Class with methods for projection of vectors on a plane. More...

#include "Decomposer.h"

Public Types
using	AffinePlaneBase_t = AffinePlaneBase< Vector, Point >

using	DecomposedVector_t = DecomposedVector< ProjVector >
	Type of decomposed vector. More...

using	Point_t = typename AffinePlaneBase_t::Point_t
	Type for a point. More...

using	Vector_t = typename AffinePlaneBase_t::Vector_t
	Type for a vector. More...

using	Projection_t = typename DecomposedVector_t::Projection_t
	Type representing the projection vector. More...

using	Distance_t = typename DecomposedVector_t::Distance_t
	Type representing the signed distance from the projection plane. More...

Public Member Functions
	PlaneDecomposer ()
	Default constructor: projection on (x,y) with origin (0, 0, 0) More...

	PlaneDecomposer (AffinePlaneBase_t &&base)
	Constructor: specifies a base (an origin and two direction vectors) More...

	PlaneDecomposer (AffinePlaneBase_t const &base)
	Constructor: specifies a base (an origin and two direction vectors) More...

Setters
void	SetBase (AffinePlaneBase_t &&base)
	Change projection base. More...

void	SetBase (AffinePlaneBase_t const &base)
	Change projection base. More...

void	SetOrigin (Point_t const &point)
	Change the 3D point of the reference frame origin. More...

void	SetMainDir (Vector_t const &dir)
	Change the main direction of the projection base. More...

void	SetSecondaryDir (Vector_t const &dir)
	Change the secondary direction of the projection base. More...

Reference point and base
Point_t	ReferencePoint () const
	Returns the reference point for the plane coordinate, as a 3D point. More...

Vector_t const &	MainDir () const
	Returns the plane main axis direction. More...

Vector_t const &	SecondaryDir () const
	Returns the plane secondary axis direction. More...

AffinePlaneBase_t const &	Base () const
	Returns the complete base representation. More...

Projection coordinate access
These methods act on 2D (vector) projections.
auto	MainComponent (Projection_t const &v) const
	Returns the main component of a projection vector. More...

auto	SecondaryComponent (Projection_t const &v) const
	Returns the secondary component of a projection vector. More...

Projection on plane
auto	PointMainComponent (Point_t const &point) const
	Returns the main component of a 3D point. More...

auto	PointSecondaryComponent (Point_t const &point) const
	Returns the secondary component of a 3D point. More...

Projection_t	PointProjection (Point_t const &point) const
	Returns the projection of the specified point on the plane. More...

auto	VectorMainComponent (Vector_t const &v) const
	Returns the main component of a projection vector. More...

auto	VectorSecondaryComponent (Vector_t const &v) const
	Returns the secondary component of a projection vector. More...

Projection_t	VectorProjection (Vector_t const &v) const
	Returns the projection of the specified vector on the plane. More...

double	Angle (Vector_t const &v) const
	Returns the angle of the projection from main direction. More...

Composition from plane to 3D
Vector_t	ComposeVector (Projection_t const &projection) const
	Returns the 3D vector from the specified projection. More...

Point_t	ComposePoint (Projection_t const &projection) const
	Returns the 3D point from the specified projection. More...

Private Attributes
AffinePlaneBase_t	fPlaneBase
	Reference base. More...

Detailed Description

template<typename Vector, typename Point, typename ProjVector>
class geo::PlaneDecomposer< Vector, Point, ProjVector >

Class with methods for projection of vectors on a plane.

Template Parameters

Vector	type to represent 3D vectors
Point	type to represent 3D points
ProjVector	type to represent 2D projection on plane

These methods deal with projection of points and vectors on a plane.

The plane is defined in a 3D space, with two axes, the "main" and the "auxiliary" one, which are orthogonal.

Definition at line 179 of file Decomposer.h.

