Inkscape: Geom::BezierCurveN< degree > Class Template Reference

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Bezier curve with compile-time specified order. More...

#include <bezier-curve.h>

Inheritance diagram for Geom::BezierCurveN< degree >:

Public Member Functions
std::pair< BezierCurveN, BezierCurveN >	subdivide (Coord t) const
	Divide a Bezier curve into two curves.

bool	isDegenerate () const override
	Check whether the curve has exactly zero length.

bool	isLineSegment () const override
	Return false if there are at least 3 distinct control points, true otherwise.

Curve *	duplicate () const override
	Create an exact copy of this curve.

Curve *	portion (Coord f, Coord t) const override
	Create a curve that corresponds to a part of this curve.

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

Curve *	derivative () const override
	Create a derivative of this curve.

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

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

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

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

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

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

bool	isLineSegment () const
	Return false if there are at least 3 distinct control points, true otherwise.

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

Coord	nearestTime (Point const &, Coord, Coord) const
	Compute a time value at which the curve comes closest to a specified point.

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

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

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

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

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

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

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

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

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

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

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

Coord	nearestTime (Point const &p, Coord from, Coord to) const
	Compute a time value at which the curve comes closest to a specified point.

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

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

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

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

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

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

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

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

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

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

Construct Bezier curves
	BezierCurveN ()
	Construct a Bezier curve of the specified order with all points zero.

	BezierCurveN (D2< Bezier > const &x)
	Construct from 2D Bezier polynomial.

	BezierCurveN (Bezier x, Bezier y)
	Construct from two 1D Bezier polynomials of the same order.

	BezierCurveN (std::vector< Point > const &points)
	Construct a Bezier curve from a vector of its control points.

	BezierCurveN (Point c0, Point c1)
	Construct a linear segment from its endpoints.

	BezierCurveN (Point c0, Point c1, Point c2)
	Construct a quadratic Bezier curve from its control points.

	BezierCurveN (Point c0, Point c1, Point c2, Point c3)
	Construct a cubic Bezier curve from its control points.

Public Member Functions inherited from Geom::BezierCurve
	BezierCurve (D2< Bezier > const &b)

Point	initialPoint () const override
	Retrieve the start of the curve.

Point	finalPoint () const override
	Retrieve the end of the curve.

void	setInitial (Point const &v) override
	Change the starting point of the curve.

void	setFinal (Point const &v) override
	Change the ending point of the curve.

Rect	boundsFast () const override
	Quickly compute the curve's approximate bounding box.

Rect	boundsExact () const override
	Compute the curve's exact bounding box.

OptRect	boundsLocal (OptInterval const &i, unsigned deg) const override

void	operator*= (Translate const &tr) override

void	operator*= (Scale const &s) override

void	operator*= (Affine const &m) override

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

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

Coord	length (Coord tolerance) const override
	Compute the arc length of this curve.

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

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

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

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

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

std::vector< Coord >	timesWithRadiusOfCurvature (double radius) const
	Computes the times where the radius of curvature of the bezier curve equals the given radius.

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

unsigned	order () const
	Get the order of the Bezier curve.

unsigned	size () const
	Get the number of control points.

Point	controlPoint (unsigned ix) const
	Access control points of the curve.

Point	operator[] (unsigned ix) const

std::vector< Point >	controlPoints () const
	Get the control points.

D2< Bezier > const &	fragment () const

void	setPoint (unsigned ix, Point const &v)
	Modify a control point.

virtual void	setPoints (std::vector< Point > const &ps)
	Set new control points.

Public Member Functions inherited from Geom::Curve
virtual	~Curve ()

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

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

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

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

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

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

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 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.

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

Static Private Member Functions
template<unsigned required_degree>
static void	assert_degree (BezierCurveN< required_degree > const *)

Additional Inherited Members
Static Public Member Functions inherited from Geom::BezierCurve
static BezierCurve *	create (std::vector< Point > const &pts)
	Construct a curve from a vector of control points.

