Inkscape: Geom::detail::bezier_clipping Namespace Reference

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Functions
void	portion (std::vector< Point > &B, Interval const &I)

void	derivative (std::vector< Point > &D, std::vector< Point > const &B)

void	print (std::vector< Point > const &cp, const char *msg="")

template<class charT >
std::basic_ostream< charT > &	operator<< (std::basic_ostream< charT > &os, const Interval &I)

double	angle (std::vector< Point > const &A)

size_t	get_precision (Interval const &I)

void	range_assertion (int k, int m, int n, const char *msg)

double	det (Point const &P1, Point const &P2)

bool	solve (Point &P, Point const &P1, Point const &P2, Point const &Q)

void	map_to (Interval &J, Interval const &I)

bool	is_constant (std::vector< Point > const &A, double precision)

void	normal (std::vector< Point > &N, std::vector< Point > const &B)

void	left_portion (Coord t, std::vector< Point > &B)

void	right_portion (Coord t, std::vector< Point > &B)

template<typename Tag >
OptInterval	clip (std::vector< Point > const &A, std::vector< Point > const &B, double precision)

template<typename Tag >
void	iterate (std::vector< Interval > &domsA, std::vector< Interval > &domsB, std::vector< Point > const &A, std::vector< Point > const &B, Interval const &domA, Interval const &domB, double precision)

void	orientation_line (std::vector< double > &l, std::vector< Point > const &c, size_t i, size_t j)

Line	pick_orientation_line (std::vector< Point > const &c, double precision)

Line	orthogonal_orientation_line (std::vector< Point > const &c, Point const &p, double precision)

double	signed_distance (Point const &p, Line const &l)

Interval	fat_line_bounds (std::vector< Point > const &c, Line const &l)

double	intersect (Point const &p1, Point const &p2, double y)

OptInterval	clip_interval (std::vector< Point > const &B, Line const &l, Interval const &bound)

template<>
OptInterval	clip< intersection_point_tag > (std::vector< Point > const &A, std::vector< Point > const &B, double precision)

void	make_focus (std::vector< Point > &F, std::vector< Point > const &B)

void	distance_control_points (std::vector< Point > &D, std::vector< Point > const &B, std::vector< Point > const &F)

OptInterval	clip_interval (std::vector< Point > const &B, std::vector< Point > const &F)

template<>
OptInterval	clip< collinear_normal_tag > (std::vector< Point > const &A, std::vector< Point > const &B, double)

template<>
void	iterate< intersection_point_tag > (std::vector< Interval > &domsA, std::vector< Interval > &domsB, std::vector< Point > const &A, std::vector< Point > const &B, Interval const &domA, Interval const &domB, double precision)

template<>
void	iterate< collinear_normal_tag > (std::vector< Interval > &domsA, std::vector< Interval > &domsB, std::vector< Point > const &A, std::vector< Point > const &B, Interval const &domA, Interval const &domB, double precision)

template<typename Tag >
void	get_solutions (std::vector< std::pair< double, double > > &xs, std::vector< Point > const &A, std::vector< Point > const &B, double precision)

void	print (std::vector< Point > const &cp)

void	pick_orientation_line (std::vector< double > &l, std::vector< Point > const &c)

double	distance (Point const &P, std::vector< double > const &l)

void	fat_line_bounds (Interval &bound, std::vector< Point > const &c, std::vector< double > const &l)

void	clip (Interval &dom, std::vector< Point > const &B, std::vector< double > const &l, Interval const &bound)

Interval	make_empty_interval ()

const Interval	H2_INTERVAL (0.5+MAX_PRECISION, 1.0)

void	intersection (std::vector< Interval > &domsA, std::vector< Interval > &domsB, std::vector< Point > const &A, std::vector< Point > const &B, Interval const &domA, Interval const &domB, double precision)

Variables
const double	MAX_PRECISION = 1e-8

const double	MIN_CLIPPED_SIZE_THRESHOLD = 0.8

const Interval	UNIT_INTERVAL (0, 1)

const OptInterval	EMPTY_INTERVAL = make_empty_interval()

const Interval	H1_INTERVAL (0, 0.5)

const Interval	H2_INTERVAL (nextafter(0.5, 1.0), 1.0)

Function Documentation

◆ angle()

double Geom::detail::bezier_clipping::angle ( std::vector< Point > const & A )

inline

Definition at line 81 of file bezier-clipping.cpp.

