Slab Class Reference

A simple slab class. More...

#include <slab.h>

Inheritance diagram for Slab:

Public Member Functions
	Slab (const Plane &, const double &=0.0)
	Create a slab given a normal direction and two points.
	Slab (const QVector< Vector > &, const Vector &)
	Create a slab given a normal direction and a set of points.
	Slab ()
	Empty.
	~Slab ()
	Empty.
Vector	Normal () const
	Return the normal direction of the slab.
double	R (const Vector &) const
	Compute the squared distance to the slab.
double	Signed (const Vector &) const
	Compute the signed distance to the slab.
Vector	Normal (const Vector &) const
	Compute the distance vector between a slab and a given point.
void	Scale (const double &)
	Scale a slab.
bool	Intersect (const Ray &, double &, double &) const
	Compute the intersection between a slab and a ray.
bool	Inside (const Vector &) const
	Check if a point is inside the slab.
void	Rotate (const Matrix &)
	Rotate a plane.
void	Translate (const double &)
	Translates a plane in the direction of its normal.

Static Public Attributes
static double	epsilon = 1.0e-5
	Internal epsilon constant.

Protected Attributes
double	e = 0.0
	Thickness.
Protected Attributes inherited from Plane
Vector	n = Vector::Z
	Plane normal.
double	cqc = 0.0
	Plane coefficient.

Additional Inherited Members
Protected Member Functions inherited from Plane
	Plane ()
	Empty.
	Plane (const Vector &, const double &)
	Creates a plane given normal and distance.
	Plane (const Vector &, const Vector &)
	Creates a plane given normal and vertex.
	Plane (const Vector &)
	Creates a plane given normal passing through the origin.
	~Plane ()
	Empty.
bool	Intersect (const Ray &, double &) const
	Compute the intersection between a plane and a ray.
bool	Inside (const Vector &) const
	Check if a point is inside or outside the plane.
int	Side (const Vector &) const
	Check if a point lies inside, outside or even on the plane.
Vector	Normal () const
	Returns the normal to the plane.
Vector	Vertex () const
	Finds a vertex on the plane.
double	Coeff () const
	Returns the coefficient of the plane.
double	R (const Vector &) const
	Compute the squared distance to the half space delimited by the plane.
double	Signed (const Vector &) const
	Compute the signed distance between a point and the plane.
double	Eval (const Vector &) const
	Evaluates the equation of the plane.
void	Transform (const Matrix4 &)
	Transforms a plane given a homogeneous transformation matrix.
void	Translate (const double &)
	Translates a plane in the direction of its normal.
void	Rotate (const Matrix &)
	Rotate a plane.
void	Scale (const double &)
	Scale a plane.
Vector	Symmetry (const Vector &) const
	Compute the point symmetric to the argument point.
Box	Symmetric (const Box &) const
	Compute the bounding box of the symmetric argument box.
Segment	Symmetric (const Segment &) const
	Compute the symmetric segment.
Sphere	Symmetric (const Sphere &) const
	Compute the symmetric sphere.
Vector	Reflect (const Vector &) const
	Compute the reflected direction.
bool	Refract (const Vector &, const double &, Vector &) const
	Compute the refracted direction.
Vector	Intersect (const Line &) const
	Compute the intersection between a plane and a line.
bool	Intersect (const Segment &, double &) const
	Compute the intersection between a plane and a segment.
Quadric	Equation (const Ray &) const
	Compute the quadric equation of the Euclidean distance to the plane.
Frame	GetFrame () const
	Return a Frame attached to the plane.
Axis	Intersect (const Plane &) const
	Compute the intesection between two planes.
Static Protected Member Functions inherited from Plane
static void	Cast (const Vector &, double &, double &)
	Compute the inverse mapping coordinates of a point.
static Vector	Intersection (const Plane &, const Plane &, const Plane &)
	Compute the intersection between three planes.
static QVector< Vector >	ConvexPoints (const QVector< Plane > &)
	Compute the intersection of a set of half spaces.
static Vector	Reflect (const Vector &, const Vector &)
	Given an input (normalized) normal, compute a reflected direction. The code is the same as:
static bool	Refract (const Vector &, const Vector &, const double &, Vector &)
	Compute the refracted direction.
Static Protected Attributes inherited from Plane
static const double	epsilon = 1e-06
	Small value for checking intersection with a ray.
static const Plane	XY
	Reference z-axis horizontal plane.
static const Plane	YZ
	Reference x-axis plane.
static const Plane	ZX
	Reference y-axis plane.

Detailed Description

A simple slab class.

The class stores the normal and the constant coefficient of the plane equations.

This class implements some optimized functions, such as the intersection with a ray.

Constructor & Destructor Documentation

Slab() [1/2]

Slab::Slab ( const Plane & plane, const double & t = 0.0 )

explicit

Create a slab given a normal direction and two points.

Parameters

plane	Plane.
t	Thickness.

Slab() [2/2]

Slab::Slab ( const QVector< Vector > & p, const Vector & n )

explicit

Create a slab given a normal direction and a set of points.

Parameters

p	Set of points.
n	Plane normal.

Member Function Documentation

Inside()

bool Slab::Inside

(

const Vector &

p

)

const

Check if a point is inside the slab.

Parameters

p

Point.

Intersect()

bool Slab::Intersect	(	const Ray &	ray,
		double &	tmin,
		double &	tmax ) const

Compute the intersection between a slab and a ray.

Sorted intersection depths are returned if intersection occurs.

Parameters

ray	The ray.
tmin,tmax	Intersection depths.

Normal()

Vector Slab::Normal

(

const Vector &

p

)

const

Compute the distance vector between a slab and a given point.

Parameters

p

Point.

R()

double Slab::R

(

const Vector &

p

)

const

Compute the squared distance to the slab.

Parameters

p

Point.

Rotate()

void Plane::Rotate

(

const Matrix &

r

)

Rotate a plane.

Parameters

r	Rotation matrix.

\((R \en)\cdot(\ep-(R v))=(R \en)\cdot \ep-(R \en)\cdot(R v)=(R \en)\cdot \ep-\en\cdot v\) as an orthonormal matrix preserves the dot product ( \((Ra)\cdot (Rb)=(Ra)^t \cdot(Rb)\) and use the property of transpose and orthonormality of R).

Scale()

void Slab::Scale

(

const double &

s

)

Scale a slab.

Parameters

s	Scaling factor.

Signed()

double Slab::Signed

(

const Vector &

p

)

const

Compute the signed distance to the slab.

Parameters

p

Point.

Translate()

void Plane::Translate

(

const double &

t

)

Translates a plane in the direction of its normal.

Parameters

t	Translation distance.