TPainter3dAlgorithms.cxx

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// @(#)root/histpainter:$Id$
// Author: Rene Brun, Evgueni Tcherniaev, Olivier Couet   12/12/94
 
/*************************************************************************
 * Copyright (C) 1995-2000, Rene Brun and Fons Rademakers.               *
 * All rights reserved.                                                  *
 *                                                                       *
 * For the licensing terms see $ROOTSYS/LICENSE.                         *
 * For the list of contributors see $ROOTSYS/README/CREDITS.             *
 *************************************************************************/
 
/*! \class TPainter3dAlgorithms
    \ingroup Histpainter
    \brief The Legos and Surfaces painter class.
 
3D graphics representations package.
 
This package was originally written by Evgueni Tcherniaev from IHEP/Protvino.
 
The original Fortran implementation was adapted to HIGZ/PAW by Olivier Couet
and Evgueni Tcherniaev.
 
This class is a subset of the original system. It has been converted to a C++
class by Rene Brun.
*/
 
#include <cstdlib>
 
#include "TROOT.h"
#include "TPainter3dAlgorithms.h"
#include "TVirtualPad.h"
#include "THistPainter.h"
#include "TH1.h"
#include "TF3.h"
#include "TView.h"
#include "Hoption.h"
#include "Hparam.h"
#include "TMath.h"
#include "TStyle.h"
#include "THLimitsFinder.h"
#include "TColor.h"
 
const Double_t kRad  = TMath::ATan(1)*Double_t(4)/Double_t(180);
const Double_t kFdel = 0.;
const Double_t kDel  = 0.0001;
const Int_t kNiso  = 4;
const Int_t kNmaxp = kNiso*13;
const Int_t kNmaxt = kNiso*12;
const Int_t kLmax  = 12;
const Int_t kF3FillColor1 = 201;
const Int_t kF3FillColor2 = 202;
const Int_t kF3LineColor  = 203;
 
extern TH1  *gCurrentHist; //these 3 globals should be replaced by class members
extern Hoption_t Hoption;
extern Hparam_t  Hparam;
 
////////////////////////////////////////////////////////////////////////////////
/// Lego default constructor
 
TPainter3dAlgorithms::TPainter3dAlgorithms(): TAttLine(1,1,1), TAttFill(1,0)
{
   Int_t i;
   fNaphi           = 0;
   fIfrast          = 0;
   fMesh            = 1;
   fColorTop        = 1;
   fColorBottom     = 1;
   fEdgeIdx         = -1;
   fNlevel          = 0;
   fSystem          = kCARTESIAN;
   fDrawFace        = nullptr;
   fLegoFunction    = nullptr;
   fSurfaceFunction = nullptr;
 
   TList *stack = nullptr;
   if (gCurrentHist) stack = gCurrentHist->GetPainter()->GetStack();
   fNStack = stack ? stack->GetSize() : 0;
   fColorMain.resize(fNStack+1);
   fColorDark.resize(fNStack+1);
   fEdgeColor.resize(fNStack+1);
   fEdgeStyle.resize(fNStack+1);
   fEdgeWidth.resize(fNStack+1);
 
   for (i=0;i<fNStack;i++) { fColorMain[i] = 1; fColorDark[i] = 1; fEdgeColor[i] = 1; fEdgeStyle[i] = 1; fEdgeWidth[i] = 1; }
   for (i=0;i<3;i++)       { fRmin[i] = 0; fRmax[i] = 1; }
   for (i=0;i<4;i++)       { fYls[i] = 0; }
 
   for (i=0;i<30;i++)      { fJmask[i] = 0; }
   for (i=0;i<200;i++)     { fLevelLine[i] = 0; }
   for (i=0;i<465;i++)     { fMask[i] = 0; }
   for (i=0;i<258;i++)     { fColorLevel[i] = 0; }
   for (i=0;i<1200;i++)    { fPlines[i] = 0.; }
   for (i=0;i<200;i++)     { fT[i] = 0.; }
   for (i=0;i<2*NumOfSlices;i++)  { fU[i] = 0.; fD[i] = 0.; }
   for (i=0;i<12;i++)      { fVls[i] = 0.; }
   for (i=0;i<257;i++)     { fFunLevel[i] = 0.; }
   for (i=0;i<8;i++)       { fF8[i] = 0.; }
 
   fLoff   = 0;
   fNT     = 0;
   fNcolor = 0;
   fNlines = 0;
   fNqs    = 0;
   fNxrast = 0;
   fNyrast = 0;
   fIc1    = 0;
   fIc2    = 0;
   fIc3    = 0;
   fQA     = 0.;
   fQD     = 0.;
   fQS     = 0.;
   fX0     = 0.;
   fYdl    = 0.;
   fXrast  = 0.;
   fYrast  = 0.;
   fFmin   = 0.;
   fFmax   = 0.;
   fDXrast = 0.;
   fDYrast = 0.;
   fDX     = 0.;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Normal default constructor
///
///  rmin[3], rmax[3] are the limits of the lego object depending on
///  the selected coordinate system
 
TPainter3dAlgorithms::TPainter3dAlgorithms(Double_t *rmin, Double_t *rmax, Int_t system)
      : TAttLine(1,1,1), TAttFill(1,0)
{
   Int_t i;
   Double_t psi;
 
   fNaphi        = 0;
   fIfrast       = 0;
   fMesh         = 1;
   fColorTop     = 1;
   fColorBottom  = 1;
   fEdgeIdx      = -1;
   fNlevel       = 0;
   fSystem       = system;
   if (system == kCARTESIAN || system == kPOLAR) psi =  0;
   else                                          psi = 90;
   fDrawFace        = nullptr;
   fLegoFunction    = nullptr;
   fSurfaceFunction = nullptr;
 
   TList *stack = gCurrentHist->GetPainter()->GetStack();
   fNStack = stack ? stack->GetSize() : 0;
 
   fColorMain.resize(fNStack+1);
   fColorDark.resize(fNStack+1);
   fEdgeColor.resize(fNStack+1);
   fEdgeStyle.resize(fNStack+1);
   fEdgeWidth.resize(fNStack+1);
 
   for (i=0;i<fNStack;i++) { fColorMain[i] = 1; fColorDark[i] = 1; fEdgeColor[i] = 1; fEdgeStyle[i] = 1; fEdgeWidth[i] = 1; }
   for (i=0;i<3;i++)       { fRmin[i] = rmin[i]; fRmax[i] = rmax[i]; }
   for (i=0;i<4;i++)       { fYls[i] = 0; }
 
   for (i=0;i<30;i++)      { fJmask[i] = 0; }
   for (i=0;i<200;i++)     { fLevelLine[i] = 0; }
   for (i=0;i<465;i++)     { fMask[i] = 0; }
   for (i=0;i<258;i++)     { fColorLevel[i] = 0; }
   for (i=0;i<1200;i++)    { fPlines[i] = 0.; }
   for (i=0;i<200;i++)     { fT[i] = 0.; }
   for (i=0;i<2*NumOfSlices;i++)  { fU[i] = 0.; fD[i] = 0.; }
   for (i=0;i<12;i++)      { fVls[i] = 0.; }
   for (i=0;i<257;i++)     { fFunLevel[i] = 0.; }
   for (i=0;i<8;i++)       { fF8[i] = 0.; }
 
   fLoff   = 0;
   fNT     = 0;
   fNcolor = 0;
   fNlines = 0;
   fNqs    = 0;
   fNxrast = 0;
   fNyrast = 0;
   fIc1    = 0;
   fIc2    = 0;
   fIc3    = 0;
   fQA     = 0.;
   fQD     = 0.;
   fQS     = 0.;
   fX0     = 0.;
   fYdl    = 0.;
   fXrast  = 0.;
   fYrast  = 0.;
   fFmin   = 0.;
   fFmax   = 0.;
   fDXrast = 0.;
   fDYrast = 0.;
   fDX     = 0.;
 
   TView *view = gPad ? gPad->GetView() : nullptr;
   if (!view)
      view = TView::CreateView(fSystem, rmin, rmax);
   if (view) {
      view->SetView(gPad->GetPhi(), gPad->GetTheta(), psi, i);
      view->SetRange(rmin,rmax);
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// destructor
 
TPainter3dAlgorithms::~TPainter3dAlgorithms()
{
}
 
////////////////////////////////////////////////////////////////////////////////
/// Draw back surfaces of surrounding box
///
/// \param[in] ang   angle between X and Y axis
 
void TPainter3dAlgorithms::BackBox(Double_t ang)
{
   static Int_t iface1[4] = { 1, 4, 8, 5 };
   static Int_t iface2[4] = { 4, 3, 7, 8 };
 
   TView *view = gPad ? gPad->GetView() : nullptr;
   if (!view) {
      Error("BackBox", "no TView in current pad");
      return;
   }
 
   //          Get corners of surrounding box
   Double_t r[3*8], av[3*8];
   Int_t ix1, ix2, iy1, iy2, iz1, iz2;
   Double_t cosa = TMath::Cos(kRad*ang);
   Double_t sina = TMath::Sin(kRad*ang);
   view->AxisVertex(ang, av, ix1, ix2, iy1, iy2, iz1, iz2);
   for (Int_t i = 0; i < 8; ++i) {
      r[i*3 + 0] = av[i*3 + 0] + av[i*3 + 1]*cosa;
      r[i*3 + 1] = av[i*3 + 1]*sina;
      r[i*3 + 2] = av[i*3 + 2];
   }
 
   //          Draw back faces
   Int_t icodes[3] = { 0, 0, 0 };
   Double_t tt[4];
   tt[0] = r[(iface1[0]-1)*3 + 2];
   tt[1] = r[(iface1[1]-1)*3 + 2];
   tt[2] = r[(iface1[2]-1)*3 + 2];
   tt[3] = r[(iface1[3]-1)*3 + 2];
   (this->*fDrawFace)(icodes, r, 4, iface1, tt);
   tt[0] = r[(iface2[0]-1)*3 + 2];
   tt[1] = r[(iface2[1]-1)*3 + 2];
   tt[2] = r[(iface2[2]-1)*3 + 2];
   tt[3] = r[(iface2[3]-1)*3 + 2];
   (this->*fDrawFace)(icodes, r, 4, iface2, tt);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Draw front surfaces of surrounding box & axes
///
/// \param[in] ang   angle between X and Y axis
 
void TPainter3dAlgorithms::FrontBox(Double_t ang)
{
   static Int_t iface1[4] = { 1, 2, 6, 5 };
   static Int_t iface2[4] = { 2, 3, 7, 6 };
 
   TView *view = gPad ? gPad->GetView() : nullptr;
   if (!view) {
      Error("FrontBox", "no TView in current pad");
      return;
   }
 
   //          Get corners of surrounding box
   Double_t r[3*8], av[3*8], x[4], y[4];
   Int_t ix1, ix2, iy1, iy2, iz1, iz2;
   Double_t cosa = TMath::Cos(kRad*ang);
   Double_t sina = TMath::Sin(kRad*ang);
   view->AxisVertex(ang, av, ix1, ix2, iy1, iy2, iz1, iz2);
   for (Int_t i = 0; i < 8; ++i) {
      r[i*3 + 0] = av[i*3 + 0] + av[i*3 + 1]*cosa;
      r[i*3 + 1] = av[i*3 + 1]*sina;
      r[i*3 + 2] = av[i*3 + 2];
      view->WCtoNDC(&r[i*3],&r[i*3]);
   }
 
   //          Draw frame
   SetLineColor(1);
   SetLineStyle(1);
   SetLineWidth(1);
   TAttLine::Modify();
   for (Int_t i = 0; i < 4; ++i) {
      Int_t k = iface1[i] - 1;
      x[i] = r[k*3 + 0];
      y[i] = r[k*3 + 1];
   }
   gPad->PaintPolyLine(4, x, y);
   for (Int_t i = 0; i < 4; ++i) {
      Int_t k = iface2[i] - 1;
      x[i] = r[k*3 + 0];
      y[i] = r[k*3 + 1];
   }
   gPad->PaintPolyLine(4, x, y);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Clear screen
 
void TPainter3dAlgorithms::ClearRaster()
{
   Int_t nw = (fNxrast*fNyrast + 29) / 30;
   for (Int_t i = 0; i < nw; ++i) fRaster[i] = 0;
   fIfrast = 0;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Set correspondence between function and color levels
///
/// \param[in] nl   number of levels
/// \param[in] fl   function levels
/// \param[in] icl   colors for levels
///
/// \param[out] irep   return code (0 OK, -1 error).
 
void TPainter3dAlgorithms::ColorFunction(Int_t nl, Double_t *fl, Int_t *icl, Int_t &irep)
{
   static const char *where = "ColorFunction";
 
   irep = 0;
   if (nl == 0) {
      fNlevel = 0;
      return;
   }
 
   //          Check parameters
   if (nl < 0 || nl > 256) {
      Error(where, "illegal number of levels (%d)", nl);
      irep = -1;
      return;
   }
 
   for (Int_t i = 1; i < nl; ++i) {
      if (fl[i] <= fl[i - 1]) {
   //         Error(where, "function levels must be in increasing order");
         irep = -1;
         return;
      }
   }
 
   for (Int_t i = 0; i < nl; ++i) {
      if (icl[i] < 0) {
   //         Error(where, "negative color index (%d)", icl[i]);
         irep = -1;
         return;
      }
   }
 
   //          Set levels
   fNlevel = nl;
   for (Int_t i = 0; i < fNlevel;   ++i) fFunLevel[i] = Hparam.factor*fl[i];
   for (Int_t i = 0; i < fNlevel+1; ++i) fColorLevel[i] = icl[i];
}
 
////////////////////////////////////////////////////////////////////////////////
/// Define the grid levels drawn in the background of surface and lego plots.
/// The grid levels are aligned on the  Z axis' main tick marks.
 
void TPainter3dAlgorithms::DefineGridLevels(Int_t ndivz)
{
   TView *view = gPad ? gPad->GetView() : nullptr;
   if (!view) {
      Error("GridLevels", "no TView in current pad");
      return;
   }
 
   //          Find the main tick marks positions
   Int_t nbins = 0;
   Double_t binLow = 0, binHigh = 0, binWidth = 0;
   Double_t *rmin = view->GetRmin();
   Double_t *rmax = view->GetRmax();
   if (!rmin || !rmax) return;
   if (ndivz > 0) {
      THLimitsFinder::Optimize(rmin[2], rmax[2], ndivz,
                               binLow, binHigh, nbins, binWidth, " ");
   } else {
      nbins = TMath::Abs(ndivz);
      binLow = rmin[2];
      binHigh = rmax[2];
      binWidth = (binHigh - binLow)/nbins;
   }
 
   //          Define the grid levels
   fNlevel = nbins + 1;
   for (Int_t i = 0; i < fNlevel; ++i) {
      fFunLevel[i] = binLow + i*binWidth;
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Draw face - 1st variant (2 colors: 1st for external surface, 2nd for internal)
///
/// \param[in] icodes   set of codes for the line (not used in this method)
/// \param[in] xyz   coordinates of nodes
/// \param[in] np   number of nodes in face
/// \param[in] iface   face
/// \param[in] t   additional function defined on this face (not used in this method)
 
void TPainter3dAlgorithms::DrawFaceMode1(Int_t *, Double_t *xyz, Int_t np, Int_t *iface, Double_t *)
{
   TView *view = gPad ? gPad->GetView() : nullptr;
   if (!view) return;
 
   //          Transfer to normalised coordinates
   Bool_t ifneg = false;
   Double_t x[12+1] = {0}, y[12+1] = {0}, p3[3];
   for (Int_t i = 0; i < np; ++i) {
      Int_t k = iface[i];
      if (k < 0) { k = -k; ifneg = true; }
      view->WCtoNDC(&xyz[(k-1)*3], p3);
      x[i] = p3[0]; y[i] = p3[1];
   }
   x[np] = x[0]; y[np] = y[0];
 
   //          Find normal
   Double_t z = 0;
   for (Int_t i = 0; i < np; ++i) {
      z += y[i]*x[i+1] - x[i]*y[i+1];
   }
 
   //          Draw face
   SetFillColor((z > 0) ? kF3FillColor1 : kF3FillColor2);
   SetFillStyle(1001);
   TAttFill::Modify();
   gPad->PaintFillArea(np, x, y);
 
   //          Draw border
   SetLineColor(kF3LineColor);
   TAttLine::Modify();
   if (ifneg) {
      for (Int_t i = 0; i < np; ++i) { // draw visible edges, skip invisible
         if (iface[i] > 0) gPad->PaintPolyLine(2, &x[i], &y[i]);
      }
   } else {
      gPad->PaintPolyLine(np+1, x, y); // all edges are visible
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Draw face - 2nd option (fill in correspondence with function levels)
///
/// \param[in] icodes   set of codes for the line (not used in this method)
/// \param[in] xyz   coordinates of nodes
/// \param[in] np   number of nodes
/// \param[in] iface   face
/// \param[in] t   additional function defined on this face
 
void TPainter3dAlgorithms::DrawFaceMode2(Int_t *, Double_t *xyz, Int_t np, Int_t *iface, Double_t *t)
{
   TView *view = gPad ? gPad->GetView() : nullptr;
   if (!view) return;
 
   //          Transfer to normalised coordinates
   Double_t x[12+1] = {0}, y[12+1] = {0}, p3[3*12];
   for (Int_t i = 0; i < np; ++i) {
      Int_t k = iface[i];
      view->WCtoNDC(&xyz[(k-1)*3], &p3[i*3]);
      x[i] = p3[i*3+0]; y[i] = p3[i*3+1];
   }
   x[np] = x[0]; y[np] = y[0];
 
   //          Draw face
   SetLineColor(fEdgeColor[fEdgeIdx]);
   SetLineStyle(fEdgeStyle[fEdgeIdx]);
   SetLineWidth(fEdgeWidth[fEdgeIdx]);
   TAttLine::Modify();
   if (np == 4) {
      Double_t ttt[5] = { t[0], t[1], t[2], t[3], t[0] };
      for (Int_t i = 0; i<3; ++i) { p3[3*4+i] = p3[i]; }
      Int_t k1 = 0, k2 = 2;
      Double_t z1 = (x[k1+1] - x[k1+0])*(y[k1+2] - y[k1+1]) - (y[k1+1] - y[k1+0])*(x[k1+2] - x[k1+1]);
      Double_t z2 = (x[k2+1] - x[k2+0])*(y[k2+2] - y[k2+1]) - (y[k2+1] - y[k2+0])*(x[k2+2] - x[k2+1]);
      if (z1 > z2) { k1 = 2; k2 = 0; }
      FillPolygon(3, &p3[3*k1], &ttt[k1]);
      if (fMesh == 1) {   // Draw border
         gPad->PaintPolyLine(3, &x[k1], &y[k1]);
      }
      FillPolygon(3, &p3[3*k2], &ttt[k2]);
      if (fMesh == 1) {   // Draw border
         gPad->PaintPolyLine(3, &x[k2], &y[k2]);
         if (z1*z2 <= 0) { // Draw middle line
            x[1] = x[2]; y[1] = y[2];
            gPad->PaintPolyLine(2, &x[0], &y[0]);
         }
      }
   } else {
      FillPolygon(np, p3, t);
      if (fMesh == 1) {   // Draw border
         gPad->PaintPolyLine(np+1, x, y);
      }
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Draw face - 3rd option (draw face for stacked lego plot)
///
/// \param[in] icodes   set of codes for the line
/// \param[in] xyz   coordinates of nodes
/// \param[in] np   number of nodes
/// \param[in] iface   face
/// \param[in] t   additional function defined on this face (not used in this method)
 
void TPainter3dAlgorithms::DrawFaceMode3(Int_t *icodes, Double_t *xyz, Int_t np, Int_t *iface, Double_t *)
{
   TView *view = gPad ? gPad->GetView() : nullptr;
   if (!view) return;
 
   //          Transfer to normalised coordinates
   Double_t x[4+1] = {0}, y[4+1] = {0}, p3[3];
   for (Int_t i = 0; i < np; ++i) {
      Int_t k = iface[i];
      view->WCtoNDC(&xyz[(k-1)*3], p3);
      x[i] = p3[0]; y[i] = p3[1];
   }
   x[np] = x[0]; y[np] = y[0];
 
   //          Draw face
   Int_t icol = 0;
   if (icodes[3] == 6) icol = fColorTop;
   if (icodes[3] == 5) icol = fColorBottom;
   if (icodes[3] == 1) icol = fColorMain[icodes[2] - 1];
   if (icodes[3] == 2) icol = fColorDark[icodes[2] - 1];
   if (icodes[3] == 3) icol = fColorMain[icodes[2] - 1];
   if (icodes[3] == 4) icol = fColorDark[icodes[2] - 1];
   SetFillStyle(1001);
   SetFillColor(icol);
   TAttFill::Modify();
   gPad->PaintFillArea(np, x, y);
 
   //          Draw border
   if (fMesh) {
      SetLineColor(fEdgeColor[fEdgeIdx]);
      SetLineStyle(fEdgeStyle[fEdgeIdx]);
      SetLineWidth(fEdgeWidth[fEdgeIdx]);
      TAttLine::Modify();
      gPad->PaintPolyLine(np+1, x, y);
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Draw face - 1st variant for "MOVING SCREEN" algorithm (draw face with level lines)
///
/// \param[in] icodes   set of codes for the line
/// \param[in] xyz   coordinates of nodes
/// \param[in] np   number of nodes
/// \param[in] iface   face
/// \param[in] tt   additional function defined on this face
 
void TPainter3dAlgorithms::DrawFaceMove1(Int_t *icodes, Double_t *xyz, Int_t np,
                                         Int_t *iface, Double_t *tt)
{
   TView *view = gPad ? gPad->GetView() : nullptr;
   if (!view) return;
 
   //          Copy points to array
   Double_t p3[3*12] = {0};
   for (Int_t i = 0; i < np; ++i) {
      Int_t k = iface[i];
      p3[i*3 + 0] = xyz[(k-1)*3 + 0];
      p3[i*3 + 1] = xyz[(k-1)*3 + 1];
      p3[i*3 + 2] = xyz[(k-1)*3 + 2];
   }
 
   //          Find level lines
   FindLevelLines(np, p3, tt);
 
   //          Draw level lines
   Double_t p1[3], p2[3], x[2], y[2];
   SetLineStyle(3);
   if (icodes[2] == 0) {  // front & back boxes
      SetLineColor(1);
      SetLineWidth(1);
   } else {
      SetLineColor(fEdgeColor[fEdgeIdx]);
      SetLineWidth(fEdgeWidth[fEdgeIdx]);
   }
   TAttLine::Modify();
   for (Int_t il = 0; il < fNlines; ++il) {
      FindVisibleDraw(&fPlines[6*il + 0], &fPlines[6*il + 3]);
      view->WCtoNDC(&fPlines[6*il + 0], p1);
      view->WCtoNDC(&fPlines[6*il + 3], p2);
      Double_t xdel = p2[0] - p1[0];
      Double_t ydel = p2[1] - p1[1];
      for (Int_t it = 0; it < fNT; ++it) {
         x[0] = p1[0] + xdel*fT[2*it + 0];
         y[0] = p1[1] + ydel*fT[2*it + 0];
         x[1] = p1[0] + xdel*fT[2*it + 1];
         y[1] = p1[1] + ydel*fT[2*it + 1];
         gPad->PaintPolyLine(2, x, y);
      }
   }
 
   //          Draw face
   if (icodes[2] == 0) {  // front & back boxes
      SetLineColor(1);
      SetLineStyle(1);
      SetLineWidth(1);
   } else {
      SetLineColor(fEdgeColor[fEdgeIdx]);
      SetLineStyle(fEdgeStyle[fEdgeIdx]);
      SetLineWidth(fEdgeWidth[fEdgeIdx]);
   }
   TAttLine::Modify();
   for (Int_t i = 0; i < np; ++i) {
      Int_t i1 = i;
      Int_t i2 = (i == np-1) ? 0 : i + 1;
      FindVisibleDraw(&p3[i1*3], &p3[i2*3]);
      view->WCtoNDC(&p3[i1*3], p1);
      view->WCtoNDC(&p3[i2*3], p2);
      Double_t xdel = p2[0] - p1[0];
      Double_t ydel = p2[1] - p1[1];
      for (Int_t it = 0; it < fNT; ++it) {
         x[0] = p1[0] + xdel*fT[2*it + 0];
         y[0] = p1[1] + ydel*fT[2*it + 0];
         x[1] = p1[0] + xdel*fT[2*it + 1];
         y[1] = p1[1] + ydel*fT[2*it + 1];
         gPad->PaintPolyLine(2, x, y);
      }
   }
 
   //          Modify screen
   for (Int_t i = 0; i < np; ++i) {
      Int_t i1 = i;
      Int_t i2 = (i == np-1) ? 0 : i + 1;
      ModifyScreen(&p3[i1*3], &p3[i2*3]);
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Draw face - 2nd variant for "MOVING SCREEN" algorithm (draw face for stacked lego plot)
///
/// \param[in] icodes   set of codes for the line
/// \param[in] xyz   coordinates of nodes
/// \param[in] np   number of nodes
/// \param[in] iface   face
/// \param[in] tt   additional function defined on this face (not used in this method)
 
void TPainter3dAlgorithms::DrawFaceMove2(Int_t *icodes, Double_t *xyz, Int_t np, Int_t *iface, Double_t *)
{
   TView *view = gPad ? gPad->GetView() : nullptr;
   if (!view) return;
 
   //          Copy points to array
   Double_t p3[3*12];
   for (Int_t i = 0; i < np; ++i) {
      Int_t k = iface[i];
      p3[i*3 + 0] = xyz[(k-1)*3 + 0];
      p3[i*3 + 1] = xyz[(k-1)*3 + 1];
      p3[i*3 + 2] = xyz[(k-1)*3 + 2];
   }
 
   //          Draw face
   Double_t p1[3], p2[3], x[2], y[2];
   if (icodes[2] == 0) {  // front & back boxes
      SetLineColor(1);
      SetLineStyle(1);
      SetLineWidth(1);
   } else {
      SetLineColor(fEdgeColor[fEdgeIdx]);
      SetLineStyle(fEdgeStyle[fEdgeIdx]);
      SetLineWidth(fEdgeWidth[fEdgeIdx]);
   }
   TAttLine::Modify();
   for (Int_t i = 0; i < np; ++i) {
      Int_t i1 = i;
      Int_t i2 = (i == np-1) ? 0 : i + 1;
      FindVisibleDraw(&p3[i1*3], &p3[i2*3]);
      view->WCtoNDC(&p3[i1*3], p1);
      view->WCtoNDC(&p3[i2*3], p2);
      Double_t xdel = p2[0] - p1[0];
      Double_t ydel = p2[1] - p1[1];
      for (Int_t it = 0; it < fNT; ++it) {
         x[0] = p1[0] + xdel*fT[2*it + 0];
         y[0] = p1[1] + ydel*fT[2*it + 0];
         x[1] = p1[0] + xdel*fT[2*it + 1];
         y[1] = p1[1] + ydel*fT[2*it + 1];
         gPad->PaintPolyLine(2, x, y);
      }
   }
 
   //          Modify screen
   for (Int_t i = 0; i < np; ++i) {
      Int_t i1 = i;
      Int_t i2 = (i == np-1) ? 0 : i + 1;
      ModifyScreen(&p3[i1*3], &p3[i2*3]);
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Draw face - 3rd variant for "MOVING SCREEN" algorithm (draw level lines only)
///
/// \param[in] icodes   set of codes for the line
/// \param[in] xyz   coordinates of nodes
/// \param[in] np   number of nodes
/// \param[in] iface   face
/// \param[in] tt   additional function defined on this face
 
void TPainter3dAlgorithms::DrawFaceMove3(Int_t *icodes, Double_t *xyz, Int_t np,
                                         Int_t *iface, Double_t *tt)
{
   TView *view = gPad ? gPad->GetView() : nullptr;
   if (!view) return;
 
   //          Set graphics attributes
   if (icodes[2] == 0) {  // frame
      SetLineColor(1);
      SetLineStyle(1);
      SetLineWidth(1);
   } else {
      SetLineColor(fEdgeColor[fEdgeIdx]);
      SetLineStyle(fEdgeStyle[fEdgeIdx]);
      SetLineWidth(fEdgeWidth[fEdgeIdx]);
   }
   TAttLine::Modify();
 
   //          Copy points to array
   Double_t p3[3*12] = {0}, ttt[12] = {0};
   for (Int_t i = 0; i < np; ++i) {
      Int_t k = iface[i];
      p3[i*3 + 0] = xyz[(k-1)*3 + 0];
      p3[i*3 + 1] = xyz[(k-1)*3 + 1];
      p3[i*3 + 2] = xyz[(k-1)*3 + 2];
      ttt[i] = tt[i];
   }
 
   //          Subdivide quadrilateral in two triangles
   Int_t npol[2] = { np, 0 }; // number of vertices in sub-polygons
   Int_t ipol[2] = {  0, 0 }; // first vertices in sub-polygons
   if (np == 4 && icodes[2] != 0) {
      p3[4*3 + 0] = p3[0];
      p3[4*3 + 1] = p3[1];
      p3[4*3 + 2] = p3[2];
      ttt[4] = tt[0];
      npol[0] = 3;  npol[1] = 3;
      ipol[0] = 0;  ipol[1] = 2;
   }
 
   Double_t p1[3], p2[3], x[2], y[2];
   for (Int_t kpol = 0; kpol < 2; ++kpol) {
      if (npol[kpol] == 0) continue;
      Int_t nv = npol[kpol];
      Int_t iv = ipol[kpol];
 
      //          Find level lines
      FindLevelLines(nv, &p3[3*iv], &ttt[iv]);
 
      //          Draw level lines
      for (Int_t il = 0; il < fNlines; ++il) {
         FindVisibleDraw(&fPlines[6*il + 0], &fPlines[6*il + 3]);
         view->WCtoNDC(&fPlines[6*il + 0], p1);
         view->WCtoNDC(&fPlines[6*il + 3], p2);
         Double_t xdel = p2[0] - p1[0];
         Double_t ydel = p2[1] - p1[1];
         for (Int_t it = 0; it < fNT; ++it) {
            x[0] = p1[0] + xdel*fT[2*it + 0];
            y[0] = p1[1] + ydel*fT[2*it + 0];
            x[1] = p1[0] + xdel*fT[2*it + 1];
            y[1] = p1[1] + ydel*fT[2*it + 1];
            gPad->PaintPolyLine(2, x, y);
         }
      }
   }
 
