Bezier basis classes which maintain knot vectors. More...

#include <GA_BezBasis.h>

Inheritance diagram for GA_BezBasis:

Public Member Functions
	GA_BezBasis (int length=-1, int order=-1)

	GA_BezBasis (fpreal start, fpreal step, int length, int order=-1)

	GA_BezBasis (const GA_BezBasis &src)

bool	isEqual (const GA_Basis &basis) const override
	Test to see if two bases are equal. More...

bool	operator== (const GA_BezBasis &a) const

bool	operator!= (const GA_BezBasis &a) const

void	reset () override
	Re-initializes the basis to default values. More...

GA_BASIS_TYPE	getType () const override
	Return the type of the basis. More...

const char *	getTypeName () const override
	Return the name of the basis. More...

int	getDimension () const override

bool	getValidInterval (int &a, int &b) const override
	Get the boundaries of the valid evaluation interval (as indices) More...

void	evalInterval (fpreal u, int offset, int deriv, fpreal64 *vals) const override

void	evalInterval (fpreal u, int offset, int deriv, fpreal32 *vals) const override

void	evalDerivativeMatrix (fpreal u, int offset, int deriv, fpreal64 bmatx[][GA_MAXORDER]) const override
	Evaluate all the derivatives of the basis from 0 to deriv (inclusive). More...

void	evalDerivativeMatrix (fpreal u, int offset, int deriv, fpreal32 bmatx[][GA_MAXORDER]) const override

int	findStartOffset (fpreal u, int uoffset) const override
	Return the first break-point. Returns -1 on an error. More...

fpreal	computeBValue (int index, fpreal u) const override

int	getBreakCount () const override

int	knotToBreakpoint (int &kidx, int a, int b) const override

int	getBreakpoints (GA_KnotVector &a, fpreal tol=theBasisTolerance) const override

int	getMultiplicity (fpreal u, int &uidx) const override

int	getEndMultiplicity () const override
	Return the expected multiplicity of the end knots (1 by default): More...

void	getCvRangeOfDomain (int ustartidx, int ustopidx, int &start_cv, int &end_cv) const override

void	getCvRangeOfDomain (fpreal ustart, fpreal ustop, int &start_cv, int &end_cv) const override

void	getCvRangeOfBreakpoint (int bkp, int &startcv, int &stopcv) const override

bool	saveH9 (std::ostream &os, bool wrapped, bool binary) const override
	I/O functions for houdini9 format. More...

bool	loadH9 (UT_IStream &is, int cvs, bool wrapped) override

bool	import (int order, const UT_FloatArray &knots)

bool	validate (int adapt=GA_Basis::GA_BASIS_ADAPT_NONE) override

bool	checkValid (int cv_len, int b_len, bool does_wrap) const override

fpreal	getGreville (int idx, bool clamp=true, bool wrap=false) const override

int	grow (bool wrapped=false) override

int	shrink (bool wrapped=false) override

bool	attach (const GA_Basis &b, bool overlap=true, bool spread=false) override

void	setWrapping (bool wrap) override

void	reverse (bool wrapped) override
	Reverse the breakpoints in the basis. More...

int	findOffset (fpreal k, int start_idx=0) const override
	Find index in the knot vector for the break point corresponding to k. More...

void	rebuild (fpreal ustart=0, fpreal ustep=1) override
	Rebuild the basis as a uniform sequence with a given step. More...

void	makeUniform (fpreal ustep=1) override
	Make the basis uniform of just find out if it is uniform: More...

void	chord (UT_Vector4Array &cvs) override

bool	slideRange (fpreal umin, fpreal umax, fpreal ubias=0.5) override

Public Member Functions inherited from GA_Basis
	GA_Basis ()
	The default constructor will initialize order=0 and length=0. More...

