Inkscape: Geom::Curve Class Reference

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Abstract continuous curve on a plane defined on [0,1]. More...

#include <curve.h>

Inheritance diagram for Geom::Curve:

Public Member Functions
virtual	~Curve ()

Evaluate the curve
virtual Point	initialPoint () const =0
	Retrieve the start of the curve.

virtual Point	finalPoint () const =0
	Retrieve the end of the curve.

virtual bool	isDegenerate () const =0
	Check whether the curve has exactly zero length.

virtual bool	isLineSegment () const
	Check whether the curve is a line segment.

virtual Interval	timeRange () const
	Get the interval of allowed time values.

virtual Point	pointAt (Coord t) const
	Evaluate the curve at a specified time value.

virtual Coord	valueAt (Coord t, Dim2 d) const
	Evaluate one of the coordinates at the specified time value.

virtual Point	operator() (Coord t) const
	Evaluate the function at the specified time value.

virtual std::vector< Point >	pointAndDerivatives (Coord t, unsigned n) const =0
	Evaluate the curve and its derivatives.

Change the curve's endpoints
virtual void	setInitial (Point const &v)=0
	Change the starting point of the curve.

virtual void	setFinal (Point const &v)=0
	Change the ending point of the curve.

Compute the bounding box
virtual Rect	boundsFast () const =0
	Quickly compute the curve's approximate bounding box.

virtual Rect	boundsExact () const =0
	Compute the curve's exact bounding box.

virtual void	expandToTransformed (Rect &bbox, Affine const &transform) const =0
	Expand the given rectangle to include the transformed curve, assuming it already contains its initial point.

virtual OptRect	boundsLocal (OptInterval const &i, unsigned deg) const =0

OptRect	boundsLocal (OptInterval const &a) const
	Compute the bounding box of a part of the curve.

Create new curves based on this one
virtual Curve *	duplicate () const =0
	Create an exact copy of this curve.

void	transform (Affine const &m)
	Transform this curve by an affine transformation.

virtual void	operator*= (Translate const &tr)

virtual void	operator*= (Scale const &s)

virtual void	operator*= (Rotate const &r)

virtual void	operator*= (HShear const &hs)

virtual void	operator*= (VShear const &vs)

virtual void	operator*= (Zoom const &z)

virtual void	operator*= (Affine const &m)=0

virtual Curve *	transformed (Affine const &m) const
	Create a curve transformed by an affine transformation.

virtual Curve *	portion (Coord a, Coord b) const =0
	Create a curve that corresponds to a part of this curve.

Curve *	portion (Interval const &i) const
	A version of that accepts an Interval.

virtual Curve *	reverse () const
	Create a reversed version of this curve.

virtual Curve *	derivative () const =0
	Create a derivative of this curve.

Advanced operations
virtual Coord	nearestTime (Point const &p, Coord a=0, Coord b=1) const
	Compute a time value at which the curve comes closest to a specified point.

Coord	nearestTime (Point const &p, Interval const &i) const
	A version that takes an Interval.

virtual std::vector< Coord >	allNearestTimes (Point const &p, Coord from=0, Coord to=1) const
	Compute time values at which the curve comes closest to a specified point.

std::vector< Coord >	allNearestTimes (Point const &p, Interval const &i)
	A version that takes an Interval.

virtual Coord	length (Coord tolerance=0.01) const
	Compute the arc length of this curve.

virtual std::vector< Coord >	roots (Coord v, Dim2 d) const =0
	Computes time values at which the curve intersects an axis-aligned line.

virtual int	winding (Point const &p) const
	Compute the partial winding number of this curve.

virtual std::vector< CurveIntersection >	intersect (Curve const &other, Coord eps=EPSILON) const
	Compute intersections with another curve.

virtual std::vector< CurveIntersection >	intersectSelf (Coord eps=EPSILON) const
	Compute intersections of this curve with itself.

virtual Point	unitTangentAt (Coord t, unsigned n=3) const
	Compute a vector tangent to the curve.

virtual D2< SBasis >	toSBasis () const =0
	Convert the curve to a symmetric power basis polynomial.

Miscellaneous
virtual int	degreesOfFreedom () const
	Return the number of independent parameters required to represent all variations of this curve.

bool	operator== (Curve const &c) const
	Test equality of two curves.

virtual bool	isNear (Curve const &c, Coord precision) const =0
	Test whether two curves are approximately the same.

virtual void	feed (PathSink &sink, bool moveto_initial) const
	Feed the curve to a PathSink.

