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.
	Triangle2 (const Triangle &)
	Create a triangle.
	~Triangle2 ()
	Empty.
Vector2	operator[] (int) const
	Return the i-th vertex.
Vector2	Center () const
	Compute the barycenter of the triangle.
Vector2	BaryCenter (const Vector &) const
	Compute the barycenter given barycentric coordinates.
Vector2	OrthoCenter () const
	Compute the orthocenter.
Circle2	Inscribed () const
	Compute the circle inscribed in the triangle.
Circle2	Circumscribed () const
	Compute the circle circumscribing the triangle.
double	R (const Vector2 &) const
	Computes the squared distance between a point and a triangle.
double	Signed (const Vector2 &) const
	Computes the signed Euclidean distance between a point and a triangle.
Vector2	Normal (const Vector2 &) const
	Computes the normal vector to a triangle.
bool	Intersect (const Circle2 &) const
	Check the intersection with a circle.
bool	Intersect (const Box2 &) const
	Check the intersection with a box.
bool	Intersect (const Segment2 &) const
	Check the intersection with a segment.
bool	Intersect (const Ray2 &, double &, double &) const
	Compute the intersection with a ray.
double	Area () const
	Compute the area of the triangle.
double	SignedArea () 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.
QVector< Vector2 >	Poisson (const double &, int, Random &=Random::R239) const
	Compute a Poisson disc distribution inside the triangle.
Vector	BarycentricCoordinates (const Vector2 &) const
	Compute the barycentric coordinates of an argument vector with respect to the triangle.
double	InscribedRadius () const
	Compute the radius of the circle inscribed in the triangle.
double	CircumscribedRadius () const
	Compute the radius of the circumscribed circle of the triangle.
double	Aspect () const
	Computes the aspect ratio of the triangle.
bool	Inside (const Box2 &) const
	Test if a box lies inside the triangle.
bool	Inside (const Circle2 &) const
	Test if a circle lies inside the triangle.
bool	Inside (const Vector2 &) const
	Test if a point lies inside the triangle.
bool	Inside (const Vector2 &, double &, double &) const
	Test if a point lies inside the triangle and computes its uv-coordinates.
Vector2	RandomInside (Random &=Random::R239) const
	Generate a random vector inside the triangle.
void	Rotate (const Matrix2 &)
	Rotate the triangle.
void	Translate (const Vector2 &)
	Translate the triangle.
void	Scale (const double &)
	Scale the triangle.
void	Scale (const Vector2 &)
	Scale the triangle.
Triangle2	Rotated (const Matrix2 &) const
	Rotate the triangle.
Triangle2	Translated (const Vector2 &) const
	Translate the triangle.
Triangle2	Scaled (const double &) const
	Scale the triangle.
Triangle2	Scaled (const Vector2 &) const
	Scale the triangle.
void	Shrink (const double &)
	Shrinks a triangle.
bool	Overlap (const Triangle2 &) const
	Test if two triangles overlap.
bool	Intersect (const Triangle2 &) const
	Test if two triangles intersect.
void	Draw (QGraphicsScene &, const QPen &=QPen(), const QBrush &=QBrush()) const
	Draw a triangle.

Static Public Member Functions
static Triangle2	Equilateral (const Vector2 &, const double &=1.0, const double &=0.0)
	Create an equilateral triangle.

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

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 &s, const Triangle2 &t)
	Overloaded.

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

Area()

double Triangle2::Area

(

)

const

Compute the area of the triangle.

See also

Triangle2::SignedArea

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()

BaryCenter()

Vector2 Triangle2::BaryCenter

(

const Vector &

weights

)

const

Compute the barycenter given barycentric coordinates.

See also

Triangle2::BarycentricCoordinates()

Parameters

weights

Weights.

BarycentricCoordinates()

Vector Triangle2::BarycentricCoordinates

(

const Vector2 &

p

)

const

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

If the point lies within the triangle, the coordinates are positive and form a partition of the unity. This no longer holds if the point is outside of the triangle.

Note that this function is not the most efficient, as it relies on the evaluation of the area formed by the triangles pab, pbc, and pca.

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.

Equilateral()

Triangle2 Triangle2::Equilateral ( const Vector2 & c, const double & r = 1.0, const double & a = 0.0 )

static

Create an equilateral triangle.

Parameters

c	Center.
r	Radius.
a	Rotation angle.

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 &

q

)

const

Test if a point lies inside the triangle.

Parameters

q

Point.

Author

Hugo Schott

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() [1/5]

bool Triangle2::Intersect

(

const Box2 &

box

)

const

Check the intersection with a box.

Parameters

box

The box.

Intersect() [2/5]

bool Triangle2::Intersect

(

const Circle2 &

circle

)

const

Check the intersection with a circle.

Parameters

circle

The circle.

Intersect() [3/5]

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() [4/5]

bool Triangle2::Intersect

(

const Segment2 &

segment

)

const

Check the intersection with a segment.

Parameters

segment

The segment.

Intersect() [5/5]

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.

Poisson()

QVector< Vector2 > Triangle2::Poisson	(	const double &	r,
		int	n,
		Random &	random = Random::R239 ) const

Compute a Poisson disc distribution inside the triangle.

This function uses a simple dart throwing algorithm.

Parameters

r	Radius of the discs.
n	Number of candidate points.
random	Random number generator.

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.

Rotated()

Triangle2 Triangle2::Rotated

(

const Matrix2 &

r

)

const

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.

Scaled() [1/2]

Triangle2 Triangle2::Scaled

(

const double &

s

)

const

Scale the triangle.

Parameters

s	Scaling factor.

Scaled() [2/2]

Triangle2 Triangle2::Scaled

(

const Vector2 &

s

)

const

Scale the triangle.

Parameters

s	Scaling vector.

Shrink()

void Triangle2::Shrink

(

const double &

e

)

Shrinks a triangle.

Parameters

e	Erosion radius.

Signed()

double Triangle2::Signed

(

const Vector2 &

q

)

const

Computes the signed Euclidean distance between a point and a triangle.

Parameters

q

Point.

SignedArea()

double Triangle2::SignedArea

(

)

const

Compute the area of the triangle.

See also

Triangle2::Area

Translate()

void Triangle2::Translate

(

const Vector2 &

t

)

Translate the triangle.

Parameters

t	Translation vector.

Translated()

Triangle2 Triangle2::Translated

(

const Vector2 &

t

)

const

Translate the triangle.

Parameters

t	Translation vector.

Friends And Related Symbol Documentation

operator<<

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

friend

Overloaded.

Parameters

t	Triangle.
s	Stream.