	GA_Basis (const GA_Basis &src)

virtual	~GA_Basis ()
	Destructor. More...

int	getOrder () const
	Return the order of the basis. More...

int	getLength () const
	Return the length of the knot vector. More...

bool	getValidRange (fpreal &a, fpreal &b) const
	Get the boundaries of the valid range of evaluation. More...

int	getMultiplicities (UT_IntArray &arr) const

bool	testForNan () const
	Returns true if any NANs snuck into this vector. More...

bool	jsonSave (UT_JSONWriter &w) const

bool	jsonSave (UT_JSONValue &v) const
	Save to a JSON value. More...

bool	jsonLoad (UT_JSONParser &p)
	Load basis from a JSON parser. More...

bool	jsonLoad (UT_JSONParser &p, const UT_JSONValue &v)
	Load basis from a JSON value. More...

virtual bool	copyFrom (const GA_Basis &b, bool compatible=false)

bool	checkValid (int cvLen, bool doesWrap) const
	Convenience method to check validity using the basis's length. More...

fpreal	unitToReal (fpreal u_unit, bool valid_interval=true) const

fpreal	realToUnit (fpreal u_real, bool valid_interval=true) const

int	append (fpreal v)
	Append a knot value to the end of the knot vector. More...

int	insertKnot (fpreal v, int i)

int	remove (int i)
	Remove a knot value (by index) More...

bool	merge (const GA_Basis &b)

bool	merge (GA_Basis &b)

int	findMaxSpan (int start, int stop) const

void	normalize (fpreal scale=0, const fpreal *neworig=0)
	Convenience method to normalize this basis. More...

void	map (const GA_Basis &b)

void	map (fpreal newlen=1, const fpreal *neworig=0)

int	map (const GA_Basis &b, fpreal &u, int uoffset=0) const

void	setOrder (int ord)

bool	findClosest (fpreal val, int &idx, int startidx, int endidx) const

int	findApproximate (fpreal val, int startidx, fpreal tol=theBasisTolerance) const

void	computeRaiseOrderAlphas (int increment, fpreal bezalfs[][GA_MAXORDER]) const

void	resize (int sz)

virtual int64	getMemoryUsage (bool inclusive) const
	Return the amount of memory used. More...

const GA_KnotVector &	getVector () const

GA_KnotVector &	getVector ()

const GA_KnotVector &	getKnotVector () const

GA_KnotVector &	getKnotVector ()

Additional Inherited Members
Public Types inherited from GA_Basis
enum	{ GA_BASIS_ADAPT_NONE, GA_BASIS_ADAPT_FLAGS, GA_BASIS_ADAPT_KNOTS }

Static Public Member Functions inherited from GA_Basis
static GA_Basis *	newSpecies (GA_BASIS_TYPE type)

static void	map (GA_KnotVector &knots, const GA_KnotVector &src, fpreal newlen=1, const fpreal *neworig=0)

Static Public Attributes inherited from GA_Basis
static const fpreal	theBasisTolerance

static const fpreal	theBinomial [GA_MAXORDER][GA_MAXORDER]
	Table of binomial coefficients. More...

Protected Member Functions inherited from GA_Basis
const GA_KnotFloat *	getData () const

Static Protected Member Functions inherited from GA_Basis
static void	doMerge (GA_KnotVector &avec, const GA_KnotVector &bvec, GA_KnotVector *inserts=0)

Protected Attributes inherited from GA_Basis
GA_KnotVector	myData

int	myOrder

Detailed Description

Bezier basis classes which maintain knot vectors.

The GA_BezBasis class maintains the knot vectors for Bezier splines. The basis consists of:

The order of the basis (degree+1)
The knot vector (an array of doubles)

Definition at line 37 of file GA_BezBasis.h.

Constructor & Destructor Documentation

GA_BezBasis::GA_BezBasis	(	int	length = `-1`,
		int	order = `-1`
	)

The default constructor will choose length/order based on the defaults for the basis type. default: order=4, length=2

GA_BezBasis::GA_BezBasis	(	fpreal	start,
		fpreal	step,
		int	length,
		int	order = `-1`
	)

GA_BezBasis::GA_BezBasis ( const GA_BezBasis & src )

Member Function Documentation

bool GA_BezBasis::attach	(	const GA_Basis &	b,
		bool	overlap = `true`,
		bool	spread = `false`
	)

overridevirtual

Attach another basis to us and grow our basis as a result. The bases must have the same type and order. If "overlap" is true, we overlap the beginning of b with our end. Spreading makes sense when you can have multiple knots in the basis, and causes identical knots to be spread within range of the neighbouring knots.

