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. More...

	Plane (const Vector &, const double &)
	Creates a plane given normal and distance. More...

	Plane (const Vector &, const Vector &)
	Creates a plane given normal and vertex. More...

	Plane (const Vector &)
	Creates a plane given normal passing through the origin. More...

	~Plane ()
	Empty.

bool	Intersect (const Ray &, double &) const
	Compute the intersection between a plane and a ray. More...

bool	Inside (const Vector &) const
	Check if a point is inside or outside the plane. More...

int	Side (const Vector &) const
	Check if a point lies inside, outside or even on the plane. More...

Vector	Normal () const
	Returns the normal to the plane.

Vector	Vertex () const
	Finds a vertex on the plane. More...

double	R (const Vector &) const
	Compute the squared distance to the half space delimited by the plane. More...

double	Signed (const Vector &) const
	Compute the signed distance between a point and the plane. More...

double	Eval (const Vector &) const
	Evaluates the equation of the plane. More...

void	Transform (const Matrix4 &)
	Transforms a plane given a homogeneous transformation matrix. More...

void	Translate (const double &)
	Translates a plane in the direction of its normal. More...

void	Rotate (const Matrix &)
	Rotate a plane. More...

Vector	Symmetry (const Vector &) const
	Compute the point symmetric to the argument point. More...

Box	Symmetric (const Box &) const
	Compute the boundix box of the symmetric argument box. More...

Segment	Symmetric (const Segment &) const
	Compute the symmetric segment. More...

Sphere	Symmetric (const Sphere &) const
	Compute the symmetric sphere. More...

Vector	Reflect (const Vector &) const
	Compute the reflected direction. More...

bool	Refract (const Vector &, const double &, Vector &) const
	Compute the refracted direction. More...

Vector	Intersect (const Line &) const
	Compute the intersection between a plane and a line. More...

bool	Intersect (const Segment &, double &) const
	Compute the intersection between a plane and a segment. More...

Quadric	Equation (const Ray &) const
	Compute the quadric equation of the Euclidean distance to the plane. More...

Frame	GetFrame () const
	Return a Frame attached to the plane. More...

Axis	Intersect (const Plane &) const
	Compute the intesection between two planes. More...

Static Public Member Functions
static void	Cast (const Vector &, double &, double &)
	Compute the inverse mapping coordinates of a point. More...

static Vector	Intersection (const Plane &, const Plane &, const Plane &)
	Compute the intersection between three planes. More...

static QVector< Vector >	ConvexPoints (const QVector< Plane > &)
	Compute the intersection of a set of half spaces. More...

static Vector	Reflect (const Vector &, const Vector &)
	Given an input (normalized) normal, compute a reflected direction. The code is the same as: More...

static bool	Refract (const Vector &, const Vector &, const double &, Vector &)
	Compute the refracted direction. More...

Static Public Attributes
static const double	epsilon = 1e-06
	Small value for checking intersection with a ray.

static const Plane	Horizontal
	Reference horizontal plane.

Protected Attributes
Vector	n = Vector::Z
	Plane normal.

double	c = 0.0
	Plane coefficient.

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

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;

Plane::n

Vector n

Plane normal.

Definition: plane.h:21

Vector

Vectors in three dimensions.

Definition: evector.h:21

◆ 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.

◆ 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 boundix 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 Function Documentation

◆ operator<<

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

friend

Overloaded.

Parameters

s	Stream.
plane	The plane.

Public Member Functions

Static Public Member Functions

Static Public Attributes

Protected Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ Plane() [1/4]

◆ Plane() [2/4]

◆ Plane() [3/4]

◆ Plane() [4/4]

Member Function Documentation

◆ Cast()

◆ ConvexPoints()

◆ Equation()

◆ Eval()

◆ GetFrame()

◆ Inside()

◆ Intersect() [1/4]

◆ Intersect() [2/4]

◆ Intersect() [3/4]

◆ Intersect() [4/4]

◆ Intersection()

◆ R()

◆ Reflect() [1/2]

◆ Reflect() [2/2]

◆ Refract() [1/2]

◆ Refract() [2/2]

◆ Rotate()

◆ Side()

◆ Signed()

◆ Symmetric() [1/3]

◆ Symmetric() [2/3]

◆ Symmetric() [3/3]

◆ Symmetry()

◆ Transform()

◆ Translate()

◆ Vertex()

Friends And Related Function Documentation

◆ operator<<