Protected Member Functions inherited from Geom::BezierCurve
	BezierCurve ()

	BezierCurve (Bezier const &x, Bezier const &y)

	BezierCurve (std::vector< Point > const &pts)

bool	_equalTo (Curve const &c) const override

Protected Attributes inherited from Geom::BezierCurve
D2< Bezier >	inner

Related Symbols inherited from Geom::BezierCurve
Coord	bezier_length (std::vector< Point > const &points, Coord tolerance)
	Compute the length of a bezier curve given by a vector of its control points.

Detailed Description

template<unsigned degree>
class Geom::BezierCurveN< degree >

Bezier curve with compile-time specified order.

Template Parameters

degree unsigned value indicating the order of the Bezier curve

Definition at line 179 of file bezier-curve.h.

Constructor & Destructor Documentation

◆ BezierCurveN() [1/7]

template<unsigned degree>

Geom::BezierCurveN< degree >::BezierCurveN ( )

inline

Construct a Bezier curve of the specified order with all points zero.

Definition at line 189 of file bezier-curve.h.

References degree, and Geom::BezierCurve::inner.

Referenced by Geom::BezierCurveN< degree >::duplicate(), Geom::BezierCurveN< degree >::portion(), Geom::BezierCurveN< degree >::reverse(), and Geom::BezierCurveN< degree >::subdivide().

◆ BezierCurveN() [2/7]

template<unsigned degree>

Geom::BezierCurveN< degree >::BezierCurveN ( D2< Bezier > const & x )

inlineexplicit

Construct from 2D Bezier polynomial.

Definition at line 194 of file bezier-curve.h.

References Geom::BezierCurve::inner.

◆ BezierCurveN() [3/7]

template<unsigned degree>

Geom::BezierCurveN< degree >::BezierCurveN	(	Bezier	x,
		Bezier	y
	)

inline

Construct from two 1D Bezier polynomials of the same order.

Definition at line 199 of file bezier-curve.h.

References Geom::BezierCurve::inner.

◆ BezierCurveN() [4/7]

template<unsigned degree>

Geom::BezierCurveN< degree >::BezierCurveN ( std::vector< Point > const & points )

inline

Construct a Bezier curve from a vector of its control points.

Definition at line 204 of file bezier-curve.h.

References degree, and Geom::BezierCurve::inner.

◆ BezierCurveN() [5/7]

template<unsigned degree>

Geom::BezierCurveN< degree >::BezierCurveN	(	Point	c0,
		Point	c1
	)

inline

Construct a linear segment from its endpoints.

Definition at line 215 of file bezier-curve.h.

References Geom::BezierCurve::inner.

◆ BezierCurveN() [6/7]

template<unsigned degree>

Geom::BezierCurveN< degree >::BezierCurveN	(	Point	c0,
		Point	c1,
		Point	c2
	)

inline

Construct a quadratic Bezier curve from its control points.

Definition at line 222 of file bezier-curve.h.

References Geom::BezierCurve::inner.

◆ BezierCurveN() [7/7]

template<unsigned degree>

Geom::BezierCurveN< degree >::BezierCurveN	(	Point	c0,
		Point	c1,
		Point	c2,
		Point	c3
	)

inline

Construct a cubic Bezier curve from its control points.

Definition at line 229 of file bezier-curve.h.

References Geom::BezierCurve::inner.

Member Function Documentation

◆ assert_degree()

template<unsigned degree>

template<unsigned required_degree>

static void Geom::BezierCurveN< degree >::assert_degree ( BezierCurveN< required_degree > const * )

inlinestaticprivate

Definition at line 183 of file bezier-curve.h.

◆ derivative() [1/3]

Curve * Geom::BezierCurveN< 1 >::derivative ( ) const

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 \(\mathbf{D} = \mathbf{C}'\).

Reimplemented from Geom::BezierCurve.