References Geom::X, and Geom::Y.

Referenced by iterate< collinear_normal_tag >(), and iterate< intersection_point_tag >().

◆ clip() [1/2]

void Geom::detail::bezier_clipping::clip	(	Interval &	dom,
		std::vector< Point > const &	B,
		std::vector< double > const &	l,
		Interval const &	bound
	)

Definition at line 208 of file intersection-by-bezier-clipping.cpp.

References D, distance(), intersect(), Geom::GenericInterval< C >::max(), Geom::GenericInterval< C >::min(), Geom::X, and Geom::Y.

◆ clip() [2/2]

template<typename Tag >

OptInterval Geom::detail::bezier_clipping::clip	(	std::vector< Point > const &	A,
		std::vector< Point > const &	B,
		double	precision
	)

Referenced by intersection().

◆ clip< collinear_normal_tag >()

template<>

OptInterval Geom::detail::bezier_clipping::clip< collinear_normal_tag >	(	std::vector< Point > const &	A,
		std::vector< Point > const &	B,
		double
	)

Definition at line 711 of file bezier-clipping.cpp.

References clip_interval(), and make_focus().

Referenced by iterate< collinear_normal_tag >().

◆ clip< intersection_point_tag >()

template<>

OptInterval Geom::detail::bezier_clipping::clip< intersection_point_tag >	(	std::vector< Point > const &	A,
		std::vector< Point > const &	B,
		double	precision
	)

Definition at line 480 of file bezier-clipping.cpp.

References clip_interval(), fat_line_bounds(), is_constant(), Geom::middle_point(), Geom::Line::normalize(), orthogonal_orientation_line(), and pick_orientation_line().

Referenced by iterate< intersection_point_tag >().

◆ clip_interval() [1/2]

OptInterval Geom::detail::bezier_clipping::clip_interval	(	std::vector< Point > const &	B,
		Line const &	l,
		Interval const &	bound
	)

Definition at line 379 of file bezier-clipping.cpp.

References D, intersect(), Geom::GenericInterval< C >::max(), Geom::GenericInterval< C >::min(), signed_distance(), Geom::ConvexHull::size(), Geom::ConvexHull::swap(), Geom::X, and Geom::Y.

Referenced by clip< collinear_normal_tag >(), and clip< intersection_point_tag >().

◆ clip_interval() [2/2]

OptInterval Geom::detail::bezier_clipping::clip_interval	(	std::vector< Point > const &	B,
		std::vector< Point > const &	F
	)

Definition at line 639 of file bezier-clipping.cpp.

References D, distance_control_points(), intersect(), Geom::ConvexHull::size(), Geom::ConvexHull::swap(), Geom::X, and Geom::Y.

◆ derivative()

void Geom::detail::bezier_clipping::derivative	(	std::vector< Point > &	D,
		std::vector< Point > const &	B
	)

Definition at line 173 of file bezier-clipping.cpp.

References D.

Referenced by normal().

◆ det()

double Geom::detail::bezier_clipping::det	(	Point const &	P1,
		Point const &	P2
	)

Definition at line 121 of file bezier-clipping.cpp.

References Geom::X, and Geom::Y.

Referenced by solve().

◆ distance()

double Geom::detail::bezier_clipping::distance	(	Point const &	P,
		std::vector< double > const &	l
	)

inline

Definition at line 163 of file intersection-by-bezier-clipping.cpp.

References Geom::X, and Geom::Y.

Referenced by clip(), and fat_line_bounds().

