Diamond2 Class Reference

A diamond in the plane. More...

#include <diamond2.h>

Inheritance diagram for Diamond2:

Public Member Functions
	Diamond2 (const Vector2 &, const Vector2 &)
	Creates a diamond given the vectors defining its bounding box.
	Diamond2 (const Vector2 &, const double &)
	Creates a diamond given its center and axes lengths.
	Diamond2 (const Vector2 &, const double &, const double &)
	Creates a diamond given its center and axes lengths.
double	Area () const
	Compute the area of the diamond.
double	Perimeter () const
	Compute the perimeter of the diamond.
Box2	GetBox () const
	Return the bounding box of the shape.
double	R (const Vector2 &) const
	Compute the squared distance between a point and the diamond.
Vector2	Vertex (int) const
	Return the i-th vertex.
Diamond2	Translated (const Vector2 &) const
	Translates the diamond.
Diamond2	Scaled (const Vector2 &) const
	Scales the diamond.
void	Draw (QGraphicsScene &, const QPen &, const QBrush &) const
	Draw a diamond.

Additional Inherited Members
Protected Member Functions inherited from Box2
	Box2 ()
	Empty.
	Box2 (const double &)
	Create a square box centered at the origin and of given half side length.
	Box2 (const double &, const double &)
	Create a box centered at the origin and of given dimensions.
	Box2 (const Vector2 &)
	Create a box from a single vertex.
	Box2 (const Vector2 &, const Vector2 &)
	Create a box.
	Box2 (const Vector2 &, const double &)
	Creates a box.
	Box2 (const Vector2 &, const double &, const double &)
	Create a box given a center point and its width, length, and height.
	Box2 (const Box &)
	Create a box in the plane given a box.
	Box2 (const Box2 &, const Box2 &)
	Create a box embedding two boxes.
	Box2 (const Box2 &, const Matrix2 &)
	Creates an axis aligned bounding box from a box and a transformation matrix.
	Box2 (const Box2 &, const Frame2 &)
	Creates an axis aligned bounding box from a box and a frame.
	Box2 (const QVector< Vector2 > &)
	Compute the bounding box of a set of points.
	Box2 (const QSize &)
	Create a box from a Qt size.
Vector2 &	operator[] (int)
	Returns either end vertex of the box.
Vector2	operator[] (int) const
	Overloaded.
Vector2	Size () const
	Compute the size (width and height) of a box.
double	Width () const
	Compute the width of a box.
double	Height () const
	Compute the height of a box.
Vector2	Diagonal () const
	Returns the diagonal of the box.
double	Radius () const
	Returns the radius of the box, i.e. the length of the half diagonal of the box.
double	Area () const
	Compute the surface area of a box.
double	Perimeter () const
	Compute the perimeter of the box.
Vector2	Center () const
	Returns the center of the box.
Vector2	Vertex (int) const
	Returns the k-th vertex of the box.
Vector2	Vertex (int, int, int, int) const
	Compute the coordinates of a grid aligned point.
Vector2	VertexUV (const Vector2 &) const
	Compute the coordinates of a point inside the box given uv coordinates.
Box2	Sub (int) const
	Computes the sub-box in the n-th quadrant.
double	R (const Vector2 &) const
	Compute the squared distance between the box and a point.
double	Signed (const Vector2 &) const
	Computes the signed distance between the box and a point.
double	R (const Box2 &) const
	Compute the squared Euclidean distance between two boxes.
void	Translate (const Vector2 &)
	Translates a box.
void	Scale (const Vector2 &)
	Scales a box.
void	Scale (const double &)
	Scales a box.
Box2	Translated (const Vector2 &) const
	Translated box.
Box2	Scaled (const double &) const
	Scales a box and return the scaled box.
Box2	Scaled (const Vector2 &) const
	Scales a box and return the scaled box.
Box2	Scaled (const QSize &) const
	Scales a box according to a Qt size.
Box2	ScaledTo (const double &) const
	Scale the box so that the largest side should equal the argument value.
Box2	ScaledCentered (const double &) const
	Scales a box while preserving its center.
Box2	Rotated (const double &) const
	Compute the box embedding the rotated box.
Box2	Rotated (const Matrix2 &) const
	Compute the box embedding the rotated box.
Box2	Centered () const
	Compute the box translated to origin.
void	SetCubic ()
	Creates the tightest embedding cube from an arbitrarilly shaped box.
void	SetInscribedCubic ()
	Creates the biggest cube inscribed in the box.
Box2	Cube () const
	Return the tightest embedding cube from an arbitrarilly shaped box.
void	Extend (const double &)
	Extend the limits of the box by a given distance.
void	Extend (const Vector2 &)
	Extend the limits of the box given a point.
Box2	Extended (const double &) const
	Extend the limits of the box by a given distance.
void	SetParallelepipedic (int, int &, int &)
	Inflates a box so that its dimensions should be a fraction of its maximum side length.
void	SetParallelepipedic (const double &, int &, int &)
	Creates a parallelepipedic box whose dimensions are integer multiples of a given input reference size.
bool	Inside (const Vector2 &) const
	Test if a point is inside the box.
bool	Inside (const Vector2 &, const double &) const
	Test if a point lies withing a given range of the box.
bool	Intersect (const Box2 &) const
	Check if the box intersects another box.
double	OverlapArea (const Box2 &) const
	Computes the overlapping area of two boxes.
Box2	Intersection (const Box2 &) const
	Computes the intersection between two boxes.
Box	ToBox (const double &, const double &) const
	Convert a planar Box2 to a Box.
int	Quadrant (const Vector2 &) const
	Computes quadrant index of a vertex with respect to the box center.
bool	Intersect (const Ray2 &, double &, double &) const
	Computes the intersection between a box and a ray.
bool	Intersect (const Ray2 &) const
	Computes the intersection between a box and a ray.
bool	Intersect (const Line2 &, double &, double &) const
	Computes the intersection between a box and a line.
bool	Intersect (const Segment2 &, double &, double &) const
	Compute the intersection between a box and a segment.
bool	Intersect (const Line2 &) const
	Check the intersection between a box and a line.
bool	Intersect (const Segment2 &) const
	Check the intersection between a box and a segment.
void	Draw (QGraphicsScene &, const QPen &=QPen(), const QBrush &=QBrush()) const
	Draw a rectangle.
Vector2	RandomInside (Random &=Random::R239) const
	Generate a random vector inside the box.
Vector2	RandomOn (Random &=Random::R239) const
	Generate a random vector on the perimeter of the box.
QRectF	GetQtRect () const
	Create the Qt rectangle.
QRect	TileRange (const Box2 &) const
	Compute the range of index for tiling the argument box so that it covers the box.
Box2	Tile (int, int) const
	Return the tiled the box using integer coordinates.
Box2	Tile (const QRect &) const
	Return the tiled the box using integer coordinates.
Segment2	GetSegment (const double &, bool=true) const
	Compute the horizontal or vertical segment dividing the box into u and 1-u parts.
QVector< Vector2 >	Poisson (const double &, int, Random &=Random::R239) const
	Compute a Poisson disc distribution inside a box.
QVector< Vector2 >	Poisson (const double &, int, const QVector< Vector2 > &, bool=true, Random &=Random::R239) const
	Compute a Poisson disc distribution inside a box.
Static Protected Member Functions inherited from Box2
static Box2	MinMax (const Vector2 &, const Vector2 &)
	Create a box from any two points.
Protected Attributes inherited from Box2
Vector2	b = Vector2(1.0)
	Lower and upper vertexes of the box.
Static Protected Attributes inherited from Box2
static const double	epsilon = 1.0e-5
	Epsilon value used to check intersections and some round off errors.
static const Box2	Infinity
	Huge bounding box, which should enclose any other.
static const Box2	Null
	Null box, equivalent to.
static const Box2	Unit
	Unit box, defined as.

