Geom::SBasis Class Reference

Polynomial in symmetric power basis. More...

#include <sbasis.h>

Public Types
typedef std::vector< Linear >::iterator	iterator
typedef std::vector< Linear >::const_iterator	const_iterator
typedef double	output_type

Public Member Functions
size_t	size () const
Linear	operator[] (unsigned i) const
Linear &	operator[] (unsigned i)
const_iterator	begin () const
const_iterator	end () const
iterator	begin ()
iterator	end ()
bool	empty () const
Linear &	back ()
Linear const &	back () const
void	pop_back ()
void	resize (unsigned n)
void	resize (unsigned n, Linear const &l)
void	reserve (unsigned n)
void	clear ()
void	insert (iterator before, const_iterator src_begin, const_iterator src_end)
Linear &	at (unsigned i)
bool	operator== (SBasis const &B) const
bool	operator!= (SBasis const &B) const
	SBasis ()
	SBasis (double a)
	SBasis (double a, double b)
	SBasis (SBasis const &a)
	SBasis (std::vector< Linear > ls)
	SBasis (Linear const &bo)
	SBasis (Linear *bo)
	SBasis (size_t n, Linear const &l)
	SBasis (Coord c0, Coord c1, Coord c2, Coord c3)
	SBasis (Coord c0, Coord c1, Coord c2, Coord c3, Coord c4, Coord c5)
	SBasis (Coord c0, Coord c1, Coord c2, Coord c3, Coord c4, Coord c5, Coord c6, Coord c7)
	SBasis (Coord c0, Coord c1, Coord c2, Coord c3, Coord c4, Coord c5, Coord c6, Coord c7, Coord c8, Coord c9)
template<typename Iter >
	SBasis (Iter first, Iter last)
bool	isZero (double eps=EPSILON) const
bool	isConstant (double eps=EPSILON) const
bool	isFinite () const
	test all coefficients are finite
Coord	at0 () const
Coord &	at0 ()
Coord	at1 () const
Coord &	at1 ()
int	degreesOfFreedom () const
double	valueAt (double t) const
double	operator() (double t) const
std::vector< double >	valueAndDerivatives (double t, unsigned n) const
	Compute the value and the first n derivatives.
SBasis	toSBasis () const
double	tailError (unsigned tail) const
	bound the error from term truncation
SBasis	operator() (SBasis const &g) const
void	normalize ()
void	truncate (unsigned k)

Private Member Functions
void	push_back (Linear const &l)
void	derive ()
	Compute the derivative of this inplace (Exact)

Private Attributes
std::vector< Linear >	d

Related Symbols
(Note that these are not member symbols.)
SBasis	reverse (SBasis const &a)
	Returns a function which reverses the domain of a.
unsigned	valuation (SBasis const &a, double tol=0)
	Returns the degree of the first non zero coefficient.
SBasis	portion (const SBasis &t, double from, double to)
	Returns the sbasis on domain [0,1] that was t on [from, to].

Detailed Description

Polynomial in symmetric power basis.

Definition at line 70 of file sbasis.h.

Member Typedef Documentation

const_iterator

typedef std::vector<Linear>::const_iterator Geom::SBasis::const_iterator

Definition at line 78 of file sbasis.h.

iterator

typedef std::vector<Linear>::iterator Geom::SBasis::iterator

Definition at line 77 of file sbasis.h.

output_type

typedef double Geom::SBasis::output_type

Definition at line 194 of file sbasis.h.

Constructor & Destructor Documentation

SBasis() [1/13]

Geom::SBasis::SBasis ( )

inline

Definition at line 112 of file sbasis.h.

Referenced by linear_root(), Geom::operator+=(), Geom::operator-(), Geom::operator-=(), and Geom::Linear::toSBasis().

SBasis() [2/13]

Geom::SBasis::SBasis ( double  a )

inlineexplicit

Definition at line 115 of file sbasis.h.

SBasis() [3/13]

Geom::SBasis::SBasis ( double  a, double  b  )

inlineexplicit

Definition at line 118 of file sbasis.h.

SBasis() [4/13]

Geom::SBasis::SBasis ( SBasis const &  a )

inline

Definition at line 121 of file sbasis.h.

SBasis() [5/13]

Geom::SBasis::SBasis ( std::vector< Linear >  ls )

inline

Definition at line 124 of file sbasis.h.

SBasis() [6/13]

Geom::SBasis::SBasis ( Linear const &  bo )

inline

Definition at line 127 of file sbasis.h.

SBasis() [7/13]

Geom::SBasis::SBasis ( Linear *  bo )

inline

Definition at line 130 of file sbasis.h.

SBasis() [8/13]

Geom::SBasis::SBasis ( size_t  n, Linear const &  l  )

inlineexplicit

Definition at line 133 of file sbasis.h.

SBasis() [9/13]

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

inline

Definition at line 135 of file sbasis.h.

SBasis() [10/13]

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

inline

Definition at line 143 of file sbasis.h.