Member Typedef Documentation

template<typename Vector, typename Point, typename ProjVector>

using geo::PlaneDecomposer< Vector, Point, ProjVector >::AffinePlaneBase_t = AffinePlaneBase<Vector, Point>

Definition at line 183 of file Decomposer.h.

template<typename Vector, typename Point, typename ProjVector>

using geo::PlaneDecomposer< Vector, Point, ProjVector >::DecomposedVector_t = DecomposedVector<ProjVector>

Type of decomposed vector.

Definition at line 186 of file Decomposer.h.

template<typename Vector, typename Point, typename ProjVector>

using geo::PlaneDecomposer< Vector, Point, ProjVector >::Distance_t = typename DecomposedVector_t::Distance_t

Type representing the signed distance from the projection plane.

Definition at line 198 of file Decomposer.h.

template<typename Vector, typename Point, typename ProjVector>

using geo::PlaneDecomposer< Vector, Point, ProjVector >::Point_t = typename AffinePlaneBase_t::Point_t

Type for a point.

Definition at line 189 of file Decomposer.h.

template<typename Vector, typename Point, typename ProjVector>

using geo::PlaneDecomposer< Vector, Point, ProjVector >::Projection_t = typename DecomposedVector_t::Projection_t

Type representing the projection vector.

Definition at line 195 of file Decomposer.h.

template<typename Vector, typename Point, typename ProjVector>

using geo::PlaneDecomposer< Vector, Point, ProjVector >::Vector_t = typename AffinePlaneBase_t::Vector_t

Type for a vector.

Definition at line 192 of file Decomposer.h.

Constructor & Destructor Documentation

template<typename Vector, typename Point, typename ProjVector>

geo::PlaneDecomposer< Vector, Point, ProjVector >::PlaneDecomposer ( )

inline

Default constructor: projection on (x,y) with origin (0, 0, 0)

Definition at line 202 of file Decomposer.h.

       : fPlaneBase(
         { 0.0, 0.0, 0.0 }, // origin
         { 1.0, 0.0, 0.0 }, // x axis
         { 0.0, 1.0, 0.0 }  // y axis
         )
       {}

template<typename Vector, typename Point, typename ProjVector>

geo::PlaneDecomposer< Vector, Point, ProjVector >::PlaneDecomposer ( AffinePlaneBase_t && base )

inline

Constructor: specifies a base (an origin and two direction vectors)

Definition at line 211 of file Decomposer.h.

211 : fPlaneBase(std::move(base)) {}

geo::PlaneDecomposer::fPlaneBase

AffinePlaneBase_t fPlaneBase

Reference base.

Definition: Decomposer.h:375

template<typename Vector, typename Point, typename ProjVector>

geo::PlaneDecomposer< Vector, Point, ProjVector >::PlaneDecomposer ( AffinePlaneBase_t const & base )

inline

Constructor: specifies a base (an origin and two direction vectors)

Definition at line 214 of file Decomposer.h.

214 : fPlaneBase(base) {}

geo::PlaneDecomposer::fPlaneBase

AffinePlaneBase_t fPlaneBase

Reference base.

Definition: Decomposer.h:375

Member Function Documentation

template<typename Vector, typename Point, typename ProjVector>

double geo::PlaneDecomposer< Vector, Point, ProjVector >::Angle ( Vector_t const & v ) const

inline

Returns the angle of the projection from main direction.

Parameters

v	vector to get the angle of

Returns: the angle of the projection from main direction, in radians

The projection on the plane is taken, and its angle from the main direction is returned. That angle is defined in the range $\left[ -\pi, \pi \right]$ , so that it is 0 for a projection matching the main direction and $\pi/2$ for one matching the secondary direction.

Definition at line 328 of file Decomposer.h.

       {
         double const a
           = std::atan2(VectorSecondaryComponent(v), VectorMainComponent(v));
         return (a >= M_PI)? -M_PI: a;
       }

template<typename Vector, typename Point, typename ProjVector>

AffinePlaneBase_t const& geo::PlaneDecomposer< Vector, Point, ProjVector >::Base ( ) const

inline

Returns the complete base representation.

Definition at line 250 of file Decomposer.h.