Protected Member Functions
virtual bool	_equalTo (Curve const &c) const =0

Detailed Description

Abstract continuous curve on a plane defined on [0,1].

Formally, a curve in 2Geom is defined as a function \(\mathbf{C}: [0, 1] \to \mathbb{R}^2\) (a function that maps the unit interval to points on a 2D plane). Its image (the set of points the curve passes through) will be denoted \(\mathcal{C} = \mathbf{C}[ [0, 1] ]\). All curve types available in 2Geom are continuous and differentiable on their interior, e.g. \((0, 1)\). Sometimes the curve's image (value set) is referred to as the curve itself for simplicity, but keep in mind that it's not strictly correct.

It is common to think of the parameter as time. The curve can then be interpreted as describing the position of some moving object from time \(t=0\) to \(t=1\). Because of this, the parameter is frequently called the time value.

Some methods return pointers to newly allocated curves. They are expected to be freed by the caller when no longer used. Default implementations are provided for some methods.

Definition at line 76 of file curve.h.

Constructor & Destructor Documentation

◆ ~Curve()

virtual Geom::Curve::~Curve ( )

inlinevirtual

Definition at line 80 of file curve.h.

Member Function Documentation

◆ _equalTo()

virtual bool Geom::Curve::_equalTo ( Curve const & c ) const

protectedpure virtual

Implemented in Geom::BezierCurve, Geom::EllipticalArc, and Geom::SBasisCurve.

Referenced by operator==().

◆ allNearestTimes() [1/2]

std::vector< Coord > Geom::Curve::allNearestTimes	(	Point const &	p,
		Coord	from = `0`,
		Coord	to = `1`
	)		const

virtual

Compute time values at which the curve comes closest to a specified point.

Parameters

p	Query point
a	Minimum time value to consider
b	Maximum time value to consider; \(a < b\)

Returns: Vector of points closest and equally far away from the query point

Reimplemented in Geom::SBasisCurve, and Geom::EllipticalArc.

Definition at line 51 of file curve.cpp.

References Geom::all_nearest_times(), and toSBasis().

Referenced by allNearestTimes().

◆ allNearestTimes() [2/2]

std::vector< Coord > Geom::Curve::allNearestTimes	(	Point const &	p,
		Interval const &	i
	)

inline

A version that takes an Interval.

Definition at line 270 of file curve.h.

References allNearestTimes(), Geom::GenericInterval< C >::max(), and Geom::GenericInterval< C >::min().

◆ boundsExact()

virtual Rect Geom::Curve::boundsExact ( ) const

pure virtual

Compute the curve's exact bounding box.

This method can be dramatically slower than boundsFast() depending on the curve type.

Returns: The smallest possible rectangle containing all of the curve's points.

Implemented in Geom::BezierCurve, Geom::EllipticalArc, and Geom::SBasisCurve.

Referenced by Geom::Path::boundsExact().

◆ boundsFast()

virtual Rect Geom::Curve::boundsFast ( ) const

pure virtual

Quickly compute the curve's approximate bounding box.

The resulting rectangle is guaranteed to contain all points belonging to the curve, but it might not be the smallest such rectangle. This method is usually fast.

Returns: A rectangle that contains all points belonging to the curve.

Implemented in Geom::BezierCurve, Geom::EllipticalArc, and Geom::SBasisCurve.

Referenced by Geom::Path::boundsFast().

◆ boundsLocal() [1/2]

OptRect Geom::Curve::boundsLocal ( OptInterval const & a ) const

inline

Compute the bounding box of a part of the curve.

Since this method returns the smallest possible bounding rectangle of the specified portion, it can also be rather slow.

Parameters

a	An interval specifying a part of the curve, or nothing. If \([0, 1] \subseteq a\), then the bounding box for the entire curve is calculated.

Returns: The smallest possible rectangle containing all points in \(\mathbf{C}[a]\), or nothing if the supplied interval is empty.

Definition at line 180 of file curve.h.

References boundsLocal().

Referenced by boundsLocal().

◆ boundsLocal() [2/2]

virtual OptRect Geom::Curve::boundsLocal	(	OptInterval const &	i,
		unsigned	deg
	)		const

pure virtual

Implemented in Geom::BezierCurve, and Geom::SBasisCurve.