   //          Modify screen
   for (Int_t i = 0; i < np; ++i) {
      Int_t i1 = i;
      Int_t i2 = (i == np - 1) ? 0 : i1 + 1;
      ModifyScreen(&p3[i1*3], &p3[i2*3]);
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Draw level lines without hidden line removal
///
/// \param[in] icodes   set of codes for the line
/// \param[in] xyz   coordinates of nodes
/// \param[in] np   number of nodes
/// \param[in] iface   face
/// \param[in] tt   additional function defined on this face
 
void TPainter3dAlgorithms::DrawLevelLines(Int_t *icodes, Double_t *xyz, Int_t np,
                                          Int_t *iface, Double_t *tt)
{
   TView *view = gPad ? gPad->GetView() : nullptr;
   if (!view) return;
 
   //          Set graphics attributes
   if (icodes[2] == 0) {  // frame
      SetLineColor(1);
      SetLineStyle(1);
      SetLineWidth(1);
   } else {
      SetLineColor(fEdgeColor[fEdgeIdx]);
      SetLineStyle(fEdgeStyle[fEdgeIdx]);
      SetLineWidth(fEdgeWidth[fEdgeIdx]);
   }
   TAttLine::Modify();
 
   //          Copy points to array
   Double_t p3[3*12] = {0}, ttt[12] = {0};
   for (Int_t i = 0; i < np; ++i) {
      Int_t k = iface[i];
      p3[i*3 + 0] = xyz[(k-1)*3 + 0];
      p3[i*3 + 1] = xyz[(k-1)*3 + 1];
      p3[i*3 + 2] = xyz[(k-1)*3 + 2];
      ttt[i] = tt[i];
   }
 
   //          Subdivide quadrilateral in two triangles
   Int_t npol[2] = { np, 0 }; // number of vertices in sub-polygons
   Int_t ipol[2] = {  0, 0 }; // first vertices in sub-polygons
   if (np == 4 && icodes[2] != 0) {
      p3[4*3 + 0] = p3[0];
      p3[4*3 + 1] = p3[1];
      p3[4*3 + 2] = p3[2];
      ttt[4] = tt[0];
      npol[0] = 3;  npol[1] = 3;
      ipol[0] = 0;  ipol[1] = 2;
   }
 
   Double_t p1[3], p2[3], x[2], y[2];
   for (Int_t kpol = 0; kpol < 2; ++kpol) {
      if (npol[kpol] == 0) continue;
      Int_t nv = npol[kpol];
      Int_t iv = ipol[kpol];
 
      //          Find level lines
      FindLevelLines(nv, &p3[3*iv], &ttt[iv]);
 
      //          Draw level lines
      for (Int_t il = 0; il < fNlines; ++il) {
         view->WCtoNDC(&fPlines[6*il + 0], p1);
         view->WCtoNDC(&fPlines[6*il + 3], p2);
         x[0] = p1[0]; y[0] = p1[1];
    x[1] = p2[0]; y[1] = p2[1];
         gPad->PaintPolyLine(2, x, y);
      }
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Draw face - 1st variant for "RASTER SCREEN" algorithm (draw face with level lines)
///
/// \param[in] icodes   set of codes for the line
/// \param[in] xyz   coordinates of nodes
/// \param[in] np   number of nodes
/// \param[in] iface   face
/// \param[in] tt   additional function defined on this face
 
void TPainter3dAlgorithms::DrawFaceRaster1(Int_t *icodes, Double_t *xyz, Int_t np, Int_t *iface, Double_t *tt)
{
   TView *view = gPad ? gPad->GetView() : nullptr;
   if (!view) return;
 
   //          Copy vertices to array
   Double_t p3[3*12] = {0}, pp[2*12] = {0};
   for (Int_t i = 0; i < np; ++i) {
      Int_t k = iface[i];
      if (k < 0) k = -k;
      p3[i*3 + 0] = xyz[(k-1)*3 + 0];
      p3[i*3 + 1] = xyz[(k-1)*3 + 1];
      p3[i*3 + 2] = xyz[(k-1)*3 + 2];
      Double_t p[3];
      view->WCtoNDC(&p3[i*3], p);
      pp[2*i + 0] = p[0];
      pp[2*i + 1] = p[1];
   }
 
   //          Find level lines
   FindLevelLines(np, p3, tt);
 
   //          Draw level lines
   Double_t p1[3], p2[3], x[2], y[2];
   SetLineStyle(3);
   if (icodes[2] == 0) {  // front & back boxes
      SetLineColor(1);
      SetLineWidth(1);
   } else {
      SetLineColor(fEdgeColor[fEdgeIdx]);
      SetLineWidth(fEdgeWidth[fEdgeIdx]);
   }
   TAttLine::Modify();
   for (Int_t il = 0; il < fNlines; ++il) {
      view->WCtoNDC(&fPlines[6*il + 0], p1);
      view->WCtoNDC(&fPlines[6*il + 3], p2);
      FindVisibleLine(p1, p2, 100, fNT, fT);
      Double_t xdel = p2[0] - p1[0];
      Double_t ydel = p2[1] - p1[1];
      for (Int_t it = 0; it < fNT; ++it) {
         x[0] = p1[0] + xdel*fT[2*it + 0];
         y[0] = p1[1] + ydel*fT[2*it + 0];
         x[1] = p1[0] + xdel*fT[2*it + 1];
         y[1] = p1[1] + ydel*fT[2*it + 1];
         gPad->PaintPolyLine(2, x, y);
      }
   }
 
   //          Draw face
   if (icodes[2] == 0) {  // front & back boxes
      SetLineColor(1);
      SetLineStyle(1);
      SetLineWidth(1);
   } else {
      SetLineColor(fEdgeColor[fEdgeIdx]);
      SetLineStyle(fEdgeStyle[fEdgeIdx]);
      SetLineWidth(fEdgeWidth[fEdgeIdx]);
   }
   TAttLine::Modify();
   for (Int_t i = 0; i < np; ++i) {
      if (iface[i] < 0) continue;
      Int_t i1 = i;
      Int_t i2 = (i == np-1) ? 0 : i + 1;
      FindVisibleLine(&pp[2*i1], &pp[2*i2], 100, fNT, fT);
      Double_t xdel = pp[2*i2 + 0] - pp[2*i1 + 0];
      Double_t ydel = pp[2*i2 + 1] - pp[2*i1 + 1];
      for (Int_t it = 0; it < fNT; ++it) {
         x[0] = pp[2*i1 + 0] + xdel*fT[2*it + 0];
         y[0] = pp[2*i1 + 1] + ydel*fT[2*it + 0];
         x[1] = pp[2*i1 + 0] + xdel*fT[2*it + 1];
         y[1] = pp[2*i1 + 1] + ydel*fT[2*it + 1];
         gPad->PaintPolyLine(2, x, y);
      }
   }
 
   //          Modify raster screen
   FillPolygonBorder(np, pp);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Draw face - 2nd variant for "RASTER SCREEN" algorithm (draw face for stacked lego plot)
///
/// \param[in] icodes   set of codes for the line (not used in this method)
/// \param[in] xyz   coordinates of nodes
/// \param[in] np   number of nodes
/// \param[in] iface   face
/// \param[in] tt   additional function defined on this face (not used in this method)
 
void TPainter3dAlgorithms::DrawFaceRaster2(Int_t *, Double_t *xyz, Int_t np, Int_t *iface, Double_t *)
{
   TView *view = gPad ? gPad->GetView() : nullptr;
   if (!view) return;
 
   //          Copy vertices to array
   Double_t x[2], y[2], pp[2*12];
   for (Int_t i = 0; i < np; ++i) {
      Int_t k = iface[i];
      if (k < 0) k = -k;
      Double_t p[3];
      view->WCtoNDC(&xyz[(k-1)*3], p);
      pp[2*i + 0] = p[0];
      pp[2*i + 1] = p[1];
   }
 
   //          Draw face
   SetLineColor(fEdgeColor[fEdgeIdx]);
   SetLineStyle(fEdgeStyle[fEdgeIdx]);
   SetLineWidth(fEdgeWidth[fEdgeIdx]);
   TAttLine::Modify();
   for (Int_t i = 0; i < np; ++i) {
      if (iface[i] < 0) continue;
      Int_t i1 = i;
      Int_t i2 = (i == np-1) ? 0 : i + 1;
      FindVisibleLine(&pp[2*i1], &pp[2*i2], 100, fNT, fT);
      Double_t xdel = pp[2*i2 + 0] - pp[2*i1 + 0];
      Double_t ydel = pp[2*i2 + 1] - pp[2*i1 + 1];
      for (Int_t it = 0; it < fNT; ++it) {
         x[0] = pp[2*i1 + 0] + xdel*fT[2*it + 0];
         y[0] = pp[2*i1 + 1] + ydel*fT[2*it + 0];
         x[1] = pp[2*i1 + 0] + xdel*fT[2*it + 1];
         y[1] = pp[2*i1 + 1] + ydel*fT[2*it + 1];
         gPad->PaintPolyLine(2, x, y);
      }
   }
 
   //          Modify raster screen
   FillPolygonBorder(np, pp);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Fill polygon with function values at vertexes
///
/// \param[in] n   number of vertexes
/// \param[in] p   polygon
/// \param[in] f   function values at nodes
///
/// Errors:
/// - illegal number of vertexes in polygon
/// - illegal call of FillPolygon: no levels
 
void TPainter3dAlgorithms::FillPolygon(Int_t n, Double_t *p, Double_t *f)
{
   Int_t ilev, i, k, icol, i1, i2, nl, np;
   Double_t fmin, fmax;
   Double_t x[12], y[12], f1, f2;
   Double_t p3[36]        /* was [3][12] */;
   Double_t funmin, funmax;
 
   /* Parameter adjustments */
   --f;
   p -= 4;
 
   if (n < 3) {
      Error("FillPolygon", "illegal number of vertices in polygon (%d)", n);
      return;
   }
 
   if (fNlevel == 0) {
      // Illegal call of FillPolygon: no levels
      return;
   }
   np = n;
   nl = fNlevel;
   if (nl < 0) nl = -nl;
   fmin = f[1];
   fmax = f[1];
   for (i = 2; i <= np; ++i) {
      if (fmin > f[i]) fmin = f[i];
      if (fmax < f[i]) fmax = f[i];
   }
   funmin = fFunLevel[0] - 1;
   if (fmin < funmin) funmin = fmin - 1;
   funmax = fFunLevel[nl - 1] + 1;
   if (fmax > funmax) funmax = fmax + 1;
 
   //          F I N D   A N D   D R A W   S U B P O L Y G O N S
   f2 = funmin;
   for (ilev = 1; ilev <= nl+1; ++ilev) {
   //         S E T   L E V E L   L I M I T S
      f1 = f2;
      if (ilev == nl + 1) f2 = funmax;
      else                f2 = fFunLevel[ilev - 1];
      if (fmax < f1)  return;
      if (fmin > f2)  continue;
   //         F I N D   S U B P O L Y G O N
      k = 0;
      for (i = 1; i <= np; ++i) {
         i1 = i;
         i2 = i + 1;
         if (i == np) i2 = 1;
         FindPartEdge(&p[i1*3 + 1], &p[i2*3 + 1], f[i1], f[i2], f1, f2, k, p3);
      }
   //         D R A W   S U B P O L Y G O N
      if (k < 3) continue;
      for (i = 1; i <= k; ++i) {
         x[i-1] = p3[i*3-3];
         y[i-1] = p3[i*3-2];
         if (TMath::IsNaN(x[i-1]) || TMath::IsNaN(y[i-1])) return;
      }
      if (ilev==1) {
         icol=gPad->GetFillColor();
      } else {
         icol = fColorLevel[ilev - 2];
      }
      SetFillColor(icol);
      SetFillStyle(1001);
      TAttFill::Modify();
      gPad->PaintFillArea(k, x, y);
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Fill a polygon including border ("RASTER SCREEN")
///
/// \param[in] nn   number of polygon nodes
/// \param[in] xy   polygon nodes
 
void TPainter3dAlgorithms::FillPolygonBorder(Int_t nn, Double_t *xy)
{
   Int_t kbit, nbit, step, ymin, ymax, test[kLmax], xcur[kLmax], xnex[kLmax],
      i, j, k, n, ibase, t, x, y, xscan[24]        /* was [2][kLmax] */,
      yscan, x1[kLmax+2], y1[kLmax+2], x2[kLmax+2], y2[kLmax+2],
      ib, nb, dx, dy, iw, nx, xx, yy, signdx, nstart, xx1, xx2, nxa, nxb;
 
   //          T R A N S F E R   T O   S C R E E N   C O O R D I N A T E S
   /* Parameter adjustments */
   xy -= 3;
 
   if (fIfrast) return;
 
   n = nn;
   x1[0] = 0;
   y1[0] = 0;
   for (i = 1; i <= n; ++i) {
      x1[i - 1] = Int_t(fNxrast*((xy[2*i + 1] - fXrast) /fDXrast) - 0.01);
      y1[i - 1] = Int_t(fNyrast*((xy[2*i + 2] - fYrast) /fDYrast) - 0.01);
   }
   x1[n] = x1[0];
   y1[n] = y1[0];
 
   //          F I N D   Y - M I N   A N D   Y - M A X
   //          S E T   R I G H T   E D G E   O R I E N T A T I O N
   ymin = y1[0];
   ymax = y1[0];
   for (i = 1; i <= n; ++i) {
      if (ymin > y1[i - 1])   ymin = y1[i - 1];
      if (ymax < y1[i - 1])   ymax = y1[i - 1];
      if (y1[i - 1] <= y1[i]) {x2[i - 1] = x1[i]; y2[i - 1] = y1[i];}
      else {
         x2[i - 1] = x1[i - 1];
         y2[i - 1] = y1[i - 1];
         x1[i - 1] = x1[i];
         y1[i - 1] = y1[i];
      }
   }
   if (ymin >= fNyrast) return;
   if (ymax < 0)        return;
   if (ymax >= fNyrast) ymax = fNyrast - 1;
 
   //          S O R T   L I N E S
   for (i = 1; i < n; ++i) {
      if (y1[i] >= y1[i - 1]) continue;
      y = y1[i];
      k = 1;
      for (j = i - 1; j >= 1; --j) {
         if (y < y1[j - 1]) continue;
         k = j + 1;
         break;
      }
      x = x1[i];
      xx = x2[i];
      yy = y2[i];
      for (j = i; j >= k; --j) {
         x1[j] = x1[j - 1];
         y1[j] = y1[j - 1];
         x2[j] = x2[j - 1];
         y2[j] = y2[j - 1];
      }
      x1[k - 1] = x;
      y1[k - 1] = y;
      x2[k - 1] = xx;
      y2[k - 1] = yy;
   }
 
   //          S E T   I N I T I A L   V A L U E S
   for (i = 1; i <= n; ++i) {
      xcur[i - 1] = x1[i - 1];
      dy = y2[i - 1] - y1[i - 1];
      dx = x2[i - 1] - x1[i - 1];
      signdx = 1;
      if (dx < 0)   signdx = -1;
      if (dx < 0)   dx = -dx;
      if (dx <= dy) {
         t = -(dy + 1) / 2 + dx;
         if (t < 0) {
            test[i - 1] = t;
            xnex[i - 1] = xcur[i - 1];
         } else {
            test[i - 1] = t - dy;
            xnex[i - 1] = xcur[i - 1] + signdx;
         }
      } else if (dy != 0) {
         step = (dx - 1) / (dy + dy) + 1;
         test[i - 1] = step*dy - (dx + 1) / 2 - dx;
         xnex[i - 1] = xcur[i - 1] + signdx*step;
      }
   }
 
   //          L O O P   O N   S C A N   L I N E S
   nstart = 1;
   for (yscan = ymin; yscan <= ymax; ++yscan) {
      nx  = 0;
      nxa = 0;
      nxb = kLmax + 1;
      for (i = nstart; i <= n; ++i) {
         if (y1[i - 1] > yscan) goto L500;
         if (y2[i - 1] <= yscan) {
            if (i == nstart)       ++nstart;
            if (y2[i - 1] != yscan)continue;
            --nxb;
            if (x2[i - 1] >= xcur[i - 1]) {
               xscan[2*nxb - 2] = xcur[i - 1];
               xscan[2*nxb - 1] = x2[i - 1];
            } else {
               xscan[2*nxb - 2] = x2[i - 1];
               xscan[2*nxb - 1] = xcur[i - 1];
            }
            continue;
         }
 
   //          S T O R E   C U R R E N T  X
   //          P R E P A R E   X   F O R   N E X T   S C A N - L I N E
         ++nxa;
         dy = y2[i - 1] - y1[i - 1];
         dx = x2[i - 1] - x1[i - 1];
         if (dx >= 0) {
            signdx = 1;
            xscan[2*nxa - 2] = xcur[i - 1];
            xscan[2*nxa - 1] = xnex[i - 1];
            if (xscan[2*nxa - 2] != xscan[2*nxa - 1]) {
               --xscan[2*nxa - 1];
            }
         } else {
            dx = -dx;
            signdx = -1;
            xscan[2*nxa - 2] = xnex[i - 1];
            xscan[2*nxa - 1] = xcur[i - 1];
            if (xscan[2*nxa - 2] != xscan[2*nxa - 1]) {
               ++xscan[2*nxa - 2];
            }
         }
         xcur[i - 1] = xnex[i - 1];
         if (dx <= dy) {
            test[i - 1] += dx;
            if (test[i - 1] < 0) continue;
            test[i - 1] -= dy;
            xnex[i - 1] += signdx;
            continue;
         }
         step = dx / dy;
         t = test[i - 1] + step*dy;
         if (t >= 0) {
            test[i - 1] = t - dx;
            xnex[i - 1] += signdx*step;
         } else {
            test[i - 1] = t + dy - dx;
            xnex[i - 1] += signdx*(step + 1);
         }
      }
 
   //          S O R T   P O I N T S   A L O N G   X
L500:
      if (yscan < 0) continue;
      ibase = yscan*fNxrast;
      if (nxa >= 2) {
         for (i = 1; i < nxa; ++i) {
            for (j = i; j >= 1; --j) {
               if (xscan[2*j] >= xscan[2*j - 2]) continue;
               x = xscan[2*j];
               xscan[2*j] = xscan[2*j - 2];
               xscan[2*j - 2] = x;
               x = xscan[2*j - 1];
               xscan[2*j + 1] = xscan[2*j - 1];
               xscan[2*j - 1] = x;
            }
         }
         for (i = 1; i <= nxa; i += 2) {
            ++nx;
            xscan[2*nx - 2] = xscan[2*i - 2];
            x = xscan[2*i + 1];
            if (xscan[2*i - 1] > x) x = xscan[2*i - 1];
            xscan[2*nx - 1] = x;
         }
      }
      if (nxb <= kLmax) {
         for (i = nxb; i <= kLmax; ++i) {
            ++nx;
            xscan[2*nx - 2] = xscan[2*i - 2];
            xscan[2*nx - 1] = xscan[2*i - 1];
         }
      }
   //          C O N C A T E N A T E   A N D   F I L L
      while (nx) {
         xx1 = xscan[2*nx - 2];
         xx2 = xscan[2*nx - 1];
         --nx;
         k = 1;
         while (k <= nx) {
            if ((xscan[2*k - 2] <= xx2 + 1) && (xscan[2*k - 1] >= xx1 - 1)) {
               if (xscan[2*k - 2] < xx1)     xx1 = xscan[2*k - 2];
               if (xscan[2*k - 1] > xx2)     xx2 = xscan[2*k - 1];
               xscan[2*k - 2] = xscan[2*nx - 2];
               xscan[2*k - 1] = xscan[2*nx - 1];
               --nx;
            } else  ++k;
         }
         if (xx1 < 0)        xx1 = 0;
         if (xx2 >= fNxrast) xx2 = fNxrast - 1;
         nbit = xx2 - xx1 + 1;
         kbit = ibase + xx1;
         iw = kbit / 30;
         ib = kbit - iw*30 + 1;
         iw = iw + 1;
         nb = 30 - ib + 1;
         if (nb > nbit) nb = nbit;
         fRaster[iw - 1] = fRaster[iw - 1] | fMask[fJmask[nb - 1] + ib - 1];
         nbit -= nb;
         if (nbit) {
            while(nbit > 30) {
               fRaster[iw] = fMask[464];
               ++iw;
               nbit += -30;
            }
            fRaster[iw] = fRaster[iw] | fMask[fJmask[nbit - 1]];
            ++iw;
         }
      }
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Find level lines for face
///
/// \param[in] np   number of nodes
/// \param[in] f   face
/// \param[in] t   additional function
///
///    Error: number of points for line not equal 2
 
void TPainter3dAlgorithms::FindLevelLines(Int_t np, Double_t *f, Double_t *t)
{
   fNlines = 0;
   if (fNlevel == 0) return;
   Int_t nl = TMath::Abs(fNlevel);
 
   // Find Tmin and Tmax
   Double_t tmin = t[0];
   Double_t tmax = t[0];
   for (Int_t i = 1; i < np; ++i) {
      if (t[i] < tmin) tmin = t[i];
      if (t[i] > tmax) tmax = t[i];
   }
   if (tmin >= fFunLevel[nl - 1]) return;
   if (tmax <= fFunLevel[0])      return;
 
   //          Find level lines
   for (Int_t il = 1; il <= nl; ++il) {
      if (tmin >= fFunLevel[il - 1]) continue;
      if (tmax <  fFunLevel[il - 1]) return;
      if (fNlines >= 200)            return;
      fNlines++;
      fLevelLine[fNlines - 1] = il;
      Int_t kp = 0;
      for (Int_t i = 0; i < np; ++i) {
         Int_t i1 = i;
         Int_t i2 = (i == np-1) ? 0 : i+1;
         Double_t d1 = t[i1] - fFunLevel[il - 1];
         Double_t d2 = t[i2] - fFunLevel[il - 1];
         if (d1 == 0) d1 = 1e-99;
         if (d2 == 0) d2 = 1e-99;
         if (d1*d2 > 0) continue;
 
         //          find point
         kp++;
         d1 /= t[i2] - t[i1];
         d2 /= t[i2] - t[i1];
         fPlines[(kp + 2*fNlines)*3 - 9] = d2*f[i1*3 + 0] - d1*f[i2*3 + 0];
         fPlines[(kp + 2*fNlines)*3 - 8] = d2*f[i1*3 + 1] - d1*f[i2*3 + 1];
         fPlines[(kp + 2*fNlines)*3 - 7] = d2*f[i1*3 + 2] - d1*f[i2*3 + 2];
         if (kp == 2) break;
      }
      if (kp != 2) {
         Error("FindLevelLines", "number of points for line not equal 2");
         fNlines--;
      }
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Find part of edge where function defined on this edge has value from
/// `fmin` to `fmax`
///
/// \param[in] p1   1st point
/// \param[in] p2   2nd point
/// \param[in] f1   function value at 1st point
/// \param[in] f2   function value at 2nd point
/// \param[in] fmin   min value of layer
/// \param[in] fmax   max value of layer
///
/// \param[out] kpp   current number of point
/// \param[out] pp   coordinates of new face
 
void TPainter3dAlgorithms::FindPartEdge(Double_t *p1, Double_t *p2, Double_t f1,
                                        Double_t f2, Double_t fmin,
                                        Double_t fmax, Int_t &kpp, Double_t *pp)
{
   Double_t d1, d2;
   Int_t k1, k2, kk;
 
   /* Parameter adjustments */
   pp -= 4;
   --p2;
   --p1;
 
   k1 = 0;
   if (f1 < fmin)  k1 = -2;
   if (f1 == fmin) k1 = -1;
   if (f1 == fmax) k1 = 1;
   if (f1 > fmax)  k1 = 2;
   k2 = 0;
   if (f2 < fmin)  k2 = -2;
   if (f2 == fmin) k2 = -1;
   if (f2 == fmax) k2 = 1;
   if (f2 > fmax)  k2 = 2;
   kk = (k1 + 2)*5 + (k2 + 2) + 1;
 
   //    K2:    -2  -1   0  +1  +2
   //    K1:    -2 -1 0 +1 +2
   switch ((int)kk) {
      case 1:  return;
      case 2:  return;
      case 3:  goto L200;
      case 4:  goto L200;
      case 5:  goto L600;
      case 6:  goto L100;
      case 7:  goto L100;
      case 8:  goto L100;
      case 9:  goto L100;
      case 10:  goto L500;
      case 11:  goto L400;
      case 12:  goto L100;
      case 13:  goto L100;
      case 14:  goto L100;
      case 15:  goto L500;
      case 16:  goto L400;
      case 17:  goto L100;
      case 18:  goto L100;
      case 19:  goto L100;
      case 20:  goto L100;
      case 21:  goto L700;
      case 22:  goto L300;
      case 23:  goto L300;
      case 24:  return;
      case 25:  return;
   }
 
   //          1 - S T   P O I N T
L100:
   ++kpp;
   pp[kpp*3 + 1] = p1[1];
   pp[kpp*3 + 2] = p1[2];
   pp[kpp*3 + 3] = p1[3];
   return;
 
   //           I N T E R S E C T I O N   W I T H   Fmin
L200:
   ++kpp;
   d1 = (fmin - f1) / (f1 - f2);
   d2 = (fmin - f2) / (f1 - f2);
   pp[kpp*3 + 1] = d2*p1[1] - d1*p2[1];
   pp[kpp*3 + 2] = d2*p1[2] - d1*p2[2];
   pp[kpp*3 + 3] = d2*p1[3] - d1*p2[3];
   return;
 
   //           I N T E R S E C T I O N   W I T H   Fmax
L300:
   ++kpp;
   d1 = (fmax - f1) / (f1 - f2);
   d2 = (fmax - f2) / (f1 - f2);
   pp[kpp*3 + 1] = d2*p1[1] - d1*p2[1];
   pp[kpp*3 + 2] = d2*p1[2] - d1*p2[2];
   pp[kpp*3 + 3] = d2*p1[3] - d1*p2[3];
   return;
 
   //          1 - S T   P O I N T,   I N T E R S E C T I O N  WITH  Fmin
L400:
   ++kpp;
   pp[kpp*3 + 1] = p1[1];
   pp[kpp*3 + 2] = p1[2];
   pp[kpp*3 + 3] = p1[3];
   ++kpp;
   d1 = (fmin - f1) / (f1 - f2);
   d2 = (fmin - f2) / (f1 - f2);
   pp[kpp*3 + 1] = d2*p1[1] - d1*p2[1];
   pp[kpp*3 + 2] = d2*p1[2] - d1*p2[2];
   pp[kpp*3 + 3] = d2*p1[3] - d1*p2[3];
   return;
 
   //          1 - S T   P O I N T,   I N T E R S E C T I O N  WITH  Fmax
L500:
   ++kpp;
   pp[kpp*3 + 1] = p1[1];
   pp[kpp*3 + 2] = p1[2];
   pp[kpp*3 + 3] = p1[3];
   ++kpp;
   d1 = (fmax - f1) / (f1 - f2);
   d2 = (fmax - f2) / (f1 - f2);
   pp[kpp*3 + 1] = d2*p1[1] - d1*p2[1];
   pp[kpp*3 + 2] = d2*p1[2] - d1*p2[2];
   pp[kpp*3 + 3] = d2*p1[3] - d1*p2[3];
   return;
 
   //           I N T E R S E C T I O N   W I T H   Fmin, Fmax
L600:
   ++kpp;
   d1 = (fmin - f1) / (f1 - f2);
   d2 = (fmin - f2) / (f1 - f2);
   pp[kpp*3 + 1] = d2*p1[1] - d1*p2[1];
   pp[kpp*3 + 2] = d2*p1[2] - d1*p2[2];
   pp[kpp*3 + 3] = d2*p1[3] - d1*p2[3];
   ++kpp;
   d1 = (fmax - f1) / (f1 - f2);
   d2 = (fmax - f2) / (f1 - f2);
   pp[kpp*3 + 1] = d2*p1[1] - d1*p2[1];
   pp[kpp*3 + 2] = d2*p1[2] - d1*p2[2];
   pp[kpp*3 + 3] = d2*p1[3] - d1*p2[3];
   return;
 
   //          I N T E R S E C T I O N   W I T H   Fmax, Fmin
L700:
   ++kpp;
   d1 = (fmax - f1) / (f1 - f2);
   d2 = (fmax - f2) / (f1 - f2);
   pp[kpp*3 + 1] = d2*p1[1] - d1*p2[1];
   pp[kpp*3 + 2] = d2*p1[2] - d1*p2[2];
   pp[kpp*3 + 3] = d2*p1[3] - d1*p2[3];
   ++kpp;
   d1 = (fmin - f1) / (f1 - f2);
   d2 = (fmin - f2) / (f1 - f2);
   pp[kpp*3 + 1] = d2*p1[1] - d1*p2[1];
   pp[kpp*3 + 2] = d2*p1[2] - d1*p2[2];
   pp[kpp*3 + 3] = d2*p1[3] - d1*p2[3];
}
 
////////////////////////////////////////////////////////////////////////////////
/// Find visible parts of line (draw line)
///
/// \param[in] r1   1-st point of the line
/// \param[in] r2   2-nd point of the line
 
void TPainter3dAlgorithms::FindVisibleDraw(Double_t *r1, Double_t *r2)
{
   Double_t yy1u, yy2u;
   Int_t i, icase, i1, i2, icase1, icase2, iv, ifback;
   Double_t x1, x2, y1, y2, z1, z2, dd, di;
   Double_t dt, dy;
   Double_t tt, uu, ww, yy, yy1, yy2, yy1d, yy2d;
   Double_t *tn = 0;
   const Double_t kEpsil = 1.e-6;
   /* Parameter adjustments */
   --r2;
   --r1;
   TView *view = gPad ? gPad->GetView() : nullptr;
 
   if (view) {
      tn = view->GetTN();
      if (tn) {
         x1 = tn[0]*r1[1] + tn[1]*r1[2] + tn[2]*r1[3]  + tn[3];
         x2 = tn[0]*r2[1] + tn[1]*r2[2] + tn[2]*r2[3]  + tn[3];
         y1 = tn[4]*r1[1] + tn[5]*r1[2] + tn[6]*r1[3]  + tn[7];
         y2 = tn[4]*r2[1] + tn[5]*r2[2] + tn[6]*r2[3]  + tn[7];
         z1 = tn[8]*r1[1] + tn[9]*r1[2] + tn[10]*r1[3] + tn[11];
         z2 = tn[8]*r2[1] + tn[9]*r2[2] + tn[10]*r2[3] + tn[11];
      } else {
         Error("FindVisibleDraw", "invalid TView in current pad");
         return;
      }
   } else {
      Error("FindVisibleDraw", "no TView in current pad");
      return;
   }
 
   ifback = 0;
   if (x1 >= x2) {
      ifback = 1;
      ww = x1;
      x1 = x2;
      x2 = ww;
      ww = y1;
      y1 = y2;
      y2 = ww;
      ww = z1;
      z1 = z2;
      z2 = ww;
   }
   fNT = 0;
   i1 = Int_t((x1 - fX0) / fDX) + 15;
   i2 = Int_t((x2 - fX0) / fDX) + 15;
   x1 = fX0 + (i1 - 1)*fDX;
   x2 = fX0 + (i2 - 1)*fDX;
   if (i1 != i2) {
 