SBasis() [11/13]

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

inline

Definition at line 153 of file sbasis.h.

SBasis() [12/13]

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

inline

Definition at line 166 of file sbasis.h.

SBasis() [13/13]

template<typename Iter >

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

inline

Definition at line 184 of file sbasis.h.

Member Function Documentation

at()

Linear & Geom::SBasis::at ( unsigned  i )

inline

Definition at line 107 of file sbasis.h.

Referenced by Geom::compose_inverse(), and Geom::Piecewise< T >::unitVector().

at0() [1/2]

Coord & Geom::SBasis::at0 ( )

inline

Definition at line 213 of file sbasis.h.

at0() [2/2]

Coord Geom::SBasis::at0 ( ) const

inline

Definition at line 212 of file sbasis.h.

Referenced by Geom::Piecewise< T >::arc_length_parametrization(), Geom::Piecewise< T >::centroid(), Geom::compose_pullback(), convole(), Geom::cos(), Geom::divide(), Geom::interpolate(), portion(), Geom::Piecewise< T >::pw_compose_inverse(), Geom::sqrt_internal(), and TEST_F().

at1() [1/2]

Coord & Geom::SBasis::at1 ( )

inline

Definition at line 215 of file sbasis.h.

at1() [2/2]

Coord Geom::SBasis::at1 ( ) const

inline

Definition at line 214 of file sbasis.h.

Referenced by Geom::Piecewise< T >::arc_length_parametrization(), Geom::Piecewise< T >::centroid(), Geom::compose_pullback(), Geom::cos(), Geom::divide(), Geom::interpolate(), portion(), Geom::Piecewise< T >::pw_compose_inverse(), Geom::sqrt_internal(), and TEST_F().

back() [1/2]

Linear & Geom::SBasis::back ( )

inline

Definition at line 88 of file sbasis.h.

back() [2/2]

Linear const & Geom::SBasis::back ( ) const

inline

Definition at line 89 of file sbasis.h.

begin() [1/2]

iterator Geom::SBasis::begin ( )

inline

Definition at line 85 of file sbasis.h.

begin() [2/2]

const_iterator Geom::SBasis::begin ( ) const

inline

Definition at line 83 of file sbasis.h.

Referenced by divide_by_sk().

clear()

void Geom::SBasis::clear ( )

inline

Definition at line 101 of file sbasis.h.

Referenced by Geom::bezier_to_sbasis(), and Geom::operator*=().

degreesOfFreedom()

int Geom::SBasis::degreesOfFreedom ( ) const

inline

Definition at line 217 of file sbasis.h.

References size.

derive()

void Geom::SBasis::derive ( )

private

Compute the derivative of this inplace (Exact)

Definition at line 350 of file sbasis.cpp.

References d, isZero(), pop_back(), and size().

Referenced by valueAndDerivatives().

empty()

bool Geom::SBasis::empty ( ) const

inline

Definition at line 87 of file sbasis.h.

end() [1/2]

iterator Geom::SBasis::end ( )

inline

Definition at line 86 of file sbasis.h.

end() [2/2]

const_iterator Geom::SBasis::end ( ) const

inline

Definition at line 84 of file sbasis.h.

Referenced by divide_by_sk().

insert()

void Geom::SBasis::insert ( iterator  before, const_iterator  src_begin, const_iterator  src_end  )

inline

Definition at line 106 of file sbasis.h.

Referenced by divide_by_sk(), and Geom::truncate().

isConstant()

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

inline

Definition at line 202 of file sbasis.h.

References size.

isFinite()

bool Geom::SBasis::isFinite

(

)

const

test all coefficients are finite

Definition at line 56 of file sbasis.cpp.

References size().

Referenced by TEST_F().

isZero()

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

inline

Definition at line 195 of file sbasis.h.

References size.

Referenced by Geom::Piecewise< T >::compose(), Geom::derivative(), derive(), Geom::divide(), Geom::force_continuity(), Geom::multiply(), Geom::multiply_add(), Geom::operator*=(), Geom::sbasis_to_poly(), Geom::sqrt(), Geom::sqrt_internal(), and TEST_F().

normalize()

void Geom::SBasis::normalize ( )

inline

Definition at line 247 of file sbasis.h.

References size.

Referenced by Geom::integral(), integral(), Geom::multiply(), Geom::multiply_add(), my_inverse(), and Geom::poly_to_sbasis().

operator!=()

bool Geom::SBasis::operator!= ( SBasis const &  B ) const

inline

Definition at line 110 of file sbasis.h.

operator()() [1/2]

double Geom::SBasis::operator() ( double  t ) const

inline

Definition at line 232 of file sbasis.h.

operator()() [2/2]

SBasis Geom::SBasis::operator() ( SBasis const &  g ) const

inline

Definition at line 424 of file sbasis.h.