Referenced by Geom::pair_intersect().

◆ degreesOfFreedom()

virtual int Geom::Curve::degreesOfFreedom ( ) const

inlinevirtual

Return the number of independent parameters required to represent all variations of this curve.

For example, for Bezier curves it returns the curve's order multiplied by 2.

Reimplemented in Geom::BezierCurve, Geom::EllipticalArc, and Geom::SBasisCurve.

Definition at line 333 of file curve.h.

◆ derivative()

virtual Curve * Geom::Curve::derivative ( ) const

pure virtual

Create a derivative of this curve.

It's best to think of the derivative in physical terms: if the curve describes the position of some object on the plane from time \(t=0\) to \(t=1\) as said in the introduction, then the curve's derivative describes that object's speed at the same times. The second derivative refers to its acceleration, the third to jerk, etc.

Returns: New curve \(\mathbf{D} = \mathbf{C}'\).

Implemented in Geom::BezierCurveN< degree >, Geom::BezierCurveN< 1 >, Geom::BezierCurveN< degree >, Geom::BezierCurveN< 1 >, Geom::BezierCurve, Geom::BezierCurveN< degree >, Geom::BezierCurveN< 1 >, Geom::EllipticalArc, and Geom::SBasisCurve.

Referenced by Geom::curve_mono_splits(), and intersectSelf().

◆ duplicate()

virtual Curve * Geom::Curve::duplicate ( ) const

pure virtual

Create an exact copy of this curve.

Returns: Pointer to a newly allocated curve, identical to the original

Implemented in Geom::BezierCurve, Geom::BezierCurveN< degree >, Geom::BezierCurveN< 1 >, Geom::EllipticalArc, Geom::Path::ClosingSegment, Geom::Path::StitchSegment, and Geom::SBasisCurve.

Referenced by Inkscape::LivePathEffect::LPERoughen::doEffect(), Geom::new_clone(), and transformed().

◆ expandToTransformed()

virtual void Geom::Curve::expandToTransformed	(	Rect &	bbox,
		Affine const &	transform
	)		const

pure virtual

Expand the given rectangle to include the transformed curve, assuming it already contains its initial point.

Parameters

bbox[in,out]	bbox The rectangle to expand; it is assumed to already contain (initialPoint() * transform).
transform	The transform to apply to the curve before taking its bounding box.

Implemented in Geom::BezierCurveN< degree >, Geom::BezierCurveN< 1 >, Geom::BezierCurveN< degree >, Geom::BezierCurveN< 1 >, Geom::BezierCurveN< degree >, Geom::BezierCurveN< 1 >, Geom::BezierCurveN< degree >, Geom::BezierCurveN< 1 >, Geom::BezierCurveN< degree >, Geom::BezierCurveN< 1 >, Geom::BezierCurveN< degree >, Geom::BezierCurveN< 1 >, Geom::BezierCurve, Geom::BezierCurveN< degree >, Geom::BezierCurveN< 1 >, Geom::EllipticalArc, and Geom::SBasisCurve.

◆ feed()

void Geom::Curve::feed	(	PathSink &	sink,
		bool	moveto_initial
	)		const

virtual

Feed the curve to a PathSink.

Reimplemented in Geom::BezierCurveN< degree >, Geom::BezierCurveN< 1 >, Geom::BezierCurveN< degree >, Geom::BezierCurveN< 1 >, Geom::BezierCurveN< degree >, Geom::BezierCurveN< 1 >, Geom::BezierCurveN< degree >, Geom::BezierCurveN< 1 >, Geom::BezierCurveN< degree >, Geom::BezierCurveN< 1 >, Geom::BezierCurveN< degree >, Geom::BezierCurveN< 1 >, Geom::BezierCurveN< degree >, Geom::BezierCurveN< 1 >, Geom::EllipticalArc, and Geom::BezierCurve.

Definition at line 214 of file curve.cpp.

References Geom::PathSink::curveTo(), initialPoint(), Geom::PathSink::moveTo(), Geom::sbasis_to_bezier(), and toSBasis().

Referenced by Geom::BezierCurve::feed().

◆ finalPoint()

virtual Point Geom::Curve::finalPoint ( ) const

pure virtual

Retrieve the end of the curve.

Returns: The point corresponding to \(\mathbf{C}(1)\).

Implemented in Geom::BezierCurve, Geom::EllipticalArc, and Geom::SBasisCurve.