◆ distance_control_points()

void Geom::detail::bezier_clipping::distance_control_points	(	std::vector< Point > &	D,
		std::vector< Point > const &	B,
		std::vector< Point > const &	F
	)

Definition at line 545 of file bezier-clipping.cpp.

References Geom::binomial_decrement_k(), Geom::binomial_increment_k(), D, and Geom::dot().

Referenced by clip_interval().

◆ fat_line_bounds() [1/2]

void Geom::detail::bezier_clipping::fat_line_bounds	(	Interval &	bound,
		std::vector< Point > const &	c,
		std::vector< double > const &	l
	)

inline

Definition at line 174 of file intersection-by-bezier-clipping.cpp.

References c, and distance().

◆ fat_line_bounds() [2/2]

Interval Geom::detail::bezier_clipping::fat_line_bounds	(	std::vector< Point > const &	c,
		Line const &	l
	)

Definition at line 351 of file bezier-clipping.cpp.

References c, Geom::GenericInterval< C >::expandTo(), and signed_distance().

Referenced by clip< intersection_point_tag >(), and intersection().

◆ get_precision()

size_t Geom::detail::bezier_clipping::get_precision ( Interval const & I )

inline

Definition at line 88 of file bezier-clipping.cpp.

Referenced by get_solutions().

◆ get_solutions()

template<typename Tag >

void Geom::detail::bezier_clipping::get_solutions	(	std::vector< std::pair< double, double > > &	xs,
		std::vector< Point > const &	A,
		std::vector< Point > const &	B,
		double	precision
	)

Definition at line 1084 of file bezier-clipping.cpp.

References get_precision(), and UNIT_INTERVAL.

◆ H2_INTERVAL()

const Interval Geom::detail::bezier_clipping::H2_INTERVAL	(	0.5+	MAX_PRECISION,
		1.	0
	)

◆ intersect()

double Geom::detail::bezier_clipping::intersect	(	Point const &	p1,
		Point const &	p2,
		double	y
	)

inline

Definition at line 365 of file bezier-clipping.cpp.

References Geom::X, and Geom::Y.

Referenced by clip(), clip_interval(), and clip_interval().

◆ intersection()

void Geom::detail::bezier_clipping::intersection	(	std::vector< Interval > &	domsA,
		std::vector< Interval > &	domsB,
		std::vector< Point > const &	A,
		std::vector< Point > const &	B,
		Interval const &	domA,
		Interval const &	domB,
		double	precision
	)

Definition at line 375 of file intersection-by-bezier-clipping.cpp.

References clip(), EMPTY_INTERVAL, Geom::GenericInterval< C >::extent(), fat_line_bounds(), H1_INTERVAL, H2_INTERVAL, intersection(), is_constant(), map_to(), Geom::GenericInterval< C >::max(), MAX_PRECISION, Geom::GenericInterval< C >::min(), MIN_CLIPPED_SIZE_THRESHOLD, pick_orientation_line(), and portion().

Referenced by intersection().

◆ is_constant()

bool Geom::detail::bezier_clipping::is_constant	(	std::vector< Point > const &	A,
		double	precision = `EPSILON`
	)

inline

Definition at line 159 of file bezier-clipping.cpp.

References Geom::are_near().

Referenced by clip< intersection_point_tag >(), intersection(), iterate< collinear_normal_tag >(), iterate< intersection_point_tag >(), and orthogonal_orientation_line().

◆ iterate()

template<typename Tag >

void Geom::detail::bezier_clipping::iterate	(	std::vector< Interval > &	domsA,
		std::vector< Interval > &	domsB,
		std::vector< Point > const &	A,
		std::vector< Point > const &	B,
		Interval const &	domA,
		Interval const &	domB,
		double	precision
	)

◆ iterate< collinear_normal_tag >()

template<>

void Geom::detail::bezier_clipping::iterate< collinear_normal_tag >	(	std::vector< Interval > &	domsA,
		std::vector< Interval > &	domsB,
		std::vector< Point > const &	A,
		std::vector< Point > const &	B,
		Interval const &	domA,
		Interval const &	domB,
		double	precision
	)

Definition at line 906 of file bezier-clipping.cpp.

