G4NURBS.cc

Go to the documentation of this file.

//
// ********************************************************************
// * License and Disclaimer                                           *
// *                                                                  *
// * The  Geant4 software  is  copyright of the Copyright Holders  of *
// * the Geant4 Collaboration.  It is provided  under  the terms  and *
// * conditions of the Geant4 Software License,  included in the file *
// * LICENSE and available at  http://cern.ch/geant4/license .  These *
// * include a list of copyright holders.                             *
// *                                                                  *
// * Neither the authors of this software system, nor their employing *
// * institutes,nor the agencies providing financial support for this *
// * work  make  any representation or  warranty, express or implied, *
// * regarding  this  software system or assume any liability for its *
// * use.  Please see the license in the file  LICENSE  and URL above *
// * for the full disclaimer and the limitation of liability.         *
// *                                                                  *
// * This  code  implementation is the result of  the  scientific and *
// * technical work of the GEANT4 collaboration.                      *
// * By using,  copying,  modifying or  distributing the software (or *
// * any work based  on the software)  you  agree  to acknowledge its *
// * use  in  resulting  scientific  publications,  and indicate your *
// * acceptance of all terms of the Geant4 Software license.          *
// ********************************************************************
//
//
// $Id$
//
// 
// Olivier Crumeyrolle  12 September 1996
 
// G4NURBS.cc
// Implementation of class G4NURBS
// OC 100796
 
 
#include "G4NURBS.hh"
 
// G4NURBS.hh includes globals.hh which includes a lot of others
// so no more includes required here
 
////////////////////////////////////////////////////////////////////////
//    Here start the real world. Please, check your armored jacket.   //
////////////////////////////////////////////////////////////////////////
 
std::ostream & operator << (std::ostream & inout_outStream,
                              const G4NURBS & in_kNurb)
{
  inout_outStream
  // the magic could be changed for good reasons only
      << "##ojc{NURBS}def[1.01.96.7]   Just a magic. Could be added to /etc/magic"
      << "\n# NURBS Definition File (human and computer readable format)"
      << "\n# :" << in_kNurb.Whoami()
      << "\n# U order\tV order : " 
      << '\n' << in_kNurb.GetUorder() << "\t\t" << in_kNurb.GetVorder();
  // number of knots and knots themselves for U and V
  for (G4NURBS::t_direction dir = G4NURBS::U; dir < G4NURBS::NofD;
       /*(*(G4int *)(&dir))++*/ dir=(G4NURBS::t_direction)(((G4int)(dir))+1) )
  {
    inout_outStream
      << "\n# Number of knots along " << G4NURBS::Tochar(dir)
      << '\n' << in_kNurb.GetnbrKnots(dir)
      << "\n# " << G4NURBS::Tochar(dir) << " knots vector (as a column)";
    {  // begin knots iteration
       G4double oneKnot;
       G4NURBS::KnotsIterator knotI(in_kNurb,dir);
       G4bool otherKnots;
       do 
       {
         otherKnots = knotI.pick(&oneKnot);
         inout_outStream << "\n\t\t" << oneKnot;
       }
       while (otherKnots);
    }  // end of knots iteration
  }  // end of direction loop
 
  // number of control points in U and V direction
  // and controlpoints
  inout_outStream
      << "\n# Number of control points along U and V"
      << '\n' << in_kNurb.GetUnbrCtrlPts() 
      << "   " << in_kNurb.GetVnbrCtrlPts()
      << "\n# Control Points (one by line, U increasing first)";
  { // begin of control points iteration
    G4NURBS::t_doubleCtrlPt   oneCP;
    G4NURBS::CtrlPtsIterator  cpI(in_kNurb);
    G4bool otherCPs;
    do
    {
      otherCPs = cpI.pick(&oneCP);
      inout_outStream 
        << "\n\t" << oneCP[G4NURBS::X]
        << "\t" << oneCP[G4NURBS::Y]
        << "\t" << oneCP[G4NURBS::Z]
        << "\t" << oneCP[G4NURBS::W];
    }
    while (otherCPs);
  } // end of control point iteration
 
  inout_outStream << "\n# That's all!"
                  << G4endl;  // endl do an \n and a flush
  return inout_outStream;
}
 
