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HxBSplineBasis Class Reference

Class definition for basis for BSpline curves. More...

#include <HxBSplineBasis.h>

List of all members.

Public Methods

 HxBSplineBasis ()
 Construct default basis. More...

 HxBSplineBasis (HxBSplineType typeCurve, int degree, int nIntervals, HxBSplineKnotsAlg typeKnots=uniformKnots, double minT=0.0, double maxT=1.0)
 Construct basis with uniformily distributed knots, given number of intervals, and path interval: minT <= t < maxT. More...

 HxBSplineBasis (HxBSplineType typeCurve, int degree, const std::vector< double > &knots)
 Construct basis with given knots. More...

 ~HxBSplineBasis ()
 Destructor. More...

HxBSplineType curveType () const
 Get the type of the cuve. More...

int degree () const
 Get the degree. More...

int nIntervals () const
 Get the number of intervals. More...

HxBSplineKnotsAlg knotsType () const
 Get the type of the knots generating algorithm. More...

double minT () const
 Get the minimum value for t. More...

double maxT () const
 Get the maximum value for t. More...

double knot (int j) const
 Get the value of the given knot. More...

std::vector< double > allKnots () const
 Get values of all knots. More...

int numB () const
 Get the number of basis functions. More...

double B (int index, double t) const
 Get value of given basis at path position t. More...

double dB (int order, int index, double t) const
 Get derivative of given basis at path position t. More...

HxBSplineInterval pathAffectedBy (int index) const
 Get path interval affected by given basis. More...

HxBSplineBasis insertKnot (double t, int n=1) const
 Insert one knot at given position. More...

STD_OSTREAM & dump (STD_OSTREAM &) const
 Dump the basis on the given stream. More...

double node (int i) const
int maxBasis (double t) const
double nearestKnot (double t) const

Friends

class HxBSplineCurve

Detailed Description

Class definition for basis for BSpline curves.

Based on "Curve and Surface Fitting with Splines", by "Dierckx,P.", "Oxford", "1993", chapter "Univariate Splines", and "The NURBS book", "Piegl, L. and Tiller, W.", Springer, 1997.

Constructor & Destructor Documentation

HxBSplineBasis::HxBSplineBasis (    ) 
 

Construct default basis. 

00017 {
00018     makeDefault();
00019 }

HxBSplineBasis::HxBSplineBasis (  HxBSplineType    t,
int    d,
int    n,
HxBSplineKnotsAlg    alg = uniformKnots,
double    min = 0.0,
double    max = 1.0
) 
 

Construct basis with uniformily distributed knots, given number of intervals, and path interval: minT <= t < maxT. 

00032 {
00033     _curveType = t;
00034     _degree = d;
00035     _minT = min;
00036     _maxT = max;
00037     _nIntervals = n;
00038 
00039     if ( _degree <= 0 || max <= min || _nIntervals < 1 ||
00040          ( t==closed && _nIntervals <= d ) ||
00041          alg != uniformKnots ) {
00042         message("(constructor) invalid parameters - using default");
00043         makeDefault();
00044         return;
00045     }
00046             // parameters ok
00047     _knotsType = uniformKnots;
00048     vector<double> knots = makeUniformKnots();
00049     completeKnots(knots);
00050 }

HxBSplineBasis::HxBSplineBasis (  HxBSplineType    typeCurve,
int    degree,
const std::vector< double > &    knots
) 
 

Construct basis with given knots.

The number of intervals and path are determined from the given knots.

HxBSplineBasis::~HxBSplineBasis (    ) 
 

Destructor. 

00089 {
00090 }

Member Function Documentation

HxBSplineType HxBSplineBasis::curveType (    )  const [inline]
 

Get the type of the cuve. 

00156 {
00157     return _curveType; 
00158 }

int HxBSplineBasis::degree (    )  const [inline]
 

Get the degree. 

00162 {
00163     return _degree;
00164 }

int HxBSplineBasis::nIntervals (    )  const [inline]
 

Get the number of intervals. 

00169 {
00170     return _nIntervals;
00171 }

HxBSplineKnotsAlg HxBSplineBasis::knotsType (    )  const [inline]
 

Get the type of the knots generating algorithm. 

00175 { 
00176     return _knotsType; 
00177 }

double HxBSplineBasis::minT (    )  const [inline]
 

Get the minimum value for t. 

00181 { 
00182     return _minT; 
00183 }

double HxBSplineBasis::maxT (    )  const [inline]
 

Get the maximum value for t. 

00187 { 
00188     return _maxT;
00189 }

double HxBSplineBasis::knot (  int    i )  const [inline]
 

Get the value of the given knot. 

00208 { 
00209     return _knotsVec[i];
00210 }

vector< double > HxBSplineBasis::allKnots (    )  const [inline]
 

Get values of all knots. 

00214 { 
00215     return _knotsVec;
00216 }

int HxBSplineBasis::numB (    )  const [inline]
 

Get the number of basis functions. 

