/*=========================================================================

  Program:   Visualization Toolkit
  Module:    vtkHexagonalPrism.cxx

  Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
  All rights reserved.
  See Copyright.txt or http://www.kitware.com/Copyright.htm for details.

     This software is distributed WITHOUT ANY WARRANTY; without even
     the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
     PURPOSE.  See the above copyright notice for more information.

=========================================================================*/

// Thanks to Philippe Guerville who developed this class.
// Thanks to Charles Pignerol (CEA-DAM, France) who ported this class under
// VTK 4.
// Thanks to Jean Favre (CSCS, Switzerland) who contributed to integrate this
// class in VTK.
// Please address all comments to Jean Favre (jfavre at cscs.ch).

#include "vtkHexagonalPrism.h"

#include "vtkObjectFactory.h"
#include "vtkLine.h"
#include "vtkQuad.h"
#include "vtkPolygon.h"
#include "vtkMath.h"
#include "vtkPoints.h"

vtkCxxRevisionMacro(vtkHexagonalPrism, "1.5");
vtkStandardNewMacro(vtkHexagonalPrism);

static const double VTK_DIVERGED = 1.e6;

// You can recompute the value by doing:
// const double a = sqrt(3.0)/4.0 + 0.5;
#define EXPRA 0.933012701892219298

// You can recompute the value by doing:
// const double b = 0.5 - sqrt(3.0)/4.0;
// Thus EXPRA + EXPRB = 1.0
#define EXPRB 0.066987298107780702

//----------------------------------------------------------------------------
// Construct the prism with twelve points.
vtkHexagonalPrism::vtkHexagonalPrism()
{
  int i;
  this->Points->SetNumberOfPoints(12);
  this->PointIds->SetNumberOfIds(12);

  for (i = 0; i < 12; i++)
    {
    this->Points->SetPoint(i, 0.0, 0.0, 0.0);
    this->PointIds->SetId(i,0);
    }

  this->Line = vtkLine::New();
  this->Quad = vtkQuad::New();
  this->Polygon = vtkPolygon::New();
  this->Polygon->PointIds->SetNumberOfIds(6);
  this->Polygon->Points->SetNumberOfPoints(6);

  for (i = 0; i < 6; i++)
    {
    this->Polygon->Points->SetPoint(i, 0.0, 0.0, 0.0);
    this->Polygon->PointIds->SetId(i,0);
    }
}

//----------------------------------------------------------------------------
vtkHexagonalPrism::~vtkHexagonalPrism()
{
  this->Line->Delete();
  this->Quad->Delete();
  this->Polygon->Delete();
}

//  Method to calculate parametric coordinates in an eight noded
//  linear hexahedron element from global coordinates.
//
static const int VTK_HEX_MAX_ITERATION=10;
static const double VTK_HEX_CONVERGED=1.e-03;

//----------------------------------------------------------------------------
int vtkHexagonalPrism::EvaluatePosition(double x[3], double* closestPoint,
                                        int& subId, double pcoords[3],
                                        double& dist2, double *weights)
{
  int iteration, converged;
  double  params[3];
  double  fcol[3], rcol[3], scol[3], tcol[3];
  int i, j;
  double  d, pt[3];
  double derivs[36];

  //  set initial position for Newton's method
  subId = 0;
  pcoords[0] = pcoords[1] = pcoords[2] = params[0] = params[1] = params[2]=0.5;

  //  enter iteration loop
  for (iteration=converged=0;
       !converged && (iteration < VTK_HEX_MAX_ITERATION);  iteration++)
    {
    //  calculate element interpolation functions and derivatives
    this->InterpolationFunctions(pcoords, weights);
    this->InterpolationDerivs(pcoords, derivs);