// the CC compiler issue some "maybe no value returned"
// but everything is ok
 
G4float G4NURBS::GetfloatKnot(t_direction in_dir, t_indKnot in_index) const
{
  in_dir = (t_direction)(in_dir & DMask);
  if ( in_index < m[in_dir].nbrKnots )
    return ((G4float)(m[in_dir].pKnots[in_index])); 
  else
  {
    G4cerr << "\nERROR: G4NURBS::GetfloatKnot: index out of range\n"
           << "\n\t in_dir : " << G4int(in_dir)
           << ", in_index : " << G4int(in_index)
           << "m[in_dir].nbrKnots : " << m[in_dir].nbrKnots << G4endl;
    return ((G4float)m[in_dir].pKnots[m[in_dir].nbrKnots-1]); 
  }
}
 
G4double G4NURBS::GetdoubleKnot(t_direction in_dir, t_indKnot in_index) const
{
  in_dir = (t_direction)(in_dir & DMask);
  if ( in_index < m[in_dir].nbrKnots )
    return (G4double)(m[in_dir].pKnots[in_index]);
  else
  {
    G4cerr << "\nERROR: G4NURBS::GetdoubleKnot: index out of range"
           << "\n\t in_dir : " << G4int(in_dir)
           << ", in_index : " << G4int(in_index)
           << "m[in_dir].nbrKnots : " << m[in_dir].nbrKnots
           << G4endl;
    return (G4double)(m[in_dir].pKnots[m[in_dir].nbrKnots-1]); 
  }
}
 
G4NURBS::t_floatCtrlPt*
G4NURBS::GetfloatCtrlPt(t_indCtrlPt in_onedimindex) const
{
  if (in_onedimindex < mtotnbrCtrlPts)
    return TofloatCtrlPt(mpCtrlPts[in_onedimindex]);       
  else
  {
    G4cerr << "\nERROR: G4NURBS::GetfloatCtrlPt: index out of range"
           << "\n\t in_onedimindex : " << in_onedimindex
           << " , mtotnbrCtrlPts : " << mtotnbrCtrlPts << G4endl;
    return TofloatCtrlPt(mpCtrlPts[mtotnbrCtrlPts-1]);  
  }    
}
 
G4NURBS::t_floatCtrlPt*
G4NURBS::GetfloatCtrlPt(t_inddCtrlPt in_Uindex, t_inddCtrlPt in_Vindex) const
{
  if ( (in_Uindex < m[U].nbrCtrlPts) && (in_Vindex < m[V].nbrCtrlPts) )
    return TofloatCtrlPt(mpCtrlPts[To1d(in_Uindex, in_Vindex)]);
  else
  {
    G4cerr << "\nERROR: G4NURBS::GetfloatCtrlPt: index(s) out of range"
           << "\n\t in_Uindex : " << in_Uindex
           << " , in_Vindex : " << in_Vindex
           << " , UnbrCtrlPts : " << m[U].nbrCtrlPts
           << " , VnbrCtrlPts : " << m[V].nbrCtrlPts << G4endl;
    return TofloatCtrlPt(mpCtrlPts[mtotnbrCtrlPts-1]);  
  }   
}
 
G4NURBS::t_doubleCtrlPt*
G4NURBS::GetdoubleCtrlPt(t_indCtrlPt in_onedimindex) const
{
  if ( in_onedimindex < mtotnbrCtrlPts )
    return TodoubleCtrlPt(mpCtrlPts[in_onedimindex]);
  else
  {
    G4cerr << "\nERROR: G4NURBS::getdoubleCtrlPts: index out of range"
           << "\n\t in_onedimindex : " << in_onedimindex
           << " , mtotnbrCtrlPts : " << mtotnbrCtrlPts << G4endl;
    return TodoubleCtrlPt(mpCtrlPts[mtotnbrCtrlPts-1]);  
  }   
}
 
