Inkscape: Geom::D2< T > Class Template Reference

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Adaptor that creates 2D functions from 1D ones. More...

#include <d2.h>

Public Types
typedef T	D1Value

typedef T &	D1Reference

typedef T const &	D1ConstReference

typedef Point	output_type

Public Member Functions
	D2 ()

	D2 (Point const &a)

	D2 (T const &a, T const &b)

template<typename Iter >
	D2 (Iter first, Iter last)

	D2 (std::vector< Point > const &vec)

T &	operator[] (unsigned i)

T const &	operator[] (unsigned i) const

Point	point (unsigned i) const

bool	isZero (double eps=EPSILON) const

bool	isConstant (double eps=EPSILON) const

bool	isFinite () const

Point	at0 () const

Point	at1 () const

Point	pointAt (double t) const

Point	valueAt (double t) const

std::vector< Point >	valueAndDerivatives (double t, unsigned n) const

D2< SBasis >	toSBasis () const

Point	operator() (double t) const

Point	operator() (double x, double y) const

Private Attributes
T	f [2]

Related Symbols
(Note that these are not member symbols.)
template<typename T >
T	dot (D2< T > const &a, Point const &b)
	Calculates the 'dot product' or 'inner product' of `a` and `b`.

template<typename T >
T	cross (D2< T > const &a, D2< T > const &b)
	Calculates the 'cross product' or 'outer product' of `a` and `b`.

D2< Piecewise< SBasis > >	tan2 (SBasis const &angle, double tol, unsigned order)
	tan2 is the pseudo-inverse of atan2.

void	length_integrating (D2< SBasis > const &B, double &result, double &abs_error, double tol)
	Calculates the length of a D2<SBasis> through gsl integration.

double	length (D2< SBasis > const &s, double tol)
	Calculates the length of a D2<SBasis> through gsl integration.

std::vector< D2< SBasis > >	cubics_fitting_curvature (Point const &M0, Point const &M1, Point const &dM0, Point const &dM1, double d2M0xdM0, double d2M1xdM1, int insist_on_speed_signs, double epsilon)
	returns the cubics fitting direction and curvature of a given input curve at two points.

std::vector< double >	find_tangents (Point P, D2< SBasis > const &A)
	returns all the parameter values of A whose tangent passes through P.

std::vector< double >	find_normals (Point P, D2< SBasis > const &A)
	returns all the parameter values of A whose normal passes through P.

std::vector< double >	find_normals_by_vector (Point V, D2< SBasis > const &A)
	returns all the parameter values of A whose normal is parallel to vector V.

std::vector< double >	find_tangents_by_vector (Point V, D2< SBasis > const &A)
	returns all the parameter values of A whose tangent is parallel to vector V.

Detailed Description

template<typename T>
class Geom::D2< T >

Adaptor that creates 2D functions from 1D ones.

Definition at line 54 of file d2.h.

Member Typedef Documentation

◆ D1ConstReference

template<typename T >

typedef T const& Geom::D2< T >::D1ConstReference

Definition at line 62 of file d2.h.

◆ D1Reference

template<typename T >

typedef T& Geom::D2< T >::D1Reference

Definition at line 61 of file d2.h.

◆ D1Value

template<typename T >

typedef T Geom::D2< T >::D1Value

Definition at line 60 of file d2.h.

◆ output_type

template<typename T >

typedef Point Geom::D2< T >::output_type

Definition at line 108 of file d2.h.

Constructor & Destructor Documentation

◆ D2() [1/5]

template<typename T >

Geom::D2< T >::D2 ( )

inline

Definition at line 64 of file d2.h.

References Geom::D2< T >::f, Geom::X, and Geom::Y.

◆ D2() [2/5]

template<typename T >

Geom::D2< T >::D2 ( Point const & a )

inlineexplicit

Definition at line 65 of file d2.h.

References Geom::D2< T >::f, Geom::X, and Geom::Y.

◆ D2() [3/5]

template<typename T >

Geom::D2< T >::D2	(	T const &	a,
		T const &	b
	)

inline

Definition at line 69 of file d2.h.

References Geom::D2< T >::f, Geom::X, and Geom::Y.

◆ D2() [4/5]

template<typename T >

template<typename Iter >

Geom::D2< T >::D2	(	Iter	first,
		Iter	last
	)

inline

Definition at line 75 of file d2.h.

References Geom::D2< T >::f, Geom::X, and Geom::Y.

◆ D2() [5/5]

template<typename T >

Geom::D2< T >::D2 ( std::vector< Point > const & vec )

inline

Definition at line 86 of file d2.h.

References Geom::D2< T >::f, Geom::X, and Geom::Y.

Member Function Documentation

◆ at0()

template<typename T >

Point Geom::D2< T >::at0 ( ) const

inline

◆ at1()

template<typename T >

Point Geom::D2< T >::at1 ( ) const

inline

Definition at line 125 of file d2.h.

References Geom::D2< T >::at1(), Geom::D2< T >::f, Geom::X, and Geom::Y.