◆ initialPoint()

virtual Point Geom::Curve::initialPoint ( ) const

pure virtual

Retrieve the start of the curve.

Returns: The point corresponding to \(\mathbf{C}(0)\).

Implemented in Geom::BezierCurve, Geom::EllipticalArc, and Geom::SBasisCurve.

◆ intersect()

std::vector< CurveIntersection > Geom::Curve::intersect	(	Curve const &	other,
		Coord	eps = `EPSILON`
	)		const

virtual

Compute intersections with another curve.

Reimplemented in Geom::BezierCurveN< degree >, Geom::BezierCurveN< 1 >, Geom::BezierCurveN< degree >, Geom::BezierCurveN< 1 >, Geom::BezierCurveN< degree >, Geom::BezierCurveN< 1 >, Geom::BezierCurveN< degree >, Geom::BezierCurveN< 1 >, Geom::BezierCurveN< degree >, Geom::BezierCurveN< 1 >, Geom::BezierCurveN< degree >, Geom::BezierCurveN< 1 >, Geom::BezierCurve, Geom::BezierCurveN< degree >, Geom::BezierCurveN< 1 >, and Geom::EllipticalArc.

Definition at line 97 of file curve.cpp.

Referenced by Geom::BezierCurveN< degree >::intersect(), Geom::BezierCurve::intersect(), and Geom::EllipticalArc::intersect().

◆ intersectSelf()

std::vector< CurveIntersection > Geom::Curve::intersectSelf ( Coord eps = EPSILON ) const

virtual

Compute intersections of this curve with itself.

Represents a sub-arc of the curve.

A closure to split the curve into portions at the prescribed split points.

A closure to find pairwise intersections between the passed subcurves.

Definition at line 103 of file curve.cpp.

References derivative(), Geom::EPSILON, portion(), result, roots(), Geom::split(), Geom::Interval::valueAt(), Geom::X, and Geom::Y.

◆ isDegenerate()

virtual bool Geom::Curve::isDegenerate ( ) const

pure virtual

Check whether the curve has exactly zero length.

Returns: True if the curve's initial point is exactly the same as its final point, and it contains no other points (its value set contains only one element).

Implemented in Geom::BezierCurveN< degree >, Geom::BezierCurveN< 1 >, Geom::BezierCurve, Geom::BezierCurveN< degree >, Geom::BezierCurveN< 1 >, Geom::EllipticalArc, and Geom::SBasisCurve.

Referenced by arcLengthAt(), Inkscape::LivePathEffect::LPEFilletChamfer::doEffect_path(), and timeAtArcLength().

◆ isLineSegment()

virtual bool Geom::Curve::isLineSegment ( ) const

inlinevirtual

Check whether the curve is a line segment.

Reimplemented in Geom::BezierCurveN< degree >, Geom::BezierCurveN< 1 >, Geom::BezierCurve, Geom::BezierCurveN< degree >, Geom::BezierCurveN< 1 >, Geom::EllipticalArc, and Geom::SBasisCurve.

Definition at line 98 of file curve.h.

Referenced by arcLengthAt(), Geom::BezierCurveN< degree >::intersect(), Geom::EllipticalArc::intersect(), and timeAtArcLength().

◆ isNear()

virtual bool Geom::Curve::isNear	(	Curve const &	c,
		Coord	precision
	)		const

pure virtual

Test whether two curves are approximately the same.

Implemented in Geom::SBasisCurve, Geom::BezierCurve, and Geom::EllipticalArc.

Referenced by Geom::parting_point().

◆ length()

Coord Geom::Curve::length ( Coord tolerance = 0.01 ) const

virtual

Compute the arc length of this curve.

For a curve \(\mathbf{C}(t) = (C_x(t), C_y(t))\), arc length is defined for 2D curves as

\[ \ell = \int_{0}^{1} \sqrt { [C_x'(t)]^2 + [C_y'(t)]^2 }\, \text{d}t \]

In other words, we divide the curve into infinitely small linear segments and add together their lengths. Of course we can't subdivide the curve into infinitely many segments on a computer, so this method returns an approximation. Not that there is usually no closed form solution to such integrals, so this method might be slow.

Parameters

tolerance Maximum allowed error

Returns: Total distance the curve's value travels on the plane when going from 0 to 1

Reimplemented in Geom::BezierCurve, and Geom::SBasisCurve.

