Plane Class Reference

A plane defined by its analytic equation. More...

#include <plane.h>

Inheritance diagram for Plane:

Public Member Functions
	Plane ()
	Empty.
	Plane (const double &, const double &, const double &, const double &)
	Creates a plane given its analytic equation.
	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 Public Member Functions
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 Public Attributes
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.

Protected Attributes
Vector	n = Vector::Z
	Plane normal.
double	c = 0.0
	Plane coefficient.

Friends
std::ostream &	operator<< (std::ostream &s, const Plane &plane)
	Overloaded.

Detailed Description

A plane defined by its analytic equation.

This class serves as a base core class for binary space patitionning or constructive solid geometry in ray-tracing.

Constructor & Destructor Documentation

Plane() [1/4]

Plane::Plane ( const double & a, const double & b, const double & c, const double & d )

inlineexplicit

Creates a plane given its analytic equation.

Parameters

a,b,c	Coefficients of the plane normal, the plane normal should be unit..
d	Plane constant.

Plane() [2/4]

Plane::Plane ( const Vector & n, const double & c )

inlineexplicit

Creates a plane given normal and distance.

Parameters

n	Plane normal, should be unit.
c	Plane constant.

Plane() [3/4]

Plane::Plane ( const Vector & n, const Vector & p )

explicit

Creates a plane given normal and vertex.

Parameters

n	Plane normal, should be unit.
p	Any point on the plane.

Plane() [4/4]

Plane::Plane ( const Vector & n )

explicit

Creates a plane given normal passing through the origin.

Parameters

n	Plane normal, should be unit.

Member Function Documentation

Cast()

void Plane::Cast ( const Vector & p, double & u, double & v )

static

Compute the inverse mapping coordinates of a point.

Parameters

p	Point that will be projected on the plane.
u,v	Returned coordinates.

ConvexPoints()

QVector< Vector > Plane::ConvexPoints ( const QVector< Plane > & planes )

static

Compute the intersection of a set of half spaces.

This is a O(n^4) algorithm

A better version in O(n^3) could be implemented: see Finding the Intersection of Half-Spaces in Time O(n ln n). Preparata and Muller, Theoretical Computer Science 8, 45-55, 1979.

Returns a set of point representing the minimal convex polygon embedding all half spaces. The function doesn't check if the intersection is bounded or not.

Parameters

planes

Set of planes.

Equation()

Quadric Plane::Equation

(

const Ray &

ray

)

const

Compute the quadric equation of the Euclidean distance to the plane.

Parameters

ray

The ray.

Eval()

double Plane::Eval ( const Vector & p ) const

inline

Evaluates the equation of the plane.

This can be interpreted as a signed distance to the plane.

Parameters

p

Point.

See also

Plane::R(), Plane::Signed()

GetFrame()

Frame Plane::GetFrame

(

)

const

Return a Frame attached to the plane.

See also

Axis::GetFrame()

Inside()

bool Plane::Inside

(

const Vector &

p

)

const

Check if a point is inside or outside the plane.

This function compares the sign strictly to 0.0, use Plane::Side() for a more fuzzy implementation.

Parameters

p

Point.

See also

Plane::Side().

Intersect() [1/4]

Vector Plane::Intersect

(

const Line &

l

)

const

Compute the intersection between a plane and a line.

The line should not be parallel to the plane.

Parameters

l

The line.

Intersect() [2/4]

Axis Plane::Intersect

(

const Plane &

plane

)

const

Compute the intesection between two planes.

Planes should not be coplanar.

Parameters

plane

Argument plane.

Intersect() [3/4]

bool Plane::Intersect	(	const Ray &	ray,
		double &	t ) const

Compute the intersection between a plane and a ray.

The intersection depth is returned if intersection occurs.

Parameters

ray	The ray.
t	Intersection depth.

Intersect() [4/4]

bool Plane::Intersect	(	const Segment &	s,
		double &	t ) const

Compute the intersection between a plane and a segment.

The intersection point can be computed using Segment::Vertex(const double&) if intersection occurs.

See also

Plane::Intersect(const Line&) const

Plane::Intersect(const Ray&) const

Parameters

s	The segment.
t	Position of the point if intersection occurs.

Intersection()

Vector Plane::Intersection ( const Plane & a, const Plane & b, const Plane & c )

static

Compute the intersection between three planes.

Returns Vector::Null if two planes are complanar.

Parameters

a,b,c

Three planes.

R()

double Plane::R

(

const Vector &

p

)

const

Compute the squared distance to the half space delimited by the plane.

Parameters

p

Point.

See also

Plane::Eval()

Reflect() [1/2]

Vector Plane::Reflect ( const Vector & d ) const

inline

Compute the reflected direction.

Parameters

d	Direction.

Reflect() [2/2]

Vector Plane::Reflect ( const Vector & d, const Vector & n )

inlinestatic

Given an input (normalized) normal, compute a reflected direction. The code is the same as:

Vector r=d-2.0*(n*d)*n;

Refract() [1/2]

bool Plane::Refract	(	const Vector &	d,
		const double &	eta,
		Vector &	r ) const

Compute the refracted direction.

Parameters

d	Direction.
eta	Index of incoming ray medium divided by the index of the other material.
r	Refracted direction.

Refract() [2/2]

bool Plane::Refract ( const Vector & d, const Vector & n, const double & eta, Vector & r )

static

Compute the refracted direction.

Parameters

d	Direction.
n	Normal.
eta	Index of incoming ray medium divided by the index of the other material.
r	Refracted direction.

Rotate()

void Plane::Rotate

(

const Matrix &

r

)

Rotate a plane.

Parameters

r	Rotation matrix.

Scale()

void Plane::Scale

(

const double &

s

)

Scale a plane.

Parameters

s	Scaling factor.

Side()

int Plane::Side

(

const Vector &

p

)

const

Check if a point lies inside, outside or even on the plane.

The epsilon tolerance used for testing if the point is on the plane is 10^-6.

Parameters

p

Point.

Signed()

double Plane::Signed

(

const Vector &

p

)

const

Compute the signed distance between a point and the plane.

Parameters

p	The point.

See also

Plane::Eval(const Vector&) const

Symmetric() [1/3]

Box Plane::Symmetric

(

const Box &

box

)

const

Compute the bounding box of the symmetric argument box.

Parameters

box

The box.

Symmetric() [2/3]

Segment Plane::Symmetric

(

const Segment &

segment

)

const

Compute the symmetric segment.

Parameters

segment

The segment.

Symmetric() [3/3]

Sphere Plane::Symmetric

(

const Sphere &

sphere

)

const

Compute the symmetric sphere.

Parameters

sphere

The sphere.

Symmetry()

Vector Plane::Symmetry

(

const Vector &

p

)

const

Compute the point symmetric to the argument point.

Parameters

p

Point.

Transform()

void Plane::Transform

(

const Matrix4 &

M

)

Transforms a plane given a homogeneous transformation matrix.

Parameters

M

Matrix.

Translate()

void Plane::Translate

(

const double &

t

)

Translates a plane in the direction of its normal.

Parameters

t	Translation distance.

Vertex()

Vector Plane::Vertex

(

)

const

Finds a vertex on the plane.

Basically computes the point on the plane which is nearest to the origin.

Friends And Related Symbol Documentation

operator<<

std::ostream & operator<< ( std::ostream & s, const Plane & plane )

friend

Overloaded.

Parameters

s	Stream.
plane	The plane.