Implements GA_Basis.

bool GA_BezBasis::checkValid	(	int	cv_len,
		int	b_len,
		bool	does_wrap
	)		const

overridevirtual

The checkValid() methods test to see whether th basis is valid given a curve with

cvLen vertices
A basis length of b_len
Periodicity determined by doesWrap

Implements GA_Basis.

void GA_BezBasis::chord ( UT_Vector4Array & cvs )

overridevirtual

Reparameterize the basis using the chord-length method, and clamp it to the valid interval. The origin and length of the valid domain remains unchanged.

Implements GA_Basis.

fpreal GA_BezBasis::computeBValue	(	int	index,
		fpreal	u
	)		const

overridevirtual

Compute one basis function (ie. the one with the given index) value at u.

Implements GA_Basis.

void GA_BezBasis::evalDerivativeMatrix	(	fpreal	u,
		int	offset,
		int	deriv,
		fpreal64	bmatx[][GA_MAXORDER]
	)		const

overridevirtual

Evaluate all the derivatives of the basis from 0 to deriv (inclusive).

Implements GA_Basis.

void GA_BezBasis::evalDerivativeMatrix	(	fpreal	u,
		int	offset,
		int	deriv,
		fpreal32	bmatx[][GA_MAXORDER]
	)		const

overridevirtual

Implements GA_Basis.

void GA_BezBasis::evalInterval	(	fpreal	u,
		int	offset,
		int	deriv,
		fpreal64 *	vals
	)		const

overridevirtual

Evaluate on a specific domain interval, on which at least one basis function is non-zero given domain point u.

Implements GA_Basis.

void GA_BezBasis::evalInterval	(	fpreal	u,
		int	offset,
		int	deriv,
		fpreal32 *	vals
	)		const

overridevirtual

Implements GA_Basis.

int GA_BezBasis::findOffset	(	fpreal	k,
		int	start_idx = `0`
	)		const

overridevirtual

Find index in the knot vector for the break point corresponding to k.

Implements GA_Basis.

int GA_BezBasis::findStartOffset	(	fpreal	u,
		int	uoffset
	)		const

overridevirtual

Return the first break-point. Returns -1 on an error.

Implements GA_Basis.

int GA_BezBasis::getBreakCount ( ) const

overridevirtual

Return the number of breakpoints (ie. unique knots) in the knot vector, in the valid interval.

Implements GA_Basis.

int GA_BezBasis::getBreakpoints	(	GA_KnotVector &	a,
		fpreal	tol = `theBasisTolerance`
	)		const

overridevirtual

Compute an array of breakpoints (i.e. unique knots) in the valid interval and return their number. The tolerance is used to differentiate between close knots.

Implements GA_Basis.

void GA_BezBasis::getCvRangeOfBreakpoint	(	int	bkp,
		int &	startcv,
		int &	stopcv
	)		const

overridevirtual

Given valid breakpoint index, compute the range of CVs that have a non-zero influence at the knot of the breakpoint. Since the basis doesn't know about wrapping, the endcv index might be higher than the spline's number of CVs.

Implements GA_Basis.

void GA_BezBasis::getCvRangeOfDomain	(	int	ustartidx,
		int	ustopidx,
		int &	start_cv,
		int &	end_cv
	)		const

overridevirtual

Given a domain range in the valid interval, compute the range of CVs that will be involved in the evaluation of the curve in that range. Since the basis doesn't know about wrapping, the endcv index might be higher than the spline's number of CVs.

Implements GA_Basis.

void GA_BezBasis::getCvRangeOfDomain	(	fpreal	ustart,
		fpreal	ustop,
		int &	start_cv,
		int &	end_cv
	)		const

overridevirtual

Implements GA_Basis.

int GA_BezBasis::getDimension ( ) const

overridevirtual

Return the dimension of the basis. For Beziers the dimension is equivalent to the length of the knot vector.

Implements GA_Basis.

int GA_BezBasis::getEndMultiplicity ( ) const

overridevirtual

Return the expected multiplicity of the end knots (1 by default):

Reimplemented from GA_Basis.

fpreal GA_BezBasis::getGreville	(	int	idx,
		bool	clamp = `true`,
		bool	wrap = `false`
	)		const

overridevirtual

Compute the idx'th greville abscissa of the domain vector. Clamping to the valid interval is optional and might not make any difference for some spline types.