G4NURBS::t_doubleCtrlPt*
G4NURBS::GetdoubleCtrlPt(t_inddCtrlPt in_Uindex, t_inddCtrlPt in_Vindex) const
{
  if ( (in_Uindex < m[U].nbrCtrlPts) && (in_Vindex < m[V].nbrCtrlPts) )
    return TodoubleCtrlPt(mpCtrlPts[To1d(in_Uindex, in_Vindex)]);
  else
  {
    G4cerr << "\nERROR: G4NURBS::GetdoubleCtrlPt: index(s) out of range"
           << "\n\t in_Uindex : " << in_Uindex
           << " , in_Vindex : " << in_Vindex
           << " , UnbrCtrlPts : " << m[U].nbrCtrlPts
           << " , VnbrCtrlPts : " << m[V].nbrCtrlPts << G4endl;
    return TodoubleCtrlPt(mpCtrlPts[mtotnbrCtrlPts-1]);  
  }  
}
 
// Total copy
G4float * G4NURBS::GetfloatAllKnots(t_direction in_dir) const
{
  in_dir = (t_direction)(in_dir & DMask);
  G4float * p = new G4float [m[in_dir].nbrKnots];
  for (t_indKnot i = 0; i < m[in_dir].nbrKnots; i++)
    p[i] = (G4float)m[in_dir].pKnots[i];
  return p;
}
 
G4double * G4NURBS::GetdoubleAllKnots(t_direction in_dir) const
{
  in_dir = (t_direction)(in_dir & DMask);
  G4double * p = new G4double [m[in_dir].nbrKnots];
  for (t_indKnot i = 0; i < m[in_dir].nbrKnots; i++)
    p[i] = (G4double)m[in_dir].pKnots[i];
  return p;
}
 
G4float * G4NURBS::GetfloatAllCtrlPts() const
{
  G4float * p = new G4float [mtotnbrCtrlPts*NofC];
  for (t_indKnot i = 0; i < mtotnbrCtrlPts*NofC; i++)
    p[i] = (G4float)(((t_Coord *)mpCtrlPts)[i]);
  return p;
}
 
G4double * G4NURBS::GetdoubleAllCtrlPts() const
{
  G4double * p = new G4double [mtotnbrCtrlPts*NofC];
  for (t_indKnot i = 0; i < mtotnbrCtrlPts*NofC; i++)
    p[i] = (G4double)(((t_Coord *)mpCtrlPts)[i]);
  return p;
}
 
// Iterators
 
G4NURBS::KnotsIterator::KnotsIterator(const G4NURBS & in_rNurb,
                                      G4NURBS::t_direction in_dir,
                                      t_indKnot in_startIndex)
 : kmdir((G4NURBS::t_direction)(in_dir &  G4NURBS::DMask)),
   kmpMax(in_rNurb.m[kmdir].pKnots + in_rNurb.m[kmdir].nbrKnots)
{
  if (in_startIndex < in_rNurb.m[kmdir].nbrKnots)
    mp = in_rNurb.m[kmdir].pKnots + in_startIndex;
  else
  {
    G4cerr   << "\nERROR: G4NURBS::KnotsIterator: in_startIndex out of range"
             << "\n\tin_startIndex : " << in_startIndex
             << ", nbr of knots : " << in_rNurb.m[kmdir].nbrKnots
             << "\n\t mp set to NULL, calls to picking functions will fail"
             << G4endl;
    mp = 0;
  }
}
 
G4bool G4NURBS::KnotsIterator::pick(G4double * inout_pDbl)
{
  (*inout_pDbl) = (G4double)(*mp);
  return (G4bool)((++mp)<kmpMax);
}
 
G4bool G4NURBS::KnotsIterator::pick(G4float * inout_pFlt)
{
  (*inout_pFlt) = (G4float)(*mp);
  return (G4bool)((++mp)<kmpMax);
}
 
G4NURBS::CtrlPtsCoordsIterator::CtrlPtsCoordsIterator(const G4NURBS & in_rNurb,
                                               t_indCtrlPt in_startCtrlPtIndex)
 : kmpMax((const t_Coord *)(in_rNurb.mpCtrlPts + in_rNurb.mtotnbrCtrlPts))
{
  if (in_startCtrlPtIndex < in_rNurb.mtotnbrCtrlPts )
    mp = (const t_Coord *)(in_rNurb.mpCtrlPts + in_startCtrlPtIndex);
  else
  {
    G4cerr << "\nERROR: G4NURBS::CtrlPtsCoordsIterator: "
           << "in_startCtrlPtIndex out of range"
           << "\n\tin_startCtrlPtIndex : " << in_startCtrlPtIndex
           << ", nbr of CtrlPts : " << in_rNurb.mtotnbrCtrlPts 
           << "\n\t mp set to NULL, calls to picking functions will fail"
           << G4endl;
    mp = 0;
  }
}
 
G4bool G4NURBS::CtrlPtsCoordsIterator::pick(G4double  * inout_pDbl)
{
  (*inout_pDbl) = (G4double)((*mp));
  return (G4bool)((++mp)<kmpMax);
}
 
G4bool G4NURBS::CtrlPtsCoordsIterator::pick(G4float * inout_pFlt)
{
  (*inout_pFlt) = (G4float)((*mp));
  return (G4bool)((++mp)<kmpMax);
}
 
G4NURBS::CtrlPtsIterator::CtrlPtsIterator(const G4NURBS & in_rNurb,
                                          t_indCtrlPt in_startIndex)
 : kmpMax(in_rNurb.mpCtrlPts + in_rNurb.mtotnbrCtrlPts)
{
  if (in_startIndex < in_rNurb.mtotnbrCtrlPts )
    mp = (in_rNurb.mpCtrlPts + in_startIndex);
  else
  {
    G4cerr << "\nERROR: G4NURBS::CtrlPtsIterator: in_startIndex out of range"
           << "\n\tin_startIndex : " << in_startIndex
           << ", nbr of CtrlPts : " << in_rNurb.mtotnbrCtrlPts 
           << "\n\t mp set to NULL, calls to picking functions will fail"
           << G4endl;
    mp = 0;
  }
}
 
G4bool G4NURBS::CtrlPtsIterator::pick(t_doubleCtrlPt * inout_pDblCtrlPt)
{
  for (t_indCoord i = G4NURBS::X; i < G4NURBS::NofC; i++)
    (*inout_pDblCtrlPt)[i] = (G4double)((*mp)[i]);
  return (G4bool)((++mp)<kmpMax);
}
 
G4bool G4NURBS::CtrlPtsIterator::pick(t_floatCtrlPt * inout_pFltCtrlPt)
{
  for (t_indCoord i = G4NURBS::X; i < G4NURBS::NofC; i++)
    (*inout_pFltCtrlPt)[i] = (G4float)((*mp)[i]);
  return (G4bool)((++mp)<kmpMax);
}
 
////////////////////////////////////////////////////////////////////////
// Building functions
 
G4bool G4NURBS::MakeKnotVector(t_Dir & io_d, t_KnotVectorGenFlag in_KVGFlag)
{
  G4bool isgood = (io_d.order + io_d.nbrCtrlPts == io_d.nbrKnots)
                  && (io_d.pKnots == 0);
  if ( isgood )
  {
    io_d.pKnots = new t_Knot [io_d.nbrKnots];
    if (in_KVGFlag != UserDefined)
    {  // let's do the knots
      t_indKnot indKnot = 0;
      t_index nbrCentralDistinctKnots = io_d.nbrCtrlPts-io_d.order;
      if ( (nbrCentralDistinctKnots % in_KVGFlag) == 0)
      {
        nbrCentralDistinctKnots /= in_KVGFlag; 
        // first and last knots repeated 'order' Times
        for (t_index i=0; i < io_d.order; indKnot++,i++)
        {
          io_d.pKnots[indKnot] = 0;
          io_d.pKnots[indKnot+io_d.nbrCtrlPts] = 1;
        }
 
        t_Knot stepKnot = 1.0/(t_Knot)(nbrCentralDistinctKnots+1);
        t_Knot valKnot = stepKnot;
 
        // central knots
        for (t_indKnot j=0; j<nbrCentralDistinctKnots; valKnot+=stepKnot, j++)
        {
          for (t_indKnot k=0; k<t_indKnot(in_KVGFlag); indKnot++, k++)
            io_d.pKnots[indKnot] = valKnot;
        }
      }
      else isgood = false;
    } // end of knots making
  }  
  return isgood;
}
 
 
std::ostream & operator << (std::ostream & io_ostr,
                              G4NURBS::t_KnotVectorGenFlag in_f)
{
  switch (in_f) 
  {
    case G4NURBS::UserDefined: io_ostr << "UserDefined"; break;
    case G4NURBS::Regular:     io_ostr << "Regular"; break;
    case G4NURBS::RegularRep:  io_ostr << "RegularRep"; break;
    default:                   io_ostr << (G4int)in_f;
  }
  return io_ostr;
}
 
////////////////////////////////////////////////////////////////////////
// Constructors and co
 
void G4NURBS::Conscheck() const
{
  G4int dummy;
  t_direction dir;
  for (dummy=0; (dummy?(dir=V):(dir=U)),(dummy < NofD); dummy++)
  { 
    if (m[dir].order<=0)
    { 
      G4ExceptionDescription ed;
      ed << "The order in the "
     << G4NURBS::Tochar(dir) 
     << " direction must be >= 1" << G4endl;
      G4Exception("G4NURBS::Conscheck()",
          "greps9001", FatalException, ed);
    }
    if (m[dir].nbrCtrlPts<=0)
    {
      G4ExceptionDescription ed;
      ed << "The number of control points "
             << G4NURBS::Tochar(dir) 
             << " direction must be >= 1" << G4endl;
      G4Exception("G4NURBS::Conscheck()",
          "greps9002", FatalException, ed);
    }
  }  // end of dummy
}
 
G4NURBS::G4NURBS ( t_order in_Uorder, t_order in_Vorder,
                   t_inddCtrlPt in_UnbrCtrlPts, t_inddCtrlPt in_VnbrCtrlPts,
                   t_CtrlPt * in_pCtrlPts,
                   t_Knot * in_pUKnots, t_Knot * in_pVKnots,
                   t_CheckFlag in_CheckFlag )
{
  m[U].order=in_Uorder; m[V].order=in_Vorder;
  m[U].nbrCtrlPts=in_UnbrCtrlPts; m[V].nbrCtrlPts=in_VnbrCtrlPts;
 
  mtotnbrCtrlPts = m[U].nbrCtrlPts * m[V].nbrCtrlPts;
  m[U].nbrKnots = m[U].order + m[U].nbrCtrlPts;
  m[V].nbrKnots = m[V].order + m[V].nbrCtrlPts;
    
  if (in_CheckFlag)
    Conscheck();
 
  // CtrlPts
  if (! (mpCtrlPts = in_pCtrlPts) )
  {
    G4ExceptionDescription ed;
    ed << "A NURBS MUST HAVE CONTROL POINTS!\n"
       << "\teven if they are defined later, the array must be allocated."
       << G4endl;
    G4Exception("G4NURBS::G4NURBS()",
        "greps9003", FatalException, ed);
  }
  //mnbralias = 0;
 