   //          F I N D   V I S I B L E   P A R T S   O F   T H E   L I N E
      di = (Double_t) (i2 - i1);
      dy = (y2 - y1) / di;
      dt = 1 / di;
      iv = -1;
      for (i = i1; i <= i2 - 1; ++i) {
         yy1 = y1 + dy*(i - i1);
         yy2 = yy1 + dy;
         yy1u = yy1 - fU[2*i - 2];
         yy1d = yy1 - fD[2*i - 2];
         yy2u = yy2 - fU[2*i - 1];
         yy2d = yy2 - fD[2*i - 1];
         tt = dt*(i - i1);
   //         A N A L I Z E   L E F T   S I D E
         icase1 = 1;
         if (yy1u >  kEpsil) icase1 = 0;
         if (yy1d < -kEpsil) icase1 = 2;
         if ((icase1 == 0 || icase1 == 2) && iv <= 0) {
            iv = 1;
            ++fNT;
            fT[2*fNT - 2] = tt;
         }
         if (icase1 == 1 && iv >= 0) {
            iv = -1;
            fT[2*fNT - 1] = tt;
         }
   //         A N A L I Z E   R I G H T   S I D E
         icase2 = 1;
         if (yy2u >  kEpsil) icase2 = 0;
         if (yy2d < -kEpsil) icase2 = 2;
         icase = icase1*3 + icase2;
         if (icase == 1) {
            iv = -1;
            fT[2*fNT - 1] = tt + dt*(yy1u / (yy1u - yy2u));
         }
         if (icase == 2) {
            fT[2*fNT - 1] = tt + dt*(yy1u / (yy1u - yy2u));
            ++fNT;
            fT[2*fNT - 2] = tt + dt*(yy1d / (yy1d - yy2d));
         }
         if (icase == 3) {
            iv = 1;
            ++fNT;
            fT[2*fNT - 2] = tt + dt*(yy1u / (yy1u - yy2u));
         }
         if (icase == 5) {
            iv = 1;
            ++fNT;
            fT[2*fNT - 2] = tt + dt*(yy1d / (yy1d - yy2d));
         }
         if (icase == 6) {
            fT[2*fNT - 1] = tt + dt*(yy1d / (yy1d - yy2d));
            ++fNT;
            fT[2*fNT - 2] = tt + dt*(yy1u / (yy1u - yy2u));
         }
         if (icase == 7) {
            iv = -1;
            fT[2*fNT - 1] = tt + dt*(yy1d / (yy1d - yy2d));
         }
         if (fNT + 1 >= 100) break;
      }
      if (iv > 0) fT[2*fNT - 1] = 1;
   } else {
 
   //          V E R T I C A L   L I N E
      fNT = 1;
      fT[0] = 0;
      fT[1] = 1;
      if (y2 <= y1) {
         if (y2 == y1) { fNT = 0; return;}
         ifback = 1 - ifback;
         yy = y1;
         y1 = y2;
         y2 = yy;
      }
      uu = fU[2*i1 - 2];
      dd = fD[2*i1 - 2];
      if (i1 != 1) {
         if (uu < fU[2*i1 - 3]) uu = fU[2*i1 - 3];
         if (dd > fD[2*i1 - 3]) dd = fD[2*i1 - 3];
      }
   //         F I N D   V I S I B L E   P A R T   O F   L I N E
      if (y1 <  uu && y2 >  dd) {
         if (y1 >= dd && y2 <= uu) {fNT = 0; return;}
         fNT = 0;
         if (dd > y1) {
            ++fNT;
            fT[2*fNT - 2] = 0;
            fT[2*fNT - 1] = (dd - y1) / (y2 - y1);
         }
         if (uu < y2) {
            ++fNT;
            fT[2*fNT - 2] = (uu - y1) / (y2 - y1);
            fT[2*fNT - 1] = 1;
         }
      }
   }
 
   if (ifback == 0) return;
   if (fNT == 0)    return;
   for (i = 1; i <= fNT; ++i) {
      fT[2*i - 2] = 1 - fT[2*i - 2];
      fT[2*i - 1] = 1 - fT[2*i - 1];
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Find visible part of a line ("RASTER SCREEN")
///
/// \param[in] p1   1st point of the line
/// \param[in] p2   2nd point of the line
/// \param[in] ntmax   max allowed number of visible segments
///
/// \param[out] nt   number of visible segments of the line
/// \param[out] t   visible segments
 
void TPainter3dAlgorithms::FindVisibleLine(Double_t *p1, Double_t *p2, Int_t ntmax, Int_t &nt, Double_t *t)
{
   Double_t ddtt;
   Double_t tcur;
   Int_t i, incrx, ivis, x1, y1, x2, y2, ib, kb, dx, dy, iw, ix, iy, ifinve, dx2, dy2;
   Double_t t1, t2;
   Double_t dt;
   Double_t tt;
   /* Parameter adjustments */
   t -= 3;
   --p2;
   --p1;
 
   if (fIfrast) {
      nt = 1;
      t[3] = 0;
      t[4] = 1;
      return;
   }
   x1 = Int_t(fNxrast*((p1[1] - fXrast) / fDXrast) - 0.01);
   y1 = Int_t(fNyrast*((p1[2] - fYrast) / fDYrast) - 0.01);
   x2 = Int_t(fNxrast*((p2[1] - fXrast) / fDXrast) - 0.01);
   y2 = Int_t(fNyrast*((p2[2] - fYrast) / fDYrast) - 0.01);
   ifinve = 0;
   if (y1 > y2) {
      ifinve = 1;
      iw = x1;
      x1 = x2;
      x2 = iw;
      iw = y1;
      y1 = y2;
      y2 = iw;
   }
   nt   = 0;
   ivis = 0;
   if (y1 >= fNyrast) return;
   if (y2 < 0)        return;
   if (x1 >= fNxrast && x2 >= fNxrast) return;
   if (x1 < 0 && x2 < 0)               return;
 
   //          S E T   I N I T I A L   V A L U E S
   incrx = 1;
   dx = x2 - x1;
   if (dx < 0) {
      dx = -dx;
      incrx = -1;
   }
   dy  = y2 - y1;
   dx2 = dx + dx;
   dy2 = dy + dy;
   if (dy > dx) goto L200;
 
   //          D X   . G T .   D Y
   dt = 1./ (Double_t)(dx + 1.);
   ddtt = dt*(float).5;
   tcur = -(Double_t)dt;
   tt = (Double_t) (-(dx + dy2));
   iy = y1;
   kb = iy*fNxrast + x1 - incrx;
   for (ix = x1; incrx < 0 ? ix >= x2 : ix <= x2; ix += incrx) {
      kb += incrx;
      tcur += dt;
      tt += dy2;
      if (tt >= 0) {
         ++iy;
         tt -= dx2;
         kb += fNxrast;
      }
      if (iy < 0)        goto L110;
      if (iy >= fNyrast) goto L110;
      if (ix < 0)        goto L110;
      if (ix >= fNxrast) goto L110;
      iw = kb / 30;
      ib = kb - iw*30 + 1;
      if (fRaster[iw] & fMask[ib - 1]) goto L110;
      if (ivis > 0)      continue;
      ivis = 1;
      ++nt;
      t[2*nt + 1] = tcur;
      continue;
L110:
      if (ivis == 0) continue;
      ivis = 0;
      t[2*nt + 2] = tcur;
      if (nt == ntmax)  goto L300;
   }
   if (ivis > 0) t[2*nt + 2] = tcur + dt + ddtt;
   goto L300;
 
   //          D Y   . G T .   D X
L200:
   dt = 1. / (Double_t)(dy + 1.);
   ddtt = dt*(float).5;
   tcur = -(Double_t)dt;
   tt = (Double_t) (-(dy + dx2));
   ix = x1;
   if (y2 >= fNyrast) y2 = fNyrast - 1;
   kb = (y1 - 1)*fNxrast + ix;
   for (iy = y1; iy <= y2; ++iy) {
      kb += fNxrast;
      tcur += dt;
      tt += dx2;
      if (tt >= 0) {
         ix += incrx;
         tt -= dy2;
         kb += incrx;
      }
      if (iy < 0)        goto L210;
      if (ix < 0)        goto L210;
      if (ix >= fNxrast) goto L210;
      iw = kb / 30;
      ib = kb - iw*30 + 1;
      if (fRaster[iw] & fMask[ib - 1]) goto L210;
      if (ivis > 0) continue;
      ivis = 1;
      ++nt;
      t[2*nt + 1] = tcur;
      continue;
L210:
      if (ivis == 0) continue;
      ivis = 0;
      t[2*nt + 2] = tcur;
      if (nt == ntmax) goto L300;
   }
   if (ivis > 0) t[2*nt + 2] = tcur + dt;
 
   //          C H E C K   D I R E C T I O N   O F   P A R A M E T E R
L300:
   if (nt == 0) return;
   dt *= 1.1;
   if (t[3] <= dt) t[3] = 0;
   if (t[2*nt + 2] >= 1 - dt) t[2*nt + 2] = 1;
   if (ifinve == 0) return;
   for (i = 1; i <= nt; ++i) {
      t1 = t[2*i + 1];
      t2 = t[2*i + 2];
      t[2*i + 1] = 1 - t2;
      t[2*i + 2] = 1 - t1;
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Find part of surface with luminosity in the corners. This method is used for
/// Gouraud shading
 
void TPainter3dAlgorithms::GouraudFunction(Int_t ia, Int_t ib, Double_t *face, Double_t *t)
{
   Int_t iphi;
   static Double_t f[108];        /* was [3][4][3][3] */
   Int_t i, j, k;
   Double_t r, s, x[36];        /* was [4][3][3] */
   Double_t y[36];        /* was [4][3][3] */
   Double_t z[36];        /* was [4][3][3] */
   Int_t incrx[3], incry[3];
 
   Double_t x1, x2, y1, y2, z1, z2, th, an[27];        /* was [3][3][3] */
   Double_t bn[12];    /* was [3][2][2] */
 
   Double_t rad;
   Double_t phi;
   Int_t ixt, iyt;
 
    /* Parameter adjustments */
   --t;
   face -= 4;
 
   iphi = 1;
   rad = TMath::ATan(1) * (float)4 / (float)180;
 
   //        Find real cell indexes
   ixt = ia + Hparam.xfirst - 1;
   iyt = ib + Hparam.yfirst - 1;
 
   //        Find increments of neighboring cells
   incrx[0] = -1;
   incrx[1] = 0;
   incrx[2] = 1;
   if (ixt == 1) incrx[0] = 0;
   if (ixt == Hparam.xlast - 1) incrx[2] = 0;
   incry[0] = -1;
   incry[1] = 0;
   incry[2] = 1;
   if (iyt == 1) incry[0] = 0;
   if (iyt == Hparam.ylast - 1) incry[2] = 0;
 
   //        Find neighboring faces
   Int_t i1, i2;
   for (j = 1; j <= 3; ++j) {
      for (i = 1; i <= 3; ++i) {
         i1 = ia + incrx[i - 1];
         i2 = ib + incry[j - 1];
         SurfaceFunction(i1, i2, &f[(((i + j*3) << 2) + 1)*3 - 51], &t[1]);
      }
   }
 
   //       Set face
   for (k = 1; k <= 4; ++k) {
      for (i = 1; i <= 3; ++i) {
         face[i + k*3] = f[i + (k + 32)*3 - 52];
      }
   }
 
   //       Find coordinates and normales
   for (j = 1; j <= 3; ++j) {
      for (i = 1; i <= 3; ++i) {
         for (k = 1; k <= 4; ++k) {
            if (Hoption.System == kPOLAR) {
               phi = f[iphi + (k + ((i + j*3) << 2))*3 - 52]*rad;
               r = f[3 - iphi + (k + ((i + j*3) << 2))*3 - 52];
               x[k + ((i + j*3) << 2) - 17] = r * TMath::Cos(phi);
               y[k + ((i + j*3) << 2) - 17] = r * TMath::Sin(phi);
               z[k + ((i + j*3) << 2) - 17] = f[(k + ((i + j*3) << 2))*3 - 49];
            } else if (Hoption.System == kCYLINDRICAL) {
               phi = f[iphi + (k + ((i + j*3) << 2))*3 - 52]*rad;
               r = f[(k + ((i + j*3) << 2))*3 - 49];
               x[k + ((i + j*3) << 2) - 17] = r*TMath::Cos(phi);
               y[k + ((i + j*3) << 2) - 17] = r*TMath::Sin(phi);
               z[k + ((i + j*3) << 2) - 17] = f[3 - iphi + (k + ((i + j*3) << 2))*3 - 52];
            } else if (Hoption.System == kSPHERICAL) {
               phi = f[iphi + (k + ((i + j*3) << 2))*3 - 52]*rad;
               th = f[3 - iphi + (k + ((i + j*3) << 2))*3 - 52]*rad;
               r = f[(k + ((i + j*3) << 2))*3 - 49];
               x[k + ((i + j*3) << 2) - 17] = r*TMath::Sin(th)*TMath::Cos(phi);
               y[k + ((i + j*3) << 2) - 17] = r*TMath::Sin(th)*TMath::Sin(phi);
               z[k + ((i + j*3) << 2) - 17] = r*TMath::Cos(th);
            } else if (Hoption.System == kRAPIDITY) {
               phi = f[iphi + (k + ((i + j*3) << 2))*3 - 52]*rad;
               th = f[3 - iphi + (k + ((i + j*3) << 2))*3 - 52]*rad;
               r = f[(k + ((i + j*3) << 2))*3 - 49];
               x[k + ((i + j*3) << 2) - 17] = r*TMath::Cos(phi);
               y[k + ((i + j*3) << 2) - 17] = r*TMath::Sin(phi);
               z[k + ((i + j*3) << 2) - 17] = r*TMath::Cos(th) / TMath::Sin(th);
            } else {
               x[k + ((i + j*3) << 2) - 17] = f[(k + ((i + j*3) << 2))*3 - 51];
               y[k + ((i + j*3) << 2) - 17] = f[(k + ((i + j*3) << 2))*3 - 50];
               z[k + ((i + j*3) << 2) - 17] = f[(k + ((i + j*3) << 2))*3 - 49];
            }
         }
         x1 = x[((i + j*3) << 2) - 14] - x[((i + j*3) << 2) - 16];
         x2 = x[((i + j*3) << 2) - 13] - x[((i + j*3) << 2) - 15];
         y1 = y[((i + j*3) << 2) - 14] - y[((i + j*3) << 2) - 16];
         y2 = y[((i + j*3) << 2) - 13] - y[((i + j*3) << 2) - 15];
         z1 = z[((i + j*3) << 2) - 14] - z[((i + j*3) << 2) - 16];
         z2 = z[((i + j*3) << 2) - 13] - z[((i + j*3) << 2) - 15];
         an[(i + j*3)*3 - 12] = y1*z2 - y2*z1;
         an[(i + j*3)*3 - 11] = z1*x2 - z2*x1;
         an[(i + j*3)*3 - 10] = x1*y2 - x2*y1;
         s = TMath::Sqrt(an[(i + j*3)*3 - 12]*an[(i + j*3)*3 - 12] + an[
                        (i + j*3)*3 - 11]*an[(i + j*3)*3 - 11] + an[(i
                        + j*3)*3 - 10]*an[(i + j*3)*3 - 10]);
 
         an[(i + j*3)*3 - 12] /= s;
         an[(i + j*3)*3 - 11] /= s;
         an[(i + j*3)*3 - 10] /= s;
      }
   }
 
   //         Find average normals
   for (j = 1; j <= 2; ++j) {
      for (i = 1; i <= 2; ++i) {
         for (k = 1; k <= 3; ++k) {
            bn[k + (i + 2*j)*3 - 10] = an[k + (i + j*3)*3 - 13]
              + an[k + (i + 1 + j*3)*3 - 13] + an[k + (i + 1 +
                          (j + 1)*3)*3 - 13] + an[k + (i + (j + 1)*3)*3 - 13];
         }
      }
   }
 
   TView *view = gPad ? gPad->GetView() : nullptr;
 
   //        Set luminosity
   Luminosity(view, bn,     t[1]);
   Luminosity(view, &bn[3], t[2]);
   Luminosity(view, &bn[9], t[3]);
   Luminosity(view, &bn[6], t[4]);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Initialize "MOVING SCREEN" method
///
/// \param[in] xmin   left boundary
/// \param[in] xmax   right boundary
 
void TPainter3dAlgorithms::InitMoveScreen(Double_t xmin, Double_t xmax)
{
   const Double_t VERY_BIG = 9e+99;
   fX0 = xmin;
   fDX = (xmax - xmin) / NumOfSlices;
   for (Int_t i = 0; i < NumOfSlices; ++i) {
      fU[2*i + 0] = -VERY_BIG;
      fU[2*i + 1] = -VERY_BIG;
      fD[2*i + 0] =  VERY_BIG;
      fD[2*i + 1] =  VERY_BIG;
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Initialize hidden lines removal algorithm (RASTER SCREEN)
///
/// \param[in] xmin   Xmin in the normalized coordinate system
/// \param[in] ymin   Ymin in the normalized coordinate system
/// \param[in] xmax   Xmax in the normalized coordinate system
/// \param[in] ymax   Ymax in the normalized coordinate system
/// \param[in] nx   number of pixels along X
/// \param[in] ny   number of pixels along Y
 
void TPainter3dAlgorithms::InitRaster(Double_t xmin, Double_t ymin, Double_t xmax, Double_t ymax, Int_t nx, Int_t ny  )
{
   Int_t i, j, k, ib, nb;
 
   fNxrast = nx;
   fNyrast = ny;
   fXrast  = xmin;
   fDXrast = xmax - xmin;
   fYrast  = ymin;
   fDYrast = ymax - ymin;
 
   //  Create buffer for raster
   Int_t buffersize = nx*ny/30 + 1;
   fRaster.resize(buffersize);
 
   //          S E T   M A S K S
   k = 0;
   Int_t pow2 = 1;
   for (i = 1; i <= 30; ++i) {
      fJmask[i - 1] = k;
      k = k + 30 - i + 1;
      fMask[i - 1] = pow2;
      pow2 *= 2;
   }
   j = 30;
   for (nb = 2; nb <= 30; ++nb) {
      for (ib = 1; ib <= 30 - nb + 1; ++ib) {
         k = 0;
         for (i = ib; i <= ib + nb - 1; ++i) k = k | fMask[i - 1];
         ++j;
         fMask[j - 1] = k;
      }
   }
 
   //          C L E A R   R A S T E R   S C R E E N
   ClearRaster();
}
 
////////////////////////////////////////////////////////////////////////////////
/// Service function for Legos
 
void TPainter3dAlgorithms::LegoFunction(Int_t ia, Int_t ib, Int_t &nv, Double_t *ab, Double_t *vv, Double_t *t)
{
   Int_t i, j, ixt, iyt;
   Double_t yval1l,  yval2l;
   Double_t xlab1l, xlab2l, ylab1l, ylab2l;
   Double_t rinrad = gStyle->GetLegoInnerR();
   Double_t dangle = 10; //Delta angle for Rapidity option
 
   /* Parameter adjustments */
   t -= 5;
   --vv;
   ab -= 3;
 
   ixt = ia + Hparam.xfirst - 1;
   iyt = ib + Hparam.yfirst - 1;
 
   //             Compute the cell position in cartesian coordinates
   //             and compute the LOG if necessary
   Double_t xwid = gCurrentHist->GetXaxis()->GetBinWidth(ixt);
   Double_t ywid = gCurrentHist->GetYaxis()->GetBinWidth(iyt);
   ab[3] = gCurrentHist->GetXaxis()->GetBinLowEdge(ixt) + xwid*Hparam.baroffset;
   ab[4] = gCurrentHist->GetYaxis()->GetBinLowEdge(iyt) + ywid*Hparam.baroffset;
   ab[5] = ab[3] + xwid*Hparam.barwidth;
   ab[8] = ab[4] + ywid*Hparam.barwidth;
 
   if (Hoption.Logx) {
      if (ab[3] > 0) ab[3]  = TMath::Log10(ab[3]);
      else           ab[3]  = Hparam.xmin;
      if (ab[5] > 0) ab[5]  = TMath::Log10(ab[5]);
      else           ab[5]  = Hparam.xmin;
   }
   // xval1l = Hparam.xmin;
   // xval2l = Hparam.xmax;
   if (Hoption.Logy) {
      if (ab[4] > 0) ab[4]  = TMath::Log10(ab[4]);
      else           ab[4]  = Hparam.ymin;
      if (ab[8] > 0) ab[8]  = TMath::Log10(ab[8]);
      else           ab[8]  = Hparam.ymin;
   }
   yval1l = Hparam.ymin;
   yval2l = Hparam.ymax;
 
   if (ab[3] < Hparam.xmin) ab[3] = Hparam.xmin;
   if (ab[4] < Hparam.ymin) ab[4] = Hparam.ymin;
   if (ab[5] > Hparam.xmax) ab[5] = Hparam.xmax;
   if (ab[8] > Hparam.ymax) ab[8] = Hparam.ymax;
   if (ab[5] < Hparam.xmin) ab[5] = Hparam.xmin;
   if (ab[8] < Hparam.ymin) ab[8] = Hparam.ymin;
 
   xlab1l = gCurrentHist->GetXaxis()->GetXmin();
   xlab2l = gCurrentHist->GetXaxis()->GetXmax();
   if (Hoption.Logx) {
      if (xlab2l>0) {
         if (xlab1l>0) xlab1l = TMath::Log10(xlab1l);
         else          xlab1l = TMath::Log10(0.001*xlab2l);
         xlab2l = TMath::Log10(xlab2l);
      }
   }
   ylab1l = gCurrentHist->GetYaxis()->GetXmin();
   ylab2l = gCurrentHist->GetYaxis()->GetXmax();
   if (Hoption.Logy) {
      if (ylab2l>0) {
         if (ylab1l>0) ylab1l = TMath::Log10(ylab1l);
         else          ylab1l = TMath::Log10(0.001*ylab2l);
         ylab2l = TMath::Log10(ylab2l);
      }
   }
 
   //       Transform the cell position in the required coordinate system
   if (Hoption.System == kPOLAR) {
      ab[3] = 360*(ab[3] - xlab1l) / (xlab2l - xlab1l);
      ab[5] = 360*(ab[5] - xlab1l) / (xlab2l - xlab1l);
      ab[4] = (ab[4] - yval1l) / (yval2l - yval1l);
      ab[8] = (ab[8] - yval1l) / (yval2l - yval1l);
   } else if (Hoption.System == kCYLINDRICAL) {
      ab[3] = 360*(ab[3] - xlab1l) / (xlab2l - xlab1l);
      ab[5] = 360*(ab[5] - xlab1l) / (xlab2l - xlab1l);
   } else if (Hoption.System == kSPHERICAL) {
      ab[3] = 360*(ab[3] - xlab1l) / (xlab2l - xlab1l);
      ab[5] = 360*(ab[5] - xlab1l) / (xlab2l - xlab1l);
      ab[4] = 180*(ab[4] - ylab1l) / (ylab2l - ylab1l);
      ab[8] = 180*(ab[8] - ylab1l) / (ylab2l - ylab1l);
   } else if (Hoption.System == kRAPIDITY) {
      ab[3] = 360*(ab[3] - xlab1l) / (xlab2l - xlab1l);
      ab[5] = 360*(ab[5] - xlab1l) / (xlab2l - xlab1l);
      ab[4] = (180 - dangle*2)*(ab[4] - ylab1l) / (ylab2l - ylab1l) + dangle;
      ab[8] = (180 - dangle*2)*(ab[8] - ylab1l) / (ylab2l - ylab1l) + dangle;
   }
 
   //             Complete the cell coordinates
   ab[6]  = ab[4];
   ab[7]  = ab[5];
   ab[9]  = ab[3];
   ab[10] = ab[8];
 
   //              Get the content of the table, and loop on the
   //              stack if necessary.
   vv[1] = Hparam.zmin;
   vv[2] = Hparam.factor*gCurrentHist->GetBinContent(ixt, iyt);
 
   // In linear scale, 3D boxes all start from 0.
   if (Hparam.zmin<0 && !Hoption.Logz && Hoption.MinimumZero) {
      if (vv[2]<0) {
         vv[1] = vv[2];
         vv[2] = 0;
      } else {
         vv[1] = 0;
      }
   }
 
   TList *stack = gCurrentHist->GetPainter()->GetStack();
   Int_t nids = 0; //not yet implemented
   if (stack) nids = stack->GetSize();
   if (nids) {
      for (i = 2; i <= nids + 1; ++i) {
         TH1 *hid = (TH1*)stack->At(i-2);
         vv[i + 1] = Hparam.factor*hid->GetBinContent(ixt, iyt) + vv[i];
         vv[i + 1] = TMath::Max(Hparam.zmin, vv[i + 1]);
         //vv[i + 1] = TMath::Min(Hparam.zmax, vv[i + 1]);
      }
   }
 
   nv = nids + 2;
   for (i = 2; i <= nv; ++i) {
      if (Hoption.Logz) {
         if (vv[i] > 0)
            vv[i] = TMath::Max(Hparam.zmin, (Double_t)TMath::Log10(vv[i]));
         else
            vv[i] = Hparam.zmin;
         vv[i] = TMath::Min(vv[i], Hparam.zmax);
      } else {
            vv[i] = TMath::Max(Hparam.zmin, vv[i]);
            vv[i] = TMath::Min(Hparam.zmax, vv[i]);
      }
   }
 
   if (!Hoption.Logz) {
      i = 3;
      while (i <= nv) {
         if (vv[i] < vv[i - 1]) {
            vv[i - 1] = vv[i];
            i = 3;
            continue;
         }
         ++i;
      }
   }
 
   //          For cylindrical, spherical and pseudo-rapidity, the content
   //          is mapped onto the radius
   if (Hoption.System == kCYLINDRICAL || Hoption.System == kSPHERICAL || Hoption.System == kRAPIDITY) {
      for (i = 1; i <= nv; ++i) {
         vv[i] = (1 - rinrad)*((vv[i] - Hparam.zmin) /
                 (Hparam.zmax - Hparam.zmin)) + rinrad;
      }
   }
 
   for (i = 1; i <= nv; ++i) {
      for (j = 1; j <= 4; ++j) t[j + (i << 2)] = vv[i];
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Draw stack of lego-plots in cartesian coordinates
///
/// \param[in] ang   angle between X ang Y (not used in this method)
/// \param[in] nx   number of cells along X
/// \param[in] ny   number of cells along Y
/// \param[in] chopt specific options
///
/// - `chopt` = 'BF' from BACK to FRONT
/// - `chopt` = 'FB' from FRONT to BACK
 
void TPainter3dAlgorithms::LegoCartesian(Double_t, Int_t nx, Int_t ny, const char *chopt)
{
   Int_t icodes[4], iface[4];
   Double_t xy[4*2], xyz[8*3], tface[4];
   Int_t firstStackNumberDrawn=-1 ;  // necessary to compute fColorBottom when the 0 option is set and when the stack is seen from below (bottomview, theta<0.)
 
   TView *view = gPad ? gPad->GetView() : nullptr;
   if (!view) {
      Error("LegoCartesian", "no TView in current pad");
      return;
   }
   Double_t *tnorm = view->GetTnorm();
   if (!tnorm) return;
 
   //          Allocate v and tt arrays
   Int_t vSize = fNStack+2;
   std::vector<Double_t> v(vSize), tt(4*vSize);
 
   //          Define order of drawing
   Int_t incrx = (tnorm[8] < 0.) ? -1 : +1;
   Int_t incry = (tnorm[9] < 0.) ? -1 : +1;
   if (*chopt != 'B' && *chopt != 'b') { // front to back
     incrx = -incrx; incry = -incry;
   }
   Int_t ix1 = (incrx == +1) ? 1 : nx;
   Int_t iy1 = (incry == +1) ? 1 : ny;
   Int_t ix2 = (incrx == +1) ? nx : 1;
   Int_t iy2 = (incry == +1) ? ny : 1;
 
   //          Find visibility of sides
   Double_t zn;
   Int_t ivis[6] = { 0,0,0,0,0,0 };
   view->FindNormal(0, 1, 0, zn);
   if (zn < 0) ivis[0] = 1;
   if (zn > 0) ivis[2] = 1;
   view->FindNormal(1, 0, 0, zn);
   if (zn > 0) ivis[1] = 1;
   if (zn < 0) ivis[3] = 1;
   view->FindNormal(0, 0, 1, zn);
   if (zn > 0) ivis[5] = 1;
   if (zn < 0) ivis[4] = 1;
 
   //          Draw stack of lego-plots
   Int_t nv = 0;
   THistPainter *painter = (THistPainter*)gCurrentHist->GetPainter();
   for (Int_t iy = iy1; iy != iy2+incry; iy += incry) {
      for (Int_t ix = ix1; ix != ix2+incrx; ix += incrx) {
         if (!painter->IsInside(ix,iy)) continue;
         (this->*fLegoFunction)(ix, iy, nv, xy, v.data(), tt.data());
         if (nv < 2 || nv > vSize) continue;
         if (Hoption.Zero) {
            Double_t total_content = 0;
            for (Int_t iv = 1; iv < nv; ++iv) { total_content += v[iv]; }
            if (total_content <= Hparam.zmin) continue;
         }
         icodes[0] = ix;
         icodes[1] = iy;
         for (Int_t i = 1; i <= 4; ++i) {
            xyz[i*3 - 3] = xy[2*i - 2];
            xyz[i*3 - 2] = xy[2*i - 1];
            xyz[(i + 4)*3 - 3] = xyz[i*3 - 3];
            xyz[(i + 4)*3 - 2] = xyz[i*3 - 2];
         }
         // Draw stack
         firstStackNumberDrawn = -1;
         for (Int_t iv = 1; iv < nv; ++iv) {
            for (Int_t i = 1; i <= 4; ++i) {
               xyz[i*3 - 1] = v[iv - 1];
               xyz[(i + 4)*3 - 1] = v[iv];
            }
            if (v[iv - 1] == v[iv]) continue;
            icodes[2] = iv;
            for (Int_t i = 1; i <= 4; ++i) {
               if (ivis[i - 1] == 0) continue;
               Int_t k1 = i;
               Int_t k2 = i + 1;
               if (i == 4) k2 = 1;
               icodes[3] = k1;
               iface[0] = k1;
               iface[1] = k2;
               iface[2] = k2 + 4;
               iface[3] = k1 + 4;
               tface[0] = tt[k1 + (iv << 2) - 5];
               tface[1] = tt[k2 + (iv << 2) - 5];
               tface[2] = tt[k2 + ((iv + 1) << 2) - 5];
               tface[3] = tt[k1 + ((iv + 1) << 2) - 5];
               fEdgeIdx = iv-1;
               (this->*fDrawFace)(icodes, xyz, 4, iface, tface);
            }
            if ( firstStackNumberDrawn==-1 ) firstStackNumberDrawn = fEdgeIdx;
         }
         // Draw bottom face
         if (ivis[4] > 0) {
            icodes[2] = 1;
            icodes[3] = 5;
            for (Int_t i = 1; i <= 4; ++i) {
               xyz[i*3 - 1] = v[0];
               iface[i - 1] = 5 - i;
               tface[i - 1] = tt[5 - i - 1];
            }
            if (!Hoption.Zero) fEdgeIdx = 0;
            else {
               fEdgeIdx = firstStackNumberDrawn;
               fColorBottom = fColorMain[fEdgeIdx];
            }
            (this->*fDrawFace)(icodes, xyz, 4, iface, tface);
         }
         // Draw top face
         if (ivis[5] > 0) {
            icodes[2] = nv - 1;
            icodes[3] = 6;
            for (Int_t i = 1; i <= 4; ++i) {
               iface[i - 1] = i + 4;
               tface[i - 1] = tt[i + (nv << 2) - 5];
            }
            Int_t cs = fColorTop;
            if ( nv <= 3 ) fEdgeIdx = 0 ;  // no stack or stack with only one histo
            else {
               if ( nv > 2 && (v[nv-1] == v[nv-2])) {
                  for (Int_t iv = nv-1; iv > 2; --iv) {
                     if (v[nv-1] == v[iv-1]) {
                        fColorTop = fColorMain[iv-2];
                        fEdgeIdx  = iv - 2;
                     }
                  }
               }
            }
            (this->*fDrawFace)(icodes, xyz, 4, iface, tface);
            fColorTop = cs;
         }
      }
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Draw stack of lego-plots in polar coordinates
///
/// \param[in] iordr   order of variables (0 - R,PHI; 1 - PHI,R)
/// \param[in] na   number of steps along 1st variable
/// \param[in] nb   number of steps along 2nd variable
/// \param[in] chopt specific options
///
/// - `chopt` = 'BF' from BACK to FRONT
/// - `chopt` = 'FB' from FRONT to BACK
 
void TPainter3dAlgorithms::LegoPolar(Int_t iordr, Int_t na, Int_t nb, const char *chopt)
{
 
   Int_t iphi, jphi, kphi, incr, nphi, ivis[6], iopt, iphi1, iphi2, iface[4], i, j;
   Double_t tface[4];
   Int_t incrr, k1, k2, ia, ib, ir1, ir2;
   Double_t ab[8];       // was [2][4]
   Int_t ir, jr, iv, nr, nv, icodes[4];
   Double_t xyz[24];     // was [3][8]
   ia = ib = 0;
   Int_t firstStackNumberDrawn = -1 ;  // necessary to compute fColorBottom when the 0 option is set and when the stack is seen from below (bottomview, theta<0.)
 
   TView *view = gPad ? gPad->GetView() : nullptr;
   if (!view) {
      Error("LegoPolar", "no TView in current pad");
      return;
   }
 
   if (iordr == 0) {
      jr   = 1;
      jphi = 2;
      nr   = na;
      nphi = nb;
   } else {
      jr   = 2;
      jphi = 1;
      nr   = nb;
      nphi = na;
   }
   if (fNaphi < nphi + 3) {
     fNaphi = nphi + 3;
     fAphi.resize(fNaphi);
   }
   if (fAphi.empty()) {
      Error("LegoPolar", "failed to allocate array fAphi[%d]", fNaphi);
      fNaphi = 0;
      return;
   }
   iopt = 2;
   if (*chopt == 'B' || *chopt == 'b') iopt = 1;
 
    // Allocate v and tt arrays
   Int_t vSize = fNStack+2;
   std::vector<Double_t> v(vSize), tt(4*vSize);
 
   //     P R E P A R E   P H I   A R R A Y
   //     F I N D    C R I T I C A L   S E C T O R S
   nv   = 0;
   kphi = nphi;
   if (iordr == 0) ia = nr;
   if (iordr != 0) ib = nr;
   for (i = 1; i <= nphi; ++i) {
      if (iordr == 0) ib = i;
      if (iordr != 0) ia = i;
      (this->*fLegoFunction)(ia, ib, nv, ab, v.data(), tt.data());
      if (i == 1) fAphi[0] = ab[jphi - 1];
      fAphi[i - 1] = (fAphi[i - 1] + ab[jphi - 1]) / (float)2.;
      fAphi[i] = ab[jphi + 3];
   }
   view->FindPhiSectors(iopt, kphi, fAphi.data(), iphi1, iphi2);
 
   //      E N C O D E   V I S I B I L I T Y   O F   S I D E S
   //      A N D   O R D E R   A L O N G   R
   for (i = 1; i <= nphi; ++i) {
      if (!iordr) ib = i;
      if (iordr)  ia = i;
      (this->*fLegoFunction)(ia, ib, nv, ab, v.data(), tt.data());
      SideVisibilityEncode(iopt, ab[jphi - 1]*kRad, ab[jphi + 3]*kRad, fAphi[i - 1]);
   }
 
   //       D R A W   S T A C K   O F   L E G O - P L O T S
   incr = 1;
   iphi = iphi1;
L100:
   if (iphi > nphi) goto L300;
 
   //     D E C O D E   V I S I B I L I T Y   O F   S I D E S
   SideVisibilityDecode(fAphi[iphi - 1], ivis[0], ivis[1], ivis[2], ivis[3], ivis[4], ivis[5], incrr);
   ir1 = 1;
   if (incrr < 0) ir1 = nr;
   ir2 = nr - ir1 + 1;
   //      D R A W   L E G O S   F O R   S E C T O R
   for (ir = ir1; incrr < 0 ? ir >= ir2 : ir <= ir2; ir += incrr) {
      if (iordr == 0) { ia = ir;   ib = iphi; }
      else            { ia = iphi; ib = ir; }
      (this->*fLegoFunction)(ia, ib, nv, ab, v.data(), tt.data());
      if (nv < 2 || nv > vSize) continue;
      if (Hoption.Zero) {
         Double_t total_content=0;
         for (iv = 1; iv < nv; ++iv) total_content += v[iv];
         if (total_content==0) continue;
      }
      icodes[0] = ia;
      icodes[1] = ib;
      for (i = 1; i <= 4; ++i) {
         j = i;
         if (iordr != 0 && i == 2) j = 4;
         if (iordr != 0 && i == 4) j = 2;
         xyz[j*3 - 3] = ab[jr + 2*i - 3]*TMath::Cos(ab[jphi + 2*i - 3]*kRad);
         xyz[j*3 - 2] = ab[jr + 2*i - 3]*TMath::Sin(ab[jphi + 2*i - 3]*kRad);
         xyz[(j + 4)*3 - 3] = xyz[j*3 - 3];
         xyz[(j + 4)*3 - 2] = xyz[j*3 - 2];
      }
   //      D R A W   S T A C K
      firstStackNumberDrawn = -1;
      for (iv = 1; iv < nv; ++iv) {
         for (i = 1; i <= 4; ++i) {
            xyz[i*3 - 1] = v[iv - 1];
            xyz[(i + 4)*3 - 1] = v[iv];
         }
         if (v[iv - 1] >= v[iv]) continue;
         icodes[2] = iv;
         for (i = 1; i <= 4; ++i) {
            if (ivis[i - 1] == 0) continue;
            k1 = i - 1;
            if (i == 1) k1 = 4;
            k2 = i;
            if (xyz[k1*3 - 3] == xyz[k2*3 - 3] && xyz[k1*3 - 2] ==
                xyz[k2*3 - 2]) continue;
            iface[0] = k1;
            iface[1] = k2;
            iface[2] = k2 + 4;
            iface[3] = k1 + 4;
            tface[0] = tt[k1 + (iv << 2) - 5];
            tface[1] = tt[k2 + (iv << 2) - 5];
            tface[2] = tt[k2 + ((iv + 1) << 2) - 5];
            tface[3] = tt[k1 + ((iv + 1) << 2) - 5];
            icodes[3] = i;
            fEdgeIdx  = iv-1;
            (this->*fDrawFace)(icodes, xyz, 4, iface, tface);
         }
         if ( firstStackNumberDrawn==-1 ) firstStackNumberDrawn = fEdgeIdx;
      }
   //         D R A W   B O T T O M   F A C E
      if (ivis[4] != 0) {
         icodes[2] = 1;
         icodes[3] = 5;
         for (i = 1; i <= 4; ++i) {
            xyz[i*3 - 1] = v[0];
            iface[i - 1] = 5 - i;
            tface[i - 1] = tt[5 - i - 1];
         }
         if (!Hoption.Zero) fEdgeIdx = 0;
         else {
            fEdgeIdx = firstStackNumberDrawn;
            fColorBottom = fColorMain[fEdgeIdx];
         }
         (this->*fDrawFace)(icodes, xyz, 4, iface, tface);
      }
   //         D R A W   T O P   F A C E
      if (ivis[5] != 0) {
         icodes[2] = nv - 1;
         icodes[3] = 6;
         for (i = 1; i <= 4; ++i) {
            iface[i - 1] = i + 4;
            tface[i - 1] = tt[i + (nv << 2) - 5];
         }
         Int_t cs = fColorTop;
         if ( nv <= 3 ) fEdgeIdx = 0 ;  // no stack or stack with only one histo
         else {
            if ( nv > 2 && (v[nv-1] == v[nv-2])) {
               for (iv = nv-1; iv>2; iv--) {
                  if (v[nv-1] == v[iv-1]) {
                     fColorTop = fColorMain[iv-2];
                     fEdgeIdx = iv-2;
                  }
               }
            }
         }
         (this->*fDrawFace)(icodes, xyz, 4, iface, tface);
         fColorTop = cs;
      }
   }
   //      N E X T   P H I
L300:
   iphi += incr;
   if (iphi == 0)      iphi = kphi;
   if (iphi > kphi)    iphi = 1;
   if (iphi != iphi2)  goto L100;
   if (incr == 0)
      return;
   if (incr < 0) {
      incr = 0;
      goto L100;
   }
   incr = -1;
   iphi = iphi1;
   goto L300;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Draw stack of lego-plots in cylindrical coordinates
///
/// \param[in] iordr   order of variables (0 - Z,PHI; 1 - PHI,Z)
/// \param[in] na   number of steps along 1st variable
/// \param[in] nb   number of steps along 2nd variable
/// \param[in] chopt specific options
///
/// - `chopt` = 'BF' from BACK to FRONT
/// - `chopt` = 'FB' from FRONT to BACK
 
void TPainter3dAlgorithms::LegoCylindrical(Int_t iordr, Int_t na, Int_t nb, const char *chopt)
{
 
 
   Int_t iphi, jphi, kphi, incr, nphi, ivis[6], iopt, iphi1, iphi2, iface[4], i, j;
   Double_t tface[4], z;
   Double_t ab[8];       // was [2][4]
   Int_t ia, ib, idummy, iz1, iz2, nz, incrz, k1, k2, nv;
   Int_t iv, iz, jz, icodes[4];
   Double_t cosphi[4];
   Double_t sinphi[4];
   Double_t xyz[24];     // was [3][8]
   ia = ib = 0;
   Int_t firstStackNumberDrawn=-1 ;  // necessary to compute fColorBottom when the 0 option is set and when the stack is seen from below (bottomview, theta<0.)
 
   TView *view = gPad ? gPad->GetView() : nullptr;
   if (!view) {
      Error("LegoCylindrical", "no TView in current pad");
      return;
   }
 
   if (iordr == 0) {
      jz   = 1;
      jphi = 2;
      nz   = na;
      nphi = nb;
   } else {
      jz   = 2;
      jphi = 1;
      nz   = nb;
      nphi = na;
   }
   if (fNaphi < nphi + 3) {
     fNaphi = nphi + 3;
     fAphi.resize(fNaphi);
   }
   if (fAphi.empty()) {
      Error("LegoCylindrical", "failed to allocate array fAphi[%d]", fNaphi);
      fNaphi = 0;
      return;
   }
   iopt = 2;
   if (*chopt == 'B' || *chopt == 'b') iopt = 1;
 
    // Allocate v and tt arrays
   Int_t vSize = fNStack+2;
   std::vector<Double_t> v(vSize), tt(4*vSize);
 
   //       P R E P A R E   P H I   A R R A Y
   //       F I N D    C R I T I C A L   S E C T O R S
   nv   = 0;
   kphi = nphi;
   if (iordr == 0) ia = nz;
   if (iordr != 0) ib = nz;
   for (i = 1; i <= nphi; ++i) {
      if (iordr == 0) ib = i;
      if (iordr != 0) ia = i;
      (this->*fLegoFunction)(ia, ib, nv, ab, v.data(), tt.data());
      if (i == 1)  fAphi[0] = ab[jphi - 1];
      fAphi[i - 1] = (fAphi[i - 1] + ab[jphi - 1]) / (float)2.;
      fAphi[i] = ab[jphi + 3];
   }
   view->FindPhiSectors(iopt, kphi, fAphi.data(), iphi1, iphi2);
 
   //      E N C O D E   V I S I B I L I T Y   O F   S I D E S
   //      A N D   O R D E R   A L O N G   R
   for (i = 1; i <= nphi; ++i) {
      if (iordr == 0) ib = i;
      if (iordr != 0) ia = i;
      (this->*fLegoFunction)(ia, ib, nv, ab, v.data(), tt.data());
      SideVisibilityEncode(iopt, ab[jphi - 1]*kRad, ab[jphi + 3]*kRad, fAphi[i - 1]);
   }
 
   //       F I N D   O R D E R   A L O N G   Z
   incrz = 1;
   iz1 = 1;
   view->FindNormal(0, 0, 1, z);
   if ((z <= 0 && iopt == 1) || (z > 0 && iopt == 2)) {
      incrz = -1;
      iz1 = nz;
   }
   iz2 = nz - iz1 + 1;
 
   //       D R A W   S T A C K   O F   L E G O - P L O T S
   incr = 1;
   iphi = iphi1;
L100:
   if (iphi > nphi) goto L400;
   //     D E C O D E   V I S I B I L I T Y   O F   S I D E S
   idummy = 0;
   SideVisibilityDecode(fAphi[iphi - 1], ivis[4], ivis[1], ivis[5], ivis[3], ivis[0], ivis[2], idummy);
   for (iz = iz1; incrz < 0 ? iz >= iz2 : iz <= iz2; iz += incrz) {
      if (iordr == 0) {ia = iz;   ib = iphi;}
      else            {ia = iphi; ib = iz;}
      (this->*fLegoFunction)(ia, ib, nv, ab, v.data(), tt.data());
      if (nv < 2 || nv > vSize) continue;
      icodes[0] = ia;
      icodes[1] = ib;
      for (i = 1; i <= 4; ++i) {
         j = i;
         if (iordr != 0 && i == 2) j = 4;
         if (iordr != 0 && i == 4) j = 2;
         cosphi[j - 1] = TMath::Cos(ab[jphi + 2*i - 3]*kRad);
         sinphi[j - 1] = TMath::Sin(ab[jphi + 2*i - 3]*kRad);
         xyz[j*3 - 1] = ab[jz + 2*i - 3];
         xyz[(j + 4)*3 - 1] = ab[jz + 2*i - 3];
      }
   //      D R A W   S T A C K
      firstStackNumberDrawn = -1;
      for (iv = 1; iv < nv; ++iv) {
         for (i = 1; i <= 4; ++i) {
            xyz[i*3 - 3] = v[iv - 1]*cosphi[i - 1];
            xyz[i*3 - 2] = v[iv - 1]*sinphi[i - 1];
            xyz[(i + 4)*3 - 3] = v[iv]*cosphi[i - 1];
            xyz[(i + 4)*3 - 2] = v[iv]*sinphi[i - 1];
         }
         if (v[iv - 1] >= v[iv]) continue;
         icodes[2] = iv;
         for (i = 1; i <= 4; ++i) {
            if (ivis[i - 1] == 0) continue;
            k1 = i;
            k2 = i - 1;
            if (i == 1) k2 = 4;
            iface[0] = k1;
            iface[1] = k2;
            iface[2] = k2 + 4;
            iface[3] = k1 + 4;
            tface[0] = tt[k1 + (iv << 2) - 5];
            tface[1] = tt[k2 + (iv << 2) - 5];
            tface[2] = tt[k2 + ((iv + 1) << 2) - 5];
            tface[3] = tt[k1 + ((iv + 1) << 2) - 5];
            icodes[3] = i;
            fEdgeIdx = iv-1;
            (this->*fDrawFace)(icodes, xyz, 4, iface, tface);
         }
         if ( firstStackNumberDrawn==-1 ) firstStackNumberDrawn = fEdgeIdx;
      }
   //       D R A W   B O T T O M   F A C E
      if (ivis[4] != 0 && v[0] > 0) {
         icodes[2] = 1;
         icodes[3] = 5;
         for (i = 1; i <= 4; ++i) {
            xyz[i*3 - 3] = v[0]*cosphi[i - 1];
            xyz[i*3 - 2] = v[0]*sinphi[i - 1];
            iface[i - 1] = i;
            tface[i - 1] = tt[i - 1];
         }
         if (!Hoption.Zero) fEdgeIdx = 0;
         else {
            fEdgeIdx = firstStackNumberDrawn;
            fColorBottom = fColorMain[fEdgeIdx];
         }
         (this->*fDrawFace)(icodes, xyz, 4, iface, tface);
      }
   //      D R A W   T O P   F A C E
      if (ivis[5] != 0 && v[nv - 1] > 0) {
         icodes[2] = nv - 1;
         icodes[3] = 6;
         for (i = 1; i <= 4; ++i) {
            iface[i - 1] = 5 - i + 4;
            tface[i - 1] = tt[5 - i + (nv << 2) - 5];
         }
         Int_t cs = fColorTop;
         if ( nv <= 3 ) fEdgeIdx = 0 ;  // no stack or stack with only one histo
         else {
            if ( nv > 2 && (v[nv-1] == v[nv-2])) {
               for (iv = nv-1; iv>2; iv--) {
                  if (v[nv-1] == v[iv-1]) {
                     fColorTop = fColorMain[iv-2];
                     fEdgeIdx = iv-2;
                  }
               }
            }
         }
         (this->*fDrawFace)(icodes, xyz, 4, iface, tface);
         fColorTop = cs;
      }
   }
   //      N E X T   P H I
L400:
   iphi += incr;
   if (iphi == 0)     iphi = kphi;
   if (iphi > kphi)   iphi = 1;
   if (iphi != iphi2) goto L100;
   if (incr == 0)
      return;
   if (incr < 0) {
      incr = 0;
      goto L100;
   }
   incr = -1;
   iphi = iphi1;
   goto L400;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Draw stack of lego-plots spheric coordinates
///
/// \param[in] ipsdr    pseudo-rapidity flag
/// \param[in] iordr   order of variables (0 - THETA,PHI; 1 - PHI,THETA)
/// \param[in] na   number of steps along 1st variable
/// \param[in] nb   number of steps along 2nd variable
/// \param[in] chopt specific options
///
/// - `chopt` = 'BF' from BACK to FRONT
/// - `chopt` = 'FB' from FRONT to BACK
 
void TPainter3dAlgorithms::LegoSpherical(Int_t ipsdr, Int_t iordr, Int_t na, Int_t nb, const char *chopt)
{
   Int_t iphi, jphi, kphi, incr, nphi, ivis[6], iopt, iphi1, iphi2, iface[4], i, j;
   Double_t tface[4], costh[4];
   Double_t sinth[4];
   Int_t k1, k2, ia, ib, incrth, ith, jth, kth, nth, mth, ith1, ith2, nv;
   Double_t ab[8];       // was [2][4]
   Double_t th;
   Int_t iv, icodes[4];
   Double_t zn, cosphi[4];
   Double_t sinphi[4], th1, th2, phi;
   Double_t xyz[24];     // was [3][8]
   Double_t phi1, phi2;
   ia = ib = 0;
   Int_t firstStackNumberDrawn=-1 ;  // necessary to compute fColorBottom when the 0 option is set and when the stack is seen from below (bottomview, theta<0.)
 
   TView *view = gPad ? gPad->GetView() : nullptr;
   if (!view) {
      Error("LegoSpherical", "no TView in current pad");
      return;
   }
 
   if (iordr == 0) {
      jth  = 1;
      jphi = 2;
      nth  = na;
      nphi = nb;
   } else {
      jth  = 2;
      jphi = 1;
      nth  = nb;
      nphi = na;
   }
   if (fNaphi < nth + 3 || fNaphi < nphi + 3) {
     fNaphi = TMath::Max(nth, nphi) + 3;
     fAphi.resize(fNaphi);
   }
   if (fAphi.empty()) {
      Error("LegoSpherical", "failed to allocate array fAphi[%d]", fNaphi);
      fNaphi = 0;
      return;
   }
   iopt = 2;
   if (*chopt == 'B' || *chopt == 'b') iopt = 1;
 
   // Allocate v and tt arrays
   Int_t vSize = fNStack+2;
   std::vector<Double_t> v(vSize), tt(4*vSize);
 
   //       P R E P A R E   P H I   A R R A Y
   //       F I N D    C R I T I C A L   P H I   S E C T O R S
   nv  = 0;
   kphi = nphi;
   mth = nth / 2;
   if (mth == 0)    mth = 1;
   if (iordr == 0) ia = mth;
   if (iordr != 0) ib = mth;
   for (i = 1; i <= nphi; ++i) {
      if (iordr == 0) ib = i;
      if (iordr != 0) ia = i;
      (this->*fLegoFunction)(ia, ib, nv, ab, v.data(), tt.data());
      if (i == 1)  fAphi[0] = ab[jphi - 1];
      fAphi[i - 1] = (fAphi[i - 1] + ab[jphi - 1]) / (float)2.;
      fAphi[i] = ab[jphi + 3];
   }
   view->FindPhiSectors(iopt, kphi, fAphi.data(), iphi1, iphi2);
 
   //       P R E P A R E   T H E T A   A R R A Y
   if (iordr == 0) ib = 1;
   if (iordr != 0) ia = 1;
   for (i = 1; i <= nth; ++i) {
      if (iordr == 0) ia = i;
      if (iordr != 0) ib = i;
      (this->*fLegoFunction)(ia, ib, nv, ab, v.data(), tt.data());
      if (i == 1) fAphi[0] = ab[jth - 1];
      fAphi[i - 1] = (fAphi[i - 1] + ab[jth - 1]) / (float)2.;
      fAphi[i] = ab[jth + 3];
   }
 
   //       D R A W   S T A C K   O F   L E G O - P L O T S
   kth = nth;
 
   incr = 1;
   iphi = iphi1;
L100:
   if (iphi > nphi) goto L500;
 
   //      F I N D    C R I T I C A L   T H E T A   S E C T O R S
   if (!iordr) {ia = mth;  ib = iphi; }
   else        {ia = iphi; ib = mth;  }
   (this->*fLegoFunction)(ia, ib, nv, ab, v.data(), tt.data());
   phi = (ab[jphi - 1] + ab[jphi + 3]) / (float)2.;
   view->FindThetaSectors(iopt, phi, kth, fAphi.data(), ith1, ith2);
   incrth = 1;
   ith = ith1;
L200:
   if (ith > nth)   goto L400;
   if (iordr == 0) ia = ith;
   if (iordr != 0) ib = ith;
   (this->*fLegoFunction)(ia, ib, nv, ab, v.data(), tt.data());
   if (nv < 2 || nv > vSize) goto L400;
 
   //      D E F I N E   V I S I B I L I T Y   O F   S I D E S
   for (i = 1; i <= 6; ++i) ivis[i - 1] = 0;
 
   phi1 = kRad*ab[jphi - 1];
   phi2 = kRad*ab[jphi + 3];
   th1  = kRad*ab[jth - 1];
   th2  = kRad*ab[jth + 3];
   view->FindNormal(TMath::Sin(phi1), -TMath::Cos(phi1), 0, zn);
   if (zn > 0) ivis[1] = 1;
   view->FindNormal(-TMath::Sin(phi2), TMath::Cos(phi2), 0, zn);
   if (zn > 0) ivis[3] = 1;
   phi = (phi1 + phi2) / (float)2.;
   view->FindNormal(-TMath::Cos(phi)*TMath::Cos(th1), -TMath::Sin(phi)*TMath::Cos(th1), TMath::Sin(th1), zn);
   if (zn > 0) ivis[0] = 1;
   view->FindNormal(TMath::Cos(phi)*TMath::Cos(th2), TMath::Sin(phi)*TMath::Cos(th2), -TMath::Sin(th2), zn);
   if (zn > 0) ivis[2] = 1;
   th = (th1 + th2) / (float)2.;
   if (ipsdr == 1) th = kRad*90;
   view->FindNormal(TMath::Cos(phi)*TMath::Sin(th), TMath::Sin(phi)*TMath::Sin(th), TMath::Cos(th), zn);
   if (zn < 0) ivis[4] = 1;
   if (zn > 0) ivis[5] = 1;
 
   //      D R A W   S T A C K
   icodes[0] = ia;
   icodes[1] = ib;
   for (i = 1; i <= 4; ++i) {
      j = i;
      if (iordr != 0 && i == 2) j = 4;
      if (iordr != 0 && i == 4) j = 2;
      costh[j - 1]  = TMath::Cos(kRad*ab[jth + 2*i - 3]);
      sinth[j - 1]  = TMath::Sin(kRad*ab[jth + 2*i - 3]);
      cosphi[j - 1] = TMath::Cos(kRad*ab[jphi + 2*i - 3]);
      sinphi[j - 1] = TMath::Sin(kRad*ab[jphi + 2*i - 3]);
   }
   firstStackNumberDrawn = -1;
   for (iv = 1; iv < nv; ++iv) {
      if (ipsdr == 1) {
         for (i = 1; i <= 4; ++i) {
            xyz[i*3 - 3] = v[iv - 1]*cosphi[i - 1];
            xyz[i*3 - 2] = v[iv - 1]*sinphi[i - 1];
            xyz[i*3 - 1] = v[iv - 1]*costh[i - 1] / sinth[i - 1];
            xyz[(i + 4)*3 - 3] = v[iv]*cosphi[i - 1];
            xyz[(i + 4)*3 - 2] = v[iv]*sinphi[i - 1];
            xyz[(i + 4)*3 - 1] = v[iv]*costh[i - 1] / sinth[i - 1];
         }
      } else {
         for (i = 1; i <= 4; ++i) {
            xyz[i*3 - 3] = v[iv - 1]*sinth[i - 1]*cosphi[i - 1];
            xyz[i*3 - 2] = v[iv - 1]*sinth[i - 1]*sinphi[i - 1];
            xyz[i*3 - 1] = v[iv - 1]*costh[i - 1];
            xyz[(i + 4)*3 - 3] = v[iv]*sinth[i - 1]*cosphi[i - 1];
            xyz[(i + 4)*3 - 2] = v[iv]*sinth[i - 1]*sinphi[i - 1];
            xyz[(i + 4)*3 - 1] = v[iv]*costh[i - 1];
         }
      }
      if (v[iv - 1] >= v[iv]) continue;
      icodes[2] = iv;
      for (i = 1; i <= 4; ++i) {
         if (ivis[i - 1] == 0) continue;
         k1 = i - 1;
         if (i == 1) k1 = 4;
         k2 = i;
         iface[0] = k1;
         iface[1] = k2;
         iface[2] = k2 + 4;
         iface[3] = k1 + 4;
         tface[0] = tt[k1 + (iv << 2) - 5];
         tface[1] = tt[k2 + (iv << 2) - 5];
         tface[2] = tt[k2 + ((iv + 1) << 2) - 5];
         tface[3] = tt[k1 + ((iv + 1) << 2) - 5];
         icodes[3] = i;
         fEdgeIdx = iv-1;
         (this->*fDrawFace)(icodes, xyz, 4, iface, tface);
      }
      if ( firstStackNumberDrawn==-1 ) firstStackNumberDrawn = fEdgeIdx;
   }
   //      D R A W   B O T T O M   F A C E
   if (ivis[4] != 0 && v[0] > 0) {
      icodes[2] = 1;
      icodes[3] = 5;
      for (i = 1; i <= 4; ++i) {
         if (ipsdr == 1) {
            xyz[i*3 - 3] = v[0]*cosphi[i - 1];
            xyz[i*3 - 2] = v[0]*sinphi[i - 1];
            xyz[i*3 - 1] = v[0]*costh[i - 1] / sinth[i - 1];
         } else {
            xyz[i*3 - 3] = v[0]*sinth[i - 1]*cosphi[i - 1];
            xyz[i*3 - 2] = v[0]*sinth[i - 1]*sinphi[i - 1];
            xyz[i*3 - 1] = v[0]*costh[i - 1];
         }
         iface[i - 1] = 5 - i;
         tface[i - 1] = tt[5 - i - 1];
      }
      if (!Hoption.Zero) fEdgeIdx = 0;
      else {
         fEdgeIdx = firstStackNumberDrawn;
         fColorBottom = fColorMain[fEdgeIdx];
      }
      (this->*fDrawFace)(icodes, xyz, 4, iface, tface);
   }
   //      D R A W   T O P   F A C E
   if (ivis[5] != 0 && v[nv - 1] > 0) {
      icodes[2] = nv - 1;
      icodes[3] = 6;
      for (i = 1; i <= 4; ++i) {
         iface[i - 1] = i + 4;
         tface[i - 1] = tt[i + 4 + 2*nv - 5];
      }
      Int_t cs = fColorTop;
      if ( nv <= 3 ) fEdgeIdx = 0 ;  // no stack or stack with only one histo
      else {
         if ( nv > 2 && (v[nv-1] == v[nv-2])) {
            for (iv = nv-1; iv>2; iv--) {
               if (v[nv-1] == v[iv-1]) {
                  fColorTop = fColorMain[iv-2];
                  fEdgeIdx  = iv-2;
               }
            }
         }
      }
      (this->*fDrawFace)(icodes, xyz, 4, iface, tface);
      fColorTop = cs;
   }
   //      N E X T   T H E T A
L400:
   ith += incrth;
   if (ith == 0)    ith = kth;
   if (ith > kth)   ith = 1;
   if (ith != ith2) goto L200;
   if (incrth == 0) goto L500;
   if (incrth < 0) {
      incrth = 0;
      goto L200;
   }
   incrth = -1;
   ith = ith1;
   goto L400;
   //      N E X T   P H I
L500:
   iphi += incr;
   if (iphi == 0)     iphi = kphi;
   if (iphi > kphi)   iphi = 1;
   if (iphi != iphi2) goto L100;
   if (incr == 0)
      return;
   if (incr < 0) {
      incr = 0;
      goto L100;
   }
   incr = -1;
   iphi = iphi1;
   goto L500;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Set light source
///
/// \param[in] nl   source number: 1 off all light sources, 0 set diffused light
/// \param[in] yl   intensity of the light source
/// \param[in] xscr, yscr, zscr  direction of the light (in respect of the screen)
///
/// \param[out] irep   reply (0 - O.K, -1 error)
 
 
void TPainter3dAlgorithms::LightSource(Int_t nl, Double_t yl, Double_t xscr,
                                       Double_t yscr, Double_t zscr, Int_t &irep)
{
   /* Local variables */
   Int_t i;
   Double_t s;
 
   irep = 0;
   if (nl < 0)       goto L100;
   else if (nl == 0) goto L200;
   else              goto L300;
 