Implements GA_Basis.

int GA_BezBasis::getMultiplicity	(	fpreal	u,
		int &	uidx
	)		const

overridevirtual

Return the multiplicity of a domain point or -1 if outside the domain. "uidx" is the index of the largest breakpoint <= u.

Implements GA_Basis.

GA_BASIS_TYPE GA_BezBasis::getType ( ) const

overridevirtual

Return the type of the basis.

Implements GA_Basis.

const char* GA_BezBasis::getTypeName ( ) const

overridevirtual

Return the name of the basis.

Implements GA_Basis.

bool GA_BezBasis::getValidInterval	(	int &	a,
		int &	b
	)		const

overridevirtual

Get the boundaries of the valid evaluation interval (as indices)

Implements GA_Basis.

int GA_BezBasis::grow ( bool wrapped = false )

overridevirtual

Grow the length of the basis by one, and set the value of the new entry to last knot+1. The method returns the index of the appended element.

Implements GA_Basis.

bool GA_BezBasis::import	(	int	order,
		const UT_FloatArray &	knots
	)

Transitional method while we might need to import data from a GB_Basis. Be careful calling this method as the order must be appropriate for the number of knots. TODO: Remove when no longer necessary.

bool GA_BezBasis::isEqual ( const GA_Basis & basis ) const

overridevirtual

Test to see if two bases are equal.

Implements GA_Basis.

int GA_BezBasis::knotToBreakpoint	(	int &	kidx,
		int	a,
		int	b
	)		const

overridevirtual

Given the index of a knot (kidx) and two bounds in the knot sequence (a and b) find out the index of the breakpoint that the knot represents, and possibly adjust kidx so that knot[kidx+1] > knot[kidx]. Return -1 if not found.

Implements GA_Basis.

bool GA_BezBasis::loadH9	(	UT_IStream &	is,
		int	cvs,
		bool	wrapped
	)

overridevirtual

Implements GA_Basis.

void GA_BezBasis::makeUniform ( fpreal ustep = 1 )

overridevirtual

Make the basis uniform of just find out if it is uniform:

Implements GA_Basis.

bool GA_BezBasis::operator!= ( const GA_BezBasis & a ) const

inline

Definition at line 50 of file GA_BezBasis.h.

bool GA_BezBasis::operator== ( const GA_BezBasis & a ) const

void GA_BezBasis::rebuild	(	fpreal	ustart = `0`,
		fpreal	ustep = `1`
	)

overridevirtual

Rebuild the basis as a uniform sequence with a given step.

Implements GA_Basis.

void GA_BezBasis::reset ( )

overridevirtual

Re-initializes the basis to default values.

Implements GA_Basis.

void GA_BezBasis::reverse ( bool wrapped )

overridevirtual

Reverse the breakpoints in the basis.

Implements GA_Basis.

bool GA_BezBasis::saveH9	(	std::ostream &	os,
		bool	wrapped,
		bool	binary
	)		const

overridevirtual

I/O functions for houdini9 format.

Implements GA_Basis.

void GA_BezBasis::setWrapping ( bool wrap )

overridevirtual

Change the size of the basis (and maybe some of its values too) to make it a valid basis for wrapped splines.

Implements GA_Basis.

int GA_BezBasis::shrink ( bool wrapped = false )

overridevirtual

Shrink the basis by one. The basis should not shrink beyond a valid length. Return the new length.

Implements GA_Basis.

bool GA_BezBasis::slideRange	(	fpreal	umin,
		fpreal	umax,
		fpreal	ubias = `0.5`
	)

overridevirtual

Slide the knots found in the given range left or right by an amount at most as large as the distance to the nearest knot outside the range. The bias is a percentage value of the left-right distance, its default value is 0.5 (i.e. don't change anything), and is clamped to [0,1].

Implements GA_Basis.

bool GA_BezBasis::validate ( int adapt = GA_Basis::GA_BASIS_ADAPT_NONE )

overridevirtual

The validate() method will force the basis to be valid (if possible). The adapt enum can be used to control the behaviour of this method.

Implements GA_Basis.

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

GA/GA_BezBasis.h

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation