A three dimensional spiral with owned parameters. More...

#include <C:/Trend/Development/Trax3/Code/trax/Curve.h>

Inheritance diagram for trax::HelixP:

Classes
struct	Data
	Data definig the curve. More...

Public Member Functions
virtual spat::VectorBundle2< Length, One >	Center () const noexcept=0
virtual Length	Radius () const noexcept=0
virtual One	Slope () const noexcept=0
virtual spat::SquareMatrix< One, 3 >	Jacobian (Length s) const =0
	Returns the partial derivatives of the position P to the parameters a, b and s in a matrix, customly called a 'Jacobian matrix'.
virtual const Data &	GetData () const noexcept=0
	Retrieves the data to construct this curve type. A roundtrip is guaranteed to be invariant.
Creation
virtual void	Create (const spat::Frame< Length, One > &start, AnglePerLength curvature, AnglePerLength torsion)=0
	Create the Helix.
virtual common::Interval< Length >	Create (const spat::VectorBundle< Length, One > &start, const spat::Position< Length > &end, const spat::Vector< One > &up=Up, Angle e_angle=epsilon__angle)=0
	Create an upright Helix from start to end.
virtual common::Interval< Length >	Create (const spat::Position< Length > &start, const spat::VectorBundle< Length, One > &end, const spat::Vector< One > &up=Up, Angle e_angle=epsilon__angle)=0
virtual void	Create (const spat::VectorBundle2< Length, One > &center, AnglePerLength curvature, AnglePerLength torsion)=0
	Create the Helix.
virtual common::Interval< Length >	Create (const Data &data)=0
	Create the Helix from data set for wich it is guaranteed, that no calculational drift will happen e.g. in write/read cycles.
Public Member Functions inherited from trax::Curve
virtual const char *	TypeName () const noexcept=0
virtual CurveType	GetCurveType () const noexcept=0
virtual bool	IsValid () const noexcept=0
virtual AnglePerLength	Curvature (Length s) const =0
virtual AnglePerLength	Torsion (Length s) const =0
virtual bool	IsFlat () const noexcept=0
virtual void	Transition (Length s, spat::Position< Length > &pos) const =0
	Copies the 3D Position at the specified location to pos.
virtual void	Transition (Length s, spat::Vector< One > &tan) const =0
	Copies the 3D tangential vector at the specified location to tan.
virtual void	Transition (Length s, spat::VectorBundle< Length, One > &bundle) const =0
	Copies the 3D Position and tangential vector at the specified location to bundle.
virtual void	Transition (Length s, spat::VectorBundle2< Length, One > &bundle) const =0
	Copies the 3D Position and tangential and normal vectors at the specified location to bundle.
virtual void	Transition (Length s, spat::Frame< Length, One > &frame) const =0
	Copies the 3D TBN-Frame at the specified location to frame.
virtual std::vector< Length >	ZeroSet () const =0
	Returns a list of parameters at which the normal vector flips from one side to the other.
virtual common::Interval< Length >	Range () const =0
virtual spat::Vector< One >	LocalUp () const =0
	Gives the Curve's idiosyncratic up direction. Some curves maintain some idea about where they have their upside, either because of their form (e.g Helix) or because it is extra defined (e.g. for Line). Some curves maintain no such notion (e.g. many Cubics).
virtual spat::Frame< Length, One >	GetCurveLocalTransformation () const =0
virtual std::unique_ptr< Curve >	Clone () const =0
	make an exact copy of this curve.
virtual bool	Mirror (const spat::VectorBundle< Length, One > &mirrorPlane)=0
	Make a Curve with mirrored geometry (but of course one thet returns right handed frames).
virtual bool	Equals (const Curve &toCurve, common::Interval< Length > range, Length epsilon_length=epsilon__length, Angle epsilon_angle=epsilon__angle) const =0
	Comparison.
	Curve (Curve &&)=delete
Curve &	operator= (const Curve &)=delete
Curve &	operator= (Curve &&)=delete

Static Public Member Functions
static dclspc std::unique_ptr< HelixP >	Make () noexcept
	Makes a HelixP object.

Additional Inherited Members
Public Types inherited from trax::Curve
enum class	CurveType { none = 0 , Line , Arc , Helix , LineP , ArcP , HelixP , Clothoid , Cubic , Spline , Rotator , RotatorWithOffset , RotatorChain , PolygonalChain , SampledCurve , Parallel , EEPCurve , EEPResidual , EEPAlternative , Unknown , UserDefined }
	Curve type identification values. More...
Protected Member Functions inherited from trax::Curve
	Curve (const Curve &)=default

Detailed Description

A three dimensional spiral with owned parameters.

Try to use 'Helix' instead. Only use this curve with redundant parameters if you really need it; for example to position a curve independently from the track's frame, or you want to use the create methods on a curve directly.