Definition at line 56 of file curve.cpp.

References toSBasis().

Referenced by arcLengthAt(), Inkscape::LivePathEffect::LPEPowerStroke::doEffect_path(), Inkscape::LivePathEffect::FilletChamferKnotHolderEntity::knot_set(), NodeSatellite::time(), timeAtArcLength(), unitTangentAt(), and Inkscape::LivePathEffect::NodeSatelliteArrayParam::updateCanvasIndicators().

◆ nearestTime() [1/2]

Coord Geom::Curve::nearestTime	(	Point const &	p,
		Coord	a = `0`,
		Coord	b = `1`
	)		const

virtual

Compute a time value at which the curve comes closest to a specified point.

The first value with the smallest distance is returned if there are multiple such points.

Parameters

p	Query point
a	Minimum time value to consider
b	Maximum time value to consider; \(a < b\)

Returns: \(q \in [a, b]: ||\mathbf{C}(q) - \mathbf{p}|| = \inf(\{r \in \mathbb{R} : ||\mathbf{C}(r) - \mathbf{p}||\})\)

Reimplemented in Geom::BezierCurveN< degree >, Geom::BezierCurveN< 1 >, Geom::BezierCurveN< degree >, Geom::BezierCurveN< 1 >, Geom::BezierCurve, Geom::BezierCurveN< degree >, Geom::BezierCurveN< 1 >, Geom::SBasisCurve, and Geom::EllipticalArc.

Definition at line 46 of file curve.cpp.

References Geom::nearest_time(), and toSBasis().

Referenced by nearestTime().

◆ nearestTime() [2/2]

Coord Geom::Curve::nearestTime	(	Point const &	p,
		Interval const &	i
	)		const

inline

A version that takes an Interval.

Definition at line 257 of file curve.h.

References Geom::GenericInterval< C >::max(), Geom::GenericInterval< C >::min(), and nearestTime().

◆ operator()()

virtual Point Geom::Curve::operator() ( Coord t ) const

inlinevirtual

Evaluate the function at the specified time value.

Allows curves to be used as functors.

Definition at line 120 of file curve.h.

References pointAt().

◆ operator*=() [1/7]

virtual void Geom::Curve::operator*= ( Affine const & m )

pure virtual

Implemented in Geom::BezierCurve, Geom::EllipticalArc, Geom::SBasisCurve, Geom::BezierCurve, Geom::EllipticalArc, and Geom::SBasisCurve.

◆ operator*=() [2/7]

virtual void Geom::Curve::operator*= ( HShear const & hs )

inlinevirtual

Reimplemented in Geom::BezierCurve, Geom::EllipticalArc, and Geom::SBasisCurve.

Definition at line 200 of file curve.h.

◆ operator*=() [3/7]

virtual void Geom::Curve::operator*= ( Rotate const & r )

inlinevirtual

Reimplemented in Geom::BezierCurve, Geom::EllipticalArc, Geom::SBasisCurve, and Geom::EllipticalArc.

Definition at line 199 of file curve.h.

◆ operator*=() [4/7]

virtual void Geom::Curve::operator*= ( Scale const & s )

inlinevirtual

Reimplemented in Geom::BezierCurve, Geom::EllipticalArc, Geom::SBasisCurve, Geom::BezierCurve, and Geom::EllipticalArc.

Definition at line 198 of file curve.h.

◆ operator*=() [5/7]

virtual void Geom::Curve::operator*= ( Translate const & tr )

inlinevirtual

Reimplemented in Geom::BezierCurve, Geom::EllipticalArc, Geom::SBasisCurve, Geom::BezierCurve, and Geom::EllipticalArc.

Definition at line 197 of file curve.h.

◆ operator*=() [6/7]

virtual void Geom::Curve::operator*= ( VShear const & vs )

inlinevirtual

Reimplemented in Geom::BezierCurve, Geom::EllipticalArc, and Geom::SBasisCurve.

Definition at line 201 of file curve.h.

◆ operator*=() [7/7]

virtual void Geom::Curve::operator*= ( Zoom const & z )

inlinevirtual

Reimplemented in Geom::BezierCurve, Geom::EllipticalArc, Geom::SBasisCurve, and Geom::EllipticalArc.

Definition at line 202 of file curve.h.

◆ operator==()

bool Geom::Curve::operator== ( Curve const & c ) const

inline

Test equality of two curves.