    //  calculate newton functions
    for (i=0; i<3; i++)
      {
      fcol[i] = rcol[i] = scol[i] = tcol[i] = 0.0;
      }
    for (i=0; i<12; i++)
      {
      this->Points->GetPoint(i, pt);
      for (j=0; j<3; j++)
        {
        fcol[j] += pt[j] * weights[i];
        rcol[j] += pt[j] * derivs[i];
        scol[j] += pt[j] * derivs[i+12];
        tcol[j] += pt[j] * derivs[i+24];
        }
      }

    for (i=0; i<3; i++)
      {
      fcol[i] -= x[i];
      }

    //  compute determinants and generate improvements
    d=vtkMath::Determinant3x3(rcol,scol,tcol);
    if ( fabs(d) < 1.e-20)
      {
      return -1;
      }

    pcoords[0] = params[0] - vtkMath::Determinant3x3 (fcol,scol,tcol) / d;
    pcoords[1] = params[1] - vtkMath::Determinant3x3 (rcol,fcol,tcol) / d;
    pcoords[2] = params[2] - vtkMath::Determinant3x3 (rcol,scol,fcol) / d;

    //  check for convergence
    if ( ((fabs(pcoords[0]-params[0])) < VTK_HEX_CONVERGED) &&
         ((fabs(pcoords[1]-params[1])) < VTK_HEX_CONVERGED) &&
         ((fabs(pcoords[2]-params[2])) < VTK_HEX_CONVERGED) )
      {
      converged = 1;
      }

    // Test for bad divergence (S.Hirschberg 11.12.2001)
    else if ((fabs(pcoords[0]) > VTK_DIVERGED) ||
             (fabs(pcoords[1]) > VTK_DIVERGED) ||
             (fabs(pcoords[2]) > VTK_DIVERGED))
      {
      return -1;
      }

    //  if not converged, repeat
    else
      {
      params[0] = pcoords[0];
      params[1] = pcoords[1];
      params[2] = pcoords[2];
      }
    }

  //  if not converged, set the parametric coordinates to arbitrary values
  //  outside of element
  if ( !converged )
    {
    return -1;
    }

  this->InterpolationFunctions(pcoords, weights);

  if ( pcoords[0] >= -0.001 && pcoords[0] <= 1.001 &&
  pcoords[1] >= -0.001 && pcoords[1] <= 1.001 &&
  pcoords[2] >= -0.001 && pcoords[2] <= 1.001 )
    {
    if (closestPoint)
      {
      closestPoint[0] = x[0]; closestPoint[1] = x[1]; closestPoint[2] = x[2];
      dist2 = 0.0; //inside hexahedron
      }
    return 1;
    }
  else
    {
    double pc[3], w[12];
    if (closestPoint)
      {
      for (i=0; i<3; i++) //only approximate, not really true for warped hexa
        {
        if (pcoords[i] < 0.0)
          {
          pc[i] = 0.0;
          }
        else if (pcoords[i] > 1.0)
          {
          pc[i] = 1.0;
          }
        else
          {
          pc[i] = pcoords[i];
          }
        }
      this->EvaluateLocation(subId, pc, closestPoint, (double *)w);
      dist2 = vtkMath::Distance2BetweenPoints(closestPoint,x);
      }
    return 0;
    }
}

//----------------------------------------------------------------------------
//
// Compute iso-parametric interpolation functions
//
void vtkHexagonalPrism::InterpolationFunctions(double pcoords[3], double sf[12])
{
  double r, s, t;
  r = pcoords[0];
  s = pcoords[1];
  t = pcoords[2];
  const double a = EXPRA;
  const double b = EXPRB;

  //First hexagon
  sf[0]  = -16./3.*(r - a  )*(r - b)*(s - 1.0 )*(t - 1.0);
  sf[1]  =  16./3.*(r - 0.5)*(r - b)*(s - 0.75)*(t - 1.0);
  sf[2]  = -16./3.*(r - 0.5)*(r - b)*(s - 0.25)*(t - 1.0);
  sf[3]  =  16./3.*(r - a  )*(r - b)*(s - 0.0 )*(t - 1.0);
  sf[4]  = -16./3.*(r - 0.5)*(r - a)*(s - 0.25)*(t - 1.0);
  sf[5]  =  16./3.*(r - 0.5)*(r - a)*(s - 0.75)*(t - 1.0);