Referenced by Geom::D2< T >::at1(), Geom::build_from_sbasis(), Geom::Piecewise< T >::centroid(), Geom::computeLinfinityNeighborhood(), computeLinfinityNeighborhood(), Geom::hausdorf(), Geom::hausdorfl(), Geom::monotonic_smash_intersect(), Geom::nearest_time(), and Geom::Piecewise< T >::unitVector().

◆ isConstant()

template<typename T >

bool Geom::D2< T >::isConstant ( double eps = EPSILON ) const

inline

Definition at line 113 of file d2.h.

References Geom::D2< T >::f, Geom::X, and Geom::Y.

Referenced by Geom::nearest_time().

◆ isFinite()

template<typename T >

bool Geom::D2< T >::isFinite ( ) const

inline

Definition at line 117 of file d2.h.

References Geom::D2< T >::f, Geom::X, and Geom::Y.

Referenced by Geom::build_from_sbasis().

◆ isZero()

template<typename T >

bool Geom::D2< T >::isZero ( double eps = EPSILON ) const

inline

Definition at line 109 of file d2.h.

References Geom::D2< T >::f, Geom::X, and Geom::Y.

Referenced by Geom::touching_circle().

◆ operator()() [1/2]

template<typename T >

Point Geom::D2< T >::operator() ( double t ) const

inline

Definition at line 433 of file d2.h.

◆ operator()() [2/2]

template<typename T >

Point Geom::D2< T >::operator()	(	double	x,
		double	y
	)		const

inline

Definition at line 443 of file d2.h.

◆ operator[]() [1/2]

template<typename T >

T & Geom::D2< T >::operator[] ( unsigned i )

inline

Definition at line 100 of file d2.h.

References Geom::D2< T >::f.

◆ operator[]() [2/2]

template<typename T >

T const & Geom::D2< T >::operator[] ( unsigned i ) const

inline

Definition at line 101 of file d2.h.

References Geom::D2< T >::f.

◆ point()

template<typename T >

Point Geom::D2< T >::point ( unsigned i ) const

inline

Definition at line 102 of file d2.h.

References Geom::D2< T >::f, Geom::X, and Geom::Y.

◆ pointAt()

template<typename T >

Point Geom::D2< T >::pointAt ( double t ) const

inline

Definition at line 129 of file d2.h.

◆ toSBasis()

template<typename T >

D2< SBasis > Geom::D2< T >::toSBasis ( ) const

inline

Definition at line 148 of file d2.h.

References Geom::D2< T >::f, Geom::D2< T >::toSBasis(), Geom::X, and Geom::Y.

Referenced by Geom::D2< T >::toSBasis().

◆ valueAndDerivatives()

template<typename T >

std::vector< Point > Geom::D2< T >::valueAndDerivatives	(	double	t,
		unsigned	n
	)		const

inline

Definition at line 138 of file d2.h.

References Geom::D2< T >::f, Geom::X, and Geom::Y.

Referenced by Geom::intersect_polish_root(), and Geom::unitTangentAt().

◆ valueAt()

template<typename T >

Point Geom::D2< T >::valueAt ( double t ) const

inline

Definition at line 133 of file d2.h.

Referenced by Geom::xAx::crossings(), Geom::Ellipse::intersect(), linearizeCusps(), Geom::monotonic_smash_intersect(), Geom::nearest_time(), and toPoly().

Friends And Related Symbol Documentation

◆ cross()

template<typename T >

T cross	(	D2< T > const &	a,
		D2< T > const &	b
	)

Calculates the 'cross product' or 'outer product' of a and b.

Returns: \(a \times b = a_Y b_X - a_X b_Y\).

Definition at line 386 of file d2.h.

◆ cubics_fitting_curvature()

template<typename T >

std::vector< D2< SBasis > > cubics_fitting_curvature	(	Point const &	M0,
		Point const &	M1,
		Point const &	dM0,
		Point const &	dM1,
		double	d2M0xdM0,
		double	d2M1xdM1,
		int	insist_on_speed_signs,
		double	epsilon
	)

returns the cubics fitting direction and curvature of a given input curve at two points.

The input can be the value, speed, and acceleration or value, speed, and cross(acceleration,speed) of the original curve at the both ends. (the second is often technically useful, as it avoids unnecessary division by |v|^2) Recall that K=1/R=cross(acceleration,speed)/|speed|^3.

Moreover, a 7-th argument 'insist_on_speed_signs' can be supplied to select solutions:
If insist_on_speed_signs == 1, only consider solutions where speeds at both ends are positively proportional to the given ones. If insist_on_speed_signs == 0, allow speeds to point in the opposite direction (both at the same time) If insist_on_speed_signs == -1, allow speeds to point in both direction independently.

Definition at line 630 of file sbasis-geometric.cpp.

References c, Geom::cross(), Geom::curvature(), result, solve_lambda0(), and Geom::Piecewise< T >::valueAt().