References Geom::compose().

operator==()

bool Geom::SBasis::operator== ( SBasis const &  B ) const

inline

Definition at line 109 of file sbasis.h.

operator[]() [1/2]

Linear & Geom::SBasis::operator[] ( unsigned  i )

inline

Definition at line 82 of file sbasis.h.

operator[]() [2/2]

Linear Geom::SBasis::operator[] ( unsigned  i ) const

inline

Definition at line 79 of file sbasis.h.

pop_back()

void Geom::SBasis::pop_back ( )

inline

Definition at line 90 of file sbasis.h.

Referenced by derive().

push_back()

void Geom::SBasis::push_back ( Linear const &  l )

inlineprivate

Definition at line 72 of file sbasis.h.

Referenced by Geom::cheb(), Geom::chebyshev(), and TEST_F().

reserve()

void Geom::SBasis::reserve ( unsigned  n )

inline

Definition at line 100 of file sbasis.h.

resize() [1/2]

void Geom::SBasis::resize ( unsigned  n )

inline

Definition at line 98 of file sbasis.h.

Referenced by Geom::bezier_to_sbasis(), Geom::compose_inverse(), Geom::derivative(), Geom::divide(), Geom::divide(), Geom::NL::LFMSBasis::instance(), Geom::integral(), integral(), Geom::inverse(), Geom::multiply_add(), Geom::operator+=(), Geom::operator-=(), Geom::sqrt(), and Geom::sqrt_internal().

resize() [2/2]

void Geom::SBasis::resize ( unsigned  n, Linear const &  l  )

inline

Definition at line 99 of file sbasis.h.

size()

size_t Geom::SBasis::size ( ) const

inline

Definition at line 76 of file sbasis.h.

Referenced by are_equal(), Geom::compose(), Geom::compose(), Geom::derivative(), derive(), divide_by_sk(), handle_to_sb(), Geom::inverse(), isFinite(), main(), Geom::multiply(), Geom::multiply_add(), my_inverse(), Geom::operator*(), Geom::operator+(), Geom::operator+=(), Geom::operator-(), Geom::operator-=(), Geom::Piecewise< T >::pw_compose_inverse(), sbasis_getitem(), sbasis_len(), Geom::sbasis_to_bezier(), Geom::sbasis_to_poly(), Geom::shift(), Geom::sqrt(), Geom::sqrt_internal(), and Geom::Piecewise< T >::unitVector().

tailError()

double Geom::SBasis::tailError

(

unsigned

tail

)

const

bound the error from term truncation

Parameters

tail	first term to chop

Returns

the largest possible error this truncation could give

Definition at line 49 of file sbasis.cpp.

References Geom::bounds_fast(), and bs.

Referenced by Geom::cos(), Geom::divide(), Geom::divide(), Geom::inverse(), Geom::Piecewise< T >::pw_compose_inverse(), pw_inverse(), Geom::sqrt(), Geom::sqrt_internal(), and Geom::Piecewise< T >::unitVector().

toSBasis()

SBasis Geom::SBasis::toSBasis ( ) const

inline

Definition at line 238 of file sbasis.h.

truncate()

void Geom::SBasis::truncate ( unsigned  k )

inline

Definition at line 252 of file sbasis.h.

References resize(), and size.

Referenced by Geom::compose(), Geom::compose_inverse(), Geom::cos(), Geom::divide(), Geom::inverse(), Geom::sqrt(), and Geom::sqrt_internal().

valueAndDerivatives()

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

Compute the value and the first n derivatives.

Parameters

t	position to evaluate
n	number of derivatives (not counting value)

Returns

a vector with the value and the n derivative evaluations

There is an elegant way to compute the value and n derivatives for a polynomial using a variant of horner's rule. Someone will someday work out how for sbasis.

Definition at line 71 of file sbasis.cpp.

References derive(), and valueAt().

valueAt()

double Geom::SBasis::valueAt ( double  t ) const

inline

Definition at line 219 of file sbasis.h.

References size.

Referenced by are_equal(), Geom::intersect(), portion(), TEST_F(), TEST_F(), and valueAndDerivatives().

Friends And Related Symbol Documentation

portion()

SBasis portion ( const SBasis &  t, double  from, double  to  )

related

Returns the sbasis on domain [0,1] that was t on [from, to].

Parameters

t	sbasis function
from,to	interval

Returns

sbasis

Definition at line 475 of file sbasis.cpp.

References at0(), at1(), Geom::compose(), and valueAt().

Referenced by Geom::portion().

reverse()

SBasis reverse ( SBasis const &  a )

related

Returns a function which reverses the domain of a.

Parameters

a	sbasis function

useful for reversing a parameteric curve.

Definition at line 271 of file sbasis.h.

References result, and reverse().

Referenced by reverse().

valuation()

unsigned valuation ( SBasis const &  a, double  tol = 0  )

related

Returns the degree of the first non zero coefficient.

Parameters

a	sbasis function
tol	largest abs val considered 0

Returns

first non zero coefficient

Definition at line 396 of file sbasis.h.

Member Data Documentation

d

std::vector<Linear> Geom::SBasis::d

private

Definition at line 71 of file sbasis.h.

Referenced by derive().

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

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