   //          S W I T C H   O F F   L I G H T S
L100:
   fLoff = 1;
   fYdl = 0;
   for (i = 1; i <= 4; ++i) {
      fYls[i - 1] = 0;
   }
   return;
   //          S E T   D I F F U S E D   L I G H T
L200:
   if (yl < 0) {
      Error("LightSource", "negative light intensity");
      irep = -1;
      return;
   }
   fYdl = yl;
   goto L400;
   //          S E T   L I G H T   S O U R C E
L300:
   if (nl > 4 || yl < 0) {
      Error("LightSource", "illegal light source number (nl=%d, yl=%f)", nl, yl);
      irep = -1;
      return;
   }
   s = TMath::Sqrt(xscr*xscr + yscr*yscr + zscr*zscr);
   if (s == 0) {
      Error("LightSource", "light source is placed at origin");
      irep = -1;
      return;
   }
   fYls[nl - 1] = yl;
   fVls[nl*3 - 3] = xscr / s;
   fVls[nl*3 - 2] = yscr / s;
   fVls[nl*3 - 1] = zscr / s;
   //         C H E C K   L I G H T S
L400:
   fLoff = 0;
   if (fYdl != 0) return;
   for (i = 1; i <= 4; ++i) {
      if (fYls[i - 1] != 0) return;
   }
   fLoff = 1;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Find surface luminosity at given point
///
/// \param[in] view    pointer on TView object
/// \param[in] anorm   surface normal at given point
///
/// \param[out] flum   luminosity
 
void TPainter3dAlgorithms::Luminosity(TView *view, Double_t *anorm, Double_t &flum)
{
   flum = 0;
 
   if (!view || fLoff) return;
 
   /* Local variables */
   Double_t cosn, cosr;
   Int_t i;
   Double_t s, vl[3], vn[3];
 
   //          T R A N S F E R   N O R M A L  T O   SCREEN COORDINATES
   view->NormalWCtoNDC(anorm, vn);
   s = TMath::Sqrt(vn[0]*vn[0] + vn[1]*vn[1] + vn[2]*vn[2]);
   if (vn[2] < 0) s = -(Double_t)s;
   vn[0] /= s;
   vn[1] /= s;
   vn[2] /= s;
 
   //          F I N D   L U M I N O S I T Y
   flum = fYdl*fQA;
   for (i = 1; i <= 4; ++i) {
      if (fYls[i - 1] <= 0) continue;
      vl[0] = fVls[i*3 - 3];
      vl[1] = fVls[i*3 - 2];
      vl[2] = fVls[i*3 - 1];
      cosn = vl[0]*vn[0] + vl[1]*vn[1] + vl[2]*vn[2];
      if (cosn < 0) continue;
      cosr = vn[1]*(vn[2]*vl[1] - vn[1]*vl[2]) - vn[0]*(vn[0]*vl[2]
             - vn[2]*vl[0]) + vn[2]*cosn;
      if (cosr <= 0) cosr = 0;
      flum += fYls[i - 1]*(fQD*cosn + fQS*TMath::Power(cosr, fNqs));
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Modify SCREEN
///
/// \param[in] r1   1-st point of the line
/// \param[in] r2   2-nd point of the line
 
void TPainter3dAlgorithms::ModifyScreen(Double_t *r1, Double_t *r2)
{
   /* Local variables */
   Int_t i, i1, i2;
   Double_t x1, x2, y1, y2, dy, ww, yy1, yy2, *tn;
 
   /* Parameter adjustments */
   --r2;
   --r1;
 
   TView *view = gPad ? gPad->GetView() : nullptr;
 
   if (view) {
      tn = view->GetTN();
      if (tn) {
         x1 = tn[0]*r1[1] + tn[1]*r1[2] + tn[2]*r1[3] + tn[3];
         x2 = tn[0]*r2[1] + tn[1]*r2[2] + tn[2]*r2[3] + tn[3];
         y1 = tn[4]*r1[1] + tn[5]*r1[2] + tn[6]*r1[3] + tn[7];
         y2 = tn[4]*r2[1] + tn[5]*r2[2] + tn[6]*r2[3] + tn[7];
      } else {
         Error("ModifyScreen", "invalid TView in current pad");
         return;
      }
   } else {
      Error("ModifyScreen", "no TView in current pad");
      return;
   }
 
   if (x1 >= x2) {
      ww = x1;
      x1 = x2;
      x2 = ww;
      ww = y1;
      y1 = y2;
      y2 = ww;
   }
   i1 = Int_t((x1 - fX0) / fDX) + 15;
   i2 = Int_t((x2 - fX0) / fDX) + 15;
   if (i1 == i2) return;
 
   //          M O D I F Y   B O U N D A R I E S   OF THE SCREEN
   dy = (y2 - y1) / (i2 - i1);
   for (i = i1; i <= i2 - 1; ++i) {
      yy1 = y1 + dy*(i - i1);
      yy2 = yy1 + dy;
      if (fD[2*i - 2] > yy1) fD[2*i - 2] = yy1;
      if (fD[2*i - 1] > yy2) fD[2*i - 1] = yy2;
      if (fU[2*i - 2] < yy1) fU[2*i - 2] = yy1;
      if (fU[2*i - 1] < yy2) fU[2*i - 1] = yy2;
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Store pointer to current algorithm to draw faces
 
void TPainter3dAlgorithms::SetDrawFace(DrawFaceFunc_t drface)
{
   fDrawFace = drface;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Store pointer to current lego function
 
void TPainter3dAlgorithms::SetLegoFunction(LegoFunc_t fun)
{
   fLegoFunction = fun;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Store pointer to current surface function
 
void TPainter3dAlgorithms::SetSurfaceFunction(SurfaceFunc_t fun)
{
   fSurfaceFunction = fun;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Store dark color for stack number n
 
void TPainter3dAlgorithms::SetColorDark(Color_t color, Int_t n)
{
   if (n < 0 ) {fColorBottom = color; return;}
   if (n > fNStack ) {fColorTop  = color; return;}
   fColorDark[n] = color;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Store color for stack number n
 
void TPainter3dAlgorithms::SetColorMain(Color_t color, Int_t n)
{
   if (n < 0 ) {fColorBottom = color; return;}
   if (n > fNStack ) {fColorTop = color; return;}
   fColorMain[n] = color;
}
 
////////////////////////////////////////////////////////////////////////////////
 
void TPainter3dAlgorithms::SetEdgeAtt(Color_t color, Style_t style, Width_t width, Int_t n)
{
   // Store edge attributes
 
   fEdgeColor[n] = color;
   fEdgeStyle[n] = style;
   fEdgeWidth[n] = width;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Decode side visibilities and order along R for sector
///
/// \param[in] val   encoded value
///
/// \param[out] iv1,iv2,iv3,iv4,iv5,iv6   visibility of the sides
/// \param[out] ir   increment along R
 
void TPainter3dAlgorithms::SideVisibilityDecode(Double_t val, Int_t &iv1, Int_t &iv2, Int_t &iv3, Int_t &iv4, Int_t &iv5, Int_t &iv6, Int_t &ir)
{
   Int_t ivis[6], i, k, num;
 
   k = Int_t(val);
   num = 128;
   for (i = 1; i <= 6; ++i) {
      ivis[i - 1] = 0;
      num /= 2;
      if (k < num) continue;
      k -= num;
      ivis[i - 1] = 1;
   }
   ir = 1;
   if (k == 1) ir = -1;
   iv1 = ivis[5];
   iv2 = ivis[4];
   iv3 = ivis[3];
   iv4 = ivis[2];
   iv5 = ivis[1];
   iv6 = ivis[0];
}
 
////////////////////////////////////////////////////////////////////////////////
/// Encode side visibilities and order along R for sector
///
/// \param[in] iopt   options: 1: from BACK to FRONT 'BF', 2: from FRONT to BACK 'FB'
/// \param[in] phi1   1st phi of sector
/// \param[in] phi2   2nd phi of sector
///
/// \param[out] val   encoded value
 
void TPainter3dAlgorithms::SideVisibilityEncode(Int_t iopt, Double_t phi1, Double_t phi2, Double_t &val)
{
   /* Local variables */
   Double_t zn, phi;
   Int_t k = 0;
 
   TView *view = gPad ? gPad->GetView() : nullptr;
   if (!view) {
      Error("SideVisibilityEncode", "no TView in current pad");
      return;
   }
 
   view->FindNormal(0, 0, 1, zn);
   if (zn > 0) k += 64;
   if (zn < 0) k += 32;
   view->FindNormal(-TMath::Sin(phi2), TMath::Cos(phi2), 0, zn);
   if (zn > 0) k += 16;
   view->FindNormal(TMath::Sin(phi1), -TMath::Cos(phi1), 0, zn);
   if (zn > 0) k += 4;
   phi = (phi1 + phi2) / (float)2.;
   view->FindNormal(TMath::Cos(phi), TMath::Sin(phi), 0, zn);
   if (zn > 0) k += 8;
   if (zn < 0) k += 2;
   if ((zn <= 0 && iopt == 1) || (zn > 0 && iopt == 2)) ++k;
   val = Double_t(k);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Set Spectrum
///
/// \param[in] nl   number of levels
/// \param[in] fmin   MIN function value
/// \param[in] fmax   MAX function value
/// \param[in] ic   initial color index (for 1st level)
/// \param[in] idc   color index increment
///
/// \param[out] irep   reply (0 O.K., -1 error)
 
void TPainter3dAlgorithms::Spectrum(Int_t nl, Double_t fmin, Double_t fmax, Int_t ic, Int_t idc, Int_t &irep)
{
   static const char *where = "Spectrum";
 
   /* Local variables */
   Double_t delf;
   Int_t i;
 
   irep = 0;
   if (nl == 0) {fNlevel = 0; return; }
 
   //          C H E C K   P A R A M E T E R S
   if (fmax <= fmin) {
      Error(where, "fmax (%f) less than fmin (%f)", fmax, fmin);
      irep = -1;
      return;
   }
   if (nl < 0 || nl > 256) {
      Error(where, "illegal number of levels (%d)", nl);
      irep = -1;
      return;
   }
   if (ic < 0) {
      Error(where, "initial color index is negative");
      irep = -1;
      return;
   }
   if (idc < 0) {
      Error(where, "color index increment must be positive");
      irep = -1;
   }
 
   //          S E T  S P E C T R
   const Int_t kMAXCOL = 50;
   delf    = (fmax - fmin) / nl;
   fNlevel = -(nl + 1);
   for (i = 1; i <= nl+1; ++i) {
      fFunLevel[i - 1] = fmin + (i - 1)*delf;
      fColorLevel[i] = ic + (i - 1)*idc;
      if (ic <= kMAXCOL && fColorLevel[i] > kMAXCOL) fColorLevel[i] -= kMAXCOL;
   }
   fColorLevel[0] = fColorLevel[1];
   fColorLevel[nl + 1] = fColorLevel[nl];
}
 
////////////////////////////////////////////////////////////////////////////////
/// Draw surface in cartesian coordinate system
///
/// \param[in] ang   angle between X ang Y (not used in this method)
/// \param[in] nx   number of steps along X
/// \param[in] ny   number of steps along Y
/// \param[in] chopt specific options
///
/// - `chopt` = 'BF' from BACK to FRONT
/// - `chopt` = 'FB' from FRONT to BACK
 
void TPainter3dAlgorithms::SurfaceCartesian(Double_t, Int_t nx, Int_t ny, const char *chopt)
{
   Int_t iface[4] = { 1,2,3,4 };
   Int_t icodes[3];
   Double_t f[4*3], tt[4], xyz[4*3];
 
   TView *view = gPad ? gPad->GetView() : nullptr;
   if (!view) {
     Error("SurfaceCartesian", "no TView in current pad");
     return;
   }
   Double_t *tnorm = view->GetTnorm();
   if (!tnorm) return;
 
   //          Define order of drawing
   Int_t incrx = (tnorm[8] < 0.) ? -1 : +1;
   Int_t incry = (tnorm[9] < 0.) ? -1 : +1;
   if (*chopt != 'B' && *chopt != 'b') { // front to back
      incrx = -incrx; incry = -incry;
   }
   Int_t ix1 = (incrx == +1) ? 1 : nx;
   Int_t iy1 = (incry == +1) ? 1 : ny;
   Int_t ix2 = (incrx == +1) ? nx : 1;
   Int_t iy2 = (incry == +1) ? ny : 1;
 
   //          Draw surface
   THistPainter *painter = (THistPainter*)gCurrentHist->GetPainter();
   for (Int_t iy = iy1; iy != iy2+incry; iy += incry) {
      for (Int_t ix = ix1; ix != ix2+incrx; ix += incrx) {
         if (!painter->IsInside(ix,iy)) continue;
         (this->*fSurfaceFunction)(ix, iy, f, tt);
         for (Int_t i = 0; i < 4; ++i) {
            xyz[i*3 + 0] = f[i*3 + 0];
            xyz[i*3 + 1] = f[i*3 + 1];
            xyz[i*3 + 2] = f[i*3 + 2];
            // added EJB -->
            Double_t al, ab;
            if (Hoption.Proj == 1 ) {
               THistPainter::ProjectAitoff2xy(xyz[i*3 + 0], xyz[i*3 + 1], al, ab);
               xyz[i*3 + 0] = al;
               xyz[i*3 + 1] = ab;
            } else if (Hoption.Proj == 2 ) {
               THistPainter::ProjectMercator2xy(xyz[i*3 + 0], xyz[i*3 + 1], al, ab);
               xyz[i*3 + 0] = al;
               xyz[i*3 + 1] = ab;
            } else if (Hoption.Proj == 3) {
               THistPainter::ProjectSinusoidal2xy(xyz[i*3 + 0], xyz[i*3 + 1], al, ab);
               xyz[i*3 + 0] = al;
               xyz[i*3 + 1] = ab;
            } else if (Hoption.Proj == 4) {
               THistPainter::ProjectParabolic2xy(xyz[i*3 + 0], xyz[i*3 + 1], al, ab);
               xyz[i*3 + 0] = al;
               xyz[i*3 + 1] = ab;
            }
         }
         icodes[0] = ix;
         icodes[1] = iy;
         icodes[2] = -1;   // -1 for data, 0 for front a back boxes
         fEdgeIdx = 0;   // constant since stacks are not (yet?) handled for surfaces
         (this->*fDrawFace)(icodes, xyz, 4, iface, tt);
      }
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Service function for Surfaces
 
void TPainter3dAlgorithms::SurfaceFunction(Int_t ia, Int_t ib, Double_t *f, Double_t *t)
{
   static Int_t ixadd[4] = { 0,1,1,0 };
   static Int_t iyadd[4] = { 0,0,1,1 };
 
   Double_t rinrad = gStyle->GetLegoInnerR();
   Double_t dangle = 10; //Delta angle for Rapidity option
   Double_t yval1l, yval2l;
   Double_t xlab1l, xlab2l, ylab1l, ylab2l;
   Int_t i, ixa, iya, icx, ixt, iyt;
 
    /* Parameter adjustments */
   --t;
   f -= 4;
 
   ixt = ia + Hparam.xfirst - 1;
   iyt = ib + Hparam.yfirst - 1;
 
   // xval1l = Hparam.xmin;
   // xval2l = Hparam.xmax;
   yval1l = Hparam.ymin;
   yval2l = Hparam.ymax;
 
   xlab1l = gCurrentHist->GetXaxis()->GetXmin();
   xlab2l = gCurrentHist->GetXaxis()->GetXmax();
   if (Hoption.Logx) {
      if (xlab2l>0) {
         if (xlab1l>0) xlab1l = TMath::Log10(xlab1l);
         else          xlab1l = TMath::Log10(0.001*xlab2l);
         xlab2l = TMath::Log10(xlab2l);
      }
   }
   ylab1l = gCurrentHist->GetYaxis()->GetXmin();
   ylab2l = gCurrentHist->GetYaxis()->GetXmax();
   if (Hoption.Logy) {
      if (ylab2l>0) {
         if (ylab1l>0) ylab1l = TMath::Log10(ylab1l);
         else          ylab1l = TMath::Log10(0.001*ylab2l);
         ylab2l = TMath::Log10(ylab2l);
      }
   }
 
   for (i = 1; i <= 4; ++i) {
      ixa = ixadd[i - 1];
      iya = iyadd[i - 1];
      Double_t xwid = gCurrentHist->GetXaxis()->GetBinWidth(ixt+ixa);
      Double_t ywid = gCurrentHist->GetYaxis()->GetBinWidth(iyt+iya);
 
   //          Compute the cell position in cartesian coordinates
   //          and compute the LOG if necessary
      f[i*3 + 1] = gCurrentHist->GetXaxis()->GetBinLowEdge(ixt+ixa) + 0.5*xwid;
      f[i*3 + 2] = gCurrentHist->GetYaxis()->GetBinLowEdge(iyt+iya) + 0.5*ywid;
      if (Hoption.Logx) {
         if (f[i*3 + 1] > 0) f[i*3 + 1] = TMath::Log10(f[i*3 + 1]);
         else                f[i*3 + 1] = Hparam.xmin;
      }
      if (Hoption.Logy) {
         if (f[i*3 + 2] > 0) f[i*3 + 2] = TMath::Log10(f[i*3 + 2]);
         else                f[i*3 + 2] = Hparam.ymin;
      }
 
   //     Transform the cell position in the required coordinate system
      if (Hoption.System == kPOLAR) {
         f[i*3 + 1] = 360*(f[i*3 + 1] - xlab1l) / (xlab2l - xlab1l);
         f[i*3 + 2] = (f[i*3 + 2] - yval1l) / (yval2l - yval1l);
      } else if (Hoption.System == kCYLINDRICAL) {
         f[i*3 + 1] = 360*(f[i*3 + 1] - xlab1l) / (xlab2l - xlab1l);
      } else if (Hoption.System == kSPHERICAL) {
         f[i*3 + 1] = 360*(f[i*3 + 1] - xlab1l) / (xlab2l - xlab1l);
         f[i*3 + 2] = 360*(f[i*3 + 2] - ylab1l) / (ylab2l - ylab1l);
      } else if (Hoption.System == kRAPIDITY) {
         f[i*3 + 1] = 360*(f[i*3 + 1] - xlab1l) / (xlab2l - xlab1l);
         f[i*3 + 2] = (180 - dangle*2)*(f[i*3 + 2] - ylab1l) / (ylab2l - ylab1l) + dangle;
      }
 
   //          Get the content of the table. If the X index (ICX) is
   //          greater than the X size of the table (NCX), that's mean
   //          IGTABL tried to close the surface and in this case the
   //          first channel should be used. */
      icx = ixt + ixa;
      if (icx > Hparam.xlast) icx = 1;
      f[i*3+3] = Hparam.factor*gCurrentHist->GetBinContent(icx, iyt + iya);
      if (Hoption.Logz) {
         if (f[i*3+3] > 0) f[i*3+3] = TMath::Log10(f[i*3+3]);
         else              f[i*3+3] = Hparam.zmin;
         if (f[i*3+3] < Hparam.zmin) f[i*3+3] = Hparam.zmin;
         if (f[i*3+3] > Hparam.zmax) f[i*3+3] = Hparam.zmax;
      } else {
         f[i*3+3] = TMath::Max(Hparam.zmin, f[i*3+3]);
         f[i*3+3] = TMath::Min(Hparam.zmax, f[i*3+3]);
      }
 
   // The colors on the surface can represent the content or the errors.
   // if (fSumw2.fN) t[i] = gCurrentHist->GetBinError(icx, iyt + iya);
   // else           t[i] = f[i * 3 + 3];
      t[i] = f[i * 3 + 3];
   }
 
   //          Define the position of the colored contours for SURF3
   if (Hoption.Surf == 23) {
      for (i = 1; i <= 4; ++i) f[i * 3 + 3] = fRmax[2];
   }
 
   if (Hoption.System == kCYLINDRICAL || Hoption.System == kSPHERICAL || Hoption.System == kRAPIDITY) {
      for (i = 1; i <= 4; ++i) {
         f[i*3 + 3] = (1 - rinrad)*((f[i*3 + 3] - Hparam.zmin) /
         (Hparam.zmax - Hparam.zmin)) + rinrad;
      }
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Draw surface in polar coordinates
///
/// \param[in] iordr   order of variables (0 - R,PHI, 1 - PHI,R)
/// \param[in] na   number of steps along 1st variable
/// \param[in] nb   number of steps along 2nd variable
/// \param[in] chopt specific options
///
/// - `chopt` = 'BF' from BACK to FRONT
/// - `chopt` = 'FB' from FRONT to BACK
 
void TPainter3dAlgorithms::SurfacePolar(Int_t iordr, Int_t na, Int_t nb, const char *chopt)
{
   /* Initialized data */
   static Int_t iface[4] = { 1,2,3,4 };
 
   TView *view = gPad ? gPad->GetView() : nullptr;
   if (!view) {
      Error("SurfacePolar", "no TView in current pad");
      return;
   }
 
   Int_t iphi, jphi, kphi, incr, nphi, iopt, iphi1, iphi2;
   Double_t f[12]        /* was [3][4] */;
   Int_t i, j, incrr, ir1, ir2;
   Double_t z;
   Int_t ia, ib, ir, jr, nr, icodes[3];  // was icode[2]. One element more to differentiate front & back boxes from data
   Double_t tt[4];
   Double_t phi, ttt[4], xyz[12]        /* was [3][4] */;
   ia = ib = 0;
 
   if (iordr == 0) {
      jr   = 1;
      jphi = 2;
      nr   = na;
      nphi = nb;
   } else {
      jr   = 2;
      jphi = 1;
      nr   = nb;
      nphi = na;
   }
   if (fNaphi < nphi + 3) {
     fNaphi = nphi + 3;
     fAphi.resize(fNaphi);
   }
   if (fAphi.empty()) {
      Error("SurfacePolar", "failed to allocate array fAphi[%d]", fNaphi);
      fNaphi = 0;
      return;
   }
   iopt = 2;
   if (*chopt == 'B' || *chopt == 'b') iopt = 1;
 
   //       P R E P A R E   P H I   A R R A Y
   //      F I N D    C R I T I C A L   S E C T O R S
   kphi = nphi;
   if (iordr == 0) ia = nr;
   if (iordr != 0) ib = nr;
   for (i = 1; i <= nphi; ++i) {
      if (iordr == 0) ib = i;
      if (iordr != 0) ia = i;
      (this->*fSurfaceFunction)(ia, ib, f, tt);
      if (i == 1) fAphi[0] = f[jphi - 1];
      fAphi[i - 1] = (fAphi[i - 1] + f[jphi - 1]) / (float)2.;
      fAphi[i] = f[jphi + 5];
   }
   view->FindPhiSectors(iopt, kphi, fAphi.data(), iphi1, iphi2);
 
   //       D R A W   S U R F A C E
   icodes[2] = -1;   // -1 for data, 0 for front a back boxes
   fEdgeIdx = 0;   // constant since stacks are not (yet?) handled for surfaces
   incr = 1;
   iphi = iphi1;
L100:
   if (iphi > nphi) goto L300;
 
   //      F I N D   O R D E R   A L O N G   R
   if (iordr == 0) {ia = nr;         ib = iphi;}
   else            {ia = iphi;ib = nr;}
 
   (this->*fSurfaceFunction)(ia, ib, f, tt);
   phi = kRad*((f[jphi - 1] + f[jphi + 5]) / 2);
   view->FindNormal(TMath::Cos(phi), TMath::Sin(phi), 0, z);
   incrr = 1;
   ir1 = 1;
   if ((z <= 0 && iopt == 1) || (z > 0 && iopt == 2)) {
      incrr = -1;
      ir1 = nr;
   }
   ir2 = nr - ir1 + 1;
   //      D R A W   S U R F A C E   F O R   S E C T O R
   for (ir = ir1; incrr < 0 ? ir >= ir2 : ir <= ir2; ir += incrr) {
      if (iordr == 0) ia = ir;
      if (iordr != 0) ib = ir;
 
      (this->*fSurfaceFunction)(ia, ib, f, tt);
      for (i = 1; i <= 4; ++i) {
         j = i;
         if (iordr != 0 && i == 2) j = 4;
         if (iordr != 0 && i == 4) j = 2;
         xyz[j*3 - 3] = f[jr + i*3 - 4]*TMath::Cos(f[jphi + i*3 - 4]*kRad);
         xyz[j*3 - 2] = f[jr + i*3 - 4]*TMath::Sin(f[jphi + i*3 - 4]*kRad);
         xyz[j*3 - 1] = f[i*3 - 1];
         ttt[j - 1] = tt[i - 1];
      }
      icodes[0] = ia;
      icodes[1] = ib;
      (this->*fDrawFace)(icodes, xyz, 4, iface, ttt);
   }
   //      N E X T   P H I
L300:
   iphi += incr;
   if (iphi == 0)     iphi = kphi;
   if (iphi > kphi)   iphi = 1;
   if (iphi != iphi2) goto L100;
   if (incr == 0) return;
   if (incr < 0) {
      incr = 0;
      goto L100;
   }
   incr = -1;
   iphi = iphi1;
   goto L300;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Draw surface in cylindrical coordinates
///
/// \param[in] iordr   order of variables (0 - Z,PHI; 1 - PHI,Z)
/// \param[in] na   number of steps along 1st variable
/// \param[in] nb   number of steps along 2nd variable
/// \param[in] chopt specific options
///
/// - `chopt` = 'BF' from BACK to FRONT
/// - `chopt` = 'FB' from FRONT to BACK
 
void TPainter3dAlgorithms::SurfaceCylindrical(Int_t iordr, Int_t na, Int_t nb, const char *chopt)
{
 
 
   /* Initialized data */
   static Int_t iface[4] = { 1,2,3,4 };
 
   Int_t iphi, jphi, kphi, incr, nphi, iopt, iphi1, iphi2;
   Int_t i, j, incrz, nz, iz1, iz2;
   Int_t ia, ib, iz, jz, icodes[3];  // was icode[2]. One element more to differentiate front & back boxes from data
   Double_t f[12]        /* was [3][4] */;
   Double_t z;
   Double_t tt[4];
   Double_t ttt[4], xyz[12]        /* was [3][4] */;
   ia = ib = 0;
 
   TView *view = gPad ? gPad->GetView() : nullptr;
   if (!view) {
      Error("SurfaceCylindrical", "no TView in current pad");
      return;
   }
 
   if (iordr == 0) {
      jz   = 1;
      jphi = 2;
      nz   = na;
      nphi = nb;
   } else {
      jz   = 2;
      jphi = 1;
      nz   = nb;
      nphi = na;
   }
   if (fNaphi < nphi + 3) {
     fNaphi = nphi + 3;
     fAphi.resize(fNaphi);
   }
   if (fAphi.empty()) {
      Error("SurfaceCylindrical", "failed to allocate array fAphi[%d]", fNaphi);
      fNaphi = 0;
      return;
   }
   iopt = 2;
   if (*chopt == 'B' || *chopt == 'b') iopt = 1;
 
   //       P R E P A R E   P H I   A R R A Y
   //       F I N D    C R I T I C A L   S E C T O R S
   kphi = nphi;
   if (iordr == 0) ia = nz;
   if (iordr != 0) ib = nz;
   for (i = 1; i <= nphi; ++i) {
      if (iordr == 0) ib = i;
      if (iordr != 0) ia = i;
      (this->*fSurfaceFunction)(ia, ib, f, tt);
      if (i == 1) fAphi[0] = f[jphi - 1];
      fAphi[i - 1] = (fAphi[i - 1] + f[jphi - 1]) / (float)2.;
      fAphi[i] = f[jphi + 5];
   }
   view->FindPhiSectors(iopt, kphi, fAphi.data(), iphi1, iphi2);
 
   //       F I N D   O R D E R   A L O N G   Z
   incrz = 1;
   iz1 = 1;
   view->FindNormal(0, 0, 1, z);
   if ((z <= 0 && iopt == 1) || (z > 0 && iopt == 2)) {
      incrz = -1;
      iz1 = nz;
   }
   iz2 = nz - iz1 + 1;
 
   //       D R A W   S U R F A C E
   icodes[2] = -1;   // -1 for data, 0 for front a back boxes
   fEdgeIdx = 0;   // constant since stacks are not (yet?) handled for surfaces
   incr = 1;
   iphi = iphi1;
L100:
   if (iphi > nphi) goto L400;
   for (iz = iz1; incrz < 0 ? iz >= iz2 : iz <= iz2; iz += incrz) {
      if (iordr == 0) {ia = iz;   ib = iphi;}
      else             {ia = iphi; ib = iz;}
      (this->*fSurfaceFunction)(ia, ib, f, tt);
      for (i = 1; i <= 4; ++i) {
         j = i;
         if (iordr == 0 && i == 2) j = 4;
         if (iordr == 0 && i == 4) j = 2;
         xyz[j*3 - 3] = f[i*3 - 1]*TMath::Cos(f[jphi + i*3 - 4]*kRad);
         xyz[j*3 - 2] = f[i*3 - 1]*TMath::Sin(f[jphi + i*3 - 4]*kRad);
         xyz[j*3 - 1] = f[jz + i*3 - 4];
         ttt[j - 1] = tt[i - 1];
      }
      icodes[0] = ia;
      icodes[1] = ib;
      (this->*fDrawFace)(icodes, xyz, 4, iface, ttt);
   }
   //      N E X T   P H I
L400:
   iphi += incr;
   if (iphi == 0)     iphi = kphi;
   if (iphi > kphi)   iphi = 1;
   if (iphi != iphi2) goto L100;
   if (incr ==  0) return;
   if (incr < 0) {
      incr = 0;
      goto L100;
   }
   incr = -1;
   iphi = iphi1;
   goto L400;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Draw surface in spheric coordinates
///
/// \param[in] ipsdr    pseudo-rapidity flag
/// \param[in] iordr   order of variables (0 - THETA,PHI; 1 - PHI,THETA)
/// \param[in] na   number of steps along 1st variable
/// \param[in] nb   number of steps along 2nd variable
/// \param[in] chopt specific options
///
/// - `chopt` = 'BF' from BACK to FRONT
/// - `chopt` = 'FB' from FRONT to BACK
 
void TPainter3dAlgorithms::SurfaceSpherical(Int_t ipsdr, Int_t iordr, Int_t na, Int_t nb, const char *chopt)
{
   /* Initialized data */
   static Int_t iface[4] = { 1,2,3,4 };
 