◆ dot()

template<typename T >

T dot	(	D2< T > const &	a,
		Point const &	b
	)

Calculates the 'dot product' or 'inner product' of a and b.

Returns: \(a \bullet b = a_X b_X + a_Y b_Y\).

Definition at line 370 of file d2.h.

◆ find_normals()

template<typename T >

std::vector< double > find_normals	(	Point	P,
		D2< SBasis > const &	A
	)

returns all the parameter values of A whose normal passes through P.

Definition at line 755 of file sbasis-geometric.cpp.

References Geom::derivative(), Geom::dot(), and Geom::roots().

◆ find_normals_by_vector()

template<typename T >

std::vector< double > find_normals_by_vector	(	Point	V,
		D2< SBasis > const &	A
	)

returns all the parameter values of A whose normal is parallel to vector V.

Definition at line 764 of file sbasis-geometric.cpp.

References Geom::derivative(), Geom::dot(), and Geom::roots().

◆ find_tangents()

template<typename T >

std::vector< double > find_tangents	(	Point	P,
		D2< SBasis > const &	A
	)

returns all the parameter values of A whose tangent passes through P.

Definition at line 746 of file sbasis-geometric.cpp.

References Geom::cross(), Geom::derivative(), and Geom::roots().

◆ find_tangents_by_vector()

template<typename T >

std::vector< double > find_tangents_by_vector	(	Point	V,
		D2< SBasis > const &	A
	)

returns all the parameter values of A whose tangent is parallel to vector V.

Definition at line 772 of file sbasis-geometric.cpp.

References Geom::derivative(), Geom::dot(), Geom::roots(), and Geom::rot90().

◆ length()

template<typename T >

double length	(	D2< SBasis > const &	s,
		double	tol
	)

Calculates the length of a D2<SBasis> through gsl integration.

Parameters

s	the Element.
tol	the maximum error allowed.

If you only want the total length, this routine faster and more accurate than constructing an arcLengthSb.

Definition at line 484 of file sbasis-geometric.cpp.

References Geom::length_integrating(), and result.

◆ length_integrating()

template<typename T >

void length_integrating	(	D2< SBasis > const &	B,
		double &	result,
		double &	abs_error,
		double	tol
	)

Calculates the length of a D2<SBasis> through gsl integration.

Parameters

B	the Element.
tol	the maximum error allowed.
result	variable to be incremented with the length of the path
abs_error	variable to be incremented with the estimated error

If you only want the length, this routine may be faster/more accurate.

Definition at line 458 of file sbasis-geometric.cpp.

References Geom::derivative(), Geom::dot(), result, sb_length_integrating(), and w.

◆ tan2()

template<typename T >

D2< Piecewise< SBasis > > tan2	(	SBasis const &	angle,
		double	tol,
		unsigned	order
	)

tan2 is the pseudo-inverse of atan2.

It takes an angle and returns a unit_vector that points in the direction of angle.

Parameters

angle	a piecewise function of angle wrt t.
tol	the maximum error allowed.
order	the maximum degree to use for approximation , SBasis

Definition at line 199 of file sbasis-geometric.cpp.

References order, and Geom::tan2().

Member Data Documentation

◆ f

template<typename T >

T Geom::D2< T >::f[2]

private

Definition at line 57 of file d2.h.

Referenced by Geom::D2< T >::at0(), Geom::D2< T >::at1(), Geom::D2< T >::D2(), Geom::D2< T >::D2(), Geom::D2< T >::D2(), Geom::D2< T >::D2(), Geom::D2< T >::D2(), Geom::D2< T >::isConstant(), Geom::D2< T >::isFinite(), Geom::D2< T >::isZero(), Geom::D2< T >::operator[](), Geom::D2< T >::operator[](), Geom::D2< T >::point(), Geom::D2< T >::toSBasis(), and Geom::D2< T >::valueAndDerivatives().

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

/builds/inkscape/inkscape/src/3rdparty/2geom/include/2geom/d2.h
/builds/inkscape/inkscape/src/3rdparty/2geom/src/2geom/sbasis-geometric.cpp

Public Types

Public Member Functions

Private Attributes

Related Symbols

Detailed Description

Member Typedef Documentation

◆ D1ConstReference

◆ D1Reference

◆ D1Value

◆ output_type

Constructor & Destructor Documentation

◆ D2() [1/5]

◆ D2() [2/5]

◆ D2() [3/5]

◆ D2() [4/5]

◆ D2() [5/5]

Member Function Documentation

◆ at0()

◆ at1()

◆ isConstant()

◆ isFinite()

◆ isZero()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ point()

◆ pointAt()

◆ toSBasis()

◆ valueAndDerivatives()

◆ valueAt()

Friends And Related Symbol Documentation

◆ cross()

◆ cubics_fitting_curvature()

◆ dot()

◆ find_normals()

◆ find_normals_by_vector()

◆ find_tangents()

◆ find_tangents_by_vector()

◆ length()

◆ length_integrating()

◆ tan2()

Member Data Documentation

◆ f