References angle(), clip< collinear_normal_tag >(), counter, Geom::GenericOptInterval< C >::empty(), Geom::GenericInterval< C >::extent(), H1_INTERVAL, H2_INTERVAL, is_constant(), iterate< collinear_normal_tag >(), map_to(), MAX_PRECISION, MIN_CLIPPED_SIZE_THRESHOLD, and portion().

Referenced by iterate< collinear_normal_tag >().

◆ iterate< intersection_point_tag >()

template<>

void Geom::detail::bezier_clipping::iterate< intersection_point_tag >	(	std::vector< Interval > &	domsA,
		std::vector< Interval > &	domsB,
		std::vector< Point > const &	A,
		std::vector< Point > const &	B,
		Interval const &	domA,
		Interval const &	domB,
		double	precision
	)

Definition at line 747 of file bezier-clipping.cpp.

References angle(), Geom::are_near(), clip< intersection_point_tag >(), counter, Geom::GenericOptInterval< C >::empty(), Geom::GenericInterval< C >::extent(), H1_INTERVAL, H2_INTERVAL, is_constant(), iterate< intersection_point_tag >(), map_to(), MAX_PRECISION, Geom::middle_point(), MIN_CLIPPED_SIZE_THRESHOLD, portion(), and print().

Referenced by iterate< intersection_point_tag >().

◆ left_portion()

void Geom::detail::bezier_clipping::left_portion	(	Coord	t,
		std::vector< Point > &	B
	)

Definition at line 209 of file bezier-clipping.cpp.

References Geom::lerp().

Referenced by portion().

◆ make_empty_interval()

Interval Geom::detail::bezier_clipping::make_empty_interval ( )

inline

Definition at line 341 of file intersection-by-bezier-clipping.cpp.

◆ make_focus()

void Geom::detail::bezier_clipping::make_focus	(	std::vector< Point > &	F,
		std::vector< Point > const &	B
	)

Definition at line 504 of file bezier-clipping.cpp.

References c, normal(), and solve().

Referenced by clip< collinear_normal_tag >().

◆ map_to()

void Geom::detail::bezier_clipping::map_to	(	Interval &	J,
		Interval const &	I
	)

inline

Definition at line 146 of file bezier-clipping.cpp.

References Geom::GenericInterval< C >::setEnds(), and Geom::Interval::valueAt().

Referenced by intersection(), iterate< collinear_normal_tag >(), and iterate< intersection_point_tag >().

◆ normal()

void Geom::detail::bezier_clipping::normal	(	std::vector< Point > &	N,
		std::vector< Point > const &	B
	)

Definition at line 196 of file bezier-clipping.cpp.

References derivative(), N, and Geom::rot90().

Referenced by make_focus().

◆ operator<<()

template<class charT >

std::basic_ostream< charT > & Geom::detail::bezier_clipping::operator<<	(	std::basic_ostream< charT > &	os,
		const Interval &	I
	)

inline

Definition at line 66 of file bezier-clipping.cpp.

References msg.

◆ orientation_line()

void Geom::detail::bezier_clipping::orientation_line	(	std::vector< double > &	l,
		std::vector< Point > const &	c,
		size_t	i,
		size_t	j
	)

inline

Definition at line 284 of file bezier-clipping.cpp.

References c, Geom::cross(), Geom::length(), Geom::X, and Geom::Y.

Referenced by pick_orientation_line().

◆ orthogonal_orientation_line()

Line Geom::detail::bezier_clipping::orthogonal_orientation_line	(	std::vector< Point > const &	c,
		Point const &	p,
		double	precision
	)

Definition at line 325 of file bezier-clipping.cpp.

References c, Geom::Point::cw(), and is_constant().

Referenced by clip< intersection_point_tag >().

◆ pick_orientation_line() [1/2]

void Geom::detail::bezier_clipping::pick_orientation_line	(	std::vector< double > &	l,
		std::vector< Point > const &	c
	)

inline

Definition at line 141 of file intersection-by-bezier-clipping.cpp.

