gsNurbs.h

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#pragma once
 
#include <gsCore/gsLinearAlgebra.h>
#include <gsCore/gsGeometry.h>
 
#include <gsNurbs/gsNurbsBasis.h>
#include <gsNurbs/gsKnotVector.h>
#include <gsNurbs/gsBoehm.h>
 
 
namespace gismo
{
 
template<class T>
class gsNurbs :  public gsGeoTraits<1,T>::GeometryBase
{
 
public: 
    typedef gsKnotVector<T> KnotVectorType;
 
    typedef typename gsGeoTraits<1,T>::GeometryBase Base;
 
    typedef T Scalar_t;
 
    typedef gsRationalBasis<gsBSplineBasis<T> > RBasis;
    typedef gsNurbsBasis<T> Basis;
 
    typedef memory::shared_ptr< gsNurbs > Ptr;
 
    typedef memory::unique_ptr< gsNurbs > uPtr;
 
public:
 
    gsNurbs() : Base() { }
    
    gsNurbs( const Basis & basis, const gsMatrix<T> & coefs ) :
    Base(basis, coefs) { }
 
    gsNurbs( const gsKnotVector<T>& KV, gsMatrix<T> w, gsMatrix<T> coefs )
    {
        this->m_coefs.swap(coefs);
        this->m_basis = new Basis(KV, give(w));
    }
    
    gsNurbs( const gsKnotVector<T>& KV, const gsMatrix<T> * pcoefs ) :
    Base( new Basis(KV, & pcoefs->rightCols(1) ), pcoefs) 
    {
        // TO DO: divide pcoefs by the weights
    }
    
    GISMO_CLONE_FUNCTION(gsNurbs)
 
    GISMO_BASIS_ACCESSORS
 
public:
 
// ***********************************************
// Virtual member functions required by the base class
// ***********************************************
 
    std::ostream &print(std::ostream &os) const
    { os << "NURBS curve "<< "of degree "<< this->basis().degree()
         << " over knots "<< this->basis().knots() <<",\n";
        os << "weights: ["<< this->weights().transpose()<< " ]\n ";
        os << "with control points "<< this->m_coefs << ".\n"; 
        return os; 
    };
 
 
// ***********************************************
// Additional members for univariate B-Splines
// ***********************************************
 
    T domainStart() const { return this->basis().knots().first(); };
 
    T domainEnd() const { return this->basis().knots().last(); };
 
    KnotVectorType & knots() { return this->basis().knots(); }
 
    const KnotVectorType & knots() const { return this->basis().knots(); }
 
    T & weight(int i) { return this->basis().weight(i); }
 
    const T weight(int i) const { return this->basis().weight(i); }
 
    const gsMatrix<T> & weights() const { return this->basis().weights(); }
    gsMatrix<T> & weights()       { return this->basis().weights(); }
 
    void isCompatible( gsGeometry<T> * other )
    {
        // compatible curves: same degree, same first/last p+1 knots
    };
    void makeCompatible( gsGeometry<T> * other )
    {
        // compatible curves: same degree, same first/last p+1 knots
    };
 
    void merge( gsGeometry<T> * otherG )
    {
        // See also gsBSpline::merge().
        // check geometric dimension
        GISMO_ASSERT(this->geoDim()==otherG->geoDim(),
                     "gsNurbs: cannot merge curves in different spaces ( R^"
                     << this->geoDim() << ", R^" << otherG->geoDim() << " ).");
 
        // check if the type of other is BSpline
        gsNurbs *  other = dynamic_cast<gsNurbs *>( otherG );   // TODO: to uPtr
        GISMO_ASSERT( other!=NULL, "Can only merge with B-spline curves.");
        other= other->clone().release();
 
        // TODO: check for periodic
 
        // check degree
        const int mDeg = this ->basis().degree();
        const int oDeg = other->basis().degree();
        const int deg  = math::max(mDeg,oDeg);
 
        other->gsNurbs::degreeElevate( deg - oDeg ); // degreeElevate(0) does nothing (and very quickly)
        this ->gsNurbs::degreeElevate( deg - mDeg );
 
        // check whether the resulting curve will be continuous
        // TODO: ideally, the tolerance should be a parameter of the function
        T tol = 1e-8;
        gsMatrix<T> mValue = this ->eval(this ->support().col(1));
        gsMatrix<T> oValue = other->eval(other->support().col(0));
        bool continuous = gsAllCloseAbsolute(mValue,oValue,tol);
 
        // merge knot vectors.
        KnotVectorType& mKnots = this ->basis().knots();
        KnotVectorType& oKnots = other->basis().knots();
        T lastKnot = mKnots.last();
        if (continuous) // reduce knot multiplicity
        {
            // TODO check for clamped knot vectors otherwise
            // we should do knot insertion beforehands
            mKnots.remove(lastKnot);
        }// else there is a knot of multiplicity deg + 1 at the discontinuity
 
        oKnots.addConstant(lastKnot-oKnots.first());
        mKnots.append( oKnots.begin()+deg+1, oKnots.end());
 
        // merge coefficients
        int n= this->coefsSize();
        int skip = continuous ? 1 : 0;
        this->m_coefs.conservativeResize( n + other->coefsSize() -skip, gsEigen::NoChange ) ;
 
        this->m_coefs.block( n,0,other->coefsSize()-skip,other->geoDim() ) =
            other->m_coefs.block( 1,0,other->coefsSize()-skip,other->geoDim() ) ;
 
        // merge Weights
        this->weights().conservativeResize( n + other->coefsSize() -skip, gsEigen::NoChange ) ;
            
        this->weights().block( n,0,other->coefsSize()-skip,1 ) =
            other->weights().block( 1,0,other->coefsSize()-skip, 1 ) ;
 
        delete other;
    }
    
    void insertKnot( T knot, int i = 1 )
    {
        if (i==0) return;
        
        gsMatrix<T> tmp = basis().projectiveCoefs(m_coefs);
        gsBoehm(basis().knots(), tmp, knot, i); 
        basis().setFromProjectiveCoefs(tmp, m_coefs, basis().weights());
    }
 
    template <class It>
    void insertKnots(It inBegin, It inEnd)
    {
        gsMatrix<T> tmp = basis().projectiveCoefs(m_coefs);
        gsBoehmRefine(basis().knots(), tmp, this->degree(), inBegin, inEnd);
        basis().setFromProjectiveCoefs(tmp, m_coefs, basis().weights());
    }
    
    /*
    void degreeElevate(int const i, int const dir = -1)
    {
        GISMO_ASSERT( (dir == -1) || (dir == 0),
                      "Invalid basis component "<< dir <<" requested for degree elevation" );
        
        bspline::degreeElevateBSpline(this->basis(), this->m_coefs, i);
    }
    */
 
    //void toProjective() { m_weights=w; } ;
    
 
protected:
    // TODO Check function
    // check function: check the coefficient number, degree, knot vector ...
 
private:
 
    // Avoid hidden overloads w.r.t. gsGeometry
    using Base::insertKnot;
 
// Data members
private:
 
    using Base::m_coefs;
    
    bool projective;
 
}; // class gsNurbs
 
 
} // namespace gismo