250 { return fPlaneBase; }

geo::PlaneDecomposer::fPlaneBase

AffinePlaneBase_t fPlaneBase

Reference base.

Definition: Decomposer.h:375

template<typename Vector, typename Point, typename ProjVector>

Point_t geo::PlaneDecomposer< Vector, Point, ProjVector >::ComposePoint ( Projection_t const & projection ) const

inline

Returns the 3D point from the specified projection.

Parameters

projection the projection vector on the plane

Returns: the 3D point representing the projection vector in world space

See also: Projection(), ReferencePoint()

The returned point is the 3D representation in space of the point of the plane described by the specified projection. The null projection is composed into the reference point returned by ReferencePoint().

Definition at line 369 of file Decomposer.h.

370 { return ReferencePoint() + ComposeVector(projection); }

geo::PlaneDecomposer::ComposeVector

Vector_t ComposeVector(Projection_t const &projection) const

Returns the 3D vector from the specified projection.

Definition: Decomposer.h:351

geo::PlaneDecomposer::ReferencePoint

Point_t ReferencePoint() const

Returns the reference point for the plane coordinate, as a 3D point.

Definition: Decomposer.h:241

template<typename Vector, typename Point, typename ProjVector>

Vector_t geo::PlaneDecomposer< Vector, Point, ProjVector >::ComposeVector ( Projection_t const & projection ) const

inline

Returns the 3D vector from the specified projection.

Parameters

projection the projection vector on the plane

Returns: the 3D vector representing the projection vector in world space

See also: Projection()

The returned vector is the 3D representation in space of the point of the plane described by the specified projection. The null projection is composed into a null vector.

Definition at line 351 of file Decomposer.h.

       {
         return MainComponent(projection) * MainDir()
           + SecondaryComponent(projection) * SecondaryDir()
           ;
       }

template<typename Vector, typename Point, typename ProjVector>

auto geo::PlaneDecomposer< Vector, Point, ProjVector >::MainComponent ( Projection_t const & v ) const

inline

Returns the main component of a projection vector.

Definition at line 262 of file Decomposer.h.

262 { return v.X(); }

template<typename Vector, typename Point, typename ProjVector>

Vector_t const& geo::PlaneDecomposer< Vector, Point, ProjVector >::MainDir ( ) const

inline

Returns the plane main axis direction.

Definition at line 244 of file Decomposer.h.

244 { return Base().MainDir(); }

geo::PlaneDecomposer::Base

AffinePlaneBase_t const & Base() const

Returns the complete base representation.

Definition: Decomposer.h:250

geo::AffinePlaneBase::MainDir

Vector_t const & MainDir() const

Returns the main axis direction.

Definition: Decomposer.h:108

template<typename Vector, typename Point, typename ProjVector>

auto geo::PlaneDecomposer< Vector, Point, ProjVector >::PointMainComponent ( Point_t const & point ) const

inline

Returns the main component of a 3D point.

Definition at line 274 of file Decomposer.h.

275 { return VectorMainComponent(Base().ToVector(point)); }

geo::PlaneDecomposer::VectorMainComponent

auto VectorMainComponent(Vector_t const &v) const

Returns the main component of a projection vector.

Definition: Decomposer.h:297

geo::PlaneDecomposer::Base

AffinePlaneBase_t const & Base() const

Returns the complete base representation.

Definition: Decomposer.h:250

template<typename Vector, typename Point, typename ProjVector>

Projection_t geo::PlaneDecomposer< Vector, Point, ProjVector >::PointProjection ( Point_t const & point ) const

inline

Returns the projection of the specified point on the plane.

Parameters

point the 3D point to be projected, in world coordinates

Returns: a 2D vector representing the projection of point on the plane

The returned vector is a 2D vector expressing the projection of the point (from world coordinates) on the plane. The vector is expressed as $ ( m, s ) $ , components following the main and the secondary direction, respectively. The origin point is the one returned by ReferencePoint().

