Inkscape: Geom::Bezier Class Reference

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Polynomial in Bernstein-Bezier basis. More...

#include <bezier.h>

Inheritance diagram for Geom::Bezier:

Classes
struct	Order

Public Types
typedef Coord	output_type

Public Member Functions
unsigned	order () const

unsigned	degree () const

unsigned	size () const

	Bezier ()

	Bezier (const Bezier &b)

Bezier &	operator= (Bezier const &other)

bool	operator== (Bezier const &other) const

bool	operator!= (Bezier const &other) const

	Bezier (Order ord)

void	resize (unsigned int n, Coord v=0)

void	clear ()

bool	isZero (double eps=EPSILON) const

bool	isConstant (double eps=EPSILON) const

bool	isFinite () const

Coord	at0 () const

Coord &	at0 ()

Coord	at1 () const

Coord &	at1 ()

Coord	valueAt (double t) const

Coord	operator() (double t) const

SBasis	toSBasis () const

Coord &	operator[] (unsigned ix)

Coord const &	operator[] (unsigned ix) const

void	setCoeff (unsigned ix, double val)

std::vector< Coord >	valueAndDerivatives (Coord t, unsigned n_derivs) const

void	subdivide (Coord t, Bezier left, Bezier right) const

std::pair< Bezier, Bezier >	subdivide (Coord t) const

std::vector< Coord >	roots () const

std::vector< Coord >	roots (Interval const &ivl) const

Bezier	forward_difference (unsigned k) const

Bezier	elevate_degree () const

Bezier	reduce_degree () const

Bezier	elevate_to_degree (unsigned newDegree) const

Bezier	deflate () const

Bezier &	operator+= (double v)

Bezier &	operator-= (double v)

Bezier &	operator*= (double v)

Bezier &	operator/= (double v)

Bezier &	operator+= (Bezier const &other)

Bezier &	operator-= (Bezier const &other)

Bezier	operator- () const
	Unary minus.

Construct Bezier polynomials from their control points
	Bezier (Coord c0)

	Bezier (Coord c0, Coord c1)

	Bezier (Coord c0, Coord c1, Coord c2)

	Bezier (Coord c0, Coord c1, Coord c2, Coord c3)

	Bezier (Coord c0, Coord c1, Coord c2, Coord c3, Coord c4)

	Bezier (Coord c0, Coord c1, Coord c2, Coord c3, Coord c4, Coord c5)

	Bezier (Coord c0, Coord c1, Coord c2, Coord c3, Coord c4, Coord c5, Coord c6)

	Bezier (Coord c0, Coord c1, Coord c2, Coord c3, Coord c4, Coord c5, Coord c6, Coord c7)

	Bezier (Coord c0, Coord c1, Coord c2, Coord c3, Coord c4, Coord c5, Coord c6, Coord c7, Coord c8)

	Bezier (Coord c0, Coord c1, Coord c2, Coord c3, Coord c4, Coord c5, Coord c6, Coord c7, Coord c8, Coord c9)

template<typename Iter >
	Bezier (Iter first, Iter last)

	Bezier (std::vector< Coord > const &vec)

Protected Member Functions
	Bezier (Coord const c[], unsigned ord)

Private Member Functions
void	find_bezier_roots (std::vector< double > &solutions, double l, double r) const

Private Attributes
std::valarray< Coord >	c_

Friends
class	Bernstein

Bezier	portion (const Bezier &a, Coord from, Coord to)

OptInterval	bounds_fast (Bezier const &b)

Bezier	derivative (const Bezier &a)

Detailed Description

Polynomial in Bernstein-Bezier basis.

Definition at line 122 of file bezier.h.

Member Typedef Documentation

◆ output_type

typedef Coord Geom::Bezier::output_type

Definition at line 253 of file bezier.h.

Constructor & Destructor Documentation

◆ Bezier() [1/16]

Geom::Bezier::Bezier	(	Coord const	c[],
		unsigned	ord
	)

inlineprotected

Definition at line 140 of file bezier.h.