  //Second hexagon
  sf[6]  =  16./3.*(r - a  )*(r - b)*(s - 1.0 )*(t - 0.0);
  sf[7]  = -16./3.*(r - 0.5)*(r - b)*(s - 0.75)*(t - 0.0);
  sf[8]  =  16./3.*(r - 0.5)*(r - b)*(s - 0.25)*(t - 0.0);
  sf[9]  = -16./3.*(r - a  )*(r - b)*(s - 0.0 )*(t - 0.0);
  sf[10] =  16./3.*(r - 0.5)*(r - a)*(s - 0.25)*(t - 0.0);
  sf[11] = -16./3.*(r - 0.5)*(r - a)*(s - 0.75)*(t - 0.0);
}

//----------------------------------------------------------------------------
void vtkHexagonalPrism::InterpolationDerivs(double pcoords[3], double derivs[36])
{
  double r, s, t;
  r = pcoords[0];
  s = pcoords[1];
  t = pcoords[2];
  const double a = EXPRA;
  const double b = EXPRB;
  //note: a+b=1.0

  // r-derivatives
  //First hexagon
  derivs[0]  = -16./3.*( 2*r - 1.0)    *(s - 1.0 )*(t - 1.0);
  derivs[1]  =  16./3.*( 2*r - b - 0.5)*(s - 0.75)*(t - 1.0);
  derivs[2]  = -16./3.*( 2*r - b - 0.5)*(s - 0.25)*(t - 1.0);
  derivs[3]  =  16./3.*( 2*r - 1.0)    *(s - 0.0 )*(t - 1.0);
  derivs[4]  = -16./3.*( 2*r - a - 0.5)*(s - 0.25)*(t - 1.0);
  derivs[5]  =  16./3.*( 2*r - a - 0.5)*(s - 0.75)*(t - 1.0);
  //Second hexagon
  derivs[6]  =  16./3.*( 2*r - 1.0)    *(s - 1.0 )*(t - 0.0);
  derivs[7]  = -16./3.*( 2*r - b - 0.5)*(s - 0.75)*(t - 0.0);
  derivs[8]  =  16./3.*( 2*r - b - 0.5)*(s - 0.25)*(t - 0.0);
  derivs[9]  = -16./3.*( 2*r - 1.0)    *(s - 0.0 )*(t - 0.0);
  derivs[10] =  16./3.*( 2*r - a - 0.5)*(s - 0.25)*(t - 0.0);
  derivs[11] = -16./3.*( 2*r - a - 0.5)*(s - 0.75)*(t - 0.0);

  // s-derivatives
  //First hexagon
  derivs[12] = -16./3.*(r - a  )*(r - b)*(t - 1.0);
  derivs[13] =  16./3.*(r - 0.5)*(r - b)*(t - 1.0);
  derivs[14] = -16./3.*(r - 0.5)*(r - b)*(t - 1.0);
  derivs[15] =  16./3.*(r - a  )*(r - b)*(t - 1.0);
  derivs[16] = -16./3.*(r - 0.5)*(r - a)*(t - 1.0);
  derivs[17] =  16./3.*(r - 0.5)*(r - a)*(t - 1.0);
  //Second hexagon
  derivs[18] =  16./3.*(r - a  )*(r - b)*(t - 0.0);
  derivs[19] = -16./3.*(r - 0.5)*(r - b)*(t - 0.0);
  derivs[20] =  16./3.*(r - 0.5)*(r - b)*(t - 0.0);
  derivs[21] = -16./3.*(r - a  )*(r - b)*(t - 0.0);
  derivs[22] =  16./3.*(r - 0.5)*(r - a)*(t - 0.0);
  derivs[23] = -16./3.*(r - 0.5)*(r - a)*(t - 0.0);