Definition at line 292 of file Decomposer.h.

293 { return VectorProjection(Base().ToVector(point)); }

geo::PlaneDecomposer::VectorProjection

Projection_t VectorProjection(Vector_t const &v) const

Returns the projection of the specified vector on the plane.

Definition: Decomposer.h:314

geo::PlaneDecomposer::Base

AffinePlaneBase_t const & Base() const

Returns the complete base representation.

Definition: Decomposer.h:250

template<typename Vector, typename Point, typename ProjVector>

auto geo::PlaneDecomposer< Vector, Point, ProjVector >::PointSecondaryComponent ( Point_t const & point ) const

inline

Returns the secondary component of a 3D point.

Definition at line 278 of file Decomposer.h.

279 { return VectorSecondaryComponent(Base().ToVector(point)); }

geo::PlaneDecomposer::Base

AffinePlaneBase_t const & Base() const

Returns the complete base representation.

Definition: Decomposer.h:250

geo::PlaneDecomposer::VectorSecondaryComponent

auto VectorSecondaryComponent(Vector_t const &v) const

Returns the secondary component of a projection vector.

Definition: Decomposer.h:301

template<typename Vector, typename Point, typename ProjVector>

Point_t geo::PlaneDecomposer< Vector, Point, ProjVector >::ReferencePoint ( ) const

inline

Returns the reference point for the plane coordinate, as a 3D point.

Definition at line 241 of file Decomposer.h.

241 { return Base().Origin(); }

geo::AffinePlaneBase::Origin

Point_t Origin() const

Returns the origin of the coordinate system in world coordinates.

Definition: Decomposer.h:117

geo::PlaneDecomposer::Base

AffinePlaneBase_t const & Base() const

Returns the complete base representation.

Definition: Decomposer.h:250

template<typename Vector, typename Point, typename ProjVector>

auto geo::PlaneDecomposer< Vector, Point, ProjVector >::SecondaryComponent ( Projection_t const & v ) const

inline

Returns the secondary component of a projection vector.

Definition at line 265 of file Decomposer.h.

265 { return v.Y(); }

template<typename Vector, typename Point, typename ProjVector>

Vector_t const& geo::PlaneDecomposer< Vector, Point, ProjVector >::SecondaryDir ( ) const

inline

Returns the plane secondary axis direction.

Definition at line 247 of file Decomposer.h.

247 { return Base().SecondaryDir(); }

geo::AffinePlaneBase::SecondaryDir

Vector_t const & SecondaryDir() const

Returns the secondary axis direction.

Definition: Decomposer.h:111

geo::PlaneDecomposer::Base

AffinePlaneBase_t const & Base() const

Returns the complete base representation.

Definition: Decomposer.h:250

template<typename Vector, typename Point, typename ProjVector>

void geo::PlaneDecomposer< Vector, Point, ProjVector >::SetBase ( AffinePlaneBase_t && base )

inline

Change projection base.

Definition at line 220 of file Decomposer.h.

Referenced by geo::Decomposer< Direction_t, Position_t, Projection_t >::SetBase().

220 { fPlaneBase = std::move(base); }

geo::PlaneDecomposer::fPlaneBase

AffinePlaneBase_t fPlaneBase

Reference base.

Definition: Decomposer.h:375

template<typename Vector, typename Point, typename ProjVector>

void geo::PlaneDecomposer< Vector, Point, ProjVector >::SetBase ( AffinePlaneBase_t const & base )

inline

Change projection base.

Definition at line 223 of file Decomposer.h.

223 { fPlaneBase = base; }

geo::PlaneDecomposer::fPlaneBase

AffinePlaneBase_t fPlaneBase

Reference base.

Definition: Decomposer.h:375

template<typename Vector, typename Point, typename ProjVector>

void geo::PlaneDecomposer< Vector, Point, ProjVector >::SetMainDir ( Vector_t const & dir )

inline

Change the main direction of the projection base.

Definition at line 229 of file Decomposer.h.

