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

Inheritance diagram for trax::Spline:

Public Types
enum class	WrapTypes { none = 0 , nonperiodic , periodic , pinned }
	Type of handling the ends:
using	SegmentValueType = CubicData
using	Data = std::vector<SegmentValueType>
	Data definig the curve.
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...

Public Member Functions
virtual int	CountControlPoints () const noexcept=0
virtual common::Interval< Length >	ResetControlPointAndTangent (int idx, const spat::VectorBundle< Length > &controlPointAndTangent)=0
	Resets a control point.
virtual spat::VectorBundle< Length >	GetControlPointAndTangent (int idx) const =0
virtual Length	GetParameter (int idx) const =0
virtual int	UpperBound (Length s) const =0
	The index of the control point that is the first one to have greater parameter than s.
virtual bool	HasGaps (Length epsilon=epsilon__length) const noexcept=0
	Check smoothness of the curve at the control points.
virtual bool	HasKinks (Angle epsilon=epsilon__angle) const noexcept=0
	Check smoothness of the tangets of the curve at the control points.
virtual common::Interval< Length >	Shorten (common::Interval< Length > toRange)=0
	Transforms the Spline to one with the given parameter range.
virtual const Data &	GetData () const noexcept=0
	Retrieves the data to construct this curve type. A roundtrip is guaranteed to be invariant.
Creation
virtual common::Interval< Length >	Create (const Curve &originalCurve, common::Interval< Length > range, Length maxDeviation=epsilon__length, common::Interval< Length > sampleDistanceLimits={ 1_m, 1000_m })=0
	Creates a spline curve from an existing curve.
virtual common::Interval< Length >	Create (std::pair< std::shared_ptr< const Curve >, common::Interval< Length > > originalCurve, Length maxDeviation=epsilon__length, common::Interval< Length > sampleDistanceLimits={ 1_m, 1000_m })=0
virtual common::Interval< Length >	Create (const std::vector< spat::VectorBundle< Length > > &controlPointsAndTangents)=0
	Creates a Cubic Hermite Spline, guaranteed to be C1 (points and tangents match).
virtual common::Interval< Length >	Create (const std::vector< spat::Position< Length > > &controlPoints)=0
	Natural Cubic C2 - smooth Spline (points, tangent, normal and curvature of the segments match).
virtual common::Interval< Length >	Create (const std::vector< spat::Position< Length > > &controlPoints, bool bClampedAtStart, const spat::Vector< Length > &startTangent, bool bClampedAtEnd, const spat::Vector< Length > &endTangent)=0
	Clamped Cubic C2 - smooth Spline (points, tangent, normal and curvature of the segments match).
virtual common::Interval< Length >	CreateCatmullRom (const std::vector< spat::Position< Length > > &controlPoints, One tension=0.5f, WrapTypes wrap=WrapTypes::nonperiodic)=0
	C1 Spline with Pi'th tangent being: tension * (Pi+1 - Pi-1).
virtual common::Interval< Length >	CreateCatmullRom (const std::vector< spat::VectorBundle< Length, One > > &controlPoints, One tension=0.5f, WrapTypes wrap=WrapTypes::nonperiodic)=0
	C1 Spline with Pi'th tangent being: tension * (Pi+1 - Pi-1).Length() * Ti.
virtual common::Interval< Length >	CreateBezier (const std::vector< spat::Position< Length > > &controlPoints, WrapTypes wrap=WrapTypes::nonperiodic)=0
	C0 Spline from Cubic Bezier control points.
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.
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< Spline >	Make () noexcept
	Makes a Spline object.

Additional Inherited Members
Protected Member Functions inherited from trax::Curve
	Curve (const Curve &)=default

Detailed Description

\ brief Cubic Hermite Spline.

Member Typedef Documentation

◆ Data

using trax::Spline::Data = std::vector<SegmentValueType>

Data definig the curve.

This is used for persistence. GetData() receives the data and there is a Create() method to create the curve from this data set without any calculations made that might distort the values during many read/write cycles.

◆ SegmentValueType

using trax::Spline::SegmentValueType = CubicData

Type of the segments.

Member Function Documentation

◆ CountControlPoints()

virtual int trax::Spline::CountControlPoints ( ) const

pure virtualnoexcept

Returns: the number of control points.

◆ Create() [1/6]

virtual common::Interval< Length > trax::Spline::Create	(	const Curve &	originalCurve,
		common::Interval< Length >	range,
		Length	maxDeviation = epsilon__length,
		common::Interval< Length >	sampleDistanceLimits = { 1_m, 1000_m } )

pure virtual

Creates a spline curve from an existing curve.

