template<typename T = double>
class ROOT::Math::Impl::Plane3D< T >

Class describing a geometrical plane in 3 dimensions.

A Plane3D is a 2 dimensional surface spanned by two linearly independent vectors. The plane is described by the equation \( a*x + b*y + c*z + d = 0 \) where (a,b,c) are the components of the normal vector to the plane \( n = (a,b,c) \) and \( d = - n \dot x \), where x is any point belonging to plane. More information on the mathematics describing a plane in 3D is available on MathWord. The Plane3D class contains the 4 scalar values in T which represent the four coefficients, fA, fB, fC, fD. fA, fB, fC are the normal components normalized to 1, i.e. fA**2 + fB**2 + fC**2 = 1

Definition at line 51 of file Plane3D.h.

Public Types
typedef PositionVector3D< Cartesian3D< T >, DefaultCoordinateSystemTag >	Point

typedef T	Scalar

typedef DisplacementVector3D< Cartesian3D< T >, DefaultCoordinateSystemTag >	Vector

Public Member Functions
	Plane3D ()
	default constructor create plane z = 0

template<class T1 , class T2 , class U >
	Plane3D (const DisplacementVector3D< T1, U > &n, const PositionVector3D< T2, U > &p)
	Construct from a generic DisplacementVector3D (normal vector) and PositionVector3D (point coplanar to the plane)

	Plane3D (const Plane3D &)=default

	Plane3D (const Point &p1, const Point &p2, const Point &p3)
	constructor from three Cartesian point belonging to the plane

template<class T1 , class T2 , class T3 , class U >
	Plane3D (const PositionVector3D< T1, U > &p1, const PositionVector3D< T2, U > &p2, const PositionVector3D< T3, U > &p3)
	constructor from three generic point belonging to the plane

	Plane3D (const Scalar &a, const Scalar &b, const Scalar &c, const Scalar &d)
	generic constructors from the four scalar values describing the plane according to the equation ax + by + cz + d = 0

	Plane3D (const Vector &n, const Point &p)
	constructor a Plane3D from a normal vector and a point coplanar to the plane

Scalar	A () const
	Return the a coefficient of the plane equation \( ax + by + c*z + d = 0 \).

Scalar	B () const
	Return the b coefficient of the plane equation \( ax + by + c*z + d = 0 \).

Scalar	C () const
	Return the c coefficient of the plane equation \( ax + by + c*z + d = 0 \).

Scalar	D () const
	Return the d coefficient of the plane equation \( ax + by + c*z + d = 0 \).

Scalar	Distance (const Point &p) const
	Return the signed distance to a Point.

template<class T1 , class U >
Scalar	Distance (const PositionVector3D< T1, U > &p) const
	Return the distance to a Point described with generic coordinates.

Scalar	HesseDistance () const
	Return the Hesse Distance (distance from the origin) of the plane or the d coefficient expressed in normalize form.

Vector	Normal () const
	Return normal vector to the plane as Cartesian DisplacementVector.

bool	operator!= (const Plane3D &rhs) const

Plane3D &	operator= (const Plane3D &)=default
	Assignment operator from other Plane3D class.

bool	operator== (const Plane3D &rhs) const
	Exact equality.

Point	ProjectOntoPlane (const Point &p) const
	Return the projection of a Cartesian point to a plane.

template<class T1 , class U >
PositionVector3D< T1, U >	ProjectOntoPlane (const PositionVector3D< T1, U > &p) const
	Return the projection of a point to a plane.

Protected Member Functions
template<typename SCALAR = T, typename std::enable_if< std::is_arithmetic< SCALAR >::value >::type * = nullptr>
void	Normalize ()
	Normalize the normal (a,b,c) plane components.

template<typename SCALAR = T, typename std::enable_if<!std::is_arithmetic< SCALAR >::value >::type * = nullptr>
void	Normalize ()
	Normalize the normal (a,b,c) plane components.

Private Member Functions
void	BuildFrom3Points (const Point &p1, const Point &p2, const Point &p3)

void	BuildFromVecAndPoint (const Vector &n, const Point &p)

Private Attributes
Scalar	fA

Scalar	fB

Scalar	fC

Scalar	fD

#include <Math/GenVector/Plane3D.h>

Member Typedef Documentation

◆ Point

template<typename T = double>

typedef PositionVector3D<Cartesian3D<T>, DefaultCoordinateSystemTag> ROOT::Math::Impl::Plane3D< T >::Point

Definition at line 59 of file Plane3D.h.

◆ Scalar

template<typename T = double>

typedef T ROOT::Math::Impl::Plane3D< T >::Scalar

Definition at line 56 of file Plane3D.h.

◆ Vector

template<typename T = double>

typedef DisplacementVector3D<Cartesian3D<T>, DefaultCoordinateSystemTag> ROOT::Math::Impl::Plane3D< T >::Vector

Definition at line 58 of file Plane3D.h.

Constructor & Destructor Documentation

◆ Plane3D() [1/7]

template<typename T = double>

ROOT::Math::Impl::Plane3D< T >::Plane3D ( )

inline

default constructor create plane z = 0

Definition at line 64 of file Plane3D.h.