  // Knots
  t_direction dir;
  G4int dummy;
  for (dummy=0; (dummy?(dir=V):(dir=U)),(dummy < NofD); dummy++)
  {
    if ( !(m[dir].pKnots = (dummy?in_pVKnots:in_pUKnots)) )
    {  // make some regular knots between 0 & 1
      if(!MakeKnotVector(m[dir], Regular))
      {
    G4ExceptionDescription ed;
        ed << "Unable to make a Regular knot vector along "
       << G4NURBS::Tochar(dir)
       << " direction."
       << G4endl;
        G4Exception("G4NURBS::G4NURBS()",
            "greps9004", FatalException, ed);
      }
      //m[dir].nbralias = 0;
    }  // end of knots-making
  }  // end for dummy
} // end of G4NURBS::G4NURBS 
 
// second constructor
 
G4NURBS::G4NURBS( t_order in_Uorder, t_order in_Vorder,
                  t_inddCtrlPt in_UnbrCtrlPts, t_inddCtrlPt in_VnbrCtrlPts,
                  t_KnotVectorGenFlag in_UKVGFlag,
                  t_KnotVectorGenFlag in_VKVGFlag,
                  t_CheckFlag in_CheckFlag )
{
  m[U].order=in_Uorder; m[V].order=in_Vorder;
  m[U].nbrCtrlPts=in_UnbrCtrlPts; m[V].nbrCtrlPts=in_VnbrCtrlPts;
 
  mtotnbrCtrlPts = m[U].nbrCtrlPts * m[V].nbrCtrlPts;
  m[U].nbrKnots = m[U].order + m[U].nbrCtrlPts;
  m[V].nbrKnots = m[V].order + m[V].nbrCtrlPts;
    
  if (in_CheckFlag)
    Conscheck();
 
  // Allocate CtrlPts
  mpCtrlPts = new t_CtrlPt [mtotnbrCtrlPts];
  //mnbralias = 0;
 
  // Knots
  t_direction dir;
  G4int dummy;
  for (dummy=0; (dummy?(dir=V):(dir=U)),(dummy < NofD); dummy++)
  {
    t_KnotVectorGenFlag flag = (dummy?in_VKVGFlag:in_UKVGFlag);
    m[dir].pKnots = 0;  // (allocation under our control)
    if ( flag != UserDefined && !MakeKnotVector(m[dir], flag) )
    {
      G4ExceptionDescription ed;
      ed << "Unable to make knot vector along "
     << G4NURBS::Tochar(dir)
     << " direction. (" << m[dir].nbrKnots 
     << " knots requested for a " 
     << flag 
     << " knots vector)"
     << G4endl;
      G4Exception("G4NURBS::G4NURBS()",
          "greps9005", FatalException, ed);
    }
    //m[dir].nbralias = 0;
  }
}
 
G4NURBS::G4NURBS(const G4NURBS & in_krNurb)
  : G4Visible(in_krNurb)
{
  // we assume the in nurbs is ok
 
  // the number of CtrlPts can be copied straightly
  mtotnbrCtrlPts = in_krNurb.mtotnbrCtrlPts;
 
  // the main datas
 
  // but as m is an array of t_Dir and as t_Dir
  // is just a structure and not a class with a copy cons
  // whe need to duplicate the knots
  t_direction dir;
  G4int dummy;
  for (dummy=0; (dummy?(dir=V):(dir=U)),(dummy < NofD); dummy++)
  {
    // first we do a 'stupid' copy of m[dir]
    m[dir] = in_krNurb.m[dir];
    // but as m is an array of t_Dir and as t_Dir
    // is just a structure and not a class with a copy cons
    // whe need to duplicate the knots
    m[dir].pKnots = new G4double [m[dir].nbrKnots];
    // we copy the knots with memcpy. This function should be the fastest
    memcpy(m[dir].pKnots, in_krNurb.m[dir].pKnots,
           m[dir].nbrKnots * sizeof(G4double));
  }  // end of dummy loop
 
  // the control points
  // once again we need to do the copy
  mpCtrlPts = new t_CtrlPt [mtotnbrCtrlPts];
  memcpy(mpCtrlPts, in_krNurb.mpCtrlPts, mtotnbrCtrlPts*sizeof(t_CtrlPt)); 
 