Parameters

originalCurve	valid template curve.
range	range on the template curve
maxDeviation	the maximum positional deviation.
sampleDistanceLimits	The minimum and maximum distance between the sample points

Exceptions

std::invalid_argument	if originalCurve is not a valid curve, or the range of the curve does not intersect with range, or maxDeviation <= 0_m.
std::runtime_error	if the curve could not get created.

◆ Create() [2/6]

virtual common::Interval< Length > trax::Spline::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.

Returns: The total curve range between start and end.

Exceptions

std::invalid_argument if the creation fails.

◆ Create() [3/6]

virtual common::Interval< Length > trax::Spline::Create ( const std::vector< spat::Position< Length > > & controlPoints )

pure virtual

Natural Cubic C2 - smooth Spline (points, tangent, normal and curvature of the segments match).

These are used in railroading often (or better be). The curvatures at start and end are zero.

Parameters

controlPoints A series of points to be connected by the spline.

Returns: The total curve range between start and end.

Exceptions

std::invalid_argument if there are less then two control points.

◆ Create() [4/6]

virtual common::Interval< Length > trax::Spline::Create	(	const std::vector< spat::Position< Length > > &	controlPoints,
		bool	bClampedAtStart,
		const spat::Vector< Length > &	startTangent,
		bool	bClampedAtEnd,
		const spat::Vector< Length > &	endTangent )

pure virtual

Clamped Cubic C2 - smooth Spline (points, tangent, normal and curvature of the segments match).

These are used in railroading often (or better be). The curvatures at start and end are given by the supplied tangent vectors. If both end are set to be not clamped, a Natural Cubic C2 spline will be generated.

Parameters

controlPoints	A series of points to be connected by the spline.
bClampedAtStart	If true the start tangent will be used.
bClampedAtEnd	If true the end tangent will be used.
startTangent	Tangent (and cubic overshoot) at start point.
endTangent	Tangent (and cubic overshoot) at end point.

Returns: The total curve range between start and end.

Exceptions

std::invalid_argument if there are less then two control points.

◆ Create() [5/6]

virtual common::Interval< Length > trax::Spline::Create ( const std::vector< spat::VectorBundle< Length > > & controlPointsAndTangents )

pure virtual

Creates a Cubic Hermite Spline, guaranteed to be C1 (points and tangents match).

There are methods to yield these controlPoint-tangents by different interpolation methods. See below.

Returns: The total curve range between start and end.

Exceptions

std::invalid_argument if there are less then two control points.

◆ Create() [6/6]

virtual common::Interval< Length > trax::Spline::Create	(	std::pair< std::shared_ptr< const Curve >, common::Interval< Length > >	originalCurve,
		Length	maxDeviation = epsilon__length,
		common::Interval< Length >	sampleDistanceLimits = { 1_m, 1000_m } )

pure virtual

Parameters

originalCurve	valid template curve.
maxDeviation	the maximum positional deviation.
sampleDistanceLimits	The minimum and maximum distance between the sample points

Exceptions

std::invalid_argument	if originalCurve is not a valid curve, or the range of the curve does not intersect with range, or maxDeviation <= 0_m.
std::runtime_error	if the curve could not get created.

◆ CreateBezier()

virtual common::Interval< Length > trax::Spline::CreateBezier	(	const std::vector< spat::Position< Length > > &	controlPoints,
		WrapTypes	wrap = WrapTypes::nonperiodic )

pure virtual

C0 Spline from Cubic Bezier control points.

These are 4 control points (P0,P1,P2,P3) for the first segment and 3 control points (P4,P5,P6) for each following segment.

/// p1 = P0 
/// t1 = 3(P1-P0)
/// p2 = P3
/// t2 = 3(P3-P2)
/// 
/// p1 = P3
/// t1 = 3(P4-P3)
/// p2 = P6
/// t2 = 3(P6-P5)
///

etc...

If the wrap type is periodic, the last segment will be closed with the first segment by an additional segment. For this only two additional control points are expected, since the first and last control point are the same.

Parameters

controlPoints	A series of points to define the spline. For nonperiodic splines the number of control points n is needed to define (n-4)/3 + 1 segments; for periodic it will be n/3 segments.
wrap	Type of wrapping the spline.

Returns: The total curve range between start and end.

Exceptions

std::invalid_argument if the control points are not the right count.