   Int_t iphi, jphi, kphi, incr, nphi, iopt, iphi1, iphi2;
   Int_t i, j, incrth, ith, jth, kth, nth, mth, ith1, ith2;
   Int_t ia, ib, icodes[3];  // was icode[2]. One element more to differentiate front & back boxes from data
   Double_t f[12]        /* was [3][4] */;
   Double_t tt[4];
   Double_t phi;
   Double_t ttt[4], xyz[12]        /* was [3][4] */;
   ia = ib = 0;
 
   TView *view = gPad ? gPad->GetView() : nullptr;
   if (!view) {
      Error("SurfaceSpherical", "no TView in current pad");
      return;
   }
 
   if (iordr == 0) {
      jth  = 1;
      jphi = 2;
      nth  = na;
      nphi = nb;
   } else {
      jth  = 2;
      jphi = 1;
      nth  = nb;
      nphi = na;
   }
   if (fNaphi < nth + 3 || fNaphi < nphi + 3) {
     fNaphi = TMath::Max(nth, nphi) + 3;
     fAphi.resize(fNaphi);
   }
   if (fAphi.empty()) {
      Error("SurfaceSpherical", "failed to allocate array fAphi[%d]", fNaphi);
      fNaphi = 0;
      return;
   }
   iopt = 2;
   if (*chopt == 'B' || *chopt == 'b') iopt = 1;
 
   //       P R E P A R E   P H I   A R R A Y
   //       F I N D    C R I T I C A L   P H I   S E C T O R S
   kphi = nphi;
   mth = nth / 2;
   if (mth == 0)    mth = 1;
   if (iordr == 0) ia = mth;
   if (iordr != 0) ib = mth;
   for (i = 1; i <= nphi; ++i) {
      if (iordr == 0) ib = i;
      if (iordr != 0) ia = i;
      (this->*fSurfaceFunction)(ia, ib, f, tt);
      if (i == 1) fAphi[0] = f[jphi - 1];
      fAphi[i - 1] = (fAphi[i - 1] + f[jphi - 1]) / (float)2.;
      fAphi[i] = f[jphi + 5];
   }
   view->FindPhiSectors(iopt, kphi, fAphi.data(), iphi1, iphi2);
 
   //       P R E P A R E   T H E T A   A R R A Y
   if (iordr == 0) ib = 1;
   if (iordr != 0) ia = 1;
   for (i = 1; i <= nth; ++i) {
      if (iordr == 0) ia = i;
      if (iordr != 0) ib = i;
 
      (this->*fSurfaceFunction)(ia, ib, f, tt);
      if (i == 1) fAphi[0] = f[jth - 1];
      fAphi[i - 1] = (fAphi[i - 1] + f[jth - 1]) / (float)2.;
      fAphi[i] = f[jth + 5];
   }
 
   //       D R A W   S U R F A C E
   icodes[2] = -1;   // -1 for data, 0 for front a back boxes
   fEdgeIdx = 0;   // constant since stacks are not (yet?) handled for surfaces
   kth  = nth;
   incr = 1;
   iphi = iphi1;
L100:
   if (iphi > nphi) goto L500;
 
   //      F I N D    C R I T I C A L   T H E T A   S E C T O R S
   if (iordr == 0) {ia = mth; ib = iphi;}
   else             {ia = iphi;ib = mth;}
 
   (this->*fSurfaceFunction)(ia, ib, f, tt);
   phi = (f[jphi - 1] + f[jphi + 5]) / (float)2.;
   view->FindThetaSectors(iopt, phi, kth, fAphi.data(), ith1, ith2);
   incrth = 1;
   ith = ith1;
L200:
   if (ith > nth)   goto L400;
   if (iordr == 0) ia = ith;
   if (iordr != 0) ib = ith;
 
   (this->*fSurfaceFunction)(ia, ib, f, tt);
   if (ipsdr == 1) {
      for (i = 1; i <= 4; ++i) {
         j = i;
         if (iordr != 0 && i == 2) j = 4;
         if (iordr != 0 && i == 4) j = 2;
         xyz[j * 3 - 3] = f[i*3 - 1]*TMath::Cos(f[jphi + i*3 - 4]*kRad);
         xyz[j * 3 - 2] = f[i*3 - 1]*TMath::Sin(f[jphi + i*3 - 4]*kRad);
         xyz[j * 3 - 1] = f[i*3 - 1]*TMath::Cos(f[jth  + i*3 - 4]*kRad) /
                          TMath::Sin(f[jth + i*3 - 4]*kRad);
         ttt[j - 1] = tt[i - 1];
      }
   } else {
      for (i = 1; i <= 4; ++i) {
         j = i;
         if (iordr != 0 && i == 2) j = 4;
         if (iordr != 0 && i == 4) j = 2;
         xyz[j*3 - 3] = f[i*3 - 1]*TMath::Sin(f[jth + i*3 - 4]*kRad)*TMath::Cos(f[jphi + i*3 - 4]*kRad);
         xyz[j*3 - 2] = f[i*3 - 1]*TMath::Sin(f[jth + i*3 - 4]*kRad)*TMath::Sin(f[jphi + i*3 - 4]*kRad);
         xyz[j*3 - 1] = f[i*3 - 1]*TMath::Cos(f[jth + i*3 - 4]*kRad);
         ttt[j - 1] = tt[i - 1];
      }
   }
   icodes[0] = ia;
   icodes[1] = ib;
   (this->*fDrawFace)(icodes, xyz, 4, iface, ttt);
   //      N E X T   T H E T A
L400:
   ith += incrth;
   if (ith == 0)    ith = kth;
   if (ith > kth)   ith = 1;
   if (ith != ith2) goto L200;
   if (incrth == 0)  goto L500;
   if (incrth < 0) {
      incrth = 0;
      goto L200;
   }
   incrth = -1;
   ith = ith1;
   goto L400;
   //      N E X T   P H I
L500:
   iphi += incr;
   if (iphi == 0)     iphi = kphi;
   if (iphi > kphi)   iphi = 1;
   if (iphi != iphi2) goto L100;
   if (incr == 0) return;
   if (incr < 0) {
      incr = 0;
      goto L100;
   }
   incr = -1;
   iphi = iphi1;
   goto L500;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Set surface property coefficients
///
/// \param[in] qqa   diffusion coefficient for diffused light  [0.,1.]
/// \param[in] qqd   diffusion coefficient for direct light    [0.,1.]
/// \param[in] qqs   diffusion coefficient for reflected light [0.,1.]
/// \param[in] nnqs   power coefficient for reflected light     (.GE.1)
///
///    Lightness model formula: Y = YD*QA + > YLi*(QD*cosNi+QS*cosRi)
///
/// \param[out] irep   reply (0 - O.K, -1 error)
 
void TPainter3dAlgorithms::SurfaceProperty(Double_t qqa, Double_t qqd, Double_t qqs, Int_t nnqs, Int_t &irep)
{
   irep = 0;
   if (qqa < 0 || qqa > 1 || qqd < 0 || qqd > 1 || qqs < 0 || qqs > 1 || nnqs < 1) {
      Error("SurfaceProperty", "error in coefficients");
      irep = -1;
      return;
   }
   fQA  = qqa;
   fQD  = qqd;
   fQS  = qqs;
   fNqs = nnqs;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Draw implicit function FUN(X,Y,Z) = 0 in cartesian coordinates using
/// hidden surface removal algorithm "Painter".
///
/// \param[in] f3 pointer to 3D function
/// \param[in] rmin   min scope coordinates
/// \param[in] rmax   max scope coordinates
/// \param[in] nx   number of steps along X
/// \param[in] ny   number of steps along Y
/// \param[in] nz   number of steps along Z
/// \param[in] chopt specific options
///
/// - `chopt` = 'BF' from BACK to FRONT
/// - `chopt` = 'FB' from FRONT to BACK
 
void TPainter3dAlgorithms::ImplicitFunction(TF3 *f3, Double_t *rmin, Double_t *rmax,
                             Int_t nx, Int_t ny, Int_t nz, const char *chopt)
{
   if (!f3) {
      Error("ImplicitFunction", "no TF3 function provided");
      return;
   }
 
   Int_t ix,    iy,    iz;
   Int_t ix1,   iy1,   iz1;
   Int_t ix2,   iy2,   iz2;
   Int_t incr,  incrx, incry, incrz;
   Int_t icodes[3], i, i1, i2, k, nnod, ntria;
   Double_t x1=0, x2=0, y1, y2, z1, z2;
   Double_t dx, dy, dz;
   Double_t p[8][3], pf[8], pn[8][3], t[3], fsurf, w;
 
   Double_t xyz[kNmaxp][3], xyzn[kNmaxp][3], grad[kNmaxp][3];
   Double_t dtria[kNmaxt][6], abcd[kNmaxt][4];
   Int_t    itria[kNmaxt][3], iorder[kNmaxt];
   TView *view = gPad ? gPad->GetView() : nullptr;
 
   if (!view) {
      Error("ImplicitFunction", "no TView in current pad");
      return;
   }
   Double_t *tnorm = view->GetTnorm();
   if (!tnorm) return;
 
 
   Bool_t fgF3Clipping = kFALSE;
   Double_t fgF3XClip = 0., fgF3YClip = 0., fgF3ZClip = 0.;
   const Double_t *clip = f3->GetClippingBox();
   if (clip) {
      fgF3Clipping = kTRUE;
      fgF3XClip = clip[0];
      fgF3YClip = clip[1];
      fgF3ZClip = clip[2];
   }
 
   //       D E F I N E   O R D E R   O F   D R A W I N G
   if (*chopt == 'B' || *chopt == 'b') {
      incrx = +1;
      incry = +1;
      incrz = +1;
   } else {
      incrx = -1;
      incry = -1;
      incrz = -1;
   }
   if (tnorm[8]  < 0.) incrx =-incrx;
   if (tnorm[9]  < 0.) incry =-incry;
   if (tnorm[10] < 0.) incrz =-incrz;
   ix1 = 1;
   iy1 = 1;
   iz1 = 1;
   if (incrx == -1) ix1 = nx;
   if (incry == -1) iy1 = ny;
   if (incrz == -1) iz1 = nz;
   ix2 = nx - ix1 + 1;
   iy2 = ny - iy1 + 1;
   iz2 = nz - iz1 + 1;
   dx  = (rmax[0]-rmin[0]) / nx;
   dy  = (rmax[1]-rmin[1]) / ny;
   dz  = (rmax[2]-rmin[2]) / nz;
 
   // Define the colors used to draw the function
   Float_t r=0., g=0., b=0., hue, light, satur, light2;
   TColor *colref = gROOT->GetColor(f3->GetFillColor());
   if (colref) colref->GetRGB(r, g, b);
   TColor::RGBtoHLS(r, g, b, hue, light, satur);
   TColor *acol;
   acol = gROOT->GetColor(kF3FillColor1);
   if (acol) acol->SetRGB(r, g, b);
   if (light >= 0.5) {
      light2 = .5*light;
   } else {
      light2 = 1-.5*light;
   }
   TColor::HLStoRGB(hue, light2, satur, r, g, b);
   acol = gROOT->GetColor(kF3FillColor2);
   if (acol) acol->SetRGB(r, g, b);
   colref = gROOT->GetColor(f3->GetLineColor());
   if (colref) colref->GetRGB(r, g, b);
   acol = gROOT->GetColor(kF3LineColor);
   if (acol) acol->SetRGB(r, g, b);
 
   //       D R A W   F U N C T I O N
   for (iz = iz1; incrz < 0 ? iz >= iz2 : iz <= iz2; iz += incrz) {
      z1     = (iz-1)*dz + rmin[2];
      z2     = z1 + dz;
      p[0][2] = z1;
      p[1][2] = z1;
      p[2][2] = z1;
      p[3][2] = z1;
      p[4][2] = z2;
      p[5][2] = z2;
      p[6][2] = z2;
      p[7][2] = z2;
      for (iy = iy1; incry < 0 ? iy >= iy2 : iy <= iy2; iy += incry) {
         y1      = (iy-1)*dy + rmin[1];
         y2      = y1 + dy;
         p[0][1] = y1;
         p[1][1] = y1;
         p[2][1] = y2;
         p[3][1] = y2;
         p[4][1] = y1;
         p[5][1] = y1;
         p[6][1] = y2;
         p[7][1] = y2;
         if (incrx == +1) {
            x2    = rmin[0];
            pf[1] = f3->Eval(x2,y1,z1);
            pf[2] = f3->Eval(x2,y2,z1);
            pf[5] = f3->Eval(x2,y1,z2);
            pf[6] = f3->Eval(x2,y2,z2);
         } else {
            x1    = rmax[0];
            pf[0] = f3->Eval(x1,y1,z1);
            pf[3] = f3->Eval(x1,y2,z1);
            pf[4] = f3->Eval(x1,y1,z2);
            pf[7] = f3->Eval(x1,y2,z2);
         }
         for (ix = ix1; incrx < 0 ? ix >= ix2 : ix <= ix2; ix += incrx) {
            icodes[0] = ix;
            icodes[1] = iy;
            icodes[2] = iz;
            if (incrx == +1) {
               x1     = x2;
               x2     = x2 + dx;
               pf[0]  = pf[1];
               pf[3]  = pf[2];
               pf[4]  = pf[5];
               pf[7]  = pf[6];
               pf[1]  = f3->Eval(x2,y1,z1);
               pf[2]  = f3->Eval(x2,y2,z1);
               pf[5]  = f3->Eval(x2,y1,z2);
               pf[6]  = f3->Eval(x2,y2,z2);
            } else {
               x2     = x1;
               x1     = x1 - dx;
               pf[1]  = pf[0];
               pf[2]  = pf[3];
               pf[5]  = pf[4];
               pf[6]  = pf[7];
               pf[0]  = f3->Eval(x1,y1,z1);
               pf[3]  = f3->Eval(x1,y2,z1);
               pf[4]  = f3->Eval(x1,y1,z2);
               pf[7]  = f3->Eval(x1,y2,z2);
            }
            if (pf[0] >= -kFdel) goto L110;
            if (pf[1] >= -kFdel) goto L120;
            if (pf[2] >= -kFdel) goto L120;
            if (pf[3] >= -kFdel) goto L120;
            if (pf[4] >= -kFdel) goto L120;
            if (pf[5] >= -kFdel) goto L120;
            if (pf[6] >= -kFdel) goto L120;
            if (pf[7] >= -kFdel) goto L120;
            goto L510;
L110:
            if (pf[1] < -kFdel) goto L120;
            if (pf[2] < -kFdel) goto L120;
            if (pf[3] < -kFdel) goto L120;
            if (pf[4] < -kFdel) goto L120;
            if (pf[5] < -kFdel) goto L120;
            if (pf[6] < -kFdel) goto L120;
            if (pf[7] < -kFdel) goto L120;
            goto L510;
L120:
            p[0][0] = x1;
            p[1][0] = x2;
            p[2][0] = x2;
            p[3][0] = x1;
            p[4][0] = x1;
            p[5][0] = x2;
            p[6][0] = x2;
            p[7][0] = x1;
 
            //       F I N D   G R A D I E N T S
            // Find X-gradient
            if (ix == 1) {
               pn[0][0] = (pf[1] - pf[0]) / dx;
               pn[3][0] = (pf[2] - pf[3]) / dx;
               pn[4][0] = (pf[5] - pf[4]) / dx;
               pn[7][0] = (pf[6] - pf[7]) / dx;
            } else {
               pn[0][0] = (pf[1] - f3->Eval(x1-dx,y1,z1)) / (dx + dx);
               pn[3][0] = (pf[2] - f3->Eval(x1-dx,y2,z1)) / (dx + dx);
               pn[4][0] = (pf[5] - f3->Eval(x1-dx,y1,z2)) / (dx + dx);
               pn[7][0] = (pf[6] - f3->Eval(x1-dx,y2,z2)) / (dx + dx);
            }
            if (ix == nx) {
               pn[1][0] = (pf[1] - pf[0]) / dx;
               pn[2][0] = (pf[2] - pf[3]) / dx;
               pn[5][0] = (pf[5] - pf[4]) / dx;
               pn[6][0] = (pf[6] - pf[7]) / dx;
            } else {
               pn[1][0] = (f3->Eval(x2+dx,y1,z1) - pf[0]) / (dx + dx);
               pn[2][0] = (f3->Eval(x2+dx,y2,z1) - pf[3]) / (dx + dx);
               pn[5][0] = (f3->Eval(x2+dx,y1,z2) - pf[4]) / (dx + dx);
               pn[6][0] = (f3->Eval(x2+dx,y2,z2) - pf[7]) / (dx + dx);
            }
            // Find Y-gradient
            if (iy == 1) {
               pn[0][1] = (pf[3] - pf[0]) / dy;
               pn[1][1] = (pf[2] - pf[1]) / dy;
               pn[4][1] = (pf[7] - pf[4]) / dy;
               pn[5][1] = (pf[6] - pf[5]) / dy;
            } else {
               pn[0][1] = (pf[3] - f3->Eval(x1,y1-dy,z1)) / (dy + dy);
               pn[1][1] = (pf[2] - f3->Eval(x2,y1-dy,z1)) / (dy + dy);
               pn[4][1] = (pf[7] - f3->Eval(x1,y1-dy,z2)) / (dy + dy);
               pn[5][1] = (pf[6] - f3->Eval(x2,y1-dy,z2)) / (dy + dy);
            }
            if (iy == ny) {
               pn[2][1] = (pf[2] - pf[1]) / dy;
               pn[3][1] = (pf[3] - pf[0]) / dy;
               pn[6][1] = (pf[6] - pf[5]) / dy;
               pn[7][1] = (pf[7] - pf[4]) / dy;
            } else {
               pn[2][1] = (f3->Eval(x2,y2+dy,z1) - pf[1]) / (dy + dy);
               pn[3][1] = (f3->Eval(x1,y2+dy,z1) - pf[0]) / (dy + dy);
               pn[6][1] = (f3->Eval(x2,y2+dy,z2) - pf[5]) / (dy + dy);
               pn[7][1] = (f3->Eval(x1,y2+dy,z2) - pf[4]) / (dy + dy);
            }
            // Find Z-gradient
            if (iz == 1) {
               pn[0][2] = (pf[4] - pf[0]) / dz;
               pn[1][2] = (pf[5] - pf[1]) / dz;
               pn[2][2] = (pf[6] - pf[2]) / dz;
               pn[3][2] = (pf[7] - pf[3]) / dz;
            } else {
               pn[0][2] = (pf[4] - f3->Eval(x1,y1,z1-dz)) / (dz + dz);
               pn[1][2] = (pf[5] - f3->Eval(x2,y1,z1-dz)) / (dz + dz);
               pn[2][2] = (pf[6] - f3->Eval(x2,y2,z1-dz)) / (dz + dz);
               pn[3][2] = (pf[7] - f3->Eval(x1,y2,z1-dz)) / (dz + dz);
            }
            if (iz == nz) {
               pn[4][2] = (pf[4] - pf[0]) / dz;
               pn[5][2] = (pf[5] - pf[1]) / dz;
               pn[6][2] = (pf[6] - pf[2]) / dz;
               pn[7][2] = (pf[7] - pf[3]) / dz;
            } else {
               pn[4][2] = (f3->Eval(x1,y1,z2+dz) - pf[0]) / (dz + dz);
               pn[5][2] = (f3->Eval(x2,y1,z2+dz) - pf[1]) / (dz + dz);
               pn[6][2] = (f3->Eval(x2,y2,z2+dz) - pf[2]) / (dz + dz);
               pn[7][2] = (f3->Eval(x1,y2,z2+dz) - pf[3]) / (dz + dz);
            }
            fsurf = 0.;
            MarchingCube(fsurf, p, pf, pn, nnod, ntria, xyz, grad, itria);
            if (ntria == 0)   goto L510;
 
            for ( i=1 ; i<=nnod ; i++ ) {
               view->WCtoNDC(&xyz[i-1][0], &xyzn[i-1][0]);
               Luminosity(view, &grad[i-1][0], w);
               grad[i-1][0] = w;
            }
            ZDepth(xyzn, ntria, itria, dtria, abcd, (Int_t*)iorder);
            if (ntria == 0)   goto L510;
            incr = 1;
            if (*chopt == 'B' || *chopt == 'b') incr =-1;
            i1 = 1;
            if (incr == -1) i1 = ntria;
            i2 = ntria - i1 + 1;
            // If clipping box is on do not draw the triangles
            if (fgF3Clipping) {
               if(x2<=fgF3XClip && y2 <=fgF3YClip && z2>=fgF3ZClip) goto L510;
            }
            // Draw triangles
            for (i=i1; incr < 0 ? i >= i2 : i <= i2; i += incr) {
               k      = iorder[i-1];
               t[0]   = grad[TMath::Abs(itria[k-1][0])-1][0];
               t[1]   = grad[TMath::Abs(itria[k-1][1])-1][0];
               t[2]   = grad[TMath::Abs(itria[k-1][2])-1][0];
               (this->*fDrawFace)(icodes, (Double_t*)xyz, 3, &itria[k-1][0], t);
            }
L510:
            continue;
         }
      }
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Topological decider for "Marching Cubes" algorithm Find set of triangles
/// approximating the iso-surface F(x,y,z)=Fiso inside the cube
///
/// \param[in] fiso    function value for iso-surface
/// \param[in] p   cube vertexes
/// \param[in] f   function values at the vertexes
/// \param[in] g   function gradients at the vertexes
///
/// \param[out] nnod   number of nodes     (maximum 13)
/// \param[out] ntria   number of triangles (maximum 12)
/// \param[out] xyz   nodes
/// \param[out] grad   node normales       (not normalized)
/// \param[out] itria   triangles
 
void TPainter3dAlgorithms::MarchingCube(Double_t fiso, Double_t p[8][3],
                                        Double_t f[8], Double_t g[8][3],
                                        Int_t &nnod, Int_t &ntria,
                                        Double_t xyz[][3],
                                        Double_t grad[][3],
                                        Int_t itria[][3])
{
   static Int_t irota[24][8] = { { 1,2,3,4,5,6,7,8 }, { 2,3,4,1,6,7,8,5 },
                                 { 3,4,1,2,7,8,5,6 }, { 4,1,2,3,8,5,6,7 },
                                 { 6,5,8,7,2,1,4,3 }, { 5,8,7,6,1,4,3,2 },
                                 { 8,7,6,5,4,3,2,1 }, { 7,6,5,8,3,2,1,4 },
                                 { 2,6,7,3,1,5,8,4 }, { 6,7,3,2,5,8,4,1 },
                                 { 7,3,2,6,8,4,1,5 }, { 3,2,6,7,4,1,5,8 },
                                 { 5,1,4,8,6,2,3,7 }, { 1,4,8,5,2,3,7,6 },
                                 { 4,8,5,1,3,7,6,2 }, { 8,5,1,4,7,6,2,3 },
                                 { 5,6,2,1,8,7,3,4 }, { 6,2,1,5,7,3,4,8 },
                                 { 2,1,5,6,3,4,8,7 }, { 1,5,6,2,4,8,7,3 },
                                 { 4,3,7,8,1,2,6,5 }, { 3,7,8,4,2,6,5,1 },
                                 { 7,8,4,3,6,5,1,2 }, { 8,4,3,7,5,1,2,6 } };
 
   static Int_t iwhat[21] = { 1,3,5,65,50,67,74,51,177,105,113,58,165,178,
                              254,252,250,190,205,188,181 };
   Int_t j, i, i1, i2, i3, ir, irt=0, k, k1, k2, incr, icase=0, n;
   Int_t itr[3];
 
   nnod  = 0;
   ntria = 0;
 
   // F I N D   C O N F I G U R A T I O N   T Y P E
   for ( i=1; i<=8 ; i++) {
      fF8[i-1] = f[i-1] - fiso;
   }
   for ( ir=1 ; ir<=24 ; ir++ ) {
      k    = 0;
      incr = 1;
      for ( i=1 ; i<=8 ; i++ ) {
         if (fF8[irota[ir-1][i-1]-1] >= 0.) k = k + incr;
         incr = incr + incr;
      }
      if (k==0 || k==255) return;
      for ( i=1 ; i<=21 ; i++ ) {
         if (k != iwhat[i-1]) continue;
            icase = i;
            irt   = ir;
            goto L200;
      }
   }
 
   // R O T A T E   C U B E
L200:
   for ( i=1 ; i<=8 ; i++ ) {
      k        = irota[irt-1][i-1];
      fF8[i-1] = f[k-1] - fiso;
      fP8[i-1][0] = p[k-1][0];
      fP8[i-1][1] = p[k-1][1];
      fP8[i-1][2] = p[k-1][2];
      fG8[i-1][0] = g[k-1][0];
      fG8[i-1][1] = g[k-1][1];
      fG8[i-1][2] = g[k-1][2];
   }
 
   // V A R I O U S   C O N F I G U R A T I O N S
   n = 0;
   switch ((int)icase) {
      case 1:
      case 15:
         MarchingCubeCase00(1, 4, 9, 0, 0, 0, nnod, ntria, xyz, grad, itria);
         goto L400;
      case 2:
      case 16:
         MarchingCubeCase00(2, 4, 9, 10, 0, 0, nnod, ntria, xyz, grad, itria);
         goto L400;
      case 3:
      case 17:
         MarchingCubeCase03(nnod, ntria, xyz, grad, itria);
         goto L400;
      case 4:
      case 18:
         MarchingCubeCase04(nnod, ntria, xyz, grad, itria);
         goto L400;
      case 5:
      case 19:
         MarchingCubeCase00(6, 2, 1, 9, 8, 0, nnod, ntria, xyz, grad, itria);
         goto L400;
      case 6:
      case 20:
         MarchingCubeCase06(nnod, ntria, xyz, grad, itria);
         goto L400;
      case 7:
      case 21:
         MarchingCubeCase07(nnod, ntria, xyz, grad, itria);
         goto L400;
      case 8:
         MarchingCubeCase00(2, 4, 8, 6, 0, 0, nnod, ntria, xyz, grad, itria);
         goto L500;
      case 9:
         MarchingCubeCase00(1, 4, 12, 7, 6, 10, nnod, ntria, xyz, grad, itria);
         goto L500;
      case 0:
         MarchingCubeCase10(nnod, ntria, xyz, grad, itria);
         goto L500;
      case 11:
         MarchingCubeCase00(1, 4, 8, 7, 11, 10, nnod, ntria, xyz, grad, itria);
         goto L500;
      case 12:
         MarchingCubeCase12(nnod, ntria, xyz, grad, itria);
         goto L500;
      case 13:
         MarchingCubeCase13(nnod, ntria, xyz, grad, itria);
         goto L500;
      case 14:
         MarchingCubeCase00(1, 9, 12, 7, 6, 2, nnod, ntria, xyz, grad, itria);
         goto L500;
   }
 
   // I F   N E E D E D ,   I N V E R T   T R I A N G L E S
L400:
   if (ntria == 0) return;
   if (icase <= 14) goto L500;
   for ( i=1; i<=ntria ; i++ ) {
      i1 = TMath::Abs(itria[i-1][0]);
      i2 = TMath::Abs(itria[i-1][1]);
      i3 = TMath::Abs(itria[i-1][2]);
      if (itria[i-1][2] < 0) i1 =-i1;
      if (itria[i-1][1] < 0) i3 =-i3;
      if (itria[i-1][0] < 0) i2 =-i2;
      itria[i-1][0] = i1;
      itria[i-1][1] = i3;
      itria[i-1][2] = i2;
   }
 
   // R E M O V E   V E R Y   S M A L L   T R I A N G L E S
L500:
   n = n + 1;
L510:
   if (n > ntria) return;
   for ( i=1 ; i<=3 ; i++ ) {
      i1 = i;
      i2 = i + 1;
      if (i2 == 4) i2 = 1;
      k1 = TMath::Abs(itria[n-1][i1-1]);
      k2 = TMath::Abs(itria[n-1][i2-1]);
      if (TMath::Abs(xyz[k1-1][0]-xyz[k2-1][0]) > kDel) continue;
      if (TMath::Abs(xyz[k1-1][1]-xyz[k2-1][1]) > kDel) continue;
      if (TMath::Abs(xyz[k1-1][2]-xyz[k2-1][2]) > kDel) continue;
      i3 = i - 1;
      if (i3 == 0) i3 = 3;
      goto L530;
   }
   goto L500;
 
   // R E M O V E   T R I A N G L E
L530:
   for ( i=1 ; i<=3 ; i++ ) {
      itr[i-1] = itria[n-1][i-1];
      itria[n-1][i-1] = itria[ntria-1][i-1];
   }
   ntria = ntria - 1;
   if (ntria == 0) return;
   if (itr[i2-1]*itr[i3-1] > 0) goto L510;
 