◆ derivative() [2/3]

Curve * Geom::BezierCurveN< 1 >::derivative ( ) const

virtual

Create a derivative of this curve.

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

Reimplemented from Geom::BezierCurve.

Definition at line 370 of file bezier-curve.cpp.

References inner(), Geom::X, and Geom::Y.

◆ derivative() [3/3]

template<unsigned degree>

Curve * Geom::BezierCurveN< degree >::derivative ( ) const

inlineoverridevirtual

Create a derivative of this curve.

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

Reimplemented from Geom::BezierCurve.

Definition at line 322 of file bezier-curve.h.

References degree, Geom::derivative(), inner(), Geom::X, and Geom::Y.

Referenced by Geom::EllipticalArc::derivative().

◆ duplicate()

template<unsigned degree>

Curve * Geom::BezierCurveN< degree >::duplicate ( ) const

inlineoverridevirtual

Create an exact copy of this curve.

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

Reimplemented from Geom::BezierCurve.

Reimplemented in Geom::Path::ClosingSegment, and Geom::Path::StitchSegment.

Definition at line 264 of file bezier-curve.h.

References Geom::BezierCurveN< degree >::BezierCurveN().

◆ expandToTransformed() [1/7]

void Geom::BezierCurveN< 1 >::expandToTransformed	(	Rect &	bbox,
		Affine const &	transform
	)		const

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.

Reimplemented from Geom::BezierCurve.

◆ expandToTransformed() [2/7]

void Geom::BezierCurveN< 2 >::expandToTransformed	(	Rect &	bbox,
		Affine const &	transform
	)		const

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.

Reimplemented from Geom::BezierCurve.

◆ expandToTransformed() [3/7]

void Geom::BezierCurveN< 3 >::expandToTransformed	(	Rect &	bbox,
		Affine const &	transform
	)		const

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.

Reimplemented from Geom::BezierCurve.

◆ expandToTransformed() [4/7]

void Geom::BezierCurveN< 1 >::expandToTransformed	(	Rect &	bbox,
		Affine const &	transform
	)		const

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.

Reimplemented from Geom::BezierCurve.

Definition at line 643 of file bezier-curve.cpp.

References Geom::GenericRect< C >::expandTo().

◆ expandToTransformed() [5/7]

void Geom::BezierCurveN< 2 >::expandToTransformed	(	Rect &	bbox,
		Affine const &	transform
	)		const

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.

Reimplemented from Geom::BezierCurve.

Definition at line 649 of file bezier-curve.cpp.

References Geom::bezier_expand_to_image().

◆ expandToTransformed() [6/7]

void Geom::BezierCurveN< 3 >::expandToTransformed	(	Rect &	bbox,
		Affine const &	transform
	)		const

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.

Reimplemented from Geom::BezierCurve.

Definition at line 657 of file bezier-curve.cpp.

References Geom::bezier_expand_to_image().

◆ expandToTransformed() [7/7]

template<unsigned degree>

void Geom::BezierCurveN< degree >::expandToTransformed	(	Rect &	bbox,
		Affine const &	transform
	)		const

inlineoverridevirtual

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.

Reimplemented from Geom::BezierCurve.

Definition at line 297 of file bezier-curve.h.

References Geom::BezierCurve::expandToTransformed(), and Geom::Curve::transform().

◆ feed() [1/7]

void Geom::BezierCurveN< 1 >::feed	(	PathSink &	sink,
		bool	moveto_initial
	)		const

virtual

Feed the curve to a PathSink.

Reimplemented from Geom::BezierCurve.

◆ feed() [2/7]

void Geom::BezierCurveN< 2 >::feed	(	PathSink &	sink,
		bool	moveto_initial
	)		const

virtual

Feed the curve to a PathSink.

Reimplemented from Geom::BezierCurve.

◆ feed() [3/7]

void Geom::BezierCurveN< 3 >::feed	(	PathSink &	sink,
		bool	moveto_initial
	)		const

virtual

Feed the curve to a PathSink.

Reimplemented from Geom::BezierCurve.

◆ feed() [4/7]

void Geom::BezierCurveN< 1 >::feed	(	PathSink &	sink,
		bool	moveto_initial
	)		const

virtual

Feed the curve to a PathSink.

Reimplemented from Geom::BezierCurve.

Definition at line 602 of file bezier-curve.cpp.

References Geom::PathSink::lineTo(), and Geom::PathSink::moveTo().

◆ feed() [5/7]

void Geom::BezierCurveN< 2 >::feed	(	PathSink &	sink,
		bool	moveto_initial
	)		const

virtual

Feed the curve to a PathSink.

Reimplemented from Geom::BezierCurve.

Definition at line 611 of file bezier-curve.cpp.

References Geom::PathSink::moveTo(), and Geom::PathSink::quadTo().

◆ feed() [6/7]

void Geom::BezierCurveN< 3 >::feed	(	PathSink &	sink,
		bool	moveto_initial
	)		const

virtual

Feed the curve to a PathSink.

Reimplemented from Geom::BezierCurve.

Definition at line 620 of file bezier-curve.cpp.

References Geom::PathSink::curveTo(), and Geom::PathSink::moveTo().

◆ feed() [7/7]

template<unsigned degree>

void Geom::BezierCurveN< degree >::feed	(	PathSink &	sink,
		bool	moveto_initial
	)		const

inlineoverridevirtual

Feed the curve to a PathSink.

Reimplemented from Geom::BezierCurve.

Definition at line 293 of file bezier-curve.h.

References Geom::BezierCurve::feed().

◆ intersect() [1/7]

std::vector< CurveIntersection > Geom::BezierCurveN< 1 >::intersect	(	Curve const &	other,
		Coord	eps
	)		const

virtual

Compute intersections with another curve.

Reimplemented from Geom::BezierCurve.

◆ intersect() [2/7]

std::vector< CurveIntersection > Geom::BezierCurveN< 2 >::intersect	(	Curve const &	other,
		Coord	eps
	)		const

virtual

Compute intersections with another curve.

Reimplemented from Geom::BezierCurve.

◆ intersect() [3/7]

std::vector< CurveIntersection > Geom::BezierCurveN< 3 >::intersect	(	Curve const &	other,
		Coord	eps
	)		const

virtual

Compute intersections with another curve.

Reimplemented from Geom::BezierCurve.

◆ intersect() [4/7]

std::vector< CurveIntersection > Geom::BezierCurveN< 1 >::intersect	(	Curve const &	other,
		Coord	eps
	)		const

virtual

Compute intersections with another curve.

Filter out candidate times outside of the interval [0, 1] fuzzed so as to accommodate for epsilon.

Reimplemented from Geom::BezierCurve.

Definition at line 399 of file bezier-curve.cpp.

References Geom::cross(), Geom::distance(), Geom::dot(), Geom::Curve::finalPoint(), Geom::infinity(), Geom::Curve::initialPoint(), Geom::Curve::intersect(), Geom::Curve::isLineSegment(), Geom::Point::isZero(), len, Geom::Point::length(), Geom::middle_point(), Geom::Point::normalized(), Geom::Curve::pointAt(), result, Geom::transpose_in_place(), and w.

◆ intersect() [5/7]

std::vector< CurveIntersection > Geom::BezierCurveN< 2 >::intersect	(	Curve const &	other,
		Coord	eps
	)		const

virtual

Compute intersections with another curve.

Reimplemented from Geom::BezierCurve.

Definition at line 556 of file bezier-curve.cpp.

References Geom::BezierCurve::intersect().

◆ intersect() [6/7]

std::vector< CurveIntersection > Geom::BezierCurveN< 3 >::intersect	(	Curve const &	other,
		Coord	eps
	)		const

virtual

Compute intersections with another curve.

Reimplemented from Geom::BezierCurve.