  // and as it's very strange to copy a nurbs in G4
  // we issue a warning :
  G4cerr << "\nWARNING: G4NURBS::G4NURBS(const G4NURBS &) used" << G4endl;
}
 
G4NURBS::~G4NURBS()
{
  // we must free the two knots vector
  t_direction dir;
  G4int dummy;
  for (dummy=0; (dummy?(dir=V):(dir=U)),(dummy < NofD); dummy++)
  {
    if (m[dir].pKnots)
      delete m[dir].pKnots;  // [m[dir].nbrKnots] if t_Knot become a class
    m[dir].pKnots = 0;
  }
  // now we free the CtrlPts array
  if (mpCtrlPts)
    delete [] mpCtrlPts;    // [mtotnbrCtrlPts] if t_CtrlPt become a class
  mpCtrlPts = 0;
}
 
/************************************************************************
 *                                                                      *
 * Return the current knot the parameter u is less than or equal to.    *
 * Find this "breakpoint" allows the evaluation routines to concentrate *
 * on only those control points actually effecting the curve around u.] *
 *                                                                      *
 *  np  is the number of points on the curve (or surface direction)     *
 *  k   is the order of the curve (or surface direction)                *
 *  kv  is the knot vector ([0..np+k-1]) to find the break point in.    *
 *                                                                      *
 ************************************************************************/
static G4int FindBreakPoint(G4double u, const Float *kv, G4int np, G4int k)
{
  G4int i;
  if (u == kv[np+1]) return np;      /* Special case for closed interval */
  i = np + k;
  while ((u < kv[i]) && (i > 0)) i--;
  return(i);
}
 
/************************************************************************
 *                                                                      *
 * Compute Bi,k(u), for i = 0..k.                                       *
 *  u        the parameter of the spline to find the basis functions for*
 *  brkPoint the start of the knot interval ("segment")                 *
 *  kv       the knot vector                                            *
 *  k        the order of the curve                                     *
 *  bvals    the array of returned basis values.                        *
 *                                                                      *
 * (From Bartels, Beatty & Barsky, p.387)                               *
 *                                                                      *
 ************************************************************************/
static void BasisFunctions(G4double u, G4int brkPoint,
                           const Float *kv, G4int k, G4double *bvals)
{
  G4int r, q, i;
  G4double omega;
 
  bvals[0] = 1.0;
  for (r=2; r <= k; r++)
  {
    i = brkPoint - r + 1;
    bvals[r-1] = 0.0;
    for (q=r-2; q >= 0; q--)
    {
      i++;
      if (i < 0)
      {
        omega = 0.0;
      }
      else
      {
        omega = (u - kv[i]) / (kv[i+r-1] - kv[i]);
      }
      bvals[q+1] = bvals[q+1] + (1.0-omega) * bvals[q];
      bvals[q]   = omega * bvals[q];
    }
  }
}
 
/************************************************************************
 *                                                                      *
 * Compute derivatives of the basis functions Bi,k(u)'                  *
 *                                                                      *
 ************************************************************************/
static void BasisDerivatives(G4double u, G4int brkPoint,
                             const Float *kv, G4int k, G4double *dvals)
{
  G4int q, i;
  G4double omega, knotScale;
 
  BasisFunctions(u, brkPoint, kv, k-1, dvals);
 
  dvals[k-1] = 0.0;      /* BasisFunctions misses this */
 
  knotScale = kv[brkPoint+1] - kv[brkPoint];
 
  i = brkPoint - k + 1;
  for (q=k-2; q >= 0; q--)
  {
    i++;
    omega = knotScale * ((G4double)(k-1)) / (kv[i+k-1] - kv[i]);
    dvals[q+1] += -omega * dvals[q];
    dvals[q] *= omega;
  }
}
 