   // C O R R E C T   O T H E R   T R I A N G L E S
   if (itr[i2-1] < 0) {
      k1 =-itr[i2-1];
      k2 =-TMath::Abs(itr[i3-1]);
   }
   if (itr[i3-1] < 0) {
      k1 =-itr[i3-1];
      k2 =-TMath::Abs(itr[i1-1]);
   }
   for ( j=1 ; j<=ntria ; j++ ) {
      for ( i=1 ; i<=3 ; i++ ) {
         if (itria[j-1][i-1] != k2) continue;
         i2 = TMath::Abs(itria[j-1][0]);
         if (i != 3) i2 = TMath::Abs(itria[j-1][i]);
         if (i2 == k1) itria[j-1][i-1] =-itria[j-1][i-1];
         goto L560;
      }
L560:
      continue;
   }
   goto L510;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Consideration of trivial cases: 1,2,5,8,9,11,14
///
/// \param[in] k1,k2,k3,k4,k5,k6   edges intersected with iso-surface
/// \param[out] nnod number of nodes
/// \param[out] ntria number of triangles
/// \param[out] xyz 3D points
/// \param[out] grad 3D gradients
/// \param[out] itria 3D triangle indices
 
void TPainter3dAlgorithms::MarchingCubeCase00(Int_t k1, Int_t k2, Int_t k3,
                                              Int_t k4, Int_t k5, Int_t k6,
                                              Int_t &nnod, Int_t &ntria,
                                              Double_t xyz[52][3],
                                              Double_t grad[52][3],
                                              Int_t itria[48][3])
{
   static Int_t it[4][4][3] = { { { 1,2, 3 }, { 0,0, 0 }, { 0,0, 0 }, { 0,0, 0 } },
                                { { 1,2,-3 }, {-1,3, 4 }, { 0,0, 0 }, { 0,0, 0 } },
                                { { 1,2,-3 }, {-1,3,-4 }, {-1,4, 5 }, { 0,0, 0 } },
                                { { 1,2,-3 }, {-1,3,-4 }, {-4,6,-1 }, { 4,5,-6 } }
                              };
   Int_t it2[4][3], i, j;
 
   Int_t ie[6];
 
   // S E T   N O D E S   &   N O R M A L E S
   ie[0] = k1;
   ie[1] = k2;
   ie[2] = k3;
   ie[3] = k4;
   ie[4] = k5;
   ie[5] = k6;
   nnod  = 6;
   if (ie[5] == 0) nnod = 5;
   if (ie[4] == 0) nnod = 4;
   if (ie[3] == 0) nnod = 3;
   MarchingCubeFindNodes(nnod, ie, xyz, grad);
 
   // S E T   T R I A N G L E S
   ntria = nnod - 2;
   // Copy "it" into a 2D matrix to be passed to MarchingCubeSetTriangles
   for ( i=0; i<3 ; i++) {
      for ( j=0; j<4 ; j++) {
         it2[j][i] = it[ntria-1][j][i];
      }
   }
   MarchingCubeSetTriangles(ntria, it2, itria);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Consider case No 3
 
void TPainter3dAlgorithms::MarchingCubeCase03(Int_t &nnod, Int_t &ntria,
                               Double_t xyz[52][3], Double_t grad[52][3], Int_t itria[48][3])
{
   Double_t f0;
   static Int_t ie[6]     = { 4,9,1, 2,11,3 };
   static Int_t it1[2][3] = { { 1,2,3 }, { 4,5,6 } };
   static Int_t it2[4][3] = { { 1,2,-5 }, { -1,5,6 }, { 5,-2,4 }, { -4,2,3 } };
 
   //  S E T   N O D E S   &   N O R M A L E S
   nnod = 6;
   MarchingCubeFindNodes(nnod, ie, xyz, grad);
 
   //  F I N D   C O N F I G U R A T I O N
   f0 = (fF8[0]*fF8[2]-fF8[1]*fF8[3]) / (fF8[0]+fF8[2]-fF8[1]-fF8[3]);
   if (f0>=0. && fF8[0]>=0.) goto L100;
   if (f0<0. && fF8[0]<0.) goto L100;
   ntria = 2;
   MarchingCubeSetTriangles(ntria, it1, itria);
   return;
 
   //  N O T   S E P A R A T E D   F R O N T   F A C E
L100:
   ntria = 4;
   MarchingCubeSetTriangles(ntria, it2, itria);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Consider case No 4
 
void TPainter3dAlgorithms::MarchingCubeCase04(Int_t &nnod, Int_t &ntria,
                               Double_t xyz[52][3], Double_t grad[52][3], Int_t itria[48][3])
{
   Int_t irep;
   static Int_t ie[6]     = { 4,9,1, 7,11,6 };
   static Int_t it1[2][3] = { { 1,2,3 }, { 4,5,6 } };
   static Int_t it2[6][3] = { { 1,2,4 }, { 2,3,6 }, { 3,1,5 },
                              { 4,5,1 }, { 5,6,3 }, { 6,4,2 } };
 
   //  S E T   N O D E S   &   N O R M A L E S
   nnod = 6;
   MarchingCubeFindNodes(nnod, ie, xyz, grad);
 
   //  I S   T H E R E   S U R F A C E   P E N E T R A T I O N ?
   MarchingCubeSurfacePenetration(fF8[0], fF8[1], fF8[2], fF8[3],
                                  fF8[4], fF8[5], fF8[6], fF8[7], irep);
   if (irep == 0) {
      ntria = 2;
      MarchingCubeSetTriangles(ntria, it1, itria);
   } else {
      ntria = 6;
      MarchingCubeSetTriangles(ntria, it2, itria);
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Consider case No 6
 
void TPainter3dAlgorithms::MarchingCubeCase06(Int_t &nnod, Int_t &ntria,
                               Double_t xyz[52][3], Double_t grad[52][3], Int_t itria[48][3])
{
   Double_t f0;
   Int_t irep;
 
   static Int_t ie[7]     = { 2,4,9,10, 6,7,11 };
   static Int_t it1[5][3] = { { 6,7,-1 }, { -6,1,2 }, { 6,2,3 }, { 6,3,-4 }, { -6,4,5 } };
   static Int_t it2[3][3] = { { 1,2,-3 }, { -1,3,4 }, { 5,6,7 } };
   static Int_t it3[7][3] = { { 6,7,-1 }, { -6,1,2 }, { 6,2,3 }, { 6,3,-4 }, { -6,4,5 },
                              { 1,7,-5 }, { -1,5,4 } };
 
   //  S E T   N O D E S   &   N O R M A L E S
   nnod = 7;
   MarchingCubeFindNodes(nnod, ie, xyz, grad);
 
   //  F I N D   C O N F I G U R A T I O N
   f0 = (fF8[1]*fF8[6]-fF8[5]*fF8[2]) / (fF8[1]+fF8[6]-fF8[5]-fF8[2]);
   if (f0>=0. && fF8[1]>=0.) goto L100;
   if (f0<0. && fF8[1]<0.) goto L100;
 
   //  I S   T H E R E   S U R F A C E   P E N E T R A T I O N ?
   MarchingCubeSurfacePenetration(fF8[2], fF8[1], fF8[5], fF8[6],
                                  fF8[3], fF8[0], fF8[4], fF8[7], irep);
   if (irep == 1) {
      ntria = 7;
      MarchingCubeSetTriangles(ntria, it3, itria);
   } else {
      ntria = 3;
      MarchingCubeSetTriangles(ntria, it2, itria);
   }
   return;
 
   //  N O T   S E P A R A T E D   R I G H T   F A C E
L100:
   ntria = 5;
   MarchingCubeSetTriangles(ntria, it1, itria);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Consider case No 7
 
void TPainter3dAlgorithms::MarchingCubeCase07(Int_t &nnod, Int_t &ntria,
                               Double_t xyz[52][3], Double_t grad[52][3],
                               Int_t itria[48][3])
{
   Double_t f1, f2, f3;
   Int_t icase, irep;
   static Int_t ie[9] = { 3,12,4, 1,10,2, 11,6,7 };
   static Int_t it[9][9][3] = {
   {{  1,2,3}, {  4,5,6}, {  7,8,9}, {  0,0,0}, {  0,0,0}, {  0,0,0}, {  0,0,0}, {  0,0,0}, {  0,0,0}},
   {{  1,2,3}, { 4,9,-7}, { -4,7,6}, { 9,4,-5}, { -9,5,8}, {  0,0,0}, {  0,0,0}, {  0,0,0}, {  0,0,0}},
   {{  4,5,6}, { 8,3,-1}, { -8,1,7}, { 3,8,-9}, { -3,9,2}, {  0,0,0}, {  0,0,0}, {  0,0,0}, {  0,0,0}},
   {{-10,2,3}, {10,3,-1}, {-10,1,7}, {10,7,-6}, {-10,6,4}, {10,4,-5}, {-10,5,8}, { 10,8,9}, {10,9,-2}},
   {{  7,8,9}, { 2,5,-6}, { -2,6,1}, { 5,2,-3}, { -5,3,4}, {  0,0,0}, {  0,0,0}, {  0,0,0}, {  0,0,0}},
   {{-10,1,2}, {10,2,-3}, {-10,3,4}, { 10,4,5}, {10,5,-8}, {-10,8,9}, {10,9,-7}, {-10,7,6}, {10,6,-1}},
   {{ 10,2,3}, {10,3,-4}, {-10,4,5}, {10,5,-6}, {-10,6,1}, {10,1,-7}, {-10,7,8}, {10,8,-9}, {-10,9,2}},
   {{  1,7,6}, { -4,2,3}, {-4,9,-2}, {-9,4,-5}, { -9,5,8}, {  0,0,0}, {  0,0,0}, {  0,0,0}, {  0,0,0}},
   {{ -1,9,2}, {  1,2,3}, { 1,3,-4}, { 6,-1,4}, {  6,4,5}, { 6,-5,7}, { -7,5,8}, {  7,8,9}, { 7,-9,1}}
   };
 
   Int_t it2[9][3], i, j;
 
   //  S E T   N O D E S   &   N O R M A L E S
   nnod = 9;
   MarchingCubeFindNodes(nnod, ie, xyz, grad);
 
   //  F I N D   C O N F I G U R A T I O N
   f1 = (fF8[2]*fF8[5]-fF8[1]*fF8[6]) / (fF8[2]+fF8[5]-fF8[1]-fF8[6]);
   f2 = (fF8[2]*fF8[7]-fF8[3]*fF8[6]) / (fF8[2]+fF8[7]-fF8[3]-fF8[6]);
   f3 = (fF8[2]*fF8[0]-fF8[1]*fF8[3]) / (fF8[2]+fF8[0]-fF8[1]-fF8[3]);
   icase = 1;
   if (f1>=0. && fF8[2] <0.) icase = icase + 1;
   if (f1 <0. && fF8[2]>=0.) icase = icase + 1;
   if (f2>=0. && fF8[2] <0.) icase = icase + 2;
   if (f2 <0. && fF8[2]>=0.) icase = icase + 2;
   if (f3>=0. && fF8[2] <0.) icase = icase + 4;
   if (f3 <0. && fF8[2]>=0.) icase = icase + 4;
   ntria = 5;
 
   switch ((int)icase) {
      case 1:  goto L100;
      case 2:  goto L400;
      case 3:  goto L400;
      case 4:  goto L200;
      case 5:  goto L400;
      case 6:  goto L200;
      case 7:  goto L200;
      case 8:  goto L300;
   }
 
L100:
   ntria = 3;
   goto L400;
 
   //  F I N D   A D D I T I O N A L   P O I N T
L200:
   nnod  = 10;
   ntria = 9;
 
   // Copy "it" into a 2D matrix to be passed to MarchingCubeMiddlePoint
   for ( i=0; i<3 ; i++) {
      for ( j=0; j<9 ; j++) {
         it2[j][i] = it[icase-1][j][i];
      }
   }
   MarchingCubeMiddlePoint(9, xyz, grad, it2, &xyz[nnod-1][0], &grad[nnod-1][0]);
   goto L400;
 
   //  I S   T H E R E   S U R F A C E   P E N E T R A T I O N ?
L300:
   MarchingCubeSurfacePenetration(fF8[3], fF8[2], fF8[6], fF8[7],
                                  fF8[0], fF8[1], fF8[5], fF8[4], irep);
   if (irep != 2) goto L400;
   ntria = 9;
   icase = 9;
 
   //  S E T   T R I A N G L E S
L400:
   // Copy "it" into a 2D matrix to be passed to MarchingCubeSetTriangles
   for ( i=0; i<3 ; i++) {
      for ( j=0; j<9 ; j++) {
         it2[j][i] = it[icase-1][j][i];
      }
   }
   MarchingCubeSetTriangles(ntria, it2, itria);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Consider case No 10
 
void TPainter3dAlgorithms::MarchingCubeCase10(Int_t &nnod, Int_t &ntria,
                               Double_t xyz[52][3], Double_t grad[52][3], Int_t itria[48][3])
{
   Double_t f1, f2;
   Int_t icase, irep;
   static Int_t ie[8] = { 1,3,12,9, 5,7,11,10 };
   static Int_t it[6][8][3] = {
   {{1,2,-3}, {-1,3,4}, {5,6,-7}, {-5,7,8}, { 0,0,0}, { 0,0,0}, { 0,0,0}, { 0,0,0}},
   {{ 9,1,2}, { 9,2,3}, { 9,3,4}, { 9,4,5}, { 9,5,6}, { 9,6,7}, { 9,7,8}, { 9,8,1}},
   {{ 9,1,2}, { 9,4,1}, { 9,3,4}, { 9,6,3}, { 9,5,6}, { 9,8,5}, { 9,7,8}, { 9,2,7}},
   {{1,2,-7}, {-1,7,8}, {5,6,-3}, {-5,3,4}, { 0,0,0}, { 0,0,0}, { 0,0,0}, { 0,0,0}},
   {{1,2,-7}, {-1,7,8}, {2,3,-6}, {-2,6,7}, {3,4,-5}, {-3,5,6}, {4,1,-8}, {-4,8,5}},
   {{1,2,-3}, {-1,3,4}, {2,7,-6}, {-2,6,3}, {7,8,-5}, {-7,5,6}, {8,1,-4}, {-8,4,5}}
   };
   Int_t it2[8][3], i, j;
 
   //  S E T   N O D E S   &   N O R M A L E S
   nnod = 8;
   MarchingCubeFindNodes(nnod, ie, xyz, grad);
 
   //  F I N D   C O N F I G U R A T I O N
   f1 = (fF8[0]*fF8[5]-fF8[1]*fF8[4]) / (fF8[0]+fF8[5]-fF8[1]-fF8[4]);
   f2 = (fF8[3]*fF8[6]-fF8[2]*fF8[7]) / (fF8[3]+fF8[6]-fF8[2]-fF8[5]);
   icase = 1;
   if (f1 >= 0.) icase = icase + 1;
   if (f2 >= 0.) icase = icase + 2;
   if (icase==1 || icase==4) goto L100;
 
   // D I F F E R E N T    T O P   A N D   B O T T O M
   nnod  = 9;
   ntria = 8;
   // Copy "it" into a 2D matrix to be passed to MarchingCubeMiddlePoint
   for ( i=0; i<3 ; i++) {
      for ( j=0; j<8 ; j++) {
         it2[j][i] = it[icase-1][j][i];
      }
   }
   MarchingCubeMiddlePoint(8, xyz, grad, it2, &xyz[nnod-1][0], &grad[nnod-1][0]);
   goto L200;
 
   //  I S   T H E R E   S U R F A C E   P E N E T R A T I O N ?
L100:
   MarchingCubeSurfacePenetration(fF8[0], fF8[1], fF8[5], fF8[4],
                                  fF8[3], fF8[2], fF8[6], fF8[7], irep);
   ntria = 4;
   if (irep == 0) goto L200;
   //  "B O T T L E   N E C K"
   ntria = 8;
   if (icase == 1) icase = 5;
   if (icase == 4) icase = 6;
 
   //  S E T   T R I A N G L E S
L200:
   // Copy "it" into a 2D matrix to be passed to MarchingCubeSetTriangles
   for ( i=0; i<3 ; i++) {
      for ( j=0; j<8 ; j++) {
         it2[j][i] = it[icase-1][j][i];
      }
   }
   MarchingCubeSetTriangles(ntria, it2, itria);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Consider case No 12
 
void TPainter3dAlgorithms::MarchingCubeCase12(Int_t &nnod, Int_t &ntria,
                               Double_t xyz[52][3], Double_t grad[52][3], Int_t itria[48][3])
{
   Double_t f1, f2;
   Int_t icase, irep;
   static Int_t ie[8] = { 3,12,4, 1,9,8,6,2 };
   static Int_t it[6][8][3] = {
   {{ 1,2,3},  {4,5,-6}, {-4,6,8}, { 6,7,8}, { 0,0,0}, { 0,0,0}, { 0,0,0}, { 0,0,0}},
   {{-9,1,2},  {9,2,-3}, {-9,3,4}, {9,4,-5}, {-9,5,6}, {9,6,-7}, {-9,7,8}, {9,8,-1}},
   {{9,1,-2},  {-9,2,6}, {9,6,-7}, {-9,7,8}, {9,8,-4}, {-9,4,5}, {9,5,-3}, {-9,3,1}},
   {{ 3,4,5},  {1,2,-6}, {-1,6,8}, { 6,7,8}, { 0,0,0}, { 0,0,0}, { 0,0,0}, { 0,0,0}},
   {{ 7,8,6},  {6,8,-1}, {-6,1,2}, {3,1,-8}, {-3,8,4}, { 3,4,5}, {3,5,-6}, {-3,6,2}},
   {{ 7,8,6},  {6,8,-4}, {-6,4,5}, {3,4,-8}, {-3,8,1}, { 3,1,2}, {3,2,-6}, {-3,6,5}}
   };
   Int_t it2[8][3], i, j;
 
   //  S E T   N O D E S   &   N O R M A L E S
   nnod = 8;
   MarchingCubeFindNodes(nnod, ie, xyz, grad);
 
   //  F I N D   C O N F I G U R A T I O N
   f1 = (fF8[0]*fF8[2]-fF8[1]*fF8[3]) / (fF8[0]+fF8[2]-fF8[1]-fF8[3]);
   f2 = (fF8[0]*fF8[7]-fF8[3]*fF8[4]) / (fF8[0]+fF8[7]-fF8[3]-fF8[4]);
   icase = 1;
   if (f1 >= 0.) icase = icase + 1;
   if (f2 >= 0.) icase = icase + 2;
   if (icase==1 || icase==4) goto L100;
 
   //  F I N D   A D D I T I O N A L   P O I N T
   nnod  = 9;
   ntria = 8;
   // Copy "it" into a 2D matrix to be passed to MarchingCubeMiddlePoint
   for ( i=0; i<3 ; i++) {
      for ( j=0; j<8 ; j++) {
         it2[j][i] = it[icase-1][j][i];
      }
   }
   MarchingCubeMiddlePoint(8, xyz, grad, it2, &xyz[nnod-1][0], &grad[nnod-1][0]);
   goto L200;
 
   //  I S   T H E R E   S U R F A C E   P E N E T R A T I O N ?
L100:
   MarchingCubeSurfacePenetration(fF8[0], fF8[1], fF8[2], fF8[3],
                                  fF8[4], fF8[5], fF8[6], fF8[7], irep);
   ntria = 4;
   if (irep != 1) goto L200;
   //  "B O T T L E   N E C K"
   ntria = 8;
   if (icase == 1) icase = 5;
   if (icase == 4) icase = 6;
 
   //  S E T   T R I A N G L E S
L200:
   // Copy "it" into a 2D matrix to be passed to MarchingCubeSetTriangles
   for ( i=0; i<3 ; i++) {
      for ( j=0; j<8 ; j++) {
         it2[j][i] = it[icase-1][j][i];
      }
   }
   MarchingCubeSetTriangles(ntria, it2, itria);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Consider case No 13
 
void TPainter3dAlgorithms::MarchingCubeCase13(Int_t &nnod, Int_t &ntria,
                               Double_t xyz[52][3], Double_t grad[52][3], Int_t itria[48][3])
{
   Double_t ff[8];
   Double_t f1, f2, f3, f4;
   Int_t nr, nf, i, k, incr, n, kr, icase, irep;
   static Int_t irota[12][8] = {
         {1,2,3,4,5,6,7,8}, {1,5,6,2,4,8,7,3}, {1,4,8,5,2,3,7,6},
         {3,7,8,4,2,6,5,1}, {3,2,6,7,4,1,5,8}, {3,4,1,2,7,8,5,6},
         {6,7,3,2,5,8,4,1}, {6,5,8,7,2,1,4,3}, {6,2,1,5,7,3,4,8},
         {8,4,3,7,5,1,2,6}, {8,5,1,4,7,6,2,3}, {8,7,6,5,4,3,2,1} };
   static Int_t iwhat[8] = { 63,62,54,26,50,9,1,0 };
   static Int_t ie[12] = { 1,2,3,4,5,6,7,8,9,10,11,12 };
   static Int_t iface[6][4] = {
         {1,2,3,4}, {5,6,7,8}, {1,2,6,5}, {2,6,7,3}, {4,3,7,8}, {1,5,8,4} };
   static Int_t it1[4][3] = { {1,2,10}, {9,5,8}, {6,11,7}, {3,4,12} };
   static Int_t it2[4][3] = { {5,6,10}, {1,4,9}, {2,11,3}, {7,8,12} };
   static Int_t it3[6][3] = { {10,12,-3}, {-10,3,2}, {12,10,-1}, {-12,1,4},
         {9,5,8}, {6,11,7} };
   static Int_t it4[6][3] = { {11,9,-1}, {-11,1,2}, {9,11,-3}, {-9,3,4},
         {5,6,10}, {7,8,12} };
   static Int_t it5[10][3] = { {13,2,-11}, {-13,11,7}, {13,7,-6}, {-13,6,10},
         {13,10,1}, {13,1,-4}, {-13,4,12}, {13,12,-3}, {-13,3,2}, {5,8,9} };
   static Int_t it6[10][3] = { {13,2,-10}, {-13,10,5}, {13,5,-6}, {-13,6,11},
         {13,11,3}, {13,3,-4}, {-13,4,9}, {13,9,-1}, {-13,1,2}, {12,7,8} };
   static Int_t it7[12][3] = { {13,2,-11}, {-13,11,7}, {13,7,-6}, {-13,6,10},
         {13,10,-5}, {-13,5,8}, {13,8,-9}, {-13,9,1},
         {13,1,-4}, {-13,4,12}, {13,12,-3}, {-13,3,2} };
   static Int_t it8[6][3] = { {3,8,12}, {3,-2,-8}, {-2,5,-8}, {2,10,-5},
         {7,6,11}, {1,4,9} };
   static Int_t it9[10][3] = { {7,12,-3}, {-7,3,11}, {11,3,2}, {6,11,-2}, {-6,2,10},
         {6,10,5}, {7,6,-5}, {-7,5,8}, {7,8,12}, {1,4,9} };
   static Int_t it10[10][3] = { {9,1,-10}, {-9,10,5}, {9,5,8}, {4,9,-8}, {-4,8,12},
         {4,12,3}, {1,4,-3}, {-1,3,2}, {1,2,10}, {7,6,11} };
 
      nnod = 0;
      ntria = 0;
 
   // F I N D   C O N F I G U R A T I O N   T Y P E
   for ( nr=1 ; nr<=12 ; nr++ ) {
      k = 0;
      incr = 1;
      for ( nf=1 ; nf<=6 ; nf++ ) {
         f1 = fF8[irota[nr-1][iface[nf-1][0]-1]-1];
         f2 = fF8[irota[nr-1][iface[nf-1][1]-1]-1];
         f3 = fF8[irota[nr-1][iface[nf-1][2]-1]-1];
         f4 = fF8[irota[nr-1][iface[nf-1][3]-1]-1];
         if ((f1*f3-f2*f4)/(f1+f3-f2-f4) >= 0.) k = k + incr;
         incr = incr + incr;
      }
      for ( i=1 ; i<=8 ; i++ ) {
         if (k != iwhat[i-1]) continue;
         icase = i;
         kr = nr;
         goto L200;
      }
   }
   Error("MarchingCubeCase13", "configuration is not found");
   return;
 
   //  R O T A T E   C U B E
L200:
   if (icase==1 || icase==8) goto L300;
   for ( n=1 ; n<=8 ; n++) {
      k = irota[kr-1][n-1];
      ff[n-1] = fF8[k-1];
      for ( i=1 ; i<=3 ; i++ ) {
         xyz[n-1][i-1] = fP8[k-1][i-1];
         grad[n-1][i-1] = fG8[k-1][i-1];
      }
   }
   for ( n=1 ; n<=8 ; n++ ) {
      fF8[n-1] = ff[n-1];
      for ( i=1 ; i<=3 ; i++ ) {
         fP8[n-1][i-1] = xyz[n-1][i-1];
         fG8[n-1][i-1] = grad[n-1][i-1];
      }
   }
 
   //  S E T   N O D E S   &   N O R M A L E S
L300:
   nnod = 12;
   MarchingCubeFindNodes(nnod, ie, xyz, grad);
 
   //  V A R I O U S   C O N F I G U R A T I O N S
   switch ((int)icase) {
      case 1:
         ntria = 4;
         MarchingCubeSetTriangles(ntria, it1, itria);
         return;
      case 8:
         ntria = 4;
         MarchingCubeSetTriangles(ntria, it2, itria);
         return;
      case 2:
         ntria = 6;
         MarchingCubeSetTriangles(ntria, it3, itria);
         return;
      case 7:
         ntria = 6;
         MarchingCubeSetTriangles(ntria, it4, itria);
         return;
      case 3:
         nnod = 13;
         ntria = 10;
         MarchingCubeMiddlePoint(9, xyz, grad, it5,
                                 &xyz[nnod-1][0], &grad[nnod-1][0]);
         MarchingCubeSetTriangles(ntria, it5, itria);
         return;
      case 6:
         nnod = 13;
         ntria = 10;
         MarchingCubeMiddlePoint(9, xyz, grad, it6,
                                 &xyz[nnod-1][0], &grad[nnod-1][0]);
         MarchingCubeSetTriangles(ntria, it6, itria);
         return;
      case 5:
         nnod = 13;
         ntria = 12;
         MarchingCubeMiddlePoint(12, xyz, grad, it7,
                                 &xyz[nnod-1][0], &grad[nnod-1][0]);
         MarchingCubeSetTriangles(ntria, it7, itria);
         return;
      //  I S   T H E R E   S U R F A C E   P E N E T R A T I O N ?
      case 4:
         MarchingCubeSurfacePenetration(fF8[2], fF8[3], fF8[0], fF8[1],
                                        fF8[6], fF8[7], fF8[4], fF8[5], irep);
         switch ((int)(irep+1)) {
            case 1:
               ntria = 6;
               MarchingCubeSetTriangles(ntria, it8, itria);
               return;
            case 2:
               ntria = 10;
               MarchingCubeSetTriangles(ntria, it9, itria);
               return;
            case 3:
               ntria = 10;
               MarchingCubeSetTriangles(ntria, it10, itria);
         }
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Set triangles (if parameter IALL=1, all edges will be visible)
///
/// \param[in] ntria   number of triangles
/// \param[in] it   triangles
///
/// \param[out] itria   triangles
 
void TPainter3dAlgorithms::MarchingCubeSetTriangles(Int_t ntria, Int_t it[][3],
                                                    Int_t itria[48][3])
{
   Int_t n, i, k;
 
   for ( n=1 ; n<=ntria ; n++ ) {
      for ( i=1 ; i<=3 ; i++ ) {
         k = it[n-1][i-1];
         itria[n-1][i-1] = k;
      }
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Find middle point of a polygon
///
/// \param[in] nnod   number of nodes in the polygon
/// \param[in] xyz   node coordinates
/// \param[in] grad   node normales
/// \param[in] it   division of the polygons into triangles
///
/// \param[out] pxyz   middle point coordinates
/// \param[out] pgrad   middle point normale
 
void TPainter3dAlgorithms::MarchingCubeMiddlePoint(Int_t nnod, Double_t xyz[52][3],
                                    Double_t grad[52][3],
                                    Int_t it[][3], Double_t *pxyz,
                                    Double_t *pgrad)
{
   Double_t p[3], g[3];
   Int_t i, n, k;
 
   for ( i=1 ; i<=3 ; i++ ) {
      p[i-1] = 0.;
      g[i-1] = 0.;
   }
   for ( n=1 ; n<=nnod ; n++ ) {
      k = it[n-1][2];
      if (k < 0) k =-k;
      for ( i=1 ; i<=3 ; i++ ) {
         p[i-1] = p[i-1] + xyz[k-1][i-1];
         g[i-1] = g[i-1] + grad[k-1][i-1];
      }
   }
   for ( i=1 ; i<=3 ; i++ ) {
      pxyz[i-1] = p[i-1] / nnod;
      pgrad[i-1] = g[i-1] / nnod;
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Check for surface penetration ("bottle neck")
///
/// \param[in] a00,a10,a11,a01   vertex values for 1st face
/// \param[in] b00,b10,b11,b01   vertex values for opposite face
///
/// \param[out] irep   1,2: there is surface penetration, 0: there is not surface penetration
 
void TPainter3dAlgorithms::MarchingCubeSurfacePenetration(Double_t a00, Double_t a10,
                                           Double_t a11, Double_t a01,
                                           Double_t b00, Double_t b10,
                                           Double_t b11, Double_t b01,
                                           Int_t &irep)
{
   Double_t a, b, c, d, s0, s1, s2;
   Int_t iposa, iposb;
 
   irep = 0;
   a = (a11-a01)*(b00-b10) - (a00-a10)*(b11-b01);
   if (a == 0.) return;
   b = a01*(b00-b10)-(a11-a01)*b00-(a00-a10)*b01+a00*(b11-b01);
   c = a00*b01 - a01*b00;
   d = b*b-4*a*c;
   if (d <= 0.) return;
   d = TMath::Sqrt(d);
   if (TMath::Abs(-b+d) > TMath::Abs(2*a)) return;
   s1 = (-b+d) / (2*a);
   if (s1<0. || s1>1.) return;
   if (TMath::Abs(-b-d) > TMath::Abs(2*a)) return;
   s2 = (-b-d) / (2*a);
   if (s2<0. || s2>1.) return;
 
   //  C A S E   N O   4 ?
   iposa = 0;
   if (a00 >= 0) iposa = iposa + 1;
   if (a01 >= 0) iposa = iposa + 2;
   if (a10 >= 0) iposa = iposa + 4;
   if (a11 >= 0) iposa = iposa + 8;
   if (iposa==6 || iposa==9) goto L100;
   irep = 1;
   return;
 
   //  N O T   C A S E   N O   4
L100:
   s0 = (a00-a01) / (a00+a11-a10-a01);
   if (s1>=s0 && s2<s0) return;
   if (s1<s0 && s2>=s0) return;
   irep = 1;
   if (s1 >= s0) irep = 2;
 
