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

#include <GA_NUBBasis.h>

Inheritance diagram for GA_NUBBasis:

Public Member Functions
	GA_NUBBasis (int length=-1, int order=-1, bool end_interpolation=true)

	GA_NUBBasis (fpreal start, fpreal step, int length, int order=-1, bool end_interpolation=true)

	GA_NUBBasis (int bkpoints, int multiplicity, int ord)

	GA_NUBBasis (const GA_NUBBasis &src)

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

bool	operator== (const GA_NUBBasis &a) const

bool	operator!= (const GA_NUBBasis &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	getEndInterpolation () const
	Return the end-interpolation flag. More...

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

int	findValidStart (fpreal u, int uoffset=-1) const

int	findStart (fpreal k, int start_idx=0) const

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 valid segment. Returns -1 on an error. More...

fpreal	computeBValue (int index, fpreal u) const override

bool	isSimilar (const GA_NUBBasis &b) const

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	refine (fpreal k, int kidx, int r, bool wrapped)

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 end_interpolation=true)

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

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

int	growAt (unsigned cv_idx, bool wrapped)

int	shrinkAt (unsigned cv_idx, bool wrapped)

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

void	setWrapping (bool wrap) override

void	setEndInterpolation (bool value, bool modify_knots)
	Change end interpolation. More...

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...

bool	mergePartial (const GA_NUBBasis &a, const GA_NUBBasis &b, int a0, int a1, int b0, int b1, GA_KnotVector aknots=nullptr, GA_KnotVector bknots=nullptr)

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

bool	cycle (int amount, bool keep_span)
	Cycle the knots, optionally keeping the original span length and origin. More...

void	toggleEndInterpolation ()
	TODO: Public for GD_PrimNURBCurve use. More...

void	makeNURBSPeriodic ()

void	updateEndInterpolation ()

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

bool	isUniform () const
	Test whether the basis is a uniform basis. More...


int	findBreakpoint (int idx) const

int	findBreakpoint (fpreal t) const


void	setKnotsByEqualSpacing (UT_Vector &param, bool wrapped=false)

void	setKnotsByAveraging (UT_Vector &param, bool wrapped=false)

void	setKnotsBySpreading (UT_Vector &param)

void	setKnotsByBreakpoints (UT_Vector &param)

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...

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)

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

NURBS basis classes which maintain knot vectors.

The GA_NUBBasis class maintains the knot vectors for NURBS. The basis consists of:

The order of the basis (degree+1)
The knot vector (an array of doubles)
A flag for end interpolation

Examples:: SOP/SOP_NURBS.C.

Definition at line 44 of file GA_NUBBasis.h.

Constructor & Destructor Documentation

GA_NUBBasis::GA_NUBBasis	(	int	length = `-1`,
		int	order = `-1`,
		bool	end_interpolation = `true`
	)

The default constructor will choose length/order based on the defaults for the basis type. default: order=4, length=8

GA_NUBBasis::GA_NUBBasis	(	fpreal	start,
		fpreal	step,
		int	length,
		int	order = `-1`,
		bool	end_interpolation = `true`
	)

GA_NUBBasis::GA_NUBBasis	(	int	bkpoints,
		int	multiplicity,
		int	ord
	)

GA_NUBBasis::GA_NUBBasis ( const GA_NUBBasis & src )

Member Function Documentation

bool GA_NUBBasis::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_NUBBasis::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 bLen
Periodicity determined by doesWrap

Implements GA_Basis.

void GA_NUBBasis::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_NUBBasis::computeBValue	(	int	index,
		fpreal	u
	)		const

overridevirtual

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

Implements GA_Basis.

bool GA_NUBBasis::copyFrom	(	const GA_Basis &	b,
		bool	compatible = `false`
	)

overridevirtual

Copy my data from the given source. If performing a compatible copy, we only do the copy if if b has the same order and length as we do.

Reimplemented from GA_Basis.

bool GA_NUBBasis::cycle	(	int	amount,
		bool	keep_span
	)

Cycle the knots, optionally keeping the original span length and origin.

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

overridevirtual

Implements GA_Basis.

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

overridevirtual

Implements GA_Basis.

int GA_NUBBasis::findBreakpoint ( int idx ) const

Find the index of the last knot in the sequence that defines the given breakpoint, or the breakpoint of the domain value. Returns -1 if not found.

Note: The search is done within the limits of the valid interval.

int GA_NUBBasis::findBreakpoint ( fpreal t ) const

Find the index of the last knot in the sequence that defines the given breakpoint, or the breakpoint of the domain value. Returns -1 if not found.

Note: The search is done within the limits of the valid interval.

int GA_NUBBasis::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_NUBBasis::findStart	(	fpreal	k,
		int	start_idx = `0`
	)		const

inline

Return the index in the knot vector such that knotVec[idx] <= k and k < knotVec[idx+1]. If k is less than the first valid knot, return -1, and if k is greater than the last valid knot, return the index of the last valid knot (i.e. the dimension).

Definition at line 98 of file GA_NUBBasis.h.

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

overridevirtual

Return the first valid segment. Returns -1 on an error.

Implements GA_Basis.

int GA_NUBBasis::findValidStart	(	fpreal	u,
		int	uoffset = `-1`
	)		const

inline

Return the index of the knot where the valid evaluation begins. Typically, for a cubic spline, this index is 3 in the end-point interpolating case and 1 otherwise. If u is completely outside the valid knot sequence, this method returns -1.

Equivalent to findStartOffset(u, uoffset).