Definition at line 572 of file bezier-curve.cpp.

References Geom::BezierCurve::intersect().

◆ intersect() [7/7]

template<unsigned degree>

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

inlineoverridevirtual

Compute intersections with another curve.

Reimplemented from Geom::BezierCurve.

Definition at line 286 of file bezier-curve.h.

References Geom::BezierCurve::intersect().

Referenced by Geom::BezierCurve::intersect(), Geom::EllipticalArc::intersect(), TEST(), TEST(), TEST(), TEST(), and TEST_F().

◆ isDegenerate() [1/2]

bool Geom::BezierCurveN< 1 >::isDegenerate ( ) const

inlinevirtual

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).

Reimplemented from Geom::BezierCurve.

Definition at line 327 of file bezier-curve.h.

References inner(), Geom::X, and Geom::Y.

◆ isDegenerate() [2/2]

template<unsigned degree>

bool Geom::BezierCurveN< degree >::isDegenerate ( ) const

inlineoverridevirtual

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).

Reimplemented from Geom::BezierCurve.

Definition at line 252 of file bezier-curve.h.

References Geom::BezierCurve::isDegenerate().

Referenced by Geom::Path::_includesClosingSegment(), Geom::Path::back_closed(), Geom::Path::size_closed(), and sp_gradient_reset_to_userspace().

◆ isLineSegment() [1/2]

bool Geom::BezierCurveN< 1 >::isLineSegment ( ) const

inlinevirtual

Return false if there are at least 3 distinct control points, true otherwise.

Reimplemented from Geom::BezierCurve.

Definition at line 330 of file bezier-curve.h.

◆ isLineSegment() [2/2]

template<unsigned degree>

bool Geom::BezierCurveN< degree >::isLineSegment ( ) const

inlineoverridevirtual

Return false if there are at least 3 distinct control points, true otherwise.

Reimplemented from Geom::BezierCurve.

Definition at line 256 of file bezier-curve.h.

References degree, and Geom::BezierCurve::isLineSegment().

◆ nearestTime() [1/3]

Coord Geom::BezierCurveN< 1 >::nearestTime	(	Point const &	p,
		Coord	a,
		Coord	b
	)		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 from Geom::BezierCurve.

◆ nearestTime() [2/3]

Coord Geom::BezierCurveN< 1 >::nearestTime	(	Point const &	p,
		Coord	a,
		Coord	b
	)		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 from Geom::BezierCurve.

Definition at line 376 of file bezier-curve.cpp.

References Geom::dot().

◆ nearestTime() [3/3]

template<unsigned degree>

Coord Geom::BezierCurveN< degree >::nearestTime	(	Point const &	p,
		Coord	a = `0`,
		Coord	b = `1`
	)		const

inlineoverridevirtual

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 from Geom::BezierCurve.

Definition at line 283 of file bezier-curve.h.

References Geom::BezierCurve::nearestTime().

Referenced by GrDrag::addStopNearPoint(), Geom::EllipticalArc::allNearestTimes(), Geom::distance(), Inkscape::distance_to_segment(), gr_knot_moved_midpoint_handler(), RectHandle::hit(), GrDrag::selected_move(), and sp_item_gradient_set_coords().

◆ portion()

template<unsigned degree>

Curve * Geom::BezierCurveN< degree >::portion	(	Coord	a,
		Coord	b
	)		const

inlineoverridevirtual

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 \([a?b] = [\min(a, b), \max(a, b)]\)

Reimplemented from Geom::BezierCurve.

Definition at line 267 of file bezier-curve.h.

References Geom::BezierCurveN< degree >::BezierCurveN(), degree, Geom::BezierCurve::inner, Geom::BezierCurve::pointAt(), and Geom::portion().

◆ reverse()

template<unsigned degree>

Curve * Geom::BezierCurveN< degree >::reverse ( ) const

inlineoverridevirtual

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 from Geom::BezierCurve.

