Curve with evenly (with respect to arc length) rotating tangent vector. More...

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

Inheritance diagram for trax::Rotator:

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

Public Member Functions
virtual spat::SquareMatrix< Real, 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 common::Interval< Length >	Create (const Data &data)=0
	Create the curve from data set for which it is guaranteed, that no calculational drift will happen e.g. in write/read cycles.
virtual const Data &	GetData () const noexcept=0
	Retrieves the data to construct this curve type. A roundtrip is guaranteed to be invariant.
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< Rotator >	Make (CurveType type=CurveType::Rotator) noexcept
	Makes a Rotator 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

Curve with evenly (with respect to arc length) rotating tangent vector.

The curve starts at origin with tangent in Ex direction and will rotate its tangent around Ez by a*s and around T x Ez by b*s.

By definition it is:

/// 
///              ( cos(a(s)) cos(b(s)) )
/// dP/ds = D1 = ( sin(a(s)) cos(b(s)) )
///              (           sin(b(s)) )
///
///

With some arbitray functions a(s), b(s). Since D1² = 1, the solution of the above differential equation, P(s), will be parameterized by arc length. So we have to solve the following integral:

///         s               s ( cos(a) cos(b) )
/// P(s) =  I dP(t)/dt dt = I ( sin(a) cos(b) ) dt =
///         0               0 (        sin(b) )
///
/// Bronstein 1991
/// 2.5.2.1.3.
///             s ( cos(a-b) + cos(a+b) )
///      =  1/2 I ( sin(a-b) + sin(a+b) ) dt
///             0 (          2 sin(b)   )
///
///

If we redefine a = a*s and b = b*s with now constant a,b, we get:

/// 
///             s ( cos((a-b)t) + cos((a+b)t) )
///      =  1/2 I ( sin((a-b)t) + sin((a+b)t) ) dt
///             0 (             2 sin(bt)     )
///
///             (  sin((a-b)t)/(a-b) + sin((a+b)t)/(a+b) ) s
///      =  1/2 ( -cos((a-b)t)/(a-b) - cos((a+b)t)/(a+b) ) |
///             (                   -2 cos(bt)/b         ) 0
///
///             (  sin((a-b)s)/(a-b) + sin((a+b)s)/(a+b) - 0                 )
///      =  1/2 ( -cos((a-b)s)/(a-b) - cos((a+b)s)/(a+b) + 1/(a-b) + 1/(a+b) )
///             (                   -2 cos(bs)/b         + 2/b               )
///
///             (      sin((a-b)s)/(a-b) + sin((a+b)s)/(a+b)     )
///      =  1/2 (  (1-cos((a-b)s))/(a-b) + (1-cos((a+b)s))/(a+b) )
///             (                        2 (1-cos(bs))/b         )
///
///

The Rotator has non constant curvature: k = sqrt(D2*D2) = sqrt( pow<2>(a*cos(b*s)) + pow<2>(b) ), which only for a == 0 or b == 0 becomes constant, which cases would deliver an arc with curvature b or a respectively. Note that no other values for a and b would deliver an arc or a helix and that it in general can not get Normalize() 'd.

Member Function Documentation

◆ Create()

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

pure virtual

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

Exceptions

std::invalid_argument if for a non-offest rotator a0 or b0 ain't zero.

◆ Jacobian()

virtual spat::SquareMatrix< Real, 3 > trax::Rotator::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'.

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.

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

◆ Create()

◆ Jacobian()