  // t-derivatives
  //First hexagon
  derivs[24] = -16./3.*(r - a  )*(r - b)*(s - 1.0 );
  derivs[25] =  16./3.*(r - 0.5)*(r - b)*(s - 0.75);
  derivs[26] = -16./3.*(r - 0.5)*(r - b)*(s - 0.25);
  derivs[27] =  16./3.*(r - a  )*(r - b)*(s - 0.0 );
  derivs[28] = -16./3.*(r - 0.5)*(r - a)*(s - 0.25);
  derivs[29] =  16./3.*(r - 0.5)*(r - a)*(s - 0.75);
  //Second hexagon
  derivs[30] =  16./3.*(r - a  )*(r - b)*(s - 1.0 );
  derivs[31] = -16./3.*(r - 0.5)*(r - b)*(s - 0.75);
  derivs[32] =  16./3.*(r - 0.5)*(r - b)*(s - 0.25);
  derivs[33] = -16./3.*(r - a  )*(r - b)*(s - 0.0 );
  derivs[34] =  16./3.*(r - 0.5)*(r - a)*(s - 0.25);
  derivs[35] = -16./3.*(r - 0.5)*(r - a)*(s - 0.75);
}

//----------------------------------------------------------------------------
void vtkHexagonalPrism::EvaluateLocation(int& vtkNotUsed(subId), 
                                         double pcoords[3], double x[3], 
                                         double *weights)
{
  int i, j;
  double pt[3];

  this->InterpolationFunctions(pcoords, weights);

  x[0] = x[1] = x[2] = 0.0;
  for (i = 0; i < 12; i++)
    {
    this->Points->GetPoint (i, pt);
    for (j = 0; j < 3; j++)
      {
      x[j] += pt [j] * weights [i];
      }
    }
}
//----------------------------------------------------------------------------
static int edges[18][2] = {  {0,1}, {1, 2}, {2, 3},
                             {3,4}, {4, 5}, {5, 0},
                             {6,7}, {7, 8}, {8, 9},
                             {9,10}, {10,11}, {11, 6},
                             {0,6}, {1, 7}, {2, 8},
                             {3,9}, {4, 10}, {5, 11} };

static int faces[8][6] = { {0,5,4,3,2,1}, {6,7,8,9,10,11},
                           {0,1,7,6,-1,-1}, {1,2,8,7,-1,-1},
                           {2,3,9,8,-1,-1}, {3,4,10,9,-1,-1},
                           {4,5,11,10,-1,-1}, {5,0,6,11,-1,-1} };

#define VTK_MAX(a,b)    (((a)>(b))?(a):(b))
#define VTK_MIN(a,b)    (((a)<(b))?(a):(b))

//----------------------------------------------------------------------------
// Returns the closest face to the point specified. Closeness is measured
// parametrically.
int vtkHexagonalPrism::CellBoundary(int subId, double pcoords[3],
                                    vtkIdList *pts)
{
  // load coordinates
  double *points = this->GetParametricCoords();
  for(int i=0;i<6;i++)
    {
    this->Polygon->PointIds->SetId(i, i);
    this->Polygon->Points->SetPoint(i, &points[3*i]);
    }

  this->Polygon->CellBoundary( subId, pcoords, pts);

  int min = VTK_MIN(pts->GetId( 0 ), pts->GetId( 1 ));
  int max = VTK_MAX(pts->GetId( 0 ), pts->GetId( 1 ));

  //Base on the edge find the quad that correspond:
  int index;
  if( (index = (max - min)) > 1)
    {
    index = 7;
    }
  else
    {
    index += min + 1;
    }

  double a[3], b[3], u[3], v[3];
  this->Polygon->Points->GetPoint(pts->GetId( 0 ), a);
  this->Polygon->Points->GetPoint(pts->GetId( 1 ), b);
  u[0] = b[0] - a[0];
  u[1] = b[1] - a[1];
  v[0] = pcoords[0] - a[0];
  v[1] = pcoords[1] - a[1];

  double dot = vtkMath::Dot2D(v, u);
  double uNorm = vtkMath::Norm2D( u );
  if (uNorm)
    {
    dot /= uNorm;
    }
  dot = (v[0]*v[0] + v[1]*v[1]) - dot*dot;
  // mathematically dot must be >= zero but, suprise suprise, it can actually
  // be negative
  if (dot > 0)
    {
    dot = sqrt( dot );
    }
  else
    {
    dot = 0;
    }
  int *verts;

  if(pcoords[2] < 0.5)
    {
    //could be closer to face 1
    //compare that distance to the distance to the quad.