Referenced by geo::Decomposer< Direction_t, Position_t, Projection_t >::SetMainDir().

229 { fPlaneBase.SetMainDir(dir); }

dir

TDirectory * dir

Definition: macro.C:5

geo::PlaneDecomposer::fPlaneBase

AffinePlaneBase_t fPlaneBase

Reference base.

Definition: Decomposer.h:375

geo::AffinePlaneBase::SetMainDir

void SetMainDir(Vector_t const &dir)

Change the main direction of the projection base.

Definition: Decomposer.h:127

template<typename Vector, typename Point, typename ProjVector>

void geo::PlaneDecomposer< Vector, Point, ProjVector >::SetOrigin ( Point_t const & point )

inline

Change the 3D point of the reference frame origin.

Definition at line 226 of file Decomposer.h.

Referenced by geo::Decomposer< Direction_t, Position_t, Projection_t >::SetOrigin().

226 { fPlaneBase.SetOrigin(point); }

geo::AffinePlaneBase::SetOrigin

void SetOrigin(Point_t const &point)

Change the 3D point of the reference frame origin.

Definition: Decomposer.h:124

geo::PlaneDecomposer::fPlaneBase

AffinePlaneBase_t fPlaneBase

Reference base.

Definition: Decomposer.h:375

template<typename Vector, typename Point, typename ProjVector>

void geo::PlaneDecomposer< Vector, Point, ProjVector >::SetSecondaryDir ( Vector_t const & dir )

inline

Change the secondary direction of the projection base.

Definition at line 232 of file Decomposer.h.

Referenced by geo::Decomposer< Direction_t, Position_t, Projection_t >::SetSecondaryDir().

233 { fPlaneBase.SetSecondaryDir(dir); }

dir

TDirectory * dir

Definition: macro.C:5

geo::PlaneDecomposer::fPlaneBase

AffinePlaneBase_t fPlaneBase

Reference base.

Definition: Decomposer.h:375

geo::AffinePlaneBase::SetSecondaryDir

void SetSecondaryDir(Vector_t const &dir)

Change the secondary direction of the projection base.

Definition: Decomposer.h:130

template<typename Vector, typename Point, typename ProjVector>

auto geo::PlaneDecomposer< Vector, Point, ProjVector >::VectorMainComponent ( Vector_t const & v ) const

inline

Returns the main component of a projection vector.

Definition at line 297 of file Decomposer.h.

298 { return geo::vect::dot(v, MainDir()); }

geo::vect::dot

constexpr auto dot(Vector const &a, Vector const &b)

Return cross product of two vectors.

Definition: geo_vectors_utils.h:990

geo::PlaneDecomposer::MainDir

Vector_t const & MainDir() const

Returns the plane main axis direction.

Definition: Decomposer.h:244

template<typename Vector, typename Point, typename ProjVector>

Projection_t geo::PlaneDecomposer< Vector, Point, ProjVector >::VectorProjection ( Vector_t const & v ) const

inline

Returns the projection of the specified vector on the plane.

Parameters

v	the 3D vector to be projected, in world units

Returns: a 2D vector representing the projection of v on the plane

The returned vector is a 2D vector expressing the projection of the vector (from world units) on the plane. The vector is expressed as $ ( m, s ) $ , components following the main and the secondary direction, respectively.

Definition at line 314 of file Decomposer.h.

315 { return { VectorMainComponent(v), VectorSecondaryComponent(v) }; }

geo::PlaneDecomposer::VectorMainComponent

auto VectorMainComponent(Vector_t const &v) const

Returns the main component of a projection vector.

Definition: Decomposer.h:297

geo::PlaneDecomposer::VectorSecondaryComponent

auto VectorSecondaryComponent(Vector_t const &v) const

Returns the secondary component of a projection vector.

Definition: Decomposer.h:301

template<typename Vector, typename Point, typename ProjVector>

auto geo::PlaneDecomposer< Vector, Point, ProjVector >::VectorSecondaryComponent ( Vector_t const & v ) const