Equality means that for any time value, the evaluation of either curve will yield the same value. This means non-degenerate curves are not equal to their reverses. Note that this tests for exact equality.

Returns: True if the curves are identical, false otherwise

Definition at line 340 of file curve.h.

References _equalTo(), and c.

◆ pointAndDerivatives()

virtual std::vector< Point > Geom::Curve::pointAndDerivatives	(	Coord	t,
		unsigned	n
	)		const

pure virtual

Evaluate the curve and its derivatives.

This will return a vector that contains the value of the curve and the specified number of derivatives. However, the returned vector might contain less elements than specified if some derivatives do not exist.

Parameters

t	Time value
n	The number of derivatives to compute

Returns: Vector of at most \(n+1\) elements of the form \([\mathbf{C}(t), \mathbf{C}'(t), \mathbf{C}''(t), \ldots]\)

Implemented in Geom::BezierCurve, and Geom::SBasisCurve.

Referenced by Inkscape::LivePathEffect::LPEAttachPath::doEffect(), Geom::intersect_polish_root(), pointAt(), and unitTangentAt().

◆ pointAt()

virtual Point Geom::Curve::pointAt ( Coord t ) const

inlinevirtual

Evaluate the curve at a specified time value.

Parameters

t	Time value

Returns: \(\mathbf{C}(t)\)

Reimplemented in Geom::BezierCurve, Geom::EllipticalArc, and Geom::SBasisCurve.

Definition at line 110 of file curve.h.

References pointAndDerivatives().

Referenced by Inkscape::LivePathEffect::LPERoughen::addNodesAndJitter(), Inkscape::LivePathEffect::LPERoughen::doEffect(), Inkscape::LivePathEffect::LPEFilletChamfer::doEffect_path(), Inkscape::UI::Tools::MarkerTool::get_marker_transform(), Geom::get_nodetype(), NodeSatellite::getPosition(), Geom::BezierCurveN< degree >::intersect(), Inkscape::LivePathEffect::LPERoughen::jitter(), Inkscape::LivePathEffect::FilletChamferKnotHolderEntity::knot_set(), NodeSatellite::lenToRad(), Geom::mono_intersect(), operator()(), Geom::pair_intersect(), Geom::parting_point(), Geom::PathVector::pointAt(), Geom::Path::pointAt(), Geom::PathVector::pointAt(), sp_shape_marker_get_transform(), and valueAt().

◆ portion() [1/2]

virtual Curve * Geom::Curve::portion	(	Coord	a,
		Coord	b
	)		const

pure virtual

Create a curve that corresponds to a part of this curve.

For \(a > b\), the returned portion will be reversed with respect to the original. The returned curve will always be of the same type.

Parameters

a	Beginning of the interval specifying the portion of the curve
b	End of the interval

Returns

New curve \(\mathbf{D}\) such that:

\(\mathbf{D}(0) = \mathbf{C}(a)\)
\(\mathbf{D}(1) = \mathbf{C}(b)\)
\(\mathbf{D}[ [0, 1] ] = \mathbf{C}[ [a?b] ]\), where \([a?b] = [\min(a, b), \max(a, b)]\)

Implemented in Geom::BezierCurve, Geom::BezierCurveN< degree >, Geom::BezierCurveN< 1 >, Geom::SBasisCurve, and Geom::EllipticalArc.

Referenced by Geom::Path::appendPortionTo(), arcLengthAt(), Inkscape::LivePathEffect::LPEFilletChamfer::doEffect_path(), intersectSelf(), NodeSatellite::lenToRad(), Geom::parting_point(), and reverse().

◆ portion() [2/2]

Curve * Geom::Curve::portion ( Interval const & i ) const

inline

A version of that accepts an Interval.

Definition at line 228 of file curve.h.

References Geom::GenericInterval< C >::max(), Geom::GenericInterval< C >::min(), and portion().

Referenced by portion().

◆ reverse()

virtual Curve * Geom::Curve::reverse ( ) const

inlinevirtual

Create a reversed version of this curve.

The result corresponds to portion(1, 0), but this method might be faster.

Returns: Pointer to a new curve \(\mathbf{D}\) such that \(\forall_{x \in [0, 1]} \mathbf{D}(x) = \mathbf{C}(1-x)\)

Reimplemented in Geom::BezierCurve, Geom::BezierCurveN< degree >, Geom::BezierCurveN< 1 >, Geom::EllipticalArc, Geom::Path::ClosingSegment, and Geom::Path::StitchSegment.