◆ Bezier() [2/16]

Geom::Bezier::Bezier ( )

inline

Definition at line 149 of file bezier.h.

◆ Bezier() [3/16]

Geom::Bezier::Bezier ( const Bezier & b )

inline

Definition at line 150 of file bezier.h.

◆ Bezier() [4/16]

Geom::Bezier::Bezier ( Order ord )

inline

Definition at line 186 of file bezier.h.

References order(), and Geom::Bezier::Order::order.

◆ Bezier() [5/16]

Geom::Bezier::Bezier ( Coord c0 )

inlineexplicit

Definition at line 192 of file bezier.h.

References c_.

◆ Bezier() [6/16]

Geom::Bezier::Bezier	(	Coord	c0,
		Coord	c1
	)

inline

Definition at line 195 of file bezier.h.

References c_.

◆ Bezier() [7/16]

Geom::Bezier::Bezier	(	Coord	c0,
		Coord	c1,
		Coord	c2
	)

inline

Definition at line 198 of file bezier.h.

References c_.

◆ Bezier() [8/16]

Geom::Bezier::Bezier	(	Coord	c0,
		Coord	c1,
		Coord	c2,
		Coord	c3
	)

inline

Definition at line 201 of file bezier.h.

References c_.

◆ Bezier() [9/16]

Geom::Bezier::Bezier	(	Coord	c0,
		Coord	c1,
		Coord	c2,
		Coord	c3,
		Coord	c4
	)

inline

Definition at line 204 of file bezier.h.

References c_.

◆ Bezier() [10/16]

Geom::Bezier::Bezier	(	Coord	c0,
		Coord	c1,
		Coord	c2,
		Coord	c3,
		Coord	c4,
		Coord	c5
	)

inline

Definition at line 207 of file bezier.h.

References c_.

◆ Bezier() [11/16]

Geom::Bezier::Bezier	(	Coord	c0,
		Coord	c1,
		Coord	c2,
		Coord	c3,
		Coord	c4,
		Coord	c5,
		Coord	c6
	)

inline

Definition at line 212 of file bezier.h.

References c_.

◆ Bezier() [12/16]

Geom::Bezier::Bezier	(	Coord	c0,
		Coord	c1,
		Coord	c2,
		Coord	c3,
		Coord	c4,
		Coord	c5,
		Coord	c6,
		Coord	c7
	)

inline

Definition at line 217 of file bezier.h.

References c_.

◆ Bezier() [13/16]

Geom::Bezier::Bezier	(	Coord	c0,
		Coord	c1,
		Coord	c2,
		Coord	c3,
		Coord	c4,
		Coord	c5,
		Coord	c6,
		Coord	c7,
		Coord	c8
	)

inline

Definition at line 222 of file bezier.h.

References c_.

◆ Bezier() [14/16]

Geom::Bezier::Bezier	(	Coord	c0,
		Coord	c1,
		Coord	c2,
		Coord	c3,
		Coord	c4,
		Coord	c5,
		Coord	c6,
		Coord	c7,
		Coord	c8,
		Coord	c9
	)

inline

Definition at line 227 of file bezier.h.

References c_.

◆ Bezier() [15/16]

template<typename Iter >

Geom::Bezier::Bezier	(	Iter	first,
		Iter	last
	)

inline

Definition at line 234 of file bezier.h.

References c_.

◆ Bezier() [16/16]

Geom::Bezier::Bezier ( std::vector< Coord > const & vec )

inline

Definition at line 240 of file bezier.h.

Member Function Documentation

◆ at0() [1/2]

Coord & Geom::Bezier::at0 ( )

inline

Definition at line 273 of file bezier.h.

References c_.

◆ at0() [2/2]

Coord Geom::Bezier::at0 ( ) const

inline

Definition at line 272 of file bezier.h.

References c_.

Referenced by Geom::bounds_exact(), Geom::Piecewise< T >::integral(), TEST_F(), TEST_F(), and wrap_bezier().

◆ at1() [1/2]

Coord & Geom::Bezier::at1 ( )

inline

Definition at line 275 of file bezier.h.