   //  C A S E S   N O   10, 13 ?
   iposb = 0;
   if (b00 >= 0) iposb = iposb + 1;
   if (b01 >= 0) iposb = iposb + 2;
   if (b10 >= 0) iposb = iposb + 4;
   if (b11 >= 0) iposb = iposb + 8;
   if (iposb!=6 && iposb!=9)  return;
   s0 = (b00-b01) / (b00+b11-b10-b01);
   if (iposa != iposb) goto L200;
   //  C A S E   N O   10
   if (irep==1 && s1>s0) return;
   if (irep==2 && s1<s0) return;
   irep = 0;
   return;
   //  C A S E   N O   13
L200:
   if (irep==1 && s1<s0) return;
   if (irep==2 && s1>s0) return;
   irep = 0;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Find nodes and normales
///
/// \param[in] nnod   number of nodes
/// \param[in] ie   edges which have section node
///
/// \param[out] xyz   nodes
/// \param[out] grad   ode normales (not normalized)
 
void TPainter3dAlgorithms::MarchingCubeFindNodes(Int_t nnod,
                                  Int_t *ie, Double_t xyz[52][3],
                                  Double_t grad[52][3])
{
   Int_t n, k, i, n1, n2;
   Double_t t;
   static Int_t iedge[12][2] = {
         {1,2}, {2,3}, {3,4}, {4,1}, {5,6}, {6,7}, {7,8}, {8,5}, {1,5}, {2,6}, {3,7}, {4,8} };
 
   for ( n=1 ; n<=nnod ; n++ ) {
      k = ie[n-1];
      if (k < 0) k =-k;
      n1 = iedge[k-1][0];
      n2 = iedge[k-1][1];
      t = fF8[n1-1] / (fF8[n1-1]-fF8[n2-1]);
      for ( i=1 ; i<=3 ; i++ ) {
         xyz[n-1][i-1] = (fP8[n2-1][i-1]-fP8[n1-1][i-1])*t + fP8[n1-1][i-1];
         grad[n-1][i-1] = (fG8[n2-1][i-1]-fG8[n1-1][i-1])*t + fG8[n1-1][i-1];
      }
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Z-depth algorithm for set of triangles
///
/// \param[in] xyz   nodes
/// \param[in] nface   number of triangular faces
/// \param[in] iface   faces (triangles)
///
/// \param[in] dface   array for min-max scopes
/// \param[in] abcd   array for face plane equations
///
/// \param[out] iorder   face order
 
void TPainter3dAlgorithms::ZDepth(Double_t xyz[52][3], Int_t &nface,
                                  Int_t iface[48][3], Double_t dface[48][6],
                                  Double_t abcd[48][4], Int_t *iorder)
{
   Int_t n, nf, i1, i2, i3, i, icur, k, itst, kface, kf, irep;
   Int_t nn[3], kk[3];
   Double_t wmin, wmax, a, b, c, q, zcur;
   Double_t v[2][3], abcdn[4], abcdk[4];
 
   //  S E T   I N I T I A L   O R D E R
   //  I G N O R E   V E R Y   S M A L L   F A C E S
   //  S E T   M I N - M A X   S C O P E S
   //  S E T   F A C E   P L A N E   E Q U A T I O N S
   nf = 0;
   for ( n=1 ; n<=nface ; n++ ) {
      i1 = TMath::Abs(iface[n-1][0]);
      i2 = TMath::Abs(iface[n-1][1]);
      i3 = TMath::Abs(iface[n-1][2]);
   //       A R E A   T E S T
      if (TMath::Abs(xyz[i2-1][0]-xyz[i1-1][0])<=kDel &&
          TMath::Abs(xyz[i2-1][1]-xyz[i1-1][1])<=kDel &&
          TMath::Abs(xyz[i2-1][2]-xyz[i1-1][2])<=kDel) continue;
      if (TMath::Abs(xyz[i3-1][0]-xyz[i2-1][0])<=kDel &&
          TMath::Abs(xyz[i3-1][1]-xyz[i2-1][1])<=kDel &&
          TMath::Abs(xyz[i3-1][2]-xyz[i2-1][2])<=kDel) continue;
      if (TMath::Abs(xyz[i1-1][0]-xyz[i3-1][0])<=kDel &&
          TMath::Abs(xyz[i1-1][1]-xyz[i3-1][1])<=kDel &&
          TMath::Abs(xyz[i1-1][2]-xyz[i3-1][2])<=kDel) continue;
   //       P R O J E C T I O N   T E S T
      if (TMath::Abs(xyz[i2-1][0]-xyz[i1-1][0])<=kDel &&
          TMath::Abs(xyz[i2-1][1]-xyz[i1-1][1])<=kDel &&
          TMath::Abs(xyz[i3-1][0]-xyz[i2-1][0])<=kDel &&
          TMath::Abs(xyz[i3-1][1]-xyz[i2-1][1])<=kDel &&
          TMath::Abs(xyz[i1-1][0]-xyz[i3-1][0])<=kDel &&
          TMath::Abs(xyz[i1-1][1]-xyz[i3-1][1])<=kDel) continue;
      nf = nf + 1;
      iorder[nf-1] = n;
   //       F I N D   M I N - M A X
      for ( i=1 ; i<=3 ; i++ ) {
         wmin = xyz[i1-1][i-1];
         wmax = xyz[i1-1][i-1];
         if (wmin > xyz[i2-1][i-1]) wmin = xyz[i2-1][i-1];
         if (wmax < xyz[i2-1][i-1]) wmax = xyz[i2-1][i-1];
         if (wmin > xyz[i3-1][i-1]) wmin = xyz[i3-1][i-1];
         if (wmax < xyz[i3-1][i-1]) wmax = xyz[i3-1][i-1];
         dface[n-1][i-1] = wmin;
         dface[n-1][i+2] = wmax;
      }
   //      F I N D   F A C E   E Q U A T I O N
      for ( i=1 ; i<=3 ; i++ ) {
         v[0][i-1] = xyz[i2-1][i-1] - xyz[i1-1][i-1];
         v[1][i-1] = xyz[i3-1][i-1] - xyz[i2-1][i-1];
      }
      a = (v[0][1]*v[1][2] - v[0][2]*v[1][1]);
      b = (v[0][2]*v[1][0] - v[0][0]*v[1][2]);
      c = (v[0][0]*v[1][1] - v[0][1]*v[1][0]);
      q = TMath::Sqrt(a*a+b*b+c*c);
      if (c < 0.) q =-q;
      a = a / q;
      b = b / q;
      c = c / q;
      abcd[n-1][0] = a;
      abcd[n-1][1] = b;
      abcd[n-1][2] = c;
      abcd[n-1][3] =-(a*xyz[i1-1][0] + b*xyz[i1-1][1] + c*xyz[i1-1][2]);
   }
   nface = nf;
   if (nf <= 1) return;
 
   //  S O R T   T R I A N G L E S   A L O N G   Z - M I N
   for ( icur=2 ; icur<=nface ; icur++ ) {
      k = iorder[icur-1];
      zcur = dface[k-1][2];
      for ( itst=icur-1 ; itst>=1 ; itst-- ) {
         k = iorder[itst-1];
         if (zcur < dface[k-1][2]) break;
         k = iorder[itst-1];
         iorder[itst-1] = iorder[itst];
         iorder[itst] = k;
      }
   }
 
   //  Z - D E P T H   A L G O R I T H M
   kface  = nface;
L300:
   if (kface == 1) goto L900;
   nf = iorder[kface-1];
   if (nf < 0) nf =-nf;
   abcdn[0] = abcd[nf-1][0];
   abcdn[1] = abcd[nf-1][1];
   abcdn[2] = abcd[nf-1][2];
   abcdn[3] = abcd[nf-1][3];
   nn[0] = TMath::Abs(iface[nf-1][0]);
   nn[1] = TMath::Abs(iface[nf-1][1]);
   nn[2] = TMath::Abs(iface[nf-1][2]);
 
   //  I N T E R N A L   L O O P
   for ( k=kface-1 ; k>=1 ; k-- ) {
      kf = iorder[k-1];
      if (kf < 0) kf =-kf;
      if (dface[nf-1][5] > dface[kf-1][2]+kDel) goto L400;
      if (iorder[k-1] > 0) goto L900;
      goto L800;
 
   //  M I N - M A X   T E S T
L400:
      if (dface[kf-1][0] >= dface[nf-1][3]-kDel) goto L800;
      if (dface[kf-1][3] <= dface[nf-1][0]+kDel) goto L800;
      if (dface[kf-1][1] >= dface[nf-1][4]-kDel) goto L800;
      if (dface[kf-1][4] <= dface[nf-1][1]+kDel) goto L800;
 
   //  K F   B E F O R E   N F ?
      kk[0] = TMath::Abs(iface[kf-1][0]);
      kk[1] = TMath::Abs(iface[kf-1][1]);
      kk[2] = TMath::Abs(iface[kf-1][2]);
      if (abcdn[0]*xyz[kk[0]-1][0]+abcdn[1]*xyz[kk[0]-1][1]+
          abcdn[2]*xyz[kk[0]-1][2]+abcdn[3] < -kDel) goto L500;
      if (abcdn[0]*xyz[kk[1]-1][0]+abcdn[1]*xyz[kk[1]-1][1]+
          abcdn[2]*xyz[kk[1]-1][2]+abcdn[3] < -kDel) goto L500;
      if (abcdn[0]*xyz[kk[2]-1][0]+abcdn[1]*xyz[kk[2]-1][1]+
          abcdn[2]*xyz[kk[2]-1][2]+abcdn[3] < -kDel) goto L500;
      goto L800;
 
   //  N F    A F T E R    K F ?
L500:
      abcdk[0] = abcd[kf-1][0];
      abcdk[1] = abcd[kf-1][1];
      abcdk[2] = abcd[kf-1][2];
      abcdk[3] = abcd[kf-1][3];
      if (abcdk[0]*xyz[nn[0]-1][0]+abcdk[1]*xyz[nn[0]-1][1]+
          abcdk[2]*xyz[nn[0]-1][2]+abcdk[3] > kDel) goto L600;
      if (abcdk[0]*xyz[nn[1]-1][0]+abcdk[1]*xyz[nn[1]-1][1]+
          abcdk[2]*xyz[nn[1]-1][2]+abcdk[3] > kDel) goto L600;
      if (abcdk[0]*xyz[nn[2]-1][0]+abcdk[1]*xyz[nn[2]-1][1]+
          abcdk[2]*xyz[nn[2]-1][2]+abcdk[3] > kDel) goto L600;
      goto L800;
 
   //  E D G E   B Y   E D G E   T E S T
   //  K F - E D G E S   A G A I N S T   N F
L600:
      for ( i=1 ; i<=3 ; i++ ) {
         i1 = kk[i-1];
         i2 = kk[0];
         if (i != 3) i2 = kk[i];
         TestEdge(kDel, xyz, i1, i2, nn, abcdn, irep);
         if ( irep<0 ) goto L700;
         if ( irep==0 ) continue;
         if ( irep>0 ) goto L800;
      }
   //  N F - E D G E S   A G A I N S T   K F
      for ( i=1 ; i<=3 ; i++ ) {
         i1 = nn[i-1];
         i2 = nn[0];
         if (i != 3) i2 = nn[i];
         TestEdge(kDel, xyz, i1, i2, kk, abcdk, irep);
         if ( irep<0 ) goto L800;
         if ( irep==0 ) continue;
         if ( irep>0 ) goto L700;
      }
      goto L800;
 
   //  C H A N G E   F A C E   O R D E R
L700:
      kf = iorder[k-1];
      for ( i=k+1 ; i<=kface ; i++ ) {
         iorder[i-2] = iorder[i-1];
      }
      iorder[kface-1] =-kf;
      if (kf > 0) goto L300;
      goto L900;
L800:
      continue;
   }
 
   //  N E X T   F A C E
L900:
   if (iorder[kface-1] < 0) iorder[kface-1] =-iorder[kface-1];
   kface = kface - 1;
   if (kface > 0) goto L300;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Test edge against face (triangle)
///
/// \param[in] del   precision
/// \param[in] xyz   nodes
/// \param[in] i1   1-st node of edge
/// \param[in] i2   2-nd node of edge
/// \param[in] iface   triangular face
/// \param[in] abcd   face plane
///
/// \param[out] irep   1: edge under face, 0: no decision, +1: edge before face
 
void TPainter3dAlgorithms::TestEdge(Double_t del, Double_t xyz[52][3], Int_t i1, Int_t i2,
                     Int_t iface[3], Double_t abcd[4], Int_t &irep)
{
   Int_t k, k1, k2, ixy, i;
   Double_t a, b, c, d1, d2, dd, xy, tmin, tmax, tmid, x, y, z;
   Double_t d[3], delta[3], t[2];
 
   irep  = 0;
 
   //  F I N D   I N T E R S E C T I O N   P O I N T S
   delta[0] = xyz[i2-1][0] - xyz[i1-1][0];
   delta[1] = xyz[i2-1][1] - xyz[i1-1][1];
   delta[2] = xyz[i2-1][2] - xyz[i1-1][2];
   if (TMath::Abs(delta[0])<=del && TMath::Abs(delta[1])<=del) return;
   ixy = 1;
   if (TMath::Abs(delta[1]) > TMath::Abs(delta[0])) ixy = 2;
   a = delta[1];
   b =-delta[0];
   c =-(a*xyz[i1-1][0] + b*xyz[i1-1][1]);
   d[0] = a*xyz[iface[0]-1][0] + b*xyz[iface[0]-1][1] + c;
   d[1] = a*xyz[iface[1]-1][0] + b*xyz[iface[1]-1][1] + c;
   d[2] = a*xyz[iface[2]-1][0] + b*xyz[iface[2]-1][1] + c;
   k = 0;
   for ( i=1 ; i<=3 ; i++ ) {
      k1 = i;
      k2 = i + 1;
      if (i == 3) k2 = 1;
      if (d[k1-1]>=0. && d[k2-1]>=0.) continue;
      if (d[k1-1] <0. && d[k2-1] <0.) continue;
      d1 = d[k1-1] / (d[k1-1] - d[k2-1]);
      d2 = d[k2-1] / (d[k1-1] - d[k2-1]);
      xy = d1*xyz[iface[k2-1]-1][ixy-1] - d2*xyz[iface[k1-1]-1][ixy-1];
      k = k + 1;
      t[k-1] = (xy-xyz[i1-1][ixy-1]) / delta[ixy-1];
      if (k == 2) goto L200;
   }
   return;
 
   //  C O M P A R E   Z - D E P T H
L200:
   tmin = TMath::Min(t[0],t[1]);
   tmax = TMath::Max(t[0],t[1]);
   if (tmin>1. || tmax<0) return;
   if (tmin < 0.) tmin = 0.;
   if (tmax > 1.) tmax = 1.;
   tmid = (tmin + tmax) / 2.;
   x = delta[0]*tmid + xyz[i1-1][0];
   y = delta[1]*tmid + xyz[i1-1][1];
   z = delta[2]*tmid + xyz[i1-1][2];
   dd = abcd[0]*x + abcd[1]*y + abcd[2]*z + abcd[3];
   if (dd > del) goto L997;
   if (dd <-del) goto L998;
   return;
 
L997:
   irep =+1;
   return;
L998:
   irep =-1;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Draw set of iso-surfaces for a scalar function defined on a grid.
///
/// \param[in] ns   number of iso-surfaces
/// \param[in] s   iso-surface values
/// \param[in] nx   number of slices along X
/// \param[in] ny   number of slices along Y
/// \param[in] nz   number of slices along Z
/// \param[in] x   slices along X
/// \param[in] y   slices along Y
/// \param[in] z   slices along Z
/// \param[in] chopt specific options
///
/// - chopt` = 'BF' from BACK to FRONT
/// - chopt` = 'FB' from FRONT to BACK
 
void TPainter3dAlgorithms::IsoSurface (Int_t ns, Double_t *s, Int_t nx,
                                       Int_t ny, Int_t nz,
                                       Double_t *x, Double_t *y, Double_t *z,
                                       const char *chopt)
{
   Double_t p[8][3], pf[8], pn[8][3];
   Double_t p0[3], p1[3], p2[3], p3[3], t[3];
   Double_t fsurf, w, d1, d2, df1, df2;
   Int_t icodes[3];
   Int_t i, i1, i2, j, ibase, nnod, knod, ntria, ktria, iopt, iready;
   Int_t ixcrit, iycrit, izcrit, incrx, incry, incrz, incr;
   Int_t ix, ix1=0, ix2=0, iy, iy1=0, iy2=0, iz, iz1=0, iz2=0, k, kx, ky, kz, isurf, nsurf;
 
   Double_t xyz[kNmaxp][3], xyzn[kNmaxp][3], grad[kNmaxp][3];
   Double_t dtria[kNmaxt][6], abcd[kNmaxt][4];
   Int_t    itria[kNmaxt][3], iorder[kNmaxt], iattr[kNmaxt];
 
   static Int_t ind[8][3] = { { 0,0,0 }, { 1,0,0 }, { 1,0,1 }, { 0,0,1 },
                              { 0,1,0 }, { 1,1,0 }, { 1,1,1 }, { 0,1,1 } };
   for (i=0;i<kNmaxp;i++) {
      xyzn[i][0] = 0.;
      xyzn[i][1] = 0.;
      xyzn[i][2] = 0.;
   }
 
   TView *view = gPad ? gPad->GetView() : nullptr;
   if (!view) {
      Error("ImplicitFunction", "no TView in current pad");
      return;
   }
 
   nsurf = ns;
   if (nsurf > kNiso) {
      Warning("IsoSurface","Number of iso-surfaces too large. Increase kNiso");
   }
   iopt = 2;
   if (*chopt == 'B' || *chopt == 'b') iopt = 1;
 
   //       F I N D   X - , Y - , Z - C R I T I C A L
   //       This logic works for parallel projection only.
   //       For central projection another logic should be implemented.
   p0[0] = x[0];
   p0[1] = y[0];
   p0[2] = z[0];
   view->WCtoNDC(p0, p0);
   p1[0] = x[nx-1];
   p1[1] = y[0];
   p1[2] = z[0];
   view->WCtoNDC(p1, p1);
   p2[0] = x[0];
   p2[1] = y[ny-1];
   p2[2] = z[0];
   view->WCtoNDC(p2, p2);
   p3[0] = x[0];
   p3[1] = y[0];
   p3[2] = z[nz-1];
   view->WCtoNDC(p3, p3);
   ixcrit = nx;
   iycrit = ny;
   izcrit = nz;
   if (p1[2] < p0[2]) ixcrit = 1;
   if (p2[2] < p0[2]) iycrit = 1;
   if (p3[2] < p0[2]) izcrit = 1;
 
   //       L O O P   A L O N G   G R I D
   //       This logic works for both (parallel & central) projections.
   incrx = 1;
   incry = 1;
   incrz = 1;
L110:
   if (incrz >= 0) {
      if (iopt == 1) iz1 = 1;
      if (iopt == 1) iz2 = izcrit-1;
      if (iopt == 2) iz1 = izcrit;
      if (iopt == 2) iz2 = nz - 1;
   } else {
      if (iopt == 1) iz1 = nz - 1;
      if (iopt == 1) iz2 = izcrit;
      if (iopt == 2) iz1 = izcrit-1;
      if (iopt == 2) iz2 = 1;
   }
   for (iz = iz1; incrz < 0 ? iz >= iz2 : iz <= iz2; iz += incrz) {
L120:
      if (incry >= 0) {
         if (iopt == 1) iy1 = 1;
         if (iopt == 1) iy2 = iycrit-1;
         if (iopt == 2) iy1 = iycrit;
         if (iopt == 2) iy2 = ny - 1;
      } else {
         if (iopt == 1) iy1 = ny - 1;
         if (iopt == 1) iy2 = iycrit;
         if (iopt == 2) iy1 = iycrit-1;
         if (iopt == 2) iy2 = 1;
      }
      for (iy = iy1; incry < 0 ? iy >= iy2 : iy <= iy2; iy += incry) {
L130:
         if (incrx >= 0) {
            if (iopt == 1) ix1 = 1;
            if (iopt == 1) ix2 = ixcrit-1;
            if (iopt == 2) ix1 = ixcrit;
            if (iopt == 2) ix2 = nx - 1;
         } else {
            if (iopt == 1) ix1 = nx - 1;
            if (iopt == 1) ix2 = ixcrit;
            if (iopt == 2) ix1 = ixcrit-1;
            if (iopt == 2) ix2 = 1;
         }
         for (ix = ix1; incrx < 0 ? ix >= ix2 : ix <= ix2; ix += incrx) {
            nnod = 0;
            ntria = 0;
            iready = 0;
            for ( isurf=1 ; isurf<=nsurf ; isurf++ ) {
               fsurf = s[isurf-1];
               if (gCurrentHist->GetBinContent(ix,  iy,  iz)   >= fsurf)
                  goto L210;
               if (gCurrentHist->GetBinContent(ix+1,iy,  iz)   >= fsurf)
                  goto L220;
               if (gCurrentHist->GetBinContent(ix,  iy+1,iz)   >= fsurf)
                  goto L220;
               if (gCurrentHist->GetBinContent(ix+1,iy+1,iz)   >= fsurf)
                  goto L220;
               if (gCurrentHist->GetBinContent(ix,  iy,  iz+1) >= fsurf)
                  goto L220;
               if (gCurrentHist->GetBinContent(ix+1,iy,  iz+1) >= fsurf)
                  goto L220;
               if (gCurrentHist->GetBinContent(ix,  iy+1,iz+1) >= fsurf)
                  goto L220;
               if (gCurrentHist->GetBinContent(ix+1,iy+1,iz+1) >= fsurf)
                  goto L220;
               continue;
L210:
               if (gCurrentHist->GetBinContent(ix+1,iy,  iz)   < fsurf)
                  goto L220;
               if (gCurrentHist->GetBinContent(ix,  iy+1,iz)   < fsurf)
                  goto L220;
               if (gCurrentHist->GetBinContent(ix+1,iy+1,iz)   < fsurf)
                  goto L220;
               if (gCurrentHist->GetBinContent(ix,  iy,  iz+1) < fsurf)
                  goto L220;
               if (gCurrentHist->GetBinContent(ix+1,iy,  iz+1) < fsurf)
                  goto L220;
               if (gCurrentHist->GetBinContent(ix,  iy+1,iz+1) < fsurf)
                  goto L220;
               if (gCurrentHist->GetBinContent(ix+1,iy+1,iz+1) < fsurf)
                  goto L220;
               continue;
 
   //       P R E P A R E   C U B E   ( P A R A L L E P I P E D )
L220:
               if (iready !=0) goto L310;
               iready = 1;
               for ( i=1 ; i<=8 ; i++ ) {
                  kx = ix + ind[i-1][0];
                  ky = iy + ind[i-1][1];
                  kz = iz + ind[i-1][2];
                  p[i-1][0] = x[kx-1];
                  p[i-1][1] = y[ky-1];
                  p[i-1][2] = z[kz-1];
                  pf[i-1] = gCurrentHist->GetBinContent(kx,ky,kz);
   //       F I N D   X - G R A D I E N T
                  if (kx == 1) {
                     pn[i-1][0] = (gCurrentHist->GetBinContent(2,ky,kz) -
                                   gCurrentHist->GetBinContent(1,ky,kz)) /
                                   (x[1]-x[0]);
                  } else if (kx == nx) {
                     pn[i-1][0] = (gCurrentHist->GetBinContent(kx,ky,kz) -
                                   gCurrentHist->GetBinContent(kx-1,ky,kz)) /
                                   (x[kx-1]-x[kx-2]);
                  } else {
                     d1 = x[kx-1] - x[kx-2];
                     d2 = x[kx] - x[kx-1];
                     if (d1 == d2) {
                        pn[i-1][0] = (gCurrentHist->GetBinContent(kx+1,ky,kz) -
                                      gCurrentHist->GetBinContent(kx-1,ky,kz)) /
                                      (d1+d1);
                     } else {
                        df1 = gCurrentHist->GetBinContent(kx,ky,kz) -
                              gCurrentHist->GetBinContent(kx-1,ky,kz);
                        df2 = gCurrentHist->GetBinContent(kx+1,ky,kz) -
                              gCurrentHist->GetBinContent(kx,ky,kz);
                        pn[i-1][0] = (df1*d2*d2+df2*d1*d1)/(d1*d2*d2+d2*d1*d1);
                     }
                  }
   //       F I N D   Y - G R A D I E N T
                  if (ky == 1) {
                     pn[i-1][1] = (gCurrentHist->GetBinContent(kx,2,kz) -
                                   gCurrentHist->GetBinContent(kx,1,kz)) /
                                   (y[1]-y[0]);
                  } else if (ky == ny) {
                     pn[i-1][1] = (gCurrentHist->GetBinContent(kx,ky,kz) -
                                   gCurrentHist->GetBinContent(kx,ky-1,kz)) /
                                   (y[ky-1]-y[ky-2]);
                  } else {
                     d1 = y[ky-1] - y[ky-2];
                     d2 = y[ky] - y[ky-1];
                     if (d1 == d2) {
                        pn[i-1][1] = (gCurrentHist->GetBinContent(kx,ky+1,kz) -
                                      gCurrentHist->GetBinContent(kx,ky-1,kz)) /
                                      (d1+d1);
                     } else {
                        df1 = gCurrentHist->GetBinContent(kx,ky,kz) -
                              gCurrentHist->GetBinContent(kx,ky-1,kz);
                        df2 = gCurrentHist->GetBinContent(kx,ky+1,kz) -
                              gCurrentHist->GetBinContent(kx,ky,kz);
                        pn[i-1][1] = (df1*d2*d2+df2*d1*d1)/(d1*d2*d2+d2*d1*d1);
                     }
                  }
   //       F I N D   Z - G R A D I E N T
                  if (kz == 1) {
                     pn[i-1][2] = (gCurrentHist->GetBinContent(kx,ky,2) -
                                   gCurrentHist->GetBinContent(kx,ky,1)) /
                                   (z[1]-z[0]);
                  } else if (kz == nz) {
                     pn[i-1][2] = (gCurrentHist->GetBinContent(kx,ky,kz) -
                                   gCurrentHist->GetBinContent(kx,ky,kz-1)) /
                                   (z[kz-1]-z[kz-2]);
                  } else {
                     d1 = z[kz-1] - z[kz-2];
                     d2 = z[kz] - z[kz-1];
                     if (d1 == d2) {
                        pn[i-1][2] = (gCurrentHist->GetBinContent(kx,ky,kz+1) -
                                      gCurrentHist->GetBinContent(kx,ky,kz-1)) /
                                      (d1+d1);
                     } else {
                        df1 = gCurrentHist->GetBinContent(kx,ky,kz) -
                              gCurrentHist->GetBinContent(kx,ky,kz-1);
                        df2 = gCurrentHist->GetBinContent(kx,ky,kz+1) -
                              gCurrentHist->GetBinContent(kx,ky,kz);
                        pn[i-1][2] = (df1*d2*d2+df2*d1*d1)/(d1*d2*d2+d2*d1*d1);
                     }
                  }
               }
 
   //       F I N D   S E T   O F   T R I A N G L E S
L310:
               Double_t xyz_tmp[kNmaxp][3], grad_tmp[kNmaxp][3];
               Int_t itria_tmp[kNmaxt][3], l;
 
               MarchingCube(s[isurf-1], p, pf, pn, knod, ktria,
                            xyz_tmp, grad_tmp, itria_tmp);
 
               for( l=0 ; l<knod ; l++) {
                  xyz[nnod+l][0] = xyz_tmp[l][0];
                  xyz[nnod+l][1] = xyz_tmp[l][1];
                  xyz[nnod+l][2] = xyz_tmp[l][2];
                  grad[nnod+l][0] = grad_tmp[l][0];
                  grad[nnod+l][1] = grad_tmp[l][1];
                  grad[nnod+l][2] = grad_tmp[l][2];
               }
               for( l=0 ; l<ktria ; l++) {
                  itria[ntria+l][0] = itria_tmp[l][0];
                  itria[ntria+l][1] = itria_tmp[l][1];
                  itria[ntria+l][2] = itria_tmp[l][2];
               }
 
               for ( i=ntria+1 ; i<=ntria+ktria ; i++ ) {
                 for ( j=1 ; j<=3 ; j++ ){
                     ibase = nnod;
                     if (itria[i-1][j-1] < 0) ibase =-nnod;
                     itria[i-1][j-1] = itria[i-1][j-1] + ibase;
                  }
                  iattr[i-1] = isurf;
               }
               nnod = nnod + knod;
               ntria = ntria + ktria;
            }
 
   //       D E P T H   S O R T,   D R A W I N G
            if (ntria == 0) continue;
            for ( i=1 ; i<=nnod ; i++ ) {
               view->WCtoNDC(&xyz[i-1][0], &xyzn[i-1][0]);
               Luminosity(view, &grad[i-1][0], w);
               grad[i-1][0] = w;
            }
            ZDepth(xyzn, ntria, itria, dtria, abcd, (Int_t*)iorder);
            if (ntria == 0) continue;
            incr = 1;
            if (iopt == 1) incr = -1;
            i1 = 1;
            if (incr == -1) i1 = ntria;
            i2 = ntria - i1 + 1;
            for (i = i1; incr < 0 ? i >= i2 : i <= i2; i += incr) {
               k = iorder[i-1];
               t[0] = grad[TMath::Abs(itria[k-1][0])-1][0];
               t[1] = grad[TMath::Abs(itria[k-1][1])-1][0];
               t[2] = grad[TMath::Abs(itria[k-1][2])-1][0];
               icodes[0] = iattr[k-1];
               icodes[1] = iattr[k-1];
               icodes[2] = iattr[k-1];
               DrawFaceGouraudShaded(icodes, xyz, 3, &itria[k-1][0], t);
            }
         }
         incrx = -incrx;
         if (incrx < 0) goto L130;
      }
      incry = -incry;
      if (incry < 0) goto L120;
   }
   incrz = -incrz;
   if (incrz < 0) goto L110;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Draw the faces for the Gouraud Shaded Iso surfaces
 
void TPainter3dAlgorithms::DrawFaceGouraudShaded(Int_t *icodes,
                                                 Double_t xyz[][3],
                                                 Int_t np, Int_t *iface,
                                                 Double_t *t)
{
   Int_t i, k, irep;
   Double_t p3[12][3];
 
   TView *view = gPad ? gPad->GetView() : nullptr;
   if (!view) {
      Error("ImplicitFunction", "no TView in current pad");
      return;
   }
 
   if (icodes[0]==1) Spectrum(fNcolor, fFmin, fFmax, fIc1, 1, irep);
   if (icodes[0]==2) Spectrum(fNcolor, fFmin, fFmax, fIc2, 1, irep);
   if (icodes[0]==3) Spectrum(fNcolor, fFmin, fFmax, fIc3, 1, irep);
   for ( i=1 ; i<=np ; i++) {
      k = iface[i-1];
      if (k<0) k = -k;
      view->WCtoNDC(&xyz[k-1][0], &p3[i-1][0]);
   }
   FillPolygon(np, (Double_t *)p3, (Double_t *)t);
}