    if(dot < pcoords[2])
      {
      //We are closer to the quad face
      verts = faces[index];
      for(int i=0; i<4; i++)
        {
        pts->InsertId(i, verts[i]);
        }
      }
    else
      {
      //we are closer to the hexa face 1
      for(int i=0; i<6; i++)
        {
        pts->InsertId(i, faces[0][i]);
        }
      }
    }
  else
    {
    //could be closer to face 2
    //compare that distance to the distance to the quad.

    if(dot < (1. - pcoords[2]) )
      {
      //We are closer to the quad face
      verts = faces[index];
      for(int i=0; i<4; i++)
        {
        pts->InsertId(i, verts[i]);
        }
      }
    else
      {
      //we are closer to the hexa face 2
      for(int i=0; i<6; i++)
        {
        pts->InsertId(i, faces[1][i]);
        }
      }
    }

  // determine whether point is inside of hexagon
  if ( pcoords[0] < 0.0 || pcoords[0] > 1.0 ||
       pcoords[1] < 0.0 || pcoords[1] > 1.0 ||
       pcoords[2] < 0.0 || pcoords[2] > 1.0 )
    {
    return 0;
    }
  else
    {
    return 1;
    }
}
//----------------------------------------------------------------------------
int *vtkHexagonalPrism::GetEdgeArray(int edgeId)
{
  return edges[edgeId];
}

//----------------------------------------------------------------------------
vtkCell *vtkHexagonalPrism::GetEdge(int edgeId)
{
  int *verts;

  verts = edges[edgeId];

  // load point id's
  this->Line->PointIds->SetId(0,this->PointIds->GetId(verts[0]));
  this->Line->PointIds->SetId(1,this->PointIds->GetId(verts[1]));

  // load coordinates
  this->Line->Points->SetPoint(0,this->Points->GetPoint(verts[0]));
  this->Line->Points->SetPoint(1,this->Points->GetPoint(verts[1]));

  return this->Line;
}
//----------------------------------------------------------------------------
int *vtkHexagonalPrism::GetFaceArray(int faceId)
{
  return faces[faceId];
}
//----------------------------------------------------------------------------
vtkCell *vtkHexagonalPrism::GetFace(int faceId)
{
  int *verts;

  verts = faces[faceId];

  if ( verts[4] != -1 ) // polys cell
    {
    // load point id's
    this->Polygon->PointIds->SetId(0,this->PointIds->GetId(verts[0]));
    this->Polygon->PointIds->SetId(1,this->PointIds->GetId(verts[1]));
    this->Polygon->PointIds->SetId(2,this->PointIds->GetId(verts[2]));
    this->Polygon->PointIds->SetId(3,this->PointIds->GetId(verts[3]));
    this->Polygon->PointIds->SetId(4,this->PointIds->GetId(verts[4]));
    this->Polygon->PointIds->SetId(5,this->PointIds->GetId(verts[5]));

    // load coordinates
    this->Polygon->Points->SetPoint(0,this->Points->GetPoint(verts[0]));
    this->Polygon->Points->SetPoint(1,this->Points->GetPoint(verts[1]));
    this->Polygon->Points->SetPoint(2,this->Points->GetPoint(verts[2]));
    this->Polygon->Points->SetPoint(3,this->Points->GetPoint(verts[3]));
    this->Polygon->Points->SetPoint(4,this->Points->GetPoint(verts[4]));
    this->Polygon->Points->SetPoint(5,this->Points->GetPoint(verts[5]));

    return this->Polygon;
    }
  else
    {
    // load point id's
    this->Quad->PointIds->SetId(0,this->PointIds->GetId(verts[0]));
    this->Quad->PointIds->SetId(1,this->PointIds->GetId(verts[1]));
    this->Quad->PointIds->SetId(2,this->PointIds->GetId(verts[2]));
    this->Quad->PointIds->SetId(3,this->PointIds->GetId(verts[3]));