Definition at line 91 of file GA_NUBBasis.h.

int GA_NUBBasis::getBreakCount ( ) const

overridevirtual

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

Implements GA_Basis.

int GA_NUBBasis::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_NUBBasis::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_NUBBasis::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_NUBBasis::getCvRangeOfDomain	(	fpreal	ustart,
		fpreal	ustop,
		int &	start_cv,
		int &	end_cv
	)		const

overridevirtual

Implements GA_Basis.

int GA_NUBBasis::getDimension ( ) const

overridevirtual

Return the dimension of the basis. For NURBS, this will be equivalent to (getLength()-getOrder()).

Implements GA_Basis.

bool GA_NUBBasis::getEndInterpolation ( ) const

inline

Return the end-interpolation flag.

Definition at line 79 of file GA_NUBBasis.h.

int GA_NUBBasis::getEndMultiplicity ( ) const

overridevirtual

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

Reimplemented from GA_Basis.

fpreal GA_NUBBasis::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.

int64 GA_NUBBasis::getMemoryUsage ( bool inclusive ) const

inlineoverridevirtual

Return the amount of memory used.

Reimplemented from GA_Basis.

Definition at line 306 of file GA_NUBBasis.h.

int GA_NUBBasis::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_NUBBasis::getType ( ) const

overridevirtual

Return the type of the basis.

Implements GA_Basis.

const char* GA_NUBBasis::getTypeName ( ) const

overridevirtual

Return the name of the basis.

Implements GA_Basis.

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

overridevirtual

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

Implements GA_Basis.

int GA_NUBBasis::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.

int GA_NUBBasis::growAt	(	unsigned	cv_idx,
		bool	wrapped
	)

Insert a new knot as a result of a CV insertion at index cvIdx. The knot index is cvIdx + 1, which is returned by growAt() if all goes OK. -1 is returned upon failure. (NURBS basis only)

bool GA_NUBBasis::import	(	int	order,
		const UT_FloatArray &	knots,
		bool	end_interpolation = `true`
	)

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_NUBBasis::isEqual ( const GA_Basis & basis ) const

overridevirtual

Test to see if two bases are equal.

Implements GA_Basis.

bool GA_NUBBasis::isSimilar ( const GA_NUBBasis & b ) const

Find out if two knot sequences are similar (ie if the knot spacings are the same all over) and their knot count is the same.

bool GA_NUBBasis::isUniform ( ) const

Test whether the basis is a uniform basis.

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

overridevirtual

Implements GA_Basis.

void GA_NUBBasis::makeNURBSPeriodic ( )

void GA_NUBBasis::makeUniform ( fpreal ustep = 1 )

overridevirtual

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

Implements GA_Basis.

bool GA_NUBBasis::mergePartial	(	const GA_NUBBasis &	a,
		const GA_NUBBasis &	b,
		int	a0,
		int	a1,
		int	b0,
		int	b1,
		GA_KnotVector *	aknots = `nullptr`,
		GA_KnotVector *	bknots = `nullptr`
	)

Create a new basis containing the partial merging of bases a and b If their order is different return -1. Otherwise return 0. The resultant basis contains knots a0..a1 of basis a merged with knots b0..b1 from basis b (after being mapped onto a0..a1) If the aknot or bknot array is given, they are set with the (appropriately mapped) knots values corresponding to the new insertions

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

inline

Definition at line 62 of file GA_NUBBasis.h.

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

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

overridevirtual

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

Implements GA_Basis.

void GA_NUBBasis::refine	(	fpreal	k,
		int	kidx,
		int	r,
		bool	wrapped
	)

Change the multiplicity of the knot by inserting it "r" times WITHOUT checking its current multiplicity. kidx is the index of a knot t such that k >= t.

void GA_NUBBasis::reset ( )

overridevirtual

Re-initializes the basis to default values.

Implements GA_Basis.

void GA_NUBBasis::reverse ( bool wrapped )

overridevirtual

Reverse the breakpoints in the basis.

Implements GA_Basis.

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

overridevirtual

I/O functions for houdini9 format.

Implements GA_Basis.

void GA_NUBBasis::setEndInterpolation	(	bool	value,
		bool	modify_knots
	)

Change end interpolation.

void GA_NUBBasis::setKnotsByAveraging	(	UT_Vector &	param,
		bool	wrapped = `false`
	)

Set up the knot vector with the given parameterization for the approximiation.

void GA_NUBBasis::setKnotsByBreakpoints ( UT_Vector & param )

Set up the knot vector with the given parameterization for the approximiation.

void GA_NUBBasis::setKnotsByEqualSpacing	(	UT_Vector &	param,
		bool	wrapped = `false`
	)

Set up the knot vector with the given parameterization for the approximiation.

void GA_NUBBasis::setKnotsBySpreading ( UT_Vector & param )

Set up the knot vector with the given parameterization for the approximiation.

void GA_NUBBasis::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_NUBBasis::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.

int GA_NUBBasis::shrinkAt	(	unsigned	cv_idx,
		bool	wrapped
	)

Delete a knot as a result of a CV removal at index cvIdx. The knot index is cvIdx + 1. The method returns the new length if successful, and -1 otherwise.

bool GA_NUBBasis::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.

void GA_NUBBasis::toggleEndInterpolation ( )

inline

TODO: Public for GD_PrimNURBCurve use.

Definition at line 298 of file GA_NUBBasis.h.

void GA_NUBBasis::updateEndInterpolation ( )

bool GA_NUBBasis::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_NUBBasis.h

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation