vertex intersection test. More...

Protected Attributes
Vector2	p [3]
	Array of vertices.

Static Protected Attributes
static double	epsilon = 1.0e-7
	Internal epsilon constant.

Friends
std::ostream &	operator<< (std::ostream &, const Triangle2 &)
	Overloaded. More...

Detailed Description

Base minimum storage triangle class in the plane.

Constructor & Destructor Documentation

Triangle2() [1/2]

Triangle2::Triangle2 ( const Vector2 &  a, const Vector2 &  b, const Vector2 &  c  )

inlineexplicit

Create a triangle given three points.

Parameters

a,b,c

Vertices.

Triangle2() [2/2]

Triangle2::Triangle2 ( const Triangle &  t )

explicit

Create a triangle.

Parameters

t

Triangle.

Member Function Documentation

Aspect()

double Triangle2::Aspect

(

)

const

Computes the aspect ratio of the triangle.

The aspect ratio is defined as twice the radius of the inscribed circle divided by the radius of the circumscribing circle.

See also

Triangle::Aspect()

BarycentricCoordinates()

Vector Triangle2::BarycentricCoordinates

(

const Vector2 &

p

)

const

Compute the barycentric coordinates of an argument vector with respect to the triangle.

See also

Triangle::BarycentricCoordinates()

Parameters

p

Point.

Circumscribed()

Circle2 Triangle2::Circumscribed ( ) const

inline

Compute the circle circumscribing the triangle.

This function directly relies on the constructor of the class.

See also

Circle2::Circle2(const Vector2&,const Vector2&,const Vector2&);

Draw()

void Triangle2::Draw	(	QGraphicsScene &	scene,
		const QPen &	pen = QPen(),
		const QBrush &	brush = QBrush()
	)		const

Draw a triangle.

Parameters

scene	Graphics scene.
pen	The pen.
brush	The brush, should the triangle be filled.

Inscribed()

Circle2 Triangle2::Inscribed

(

)

const

Compute the circle inscribed in the triangle.

The center of the circle is the center of (A,a), (B,b) and (C,c) where A, B and C are the vertices of the triangle and coefficients a, b and c represent the length of their facing edge.

InscribedRadius()

double Triangle2::InscribedRadius

(

)

const

Compute the radius of the circle inscribed in the triangle.

Some algebra will show that it is half the ratio of the half perimeter and the surface of the triangle.

Inside() [1/4]

bool Triangle2::Inside

(

const Box2 &

box

)

const

Test if a box lies inside the triangle.

Parameters

box

The box.

Inside() [2/4]

bool Triangle2::Inside

(

const Circle2 &

circle

)

const

Test if a circle lies inside the triangle.

Parameters

circle

The circle.

Inside() [3/4]

bool Triangle2::Inside

(

const Vector2 &

p

)

const

Test if a point lies inside the triangle.

This is an optimized version with some early tests to avoid some computations.

See also

Triangle2::Inside(const Vector2&,double&,double&)

Parameters

p

Point.

Inside() [4/4]

bool Triangle2::Inside	(	const Vector2 &	p,
		double &	u,
		double &	v
	)		const

Test if a point lies inside the triangle and computes its uv-coordinates.

Parameters

p	Point.
u,v	UV-coordinates.

Intersect() [1/3]

bool Triangle2::Intersect

(

const Circle2 &

circle

)

const

Check the intersection with a circle.

Parameters

circle

The circle.

Intersect() [2/3]

bool Triangle2::Intersect	(	const Ray2 &	ray,
		double &	ta,
		double &	tb
	)		const

Compute the intersection with a ray.

Parameters

ray	The ray.
ta,tb	Intersection depths

Intersect() [3/3]

bool Triangle2::Intersect

(

const Triangle2 &

t

)

const

Test if two triangles intersect.

Parameters

t

Triangle.

Triangles should have their vertices in trigonometric order.

IntersectEdge()

bool Triangle2::IntersectEdge ( const Triangle2 &  t ) const

protected

Test if the edges of two triangles intersect.

Parameters

t

Triangle.

IntersectVertex()

bool Triangle2::IntersectVertex ( const Triangle2 &  t ) const

protected

Test if two triangles are intersecting by performing a vertex intersection test.

Parameters

t

Triangle.

Triangles should have their vertices in trigonometric order.

Normal()

Vector2 Triangle2::Normal

(

const Vector2 &

q

)

const

Computes the normal vector to a triangle.

Parameters

q

Point.

Overlap()

bool Triangle2::Overlap

(

const Triangle2 &

t

)

const

Test if two triangles overlap.

Parameters

t

Triangle.

R()

double Triangle2::R

(

const Vector2 &

q

)

const

Computes the squared distance between a point and a triangle.

Parameters

q

Point.

RandomInside()

Vector2 Triangle2::RandomInside

(

Random &

random = Random::R239

)

const

Generate a random vector inside the triangle.

See also

Triangle::RandomInside

Parameters

random

Random number generator.

Rotate()

void Triangle2::Rotate

(

const Matrix2 &

r

)

Rotate the triangle.

Parameters

r	Rotation matrix.

Scale() [1/2]

void Triangle2::Scale

(

const double &

s

)

Scale the triangle.

Parameters

s	Scaling factor.

Scale() [2/2]

void Triangle2::Scale

(

const Vector2 &

s

)

Scale the triangle.

Parameters

s	Scaling vector.

Shrink()

void Triangle2::Shrink

(

const double &

e

)

Shrinks a triangle.

Parameters

e	Erosion radius.

Translate()

void Triangle2::Translate

(

const Vector2 &

t

)

Translate the triangle.

Parameters

t	Translation vector.

Friends And Related Function Documentation

operator<<

std::ostream & operator<< ( std::ostream &  s, const Triangle2 &  t  )

friend

Overloaded.

Parameters

t	Triangle.
s	Stream.