    // load coordinates
    this->Quad->Points->SetPoint(0,this->Points->GetPoint(verts[0]));
    this->Quad->Points->SetPoint(1,this->Points->GetPoint(verts[1]));
    this->Quad->Points->SetPoint(2,this->Points->GetPoint(verts[2]));
    this->Quad->Points->SetPoint(3,this->Points->GetPoint(verts[3]));

    return this->Quad;
    }
}
//----------------------------------------------------------------------------
//
// Intersect prism faces against line. Each prism face is a quadrilateral.
//
int vtkHexagonalPrism::IntersectWithLine(double p1[3], double p2[3], double tol,
                                         double &t, double x[3], double pcoords[3],
                                         int& subId)
{
  int intersection=0;
  double pt1[3], pt2[3], pt3[3], pt4[3], pt5[3], pt6[3];
  double tTemp;
  double pc[3], xTemp[3], dist2, weights[12];
  int faceNum;

  t = VTK_DOUBLE_MAX;

  //first intersect the penta faces
  for (faceNum=0; faceNum<2; faceNum++)
    {
    this->Points->GetPoint(faces[faceNum][0], pt1);
    this->Points->GetPoint(faces[faceNum][1], pt2);
    this->Points->GetPoint(faces[faceNum][2], pt3);
    this->Points->GetPoint(faces[faceNum][3], pt4);
    this->Points->GetPoint(faces[faceNum][4], pt5);
    this->Points->GetPoint(faces[faceNum][5], pt6);

    this->Polygon->Points->SetPoint(0,pt1);
    this->Polygon->Points->SetPoint(1,pt2);
    this->Polygon->Points->SetPoint(2,pt3);
    this->Polygon->Points->SetPoint(3,pt4);
    this->Polygon->Points->SetPoint(4,pt5);
    this->Polygon->Points->SetPoint(5,pt6);

    if ( this->Polygon->IntersectWithLine(p1, p2, tol, tTemp, xTemp,
                                          pc, subId) )
      {
      intersection = 1;
      if ( tTemp < t )
        {
        t = tTemp;
        x[0] = xTemp[0]; x[1] = xTemp[1]; x[2] = xTemp[2];
        switch (faceNum)
          {
          case 0:
            pcoords[0] = pc[0]; pcoords[1] = pc[1]; pcoords[2] = 0.0;
            break;

          case 1:
            pcoords[0] = pc[0]; pcoords[1] = pc[1]; pcoords[2] = 1.0;
            break;
          }
        }
      }
    }

  //now intersect the quad faces
  for (faceNum=2; faceNum<8; faceNum++)
    {
    this->Points->GetPoint(faces[faceNum][0], pt1);
    this->Points->GetPoint(faces[faceNum][1], pt2);
    this->Points->GetPoint(faces[faceNum][2], pt3);
    this->Points->GetPoint(faces[faceNum][3], pt4);

    this->Quad->Points->SetPoint(0,pt1);
    this->Quad->Points->SetPoint(1,pt2);
    this->Quad->Points->SetPoint(2,pt3);
    this->Quad->Points->SetPoint(3,pt4);

    if ( this->Quad->IntersectWithLine(p1, p2, tol, tTemp, xTemp, pc, subId) )
      {
      intersection = 1;
      if ( tTemp < t )
        {
        t = tTemp;
        x[0] = xTemp[0]; x[1] = xTemp[1]; x[2] = xTemp[2];
        this->EvaluatePosition(x, xTemp, subId, pcoords, dist2, weights);
        }
      }
    }