/// k                   : curvature
/// t                   : torsion
/// a                   : radius
/// b/a == tan(alpha)   : slope
///
///         { a*cos( s/sqrt(a²+b²) ) }
/// P(s) =  { a*sin( s/sqrt(a²+b²) ) }
///         { b*s/sqrt(a²+b²)        }
///
/// k = a / (a² + b²)
/// t = b / (a² + b²)
/// a = k / (k² + t²)
/// b = t / (k² + t²)
///

Member Function Documentation

◆ Center()

virtual spat::VectorBundle2< Length, One > trax::HelixP::Center ( ) const

pure virtualnoexcept

Returns: The center around wich the spiral turns. The T vector points to the spiral at parameter 0.

◆ Create() [1/5]

virtual common::Interval< Length > trax::HelixP::Create ( const Data & data )

pure virtual

Create the Helix from data set for wich it is guaranteed, that no calculational drift will happen e.g. in write/read cycles.

Exceptions

std::invalid_argument if the curve can not created from the input values.

◆ Create() [2/5]

virtual void trax::HelixP::Create	(	const spat::Frame< Length, One > &	start,
		AnglePerLength	curvature,
		AnglePerLength	torsion )

pure virtual

Create the Helix.

Parameters

start	Starting point with tangent, normal and binormal directions.
curvature	Constant curvature of the Helix. Keep in mind that the radius of the helix is r = k / (k² + t²), not 1/k.
torsion	Constant torsion (winding) of the helix.

Exceptions

std::invalid_argument if curvature <= 0.

◆ Create() [3/5]

virtual common::Interval< Length > trax::HelixP::Create	(	const spat::Position< Length > &	start,
		const spat::VectorBundle< Length, One > &	end,
		const spat::Vector< One > &	up = Up,
		Angle	e_angle = epsilon__angle )

pure virtual

Parameters

start	Starting point with starting direction perpendicular to Up.
end	End point of helix.
up	Up direction.
e_angle	the total angle of the arc that would be too small, so creation fails.

Returns: the range along the curve from start to end.

Exceptions

std::invalid_argument if a helix can not get calculated from input values, e.g. the two points are too near or the start.T points directly to end.

◆ Create() [4/5]

virtual void trax::HelixP::Create	(	const spat::VectorBundle2< Length, One > &	center,
		AnglePerLength	curvature,
		AnglePerLength	torsion )

pure virtual

Create the Helix.

Parameters

center	Center point of the helix. center.T points to starting point of the helix at s=0.
curvature	Constant curvature of the Helix. Keep in mind that the radius of the helix is r = c / (c² + t²), not 1/c.
torsion	Constant torsion (winding) of the helix.

Exceptions

std::invalid_argument if curvature <= 0.

◆ Create() [5/5]

virtual common::Interval< Length > trax::HelixP::Create	(	const spat::VectorBundle< Length, One > &	start,
		const spat::Position< Length > &	end,
		const spat::Vector< One > &	up = Up,
		Angle	e_angle = epsilon__angle )

pure virtual

Create an upright Helix from start to end.

Parameters

start	Starting point with starting direction perpendicular to Up.
end	End point of helix.
up	Up direction.
e_angle	the total angle of the arc that would be too small, so creation fails.

Returns: the range along the curve from start to end.

Exceptions

std::invalid_argument if a helix can not get calculated from input values, e.g. the two points are too near or the start.T points directly to end.

◆ Jacobian()

virtual spat::SquareMatrix< One, 3 > trax::HelixP::Jacobian ( Length s ) const

pure virtual

Returns the partial derivatives of the position P to the parameters a, b and s in a matrix, customly called a 'Jacobian matrix'.

For calculation

See also: Helix::Jacobian.

Parameters

s	parameter to evaluate the derivatives.

Returns: dP/da, dP/db and dP/ds will make up the 0th, 1st and 2nd column of the matrix.

Exceptions

std::bad_alloc on memory exhaustion.

◆ Radius()

virtual Length trax::HelixP::Radius ( ) const

pure virtualnoexcept

Returns: Radius of helix, same as value a.

◆ Slope()

virtual One trax::HelixP::Slope ( ) const

pure virtualnoexcept

Returns: Tangens of inclination angle, being: b/a.

The documentation for this struct was generated from the following file:

C:/Trend/Development/Trax3/Code/trax/Curve.h

Classes

Public Member Functions

Static Public Member Functions

Additional Inherited Members

Detailed Description

Member Function Documentation

◆ Center()

◆ Create() [1/5]

◆ Create() [2/5]

◆ Create() [3/5]

◆ Create() [4/5]

◆ Create() [5/5]

◆ Jacobian()

◆ Radius()

◆ Slope()