Detailed Description

A diamond in the plane.

Constructor & Destructor Documentation

Diamond2() [1/3]

Diamond2::Diamond2 ( const Vector2 & a, const Vector2 & b )

explicit

Creates a diamond given the vectors defining its bounding box.

Parameters

a,b

Vectors.

Diamond2() [2/3]

Diamond2::Diamond2 ( const Vector2 & c, const double & r )

explicit

Creates a diamond given its center and axes lengths.

Parameters

c	Center.
r	Radius.

Diamond2() [3/3]

Diamond2::Diamond2 ( const Vector2 & c, const double & x, const double & y )

explicit

Creates a diamond given its center and axes lengths.

Parameters

c	Center.
x,y	Axes lengths.

Member Function Documentation

Area()

double Diamond2::Area

(

)

const

Compute the area of the diamond.

It is half the area of a box.

Draw()

void Diamond2::Draw	(	QGraphicsScene &	scene,
		const QPen &	pen,
		const QBrush &	brush ) const

Draw a diamond.

Parameters

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

Perimeter()

double Diamond2::Perimeter

(

)

const

Compute the perimeter of the diamond.

It is twice the length of the diagonal of the box.

R()

double Diamond2::R

(

const Vector2 &

p

)

const

Compute the squared distance between a point and the diamond.

Parameters

p

Point.

Scaled()

Diamond2 Diamond2::Scaled

(

const Vector2 &

s

)

const

Scales the diamond.

Parameters

s	Scaling vector.

Translated()

Diamond2 Diamond2::Translated

(

const Vector2 &

t

)

const

Translates the diamond.

Parameters

t	Translation vector.

Vertex()

Vector2 Diamond2::Vertex

(

int

i

)

const

Return the i-th vertex.

Parameters

i	Vertex index.