◆ Plane3D() [2/7]

template<typename T = double>

ROOT::Math::Impl::Plane3D< T >::Plane3D	(	const Scalar &	a,
		const Scalar &	b,
		const Scalar &	c,
		const Scalar &	d
	)

inline

generic constructors from the four scalar values describing the plane according to the equation ax + by + cz + d = 0

Parameters

a	scalar value
b	scalar value
c	scalar value
d	sxcalar value

Definition at line 74 of file Plane3D.h.

◆ Plane3D() [3/7]

template<typename T = double>

ROOT::Math::Impl::Plane3D< T >::Plane3D	(	const Vector &	n,
		const Point &	p
	)

inline

constructor a Plane3D from a normal vector and a point coplanar to the plane

Parameters

n	normal expressed as a ROOT::Math::DisplacementVector3D<Cartesian3D<T> >
p	point expressed as a ROOT::Math::PositionVector3D<Cartesian3D<T> >

Definition at line 85 of file Plane3D.h.

◆ Plane3D() [4/7]

template<typename T = double>

template<class T1 , class T2 , class U >

ROOT::Math::Impl::Plane3D< T >::Plane3D	(	const DisplacementVector3D< T1, U > &	n,
		const PositionVector3D< T2, U > &	p
	)

inline

Construct from a generic DisplacementVector3D (normal vector) and PositionVector3D (point coplanar to the plane)

Parameters

n	normal expressed as a generic ROOT::Math::DisplacementVector3D
p	point expressed as a generic ROOT::Math::PositionVector3D

Definition at line 94 of file Plane3D.h.

◆ Plane3D() [5/7]

template<typename T = double>

ROOT::Math::Impl::Plane3D< T >::Plane3D	(	const Point &	p1,
		const Point &	p2,
		const Point &	p3
	)

inline

constructor from three Cartesian point belonging to the plane

Parameters

p1	point1 expressed as a generic ROOT::Math::PositionVector3D
p2	point2 expressed as a generic ROOT::Math::PositionVector3D
p3	point3 expressed as a generic ROOT::Math::PositionVector3D

Definition at line 105 of file Plane3D.h.

◆ Plane3D() [6/7]

template<typename T = double>

template<class T1 , class T2 , class T3 , class U >

ROOT::Math::Impl::Plane3D< T >::Plane3D	(	const PositionVector3D< T1, U > &	p1,
		const PositionVector3D< T2, U > &	p2,
		const PositionVector3D< T3, U > &	p3
	)

inline

constructor from three generic point belonging to the plane

Parameters

p1	point1 expressed as ROOT::Math::DisplacementVector3D<Cartesian3D<T> >
p2	point2 expressed as ROOT::Math::DisplacementVector3D<Cartesian3D<T> >
p3	point3 expressed as ROOT::Math::DisplacementVector3D<Cartesian3D<T> >

Definition at line 114 of file Plane3D.h.

◆ Plane3D() [7/7]

template<typename T = double>

ROOT::Math::Impl::Plane3D< T >::Plane3D ( const Plane3D< T > & )

default

Member Function Documentation

◆ A()

template<typename T = double>

Scalar ROOT::Math::Impl::Plane3D< T >::A ( ) const

inline

Return the a coefficient of the plane equation \( a*x + b*y + c*z + d = 0 \).

It is also the x-component of the vector perpendicular to the plane.

Definition at line 133 of file Plane3D.h.

◆ B()

template<typename T = double>

Scalar ROOT::Math::Impl::Plane3D< T >::B ( ) const

inline

Return the b coefficient of the plane equation \( a*x + b*y + c*z + d = 0 \).

It is also the y-component of the vector perpendicular to the plane

Definition at line 139 of file Plane3D.h.

◆ BuildFrom3Points()

template<typename T = double>

void ROOT::Math::Impl::Plane3D< T >::BuildFrom3Points	(	const Point &	p1,
		const Point &	p2,
		const Point &	p3
	)

inlineprivate

Definition at line 267 of file Plane3D.h.

◆ BuildFromVecAndPoint()

template<typename T = double>

void ROOT::Math::Impl::Plane3D< T >::BuildFromVecAndPoint	(	const Vector &	n,
		const Point &	p
	)

inlineprivate

Definition at line 256 of file Plane3D.h.

◆ C()

template<typename T = double>

Scalar ROOT::Math::Impl::Plane3D< T >::C ( ) const

inline

Return the c coefficient of the plane equation \( a*x + b*y + c*z + d = 0 \).

It is also the z-component of the vector perpendicular to the plane

Definition at line 145 of file Plane3D.h.

◆ D()

template<typename T = double>

Scalar ROOT::Math::Impl::Plane3D< T >::D ( ) const

inline

Return the d coefficient of the plane equation \( a*x + b*y + c*z + d = 0 \).

It is also the distance from the origin (HesseDistance)

Definition at line 151 of file Plane3D.h.

◆ Distance() [1/2]

template<typename T = double>

Scalar ROOT::Math::Impl::Plane3D< T >::Distance ( const Point & p ) const

inline

Return the signed distance to a Point.