Reimplemented in Geom::Path::ClosingSegment, and Geom::Path::StitchSegment.

Definition at line 274 of file bezier-curve.h.

References Geom::BezierCurveN< degree >::BezierCurveN(), degree, Geom::BezierCurve::finalPoint(), Geom::BezierCurve::initialPoint(), Geom::BezierCurve::inner, and Geom::reverse().

◆ subdivide()

template<unsigned degree>

std::pair< BezierCurveN, BezierCurveN > Geom::BezierCurveN< degree >::subdivide ( Coord t ) const

inline

Divide a Bezier curve into two curves.

Parameters

t	Time value

Returns: Pair of Bezier curves \((\mathbf{D}, \mathbf{E})\) such that \(\mathbf{D}[ [0,1] ] = \mathbf{C}[ [0,t] ]\) and \(\mathbf{E}[ [0,1] ] = \mathbf{C}[ [t,1] ]\)

Definition at line 245 of file bezier-curve.h.

References Geom::BezierCurveN< degree >::BezierCurveN(), Geom::BezierCurve::inner, Geom::X, and Geom::Y.

Referenced by Inkscape::LivePathEffect::LPERoughen::addNodesAndJitter(), Inkscape::LivePathEffect::path_from_piecewise_fix_cusps(), and Inkscape::UI::PathManipulator::subdivideSegment().

◆ winding() [1/3]

int Geom::BezierCurveN< 1 >::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

Reimplemented from Geom::Curve.

◆ winding() [2/3]

int Geom::BezierCurveN< 1 >::winding ( Point const & p ) const

virtual

Compute the partial winding number of this curve.

Parameters

p	Point where the winding number should be determined

Returns: Winding number contribution at p

Reimplemented from Geom::Curve.

Definition at line 585 of file bezier-curve.cpp.

References inner(), Geom::lerp(), Geom::X, and Geom::Y.

◆ winding() [3/3]

template<unsigned degree>

int Geom::BezierCurveN< degree >::winding ( Point const & p ) const

inlineoverridevirtual

Compute the partial winding number of this curve.

Parameters

p	Point where the winding number should be determined

Returns: Winding number contribution at p

Reimplemented from Geom::Curve.

Definition at line 290 of file bezier-curve.h.

References Geom::Curve::winding().

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

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

Public Member Functions

Static Private Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ BezierCurveN() [1/7]

◆ BezierCurveN() [2/7]

◆ BezierCurveN() [3/7]

◆ BezierCurveN() [4/7]

◆ BezierCurveN() [5/7]

◆ BezierCurveN() [6/7]

◆ BezierCurveN() [7/7]

Member Function Documentation

◆ assert_degree()

◆ derivative() [1/3]

◆ derivative() [2/3]

◆ derivative() [3/3]

◆ duplicate()

◆ expandToTransformed() [1/7]

◆ expandToTransformed() [2/7]

◆ expandToTransformed() [3/7]

◆ expandToTransformed() [4/7]

◆ expandToTransformed() [5/7]

◆ expandToTransformed() [6/7]

◆ expandToTransformed() [7/7]

◆ feed() [1/7]

◆ feed() [2/7]

◆ feed() [3/7]

◆ feed() [4/7]

◆ feed() [5/7]

◆ feed() [6/7]

◆ feed() [7/7]

◆ intersect() [1/7]

◆ intersect() [2/7]

◆ intersect() [3/7]

◆ intersect() [4/7]

◆ intersect() [5/7]

◆ intersect() [6/7]

◆ intersect() [7/7]

◆ isDegenerate() [1/2]

◆ isDegenerate() [2/2]

◆ isLineSegment() [1/2]

◆ isLineSegment() [2/2]

◆ nearestTime() [1/3]

◆ nearestTime() [2/3]

◆ nearestTime() [3/3]

◆ portion()

◆ reverse()

◆ subdivide()

◆ winding() [1/3]

◆ winding() [2/3]

◆ winding() [3/3]