Definition at line 234 of file curve.h.

References portion().

Referenced by Inkscape::UI::Tools::PencilTool::_fitAndSplit(), Inkscape::UI::Tools::PencilTool::_interpolate(), Inkscape::UI::Tools::PencilTool::_sketchInterpolate(), Inkscape::LivePathEffect::LPEAttachPath::doEffect(), Inkscape::UI::Tools::MarkerTool::get_marker_transform(), Geom::get_nodetype(), sp_shape_marker_get_transform(), and sp_shape_marker_get_transform_at_end().

◆ roots()

virtual std::vector< Coord > Geom::Curve::roots	(	Coord	v,
		Dim2	d
	)		const

pure virtual

Computes time values at which the curve intersects an axis-aligned line.

Parameters

v	The coordinate of the line
d	Which axis the coordinate is on. X means a vertical line, Y a horizontal line.

Implemented in Geom::BezierCurve, Geom::SBasisCurve, and Geom::EllipticalArc.

Referenced by Geom::curve_mono_splits(), intersectSelf(), and winding().

◆ setFinal()

virtual void Geom::Curve::setFinal ( Point const & v )

pure virtual

Change the ending point of the curve.

After calling this method, it is guaranteed that \(\mathbf{C}(0) = \mathbf{p}\), and the curve is still continuous. The precise new shape of the curve varies with curve type.

Parameters

p	New ending point of the curve

Implemented in Geom::EllipticalArc, Geom::BezierCurve, and Geom::SBasisCurve.

Referenced by Geom::SVGPathParser::_closePath(), and Geom::Path::appendPortionTo().

◆ setInitial()

virtual void Geom::Curve::setInitial ( Point const & v )

pure virtual

Change the starting point of the curve.

After calling this method, it is guaranteed that \(\mathbf{C}(0) = \mathbf{p}\), and the curve is still continuous. The precise new shape of the curve varies with curve type.

Parameters

p	New starting point of the curve

Implemented in Geom::EllipticalArc, Geom::BezierCurve, and Geom::SBasisCurve.

Referenced by Geom::Path::appendPortionTo(), and Inkscape::LivePathEffect::LPEFilletChamfer::doEffect_path().

◆ timeRange()

virtual Interval Geom::Curve::timeRange ( ) const

inlinevirtual

Get the interval of allowed time values.

Returns: \([0, 1]\)

Definition at line 102 of file curve.h.

◆ toSBasis()

virtual D2< SBasis > Geom::Curve::toSBasis ( ) const

pure virtual

Convert the curve to a symmetric power basis polynomial.

Symmetric power basis polynomials (S-basis for short) are numerical representations of curves with excellent numerical properties. Most high level operations provided by 2Geom are implemented in terms of S-basis operations, so every curve has to provide a method to convert it to an S-basis polynomial on two variables. See SBasis class reference for more information.

Implemented in Geom::BezierCurve, Geom::EllipticalArc, and Geom::SBasisCurve.

Referenced by Inkscape::UI::PathManipulator::_bsplineHandleReposition(), Inkscape::UI::Tools::PenTool::_bsplineSpiroMotion(), allNearestTimes(), Inkscape::LivePathEffect::LPEBSpline::doBSplineFromWidget(), feed(), length(), monotonic_smash_intersect(), nearestTime(), NodeSatellite::radToLen(), Inkscape::LivePathEffect::sp_bspline_do_effect(), Inkscape::UI::PathManipulator::subdivideSegment(), and timeAtArcLength().

◆ transform()

void Geom::Curve::transform ( Affine const & m )

inline

Transform this curve by an affine transformation.

Because of this method, all curve types must be closed under affine transformations.

Parameters

m	Affine describing the affine transformation

Definition at line 193 of file curve.h.

Referenced by Geom::Ellipse::axis(), Geom::BezierCurve::expandToTransformed(), Geom::BezierCurveN< degree >::expandToTransformed(), Geom::EllipticalArc::expandToTransformed(), Geom::SBasisCurve::expandToTransformed(), Geom::Ellipse::semiaxis(), and transformed().

◆ transformed()

virtual Curve * Geom::Curve::transformed ( Affine const & m ) const

inlinevirtual

Create a curve transformed by an affine transformation.

This method returns a new curve instead modifying the existing one.