References c_, and order().

◆ at1() [2/2]

Coord Geom::Bezier::at1 ( ) const

inline

Definition at line 274 of file bezier.h.

References c_, and order().

Referenced by Geom::bounds_exact(), TEST_F(), and wrap_bezier().

◆ clear()

void Geom::Bezier::clear ( )

inline

Definition at line 248 of file bezier.h.

References c_.

Referenced by Inkscape::LivePathEffect::LPEMirrorSymmetry::doEffect_path(), Geom::sbasis_to_bezier(), and Inkscape::LivePathEffect::LPESlice::splititem().

◆ deflate()

Bezier Geom::Bezier::deflate ( ) const

Definition at line 176 of file bezier.cpp.

References c_, and order().

Referenced by find_bezier_roots(), and TEST_F().

◆ degree()

unsigned Geom::Bezier::degree ( ) const

inline

Definition at line 146 of file bezier.h.

References order().

Referenced by elevate_to_degree(), Geom::find_bernstein_roots(), find_bezier_roots(), operator+=(), operator-=(), and operator==().

◆ elevate_degree()

Bezier Geom::Bezier::elevate_degree ( ) const

Definition at line 138 of file bezier.cpp.

References c_, order(), and size().

Referenced by elevate_to_degree(), and TEST_F().

◆ elevate_to_degree()

Bezier Geom::Bezier::elevate_to_degree ( unsigned newDegree ) const

Definition at line 167 of file bezier.cpp.

References degree(), and elevate_degree().

Referenced by operator+=(), operator-=(), and TEST_F().

◆ find_bezier_roots()

void Geom::Bezier::find_bezier_roots	(	std::vector< double > &	solutions,
		double	l,
		double	r
	)		const

private

Definition at line 40 of file solve-bezier.cpp.

References deflate(), degree(), isConstant(), Geom::sgn(), and solutions.

Referenced by roots().

◆ forward_difference()

Bezier Geom::Bezier::forward_difference ( unsigned k ) const

Definition at line 121 of file bezier.cpp.

References Geom::binomial_increment_k(), c_, order(), and size().

◆ isConstant()

bool Geom::Bezier::isConstant ( double eps = EPSILON ) const

inline

Definition at line 260 of file bezier.h.

References Geom::are_near(), c_, and order().

Referenced by find_bezier_roots().

◆ isFinite()

bool Geom::Bezier::isFinite ( ) const

inline

Definition at line 266 of file bezier.h.

References c_, and order().

Referenced by wrap_bezier().

◆ isZero()

bool Geom::Bezier::isZero ( double eps = EPSILON ) const

inline

Definition at line 254 of file bezier.h.

References Geom::are_near(), c_, and order().

Referenced by wrap_bezier().

◆ operator!=()

bool Geom::Bezier::operator!= ( Bezier const & other ) const

inline

Definition at line 173 of file bezier.h.

◆ operator()()

Coord Geom::Bezier::operator() ( double t ) const

inline

Definition at line 280 of file bezier.h.

References valueAt().

◆ operator*=()

Bezier & Geom::Bezier::operator*= ( double v )

inline

Definition at line 313 of file bezier.h.

References c_.

◆ operator+=() [1/2]

Bezier & Geom::Bezier::operator+= ( Bezier const & other )

Definition at line 195 of file bezier.cpp.

References c_, degree(), elevate_to_degree(), and size().

◆ operator+=() [2/2]

Bezier & Geom::Bezier::operator+= ( double v )

inline

Definition at line 305 of file bezier.h.

References c_.

◆ operator-()

Bezier Geom::Bezier::operator- ( ) const

inline

Unary minus.

Definition at line 325 of file bezier.h.

References c_, and result.

◆ operator-=() [1/2]

Bezier & Geom::Bezier::operator-= ( Bezier const & other )

Definition at line 208 of file bezier.cpp.

References c_, degree(), elevate_to_degree(), and size().

◆ operator-=() [2/2]

Bezier & Geom::Bezier::operator-= ( double v )

inline

Definition at line 309 of file bezier.h.