The distance is signed positive if the Point is in the same side of the normal vector to the plane.

Parameters

p	Point expressed in Cartesian Coordinates

Definition at line 170 of file Plane3D.h.

◆ Distance() [2/2]

template<typename T = double>

template<class T1 , class U >

Scalar ROOT::Math::Impl::Plane3D< T >::Distance ( const PositionVector3D< T1, U > & p ) const

inline

Return the distance to a Point described with generic coordinates.

Parameters

p	Point expressed as generic ROOT::Math::PositionVector3D

Definition at line 177 of file Plane3D.h.

◆ HesseDistance()

template<typename T = double>

Scalar ROOT::Math::Impl::Plane3D< T >::HesseDistance ( ) const

inline

Return the Hesse Distance (distance from the origin) of the plane or the d coefficient expressed in normalize form.

Definition at line 162 of file Plane3D.h.

◆ Normal()

template<typename T = double>

Vector ROOT::Math::Impl::Plane3D< T >::Normal ( ) const

inline

Return normal vector to the plane as Cartesian DisplacementVector.

Definition at line 156 of file Plane3D.h.

◆ Normalize() [1/2]

template<typename T = double>

template<typename SCALAR = T, typename std::enable_if< std::is_arithmetic< SCALAR >::value >::type * = nullptr>

void ROOT::Math::Impl::Plane3D< T >::Normalize ( )

inlineprotected

Normalize the normal (a,b,c) plane components.

Definition at line 216 of file Plane3D.h.

◆ Normalize() [2/2]

template<typename T = double>

template<typename SCALAR = T, typename std::enable_if<!std::is_arithmetic< SCALAR >::value >::type * = nullptr>

void ROOT::Math::Impl::Plane3D< T >::Normalize ( )

inlineprotected

Normalize the normal (a,b,c) plane components.

Definition at line 237 of file Plane3D.h.

◆ operator!=()

template<typename T = double>

bool ROOT::Math::Impl::Plane3D< T >::operator!= ( const Plane3D< T > & rhs ) const

inline

Definition at line 209 of file Plane3D.h.

◆ operator=()

template<typename T = double>

Plane3D & ROOT::Math::Impl::Plane3D< T >::operator= ( const Plane3D< T > & )

default

Assignment operator from other Plane3D class.

◆ operator==()

template<typename T = double>

bool ROOT::Math::Impl::Plane3D< T >::operator== ( const Plane3D< T > & rhs ) const

inline

Exact equality.

Definition at line 208 of file Plane3D.h.

◆ ProjectOntoPlane() [1/2]

template<typename T = double>

Point ROOT::Math::Impl::Plane3D< T >::ProjectOntoPlane ( const Point & p ) const

inline

Return the projection of a Cartesian point to a plane.

Parameters

p	Point expressed as PositionVector3D<Cartesian3D<T> >

Definition at line 186 of file Plane3D.h.

◆ ProjectOntoPlane() [2/2]

template<typename T = double>

template<class T1 , class U >

PositionVector3D< T1, U > ROOT::Math::Impl::Plane3D< T >::ProjectOntoPlane ( const PositionVector3D< T1, U > & p ) const

inline

Return the projection of a point to a plane.

Parameters

p	Point expressed as generic ROOT::Math::PositionVector3D

Definition at line 197 of file Plane3D.h.

Member Data Documentation

◆ fA

template<typename T = double>

Scalar ROOT::Math::Impl::Plane3D< T >::fA

private

Definition at line 282 of file Plane3D.h.

◆ fB

template<typename T = double>

Scalar ROOT::Math::Impl::Plane3D< T >::fB

private

Definition at line 283 of file Plane3D.h.

◆ fC

template<typename T = double>

Scalar ROOT::Math::Impl::Plane3D< T >::fC

private

Definition at line 284 of file Plane3D.h.

◆ fD

template<typename T = double>

Scalar ROOT::Math::Impl::Plane3D< T >::fD

private

Definition at line 285 of file Plane3D.h.

math/genvector/inc/Math/GenVector/Plane3D.h

Public Types

Public Member Functions

Protected Member Functions

Private Member Functions

Private Attributes

Member Typedef Documentation

◆ Point

◆ Scalar

◆ Vector

Constructor & Destructor Documentation

◆ Plane3D() [1/7]

◆ Plane3D() [2/7]

◆ Plane3D() [3/7]

◆ Plane3D() [4/7]

◆ Plane3D() [5/7]

◆ Plane3D() [6/7]

◆ Plane3D() [7/7]

Member Function Documentation

◆ A()

◆ B()

◆ BuildFrom3Points()

◆ BuildFromVecAndPoint()

◆ C()

◆ D()

◆ Distance() [1/2]

◆ Distance() [2/2]

◆ HesseDistance()

◆ Normal()

◆ Normalize() [1/2]

◆ Normalize() [2/2]

◆ operator!=()

◆ operator=()

◆ operator==()

◆ ProjectOntoPlane() [1/2]

◆ ProjectOntoPlane() [2/2]

Member Data Documentation

◆ fA

◆ fB

◆ fC

◆ fD