Parameters

m	Affine describing the affine transformation

Returns: Pointer to a new, transformed curve

Definition at line 209 of file curve.h.

References duplicate(), and transform().

◆ unitTangentAt()

Point Geom::Curve::unitTangentAt	(	Coord	t,
		unsigned	n = `3`
	)		const

virtual

Compute a vector tangent to the curve.

This will return an unit vector (a Point with length() equal to 1) that denotes a vector tangent to the curve. This vector is defined as \( \mathbf{v}(t) = \frac{\mathbf{C}'(t)}{||\mathbf{C}'(t)||} \). It is pointed in the direction of increasing \(t\), at the specified time value. The method uses l'Hopital's rule when the derivative is zero. A zero vector is returned if no non-zero derivative could be found.

Parameters

t	Time value
n	The maximum order of derivative to consider

Returns: Unit tangent vector \(\mathbf{v}(t)\)

Definition at line 201 of file curve.cpp.

References Geom::are_near(), length(), and pointAndDerivatives().

Referenced by Inkscape::UI::Tools::EraserTool::_accumulate(), Inkscape::UI::Tools::PencilTool::_fitAndSplit(), Inkscape::UI::Tools::PencilTool::_interpolate(), Inkscape::UI::Tools::PencilTool::_sketchInterpolate(), Geom::find_direction_of_travel(), Inkscape::UI::Tools::MarkerTool::get_marker_transform(), Geom::get_nodetype(), sp_shape_marker_get_transform(), sp_shape_marker_get_transform_at_end(), and winding().

◆ valueAt()

virtual Coord Geom::Curve::valueAt	(	Coord	t,
		Dim2	d
	)		const

inlinevirtual

Evaluate one of the coordinates at the specified time value.

Parameters

t	Time value
d	The dimension to evaluate

Returns: The specified coordinate of \(\mathbf{C}(t)\)

Reimplemented in Geom::BezierCurve, Geom::EllipticalArc, and Geom::SBasisCurve.

Definition at line 116 of file curve.h.

References pointAt().

Referenced by Geom::PathVector::valueAt(), Geom::Path::valueAt(), Geom::PathVector::valueAt(), and winding().

◆ winding()

int Geom::Curve::winding ( Point const & p ) const

virtual

Compute the partial winding number of this curve.

The partial winding number is equal to the difference between the number of roots at which the curve goes in the +Y direction and the number of roots at which the curve goes in the -Y direction. This method is mainly useful for implementing path winding calculation. It will ignore roots which are local maxima on the Y axis.

Parameters

p	Point where the winding number should be determined

Returns: Winding number contribution at p

Definition at line 61 of file curve.cpp.

References roots(), unitTangentAt(), valueAt(), Geom::X, and Geom::Y.

Referenced by Geom::BezierCurveN< degree >::winding().

The documentation for this class was generated from the following files:

/builds/inkscape/inkscape/src/3rdparty/2geom/include/2geom/curve.h
/builds/inkscape/inkscape/src/3rdparty/2geom/src/2geom/curve.cpp

Public Member Functions

Protected Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ ~Curve()

Member Function Documentation

◆ _equalTo()

◆ allNearestTimes() [1/2]

◆ allNearestTimes() [2/2]

◆ boundsExact()

◆ boundsFast()

◆ boundsLocal() [1/2]

◆ boundsLocal() [2/2]

◆ degreesOfFreedom()

◆ derivative()

◆ duplicate()

◆ expandToTransformed()

◆ feed()

◆ finalPoint()

◆ initialPoint()

◆ intersect()

◆ intersectSelf()

◆ isDegenerate()

◆ isLineSegment()

◆ isNear()

◆ length()

◆ nearestTime() [1/2]

◆ nearestTime() [2/2]

◆ operator()()

◆ operator*=() [1/7]

◆ operator*=() [2/7]

◆ operator*=() [3/7]

◆ operator*=() [4/7]

◆ operator*=() [5/7]

◆ operator*=() [6/7]

◆ operator*=() [7/7]

◆ operator==()

◆ pointAndDerivatives()

◆ pointAt()

◆ portion() [1/2]

◆ portion() [2/2]

◆ reverse()

◆ roots()

◆ setFinal()

◆ setInitial()

◆ timeRange()

◆ toSBasis()

◆ transform()

◆ transformed()

◆ unitTangentAt()

◆ valueAt()

◆ winding()