References c_.

◆ operator/=()

Bezier & Geom::Bezier::operator/= ( double v )

inline

Definition at line 317 of file bezier.h.

References c_.

◆ operator=()

Bezier & Geom::Bezier::operator= ( Bezier const & other )

inline

Definition at line 151 of file bezier.h.

References c_, and resize().

◆ operator==()

bool Geom::Bezier::operator== ( Bezier const & other ) const

inline

Definition at line 159 of file bezier.h.

References c_, and degree().

◆ operator[]() [1/2]

Coord & Geom::Bezier::operator[] ( unsigned ix )

inline

Definition at line 284 of file bezier.h.

References c_.

◆ operator[]() [2/2]

Coord const & Geom::Bezier::operator[] ( unsigned ix ) const

inline

Definition at line 285 of file bezier.h.

References c_.

◆ order()

unsigned Geom::Bezier::order ( ) const

inline

Definition at line 145 of file bezier.h.

References c_.

Referenced by at1(), at1(), Bezier(), Geom::bezier_to_sbasis(), deflate(), degree(), elevate_degree(), forward_difference(), Geom::integral(), isConstant(), isFinite(), isZero(), Geom::operator*(), Geom::operator<<(), reduce_degree(), Geom::reverse(), roots(), subdivide(), TEST_F(), valueAndDerivatives(), and valueAt().

◆ reduce_degree()

Bezier Geom::Bezier::reduce_degree ( ) const

Definition at line 150 of file bezier.cpp.

References c_, order(), and size().

◆ resize()

void Geom::Bezier::resize	(	unsigned int	n,
		Coord	v = `0`
	)

inline

Definition at line 245 of file bezier.h.

References c_.

Referenced by operator=(), and Geom::sbasis_to_bezier().

◆ roots() [1/2]

std::vector< Coord > Geom::Bezier::roots ( ) const

Definition at line 105 of file bezier.cpp.

References find_bezier_roots(), and solutions.

Referenced by Geom::bounds_exact(), Geom::Path::extrema(), Geom::find_self_intersections(), Inkscape::UI::PathManipulator::insertNodeAtExtremum(), Geom::Ellipse::intersect(), TEST_F(), TEST_F(), and TEST_F().

◆ roots() [2/2]

std::vector< Coord > Geom::Bezier::roots ( Interval const & ivl ) const

Definition at line 113 of file bezier.cpp.

References c_, Geom::find_bernstein_roots(), Geom::GenericInterval< C >::max(), Geom::GenericInterval< C >::min(), order(), and solutions.

◆ setCoeff()

void Geom::Bezier::setCoeff	(	unsigned	ix,
		double	val
	)

inline

Definition at line 287 of file bezier.h.

References c_.

Referenced by TEST_F().

◆ size()

unsigned Geom::Bezier::size ( ) const

inline

Definition at line 147 of file bezier.h.

References c_.

Referenced by are_equal(), bezier_getitem(), Inkscape::LivePathEffect::LPEMirrorSymmetry::doEffect_path(), elevate_degree(), forward_difference(), Geom::NL::LFMBezier::instance(), operator+=(), operator-=(), reduce_degree(), Inkscape::LivePathEffect::LPESlice::splititem(), subdivide(), TEST_F(), TEST_F(), and valueAndDerivatives().

◆ subdivide() [1/2]

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

Definition at line 98 of file bezier.cpp.

References subdivide().

◆ subdivide() [2/2]

void Geom::Bezier::subdivide	(	Coord	t,
		Bezier *	left,
		Bezier *	right
	)		const

Definition at line 79 of file bezier.cpp.

References c_, order(), and size().

Referenced by subdivide(), and TEST_F().

◆ toSBasis()

SBasis Geom::Bezier::toSBasis ( ) const

Definition at line 187 of file bezier.cpp.

References Geom::bezier_to_sbasis().

Referenced by wrap_bezier().