References Geom::are_near(), c, and orientation_line().

◆ pick_orientation_line() [2/2]

Line Geom::detail::bezier_clipping::pick_orientation_line	(	std::vector< Point > const &	c,
		double	precision
	)

Definition at line 302 of file bezier-clipping.cpp.

References Geom::are_near(), and c.

Referenced by clip< intersection_point_tag >(), and intersection().

◆ portion()

void Geom::detail::bezier_clipping::portion	(	std::vector< Point > &	B,
		Interval const &	I
	)

Definition at line 241 of file bezier-clipping.cpp.

References left_portion(), and right_portion().

Referenced by intersection(), iterate< collinear_normal_tag >(), and iterate< intersection_point_tag >().

◆ print() [1/2]

void Geom::detail::bezier_clipping::print ( std::vector< Point > const & cp )

inline

Definition at line 60 of file intersection-by-bezier-clipping.cpp.

◆ print() [2/2]

void Geom::detail::bezier_clipping::print	(	std::vector< Point > const &	cp,
		const char *	msg = `""`
	)

Definition at line 66 of file bezier-clipping.cpp.

Referenced by iterate< intersection_point_tag >().

◆ range_assertion()

void Geom::detail::bezier_clipping::range_assertion	(	int	k,
		int	m,
		int	n,
		const char *	msg
	)

Definition at line 102 of file bezier-clipping.cpp.

References msg.

◆ right_portion()

void Geom::detail::bezier_clipping::right_portion	(	Coord	t,
		std::vector< Point > &	B
	)

Definition at line 225 of file bezier-clipping.cpp.

References Geom::lerp().

Referenced by portion().

◆ signed_distance()

double Geom::detail::bezier_clipping::signed_distance	(	Point const &	p,
		Line const &	l
	)

Definition at line 339 of file bezier-clipping.cpp.

References c, Geom::Line::coefficients(), Geom::X, and Geom::Y.

Referenced by clip_interval(), and fat_line_bounds().

◆ solve()

bool Geom::detail::bezier_clipping::solve	(	Point &	P,
		Point const &	P1,
		Point const &	P2,
		Point const &	Q
	)

Definition at line 130 of file bezier-clipping.cpp.

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

Referenced by make_focus().

Variable Documentation

◆ EMPTY_INTERVAL

const Interval Geom::detail::bezier_clipping::EMPTY_INTERVAL = make_empty_interval()

Definition at line 725 of file bezier-clipping.cpp.

Referenced by intersection().

◆ H1_INTERVAL

const Interval Geom::detail::bezier_clipping::H1_INTERVAL	(	0	,
		0.	5
	)

Referenced by intersection(), iterate< collinear_normal_tag >(), and iterate< intersection_point_tag >().

◆ H2_INTERVAL

const Interval Geom::detail::bezier_clipping::H2_INTERVAL(nextafter(0.5, 1.0), 1.0)	(	nextafter(0.5, 1.0)	,
		1.	0
	)

Referenced by intersection(), iterate< collinear_normal_tag >(), and iterate< intersection_point_tag >().

◆ MAX_PRECISION

const double Geom::detail::bezier_clipping::MAX_PRECISION = 1e-8

Definition at line 722 of file bezier-clipping.cpp.

Referenced by intersection(), iterate< collinear_normal_tag >(), and iterate< intersection_point_tag >().

◆ MIN_CLIPPED_SIZE_THRESHOLD

const double Geom::detail::bezier_clipping::MIN_CLIPPED_SIZE_THRESHOLD = 0.8

Definition at line 723 of file bezier-clipping.cpp.

Referenced by intersection(), iterate< collinear_normal_tag >(), and iterate< intersection_point_tag >().

◆ UNIT_INTERVAL

const Interval Geom::detail::bezier_clipping::UNIT_INTERVAL	(	0	,
		1
	)

Referenced by get_solutions().