00193 { 
00194     switch ( curveType() ) {
00195       case closed:
00196             return _nIntervals; 
00197             break;
00198       case openRepeatEndPoints:
00199       case open:
00200       default:  // this case should never happen!
00201             return _nIntervals+degree(); 
00202             break;
00203     }
00204 }

double HxBSplineBasis::B (  int    i,
double    t
)  const
 

Get value of given basis at path position t. 

00102 {
00103     if ( t < minT() ) {
00104         message("(B) invalid t - setting to minT()");
00105         t = minT();
00106     }
00107     else    if ( t >= maxT() ) {
00108             message("(B) invalid t - setting near to maxT()");
00109             t = maxT() - EPS;
00110         }
00111     if ( ! inRange(i, 0, numB()) ) {
00112         message("(B) invalid index - setting to 0");
00113         i = 0;
00114     }
00115 
00116         // return 0 if i doesn't affect point at t
00117     if ( isNullAt(i, t) )
00118         return 0.0;
00119 
00120         // Calculate basis
00121     return nim(t, internalBasisIndex(i, t), degree()+1);
00122 }

double HxBSplineBasis::dB (  int    order,
int    i,
double    t
)  const
 

Get derivative of given basis at path position t. 

00135 {
00136     if ( t < minT() ) {
00137         message("(dB) invalid t - setting to minT()");
00138         t = minT();
00139     }
00140     else    if ( t >= maxT() ) {
00141             message("(dB) invalid t - setting near to maxT()");
00142             t = maxT() - EPS;
00143         }
00144     if ( ! inRange(i, 0, numB()) ) {
00145         message("(dB) invalid index - setting to 0");
00146         i = 0;
00147     }
00148     if ( ! inRange(order, 0, degree()-1) ) {
00149         message("(dB) derivative not defined - setting to zero");
00150         order = 0;
00151     }
00152 
00153         // return 0 if i doesn't affect point at t
00154     if ( isNullAt(i, t) )
00155         return 0.0;
00156 
00157         // Calculate basis or derivative
00158     int index = internalBasisIndex(i,t);
00159     if ( order )
00160         return dNim(order, t, index, degree()+1);
00161     else    return nim(t, index, degree()+1);
00162 }

HxBSplineInterval HxBSplineBasis::pathAffectedBy (  int    i )  const
 

Get path interval affected by given basis. 

00171 {
00172     if ( ! inRange(i, 0, numB()) ) {
00173         message("(pathAffectedBy) invalid i - fixing to 0");
00174         i = 0;
00175     }
00176 
00177     double t1 =  _knotsVec[i];
00178     if ( t1 < minT() ) {
00179         if ( curveType() == closed ) 
00180             t1 = maxT() - absolute(minT() - t1);
00181         else    t1 = minT(); //ZZZ
00182     }
00183     double t2 = _knotsVec[i+degree()+1];
00184     if ( t2 >= maxT() ) {
00185         if ( curveType() == closed ) 
00186             t2 = minT() + (t2 - maxT());
00187         else    t2 = maxT(); //ZZZ
00188     }
00189     
00190     HxBSplineInterval tmp( t1,t2, minT(), maxT(), curveType());
00191 
00192     return tmp;
00193 }

HxBSplineBasis HxBSplineBasis::insertKnot (  double    t,
int    n = 1
)  const
 

Insert one knot at given position. 

00203 {
00204     if ( t < minT() ) {
00205         message("(insertKnot) invalid t - setting to minT()");
00206         t = minT();
00207     }
00208     else    if ( t >= maxT() ) {
00209             message("(insertKnot) invalid t - setting near to maxT()");
00210             t = maxT() - EPS;
00211         }
00212     HxBSplineBasis tmp(*this);
00213     for (int i=degree(); i < tmp._knotsVec.size(); i++ )
00214         if ( tmp._knotsVec[i] >= t ) {
00215             tmp._nIntervals++;
00216             tmp._knotsVec.insert( tmp._knotsVec.begin()+i, n, t);
00217             tmp.correctEnds(i);
00218             break;
00219         }
00220     return tmp; 
00221 }

STD_OSTREAM & HxBSplineBasis::dump (  STD_OSTREAM &    os )  const
 

Dump the basis on the given stream. 

00229 {
00230     os << "Curve Type: " << curveType();
00231     os << "  Knots Type: " << knotsType();
00232     os << "  Degree: " << degree();
00233     os << "  Interval: [" << minT() << "," << maxT() << "]" << STD_ENDL;
00234 
00235     if ( _knotsVec.empty() ) {
00236         os << "No knots";
00237     } else {
00238         os << "Knots Vector: " << _knotsVec.size() << " knots";
00239         os << " (" << _nIntervals << " intervals,";
00240         os << " N Basis=" << numB() << ")\n";
00241         for ( int i = 0; i < _knotsVec.size(); i++ ) {
00242             os << _knotsVec[i] << ", ";
00243         }
00244     }
00245 
00246     os << STD_ENDL;
00247     return os;
00248 }

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