◆ valueAndDerivatives()

std::vector< Coord > Geom::Bezier::valueAndDerivatives	(	Coord	t,
		unsigned	n_derivs
	)		const

Definition at line 51 of file bezier.cpp.

References Geom::bernstein_value_at(), c_, order(), and size().

Referenced by TEST_F().

◆ valueAt()

Coord Geom::Bezier::valueAt ( double t ) const

inline

Definition at line 277 of file bezier.h.

References Geom::bernstein_value_at(), c_, and order().

Referenced by are_equal(), Geom::bounds_exact(), Inkscape::UI::PathManipulator::insertNodeAtExtremum(), operator()(), Geom::RatQuad::pointAt(), TEST_F(), TEST_F(), and wrap_bezier().

Friends And Related Symbol Documentation

◆ Bernstein

friend class Bernstein

friend

Definition at line 133 of file bezier.h.

◆ bounds_fast

OptInterval bounds_fast ( Bezier const & b )

friend

Definition at line 305 of file bezier.cpp.

◆ derivative

Bezier derivative ( const Bezier & a )

friend

Definition at line 282 of file bezier.cpp.

◆ portion

Bezier portion	(	const Bezier &	a,
		Coord	from,
		Coord	to
	)

friend

Definition at line 250 of file bezier.cpp.

Referenced by Inkscape::LivePathEffect::LPEMirrorSymmetry::doEffect_path(), and Inkscape::LivePathEffect::LPESlice::splititem().

Member Data Documentation

◆ c_

std::valarray<Coord> Geom::Bezier::c_

private

Definition at line 128 of file bezier.h.

Referenced by at0(), at0(), at1(), at1(), Bezier(), Bezier(), Bezier(), Bezier(), Bezier(), Bezier(), Bezier(), Bezier(), Bezier(), Bezier(), Bezier(), clear(), deflate(), elevate_degree(), forward_difference(), isConstant(), isFinite(), isZero(), operator*=(), operator+=(), operator+=(), operator-(), operator-=(), operator-=(), operator/=(), operator=(), operator==(), operator[](), operator[](), order(), reduce_degree(), resize(), roots(), setCoeff(), size(), subdivide(), valueAndDerivatives(), and valueAt().

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

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

Classes

Public Types

Public Member Functions

Protected Member Functions

Private Member Functions

Private Attributes

Friends

Detailed Description

Member Typedef Documentation

◆ output_type

Constructor & Destructor Documentation

◆ Bezier() [1/16]

◆ Bezier() [2/16]

◆ Bezier() [3/16]

◆ Bezier() [4/16]

◆ Bezier() [5/16]

◆ Bezier() [6/16]

◆ Bezier() [7/16]

◆ Bezier() [8/16]

◆ Bezier() [9/16]

◆ Bezier() [10/16]

◆ Bezier() [11/16]

◆ Bezier() [12/16]

◆ Bezier() [13/16]

◆ Bezier() [14/16]

◆ Bezier() [15/16]

◆ Bezier() [16/16]

Member Function Documentation

◆ at0() [1/2]

◆ at0() [2/2]

◆ at1() [1/2]

◆ at1() [2/2]

◆ clear()

◆ deflate()

◆ degree()

◆ elevate_degree()

◆ elevate_to_degree()

◆ find_bezier_roots()

◆ forward_difference()

◆ isConstant()

◆ isFinite()

◆ isZero()

◆ operator!=()

◆ operator()()

◆ operator*=()

◆ operator+=() [1/2]

◆ operator+=() [2/2]

◆ operator-()

◆ operator-=() [1/2]

◆ operator-=() [2/2]

◆ operator/=()

◆ operator=()

◆ operator==()

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ order()

◆ reduce_degree()

◆ resize()

◆ roots() [1/2]

◆ roots() [2/2]

◆ setCoeff()

◆ size()

◆ subdivide() [1/2]

◆ subdivide() [2/2]

◆ toSBasis()

◆ valueAndDerivatives()

◆ valueAt()

Friends And Related Symbol Documentation

◆ Bernstein

◆ bounds_fast

◆ derivative

◆ portion

Member Data Documentation

◆ c_