/***********************************************************************
 *                                                                     *
 * Calculate a point p on NurbSurface n at a specific u, v             *
 * using the tensor product.                                           *
 *                                                                     *
 * Note the valid parameter range for u and v is                       *
 * (kvU[orderU] <= u < kvU[numU), (kvV[orderV] <= v < kvV[numV])       *
 *                                                                     *
 ***********************************************************************/
void G4NURBS::CalcPoint(G4double u, G4double v, G4Point3D &p,
                        G4Vector3D &utan, G4Vector3D &vtan) const
{
#define MAXORDER 50
  struct Point4
  {
    G4double x, y, z, w;
  };
 
  G4int i, j, ri, rj;
  G4int ubrkPoint, ufirst;
  G4double bu[MAXORDER], buprime[MAXORDER];
  G4int vbrkPoint, vfirst;
  G4double bv[MAXORDER], bvprime[MAXORDER];
  Point4 r, rutan, rvtan;
 
  r.x = 0.0; r.y = 0.0; r.z = 0.0; r.w = 0.0;
  rutan = r;   rvtan = r;
 
  G4int numU   = GetUnbrCtrlPts();
  G4int numV   = GetVnbrCtrlPts();
  G4int orderU = GetUorder();
  G4int orderV = GetVorder();
  
  /* Evaluate non-uniform basis functions (and derivatives) */
  
  ubrkPoint = FindBreakPoint(u, m[U].pKnots, numU-1, orderU);
  ufirst    = ubrkPoint - orderU + 1;
  BasisFunctions  (u, ubrkPoint, m[U].pKnots, orderU, bu);
  BasisDerivatives(u, ubrkPoint, m[U].pKnots, orderU, buprime);
 
  vbrkPoint = FindBreakPoint(v, m[V].pKnots, numV-1, orderV);
  vfirst    = vbrkPoint - orderV + 1;
  BasisFunctions  (v, vbrkPoint, m[V].pKnots, orderV, bv);
  BasisDerivatives(v, vbrkPoint, m[V].pKnots, orderV, bvprime);
 
  /* Weight control points against the basis functions */
 
  t_doubleCtrlPt *cpoint;
  Point4 cp;
  G4double tmp;
 
  for (i=0; i<orderV; i++)
  {
    for (j=0; j<orderU; j++)
    {
      ri = orderV - 1 - i;
      rj = orderU - 1 - j;
 
      tmp = bu[rj] * bv[ri];
 
      cpoint = GetdoubleCtrlPt(j+ufirst, i+vfirst);
      cp.x = *cpoint[G4NURBS::X];
      cp.y = *cpoint[G4NURBS::Y];
      cp.z = *cpoint[G4NURBS::Z];
      cp.w = *cpoint[G4NURBS::W];
      delete [] cpoint;
 
      r.x += cp.x * tmp;
      r.y += cp.y * tmp;
      r.z += cp.z * tmp;
      r.w += cp.w * tmp;
      
      tmp = buprime[rj] * bv[ri];
      rutan.x += cp.x * tmp;
      rutan.y += cp.y * tmp;
      rutan.z += cp.z * tmp;
      rutan.w += cp.w * tmp;
 
      tmp = bu[rj] * bvprime[ri];
      rvtan.x += cp.x * tmp;
      rvtan.y += cp.y * tmp;
      rvtan.z += cp.z * tmp;
      rvtan.w += cp.w * tmp;
    }
  }
 
  /* Project tangents, using the quotient rule for differentiation */
  
  G4double wsqrdiv = 1.0 / (r.w * r.w);
 
  utan.setX((r.w * rutan.x - rutan.w * r.x) * wsqrdiv);
  utan.setY((r.w * rutan.y - rutan.w * r.y) * wsqrdiv);
  utan.setZ((r.w * rutan.z - rutan.w * r.z) * wsqrdiv);
 
  vtan.setX((r.w * rvtan.x - rvtan.w * r.x) * wsqrdiv);
  vtan.setY((r.w * rvtan.y - rvtan.w * r.y) * wsqrdiv);
  vtan.setZ((r.w * rvtan.z - rvtan.w * r.z) * wsqrdiv);
 
  p.setX(r.x / r.w);
  p.setY(r.y / r.w);
  p.setZ(r.z / r.w);
}