◆ CreateCatmullRom() [1/2]

virtual common::Interval< Length > trax::Spline::CreateCatmullRom	(	const std::vector< spat::Position< Length > > &	controlPoints,
		One	tension = 0.5f,
		WrapTypes	wrap = WrapTypes::nonperiodic )

pure virtual

C1 Spline with Pi'th tangent being: tension * (Pi+1 - Pi-1).

This might match well with paths on top of terrains. The tangents at start and end are tension * (P1 - P0) and tension * (Pn - Pn-1) respectively.

Parameters

controlPoints	A series of points to be connected by the spline.
tension	Streching value for the tangent's cubic overshoot. Must be > 0.
wrap	Type of wrapping the spline. If WrapTypes::periodic, the first and last control point will be connected by an additional segment.

Returns: The total curve range between start and end

Exceptions

std::invalid_argument	if there are less then two control points.
std::invalid_argument	if tension <= 0.

◆ CreateCatmullRom() [2/2]

virtual common::Interval< Length > trax::Spline::CreateCatmullRom	(	const std::vector< spat::VectorBundle< Length, One > > &	controlPoints,
		One	tension = 0.5f,
		WrapTypes	wrap = WrapTypes::nonperiodic )

pure virtual

C1 Spline with Pi'th tangent being: tension * (Pi+1 - Pi-1).Length() * Ti.

Modified Catmull-Rom for known tangent directions.

Parameters

controlPoints	A series of points and tangents to be connected by the spline.
tension	Streching value for the tangent's cubic overshoot. Must be > 0.
wrap	Type of wrapping the spline. If WrapTypes::periodic, the first and last control point will be connected by an additional segment.

Returns: The total curve range between start and end

Exceptions

std::invalid_argument	if there are less then two control points.
std::invalid_argument	if tension <= 0.

◆ GetControlPointAndTangent()

virtual spat::VectorBundle< Length > trax::Spline::GetControlPointAndTangent ( int idx ) const

pure virtual

Parameters

idx	id of the control point to retrieve [0,CountControlPoints()[.

Returns: Position and tangent (including cubic overshoot) at control point.

Exceptions

std::out_of_range	if idx is out of range.
std::logic_error	if the spline wasn't created before.

◆ GetParameter()

virtual Length trax::Spline::GetParameter ( int idx ) const

pure virtual

Parameters

idx	id of the control point to retrieve [0,CountControlPoints()[.

Returns: the arc length parameter at a control point.

Exceptions

std::out_of_range if idx is out of range.

◆ ResetControlPointAndTangent()

virtual common::Interval< Length > trax::Spline::ResetControlPointAndTangent	(	int	idx,
		const spat::VectorBundle< Length > &	controlPointAndTangent )

pure virtual

Resets a control point.

The methods will change the controlpoint only. Any property achieved by using specially interpolated data sets might get lost.

Parameters

idx	id of the control point to reset [0,CountControlPoints()[.
controlPointAndTangent	3D position and tangent including cubic overshoot.

Returns: The total curve range between start and end.

Exceptions

std::logic_error	if the spline wasn't created before.
std::out_of_range	if idx is out of range.

◆ Shorten()

virtual common::Interval< Length > trax::Spline::Shorten ( common::Interval< Length > toRange )

pure virtual

Transforms the Spline to one with the given parameter range.

Shortens the curve in a way that it will run from the starting point of toRange to the end along the same path as the original, but with parameters running between {0_m,toRange.Length()}.

Parameters

toRange Parameter range of the original Spline, to transform the Spline to. If toRange is outside the original range it will get clipped.

Returns: {0_m,toRange.Length()}, the new parameter range.

Exceptions

std::invalid_argument if the creation of the shorter spline fails.

◆ UpperBound()

virtual int trax::Spline::UpperBound ( Length s ) const

pure virtual

The index of the control point that is the first one to have greater parameter than s.

The index might become greater than CountControlPoints() - 1, in what case s is beyond the curves range.

Returns: the index of the first control point that has a parameter value greater then s.

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

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

Public Types

Public Member Functions

Static Public Member Functions

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ Data

◆ SegmentValueType

Member Function Documentation

◆ CountControlPoints()

◆ Create() [1/6]

◆ Create() [2/6]

◆ Create() [3/6]

◆ Create() [4/6]

◆ Create() [5/6]

◆ Create() [6/6]

◆ CreateBezier()

◆ CreateCatmullRom() [1/2]

◆ CreateCatmullRom() [2/2]

◆ GetControlPointAndTangent()

◆ GetParameter()

◆ ResetControlPointAndTangent()

◆ Shorten()

◆ UpperBound()