  return intersection;
}
//----------------------------------------------------------------------------
int vtkHexagonalPrism::Triangulate(int vtkNotUsed(index), vtkIdList *ptIds, vtkPoints *pts)
{
  ptIds->Reset();
  pts->Reset();

  for ( int i=0; i < 4; i++ )
    {
    ptIds->InsertId(i,this->PointIds->GetId(i));
    pts->InsertPoint(i,this->Points->GetPoint(i));
    }

  return 1;
}
//----------------------------------------------------------------------------
//
// Compute derivatives in x-y-z directions. Use chain rule in combination
// with interpolation function derivatives.
//
void vtkHexagonalPrism::Derivatives(int vtkNotUsed(subId), double pcoords[3],
                                    double *values, int dim, double *derivs)
{
  double *jI[3], j0[3], j1[3], j2[3];
  double functionDerivs[36], sum[3], value;
  int i, j, k;

  // compute inverse Jacobian and interpolation function derivatives
  jI[0] = j0; jI[1] = j1; jI[2] = j2;
  this->JacobianInverse(pcoords, jI, functionDerivs);

  // now compute derivates of values provided
  for (k=0; k < dim; k++) //loop over values per vertex
    {
    sum[0] = sum[1] = sum[2] = 0.0;
    for ( i=0; i < 12; i++) //loop over interp. function derivatives
      {
      value = values[dim*i + k];
      sum[0] += functionDerivs[i] * value;
      sum[1] += functionDerivs[12 + i] * value;
      sum[2] += functionDerivs[24 + i] * value;
      }

    for (j=0; j < 3; j++) //loop over derivative directions
      {
      derivs[3*k + j] = sum[0]*jI[j][0] + sum[1]*jI[j][1] + sum[2]*jI[j][2];
      }
    }
}
//----------------------------------------------------------------------------
// Given parametric coordinates compute inverse Jacobian transformation
// matrix. Returns 9 elements of 3x3 inverse Jacobian plus interpolation
// function derivatives.
void vtkHexagonalPrism::JacobianInverse(double pcoords[3], double **inverse,
                                        double derivs[36])
{
  int i, j;
  double *m[3], m0[3], m1[3], m2[3];
  double x[3];

  // compute interpolation function derivatives
  this->InterpolationDerivs(pcoords, derivs);

  // create Jacobian matrix
  m[0] = m0; m[1] = m1; m[2] = m2;
  for (i=0; i < 3; i++) //initialize matrix
    {
    m0[i] = m1[i] = m2[i] = 0.0;
    }

  for ( j=0; j < 12; j++ )
    {
    this->Points->GetPoint(j, x);
    for ( i=0; i < 3; i++ )
      {
      m0[i] += x[i] * derivs[j];
      m1[i] += x[i] * derivs[12 + j];
      m2[i] += x[i] * derivs[24 + j];
      }
    }

  // now find the inverse
  if ( vtkMath::InvertMatrix(m,inverse,3) == 0 )
    {
    vtkErrorMacro(<<"Jacobian inverse not found");
    return;
    }
}

//----------------------------------------------------------------------------
void vtkHexagonalPrism::GetEdgePoints(int edgeId, int* &pts)
{
  pts = this->GetEdgeArray(edgeId);
}

//----------------------------------------------------------------------------
void vtkHexagonalPrism::GetFacePoints(int faceId, int* &pts)
{
  pts = this->GetFaceArray(faceId);
}

static double vtkHexagonalPrismCellPCoords[36] = {
  0.5,   0.0 , 0.0,
  EXPRA, 0.25, 0.0,
  EXPRA, 0.75, 0.0,
  0.5,   1.0 , 0.0,
  EXPRB, 0.75, 0.0,
  EXPRB, 0.25, 0.0,
  0.5,   0.0 , 1.0,
  EXPRA, 0.25, 1.0,
  EXPRA, 0.75, 1.0,
  0.5,   1.0 , 1.0,
  EXPRB, 0.75, 1.0,
  EXPRB, 0.25, 1.0,
};

//----------------------------------------------------------------------------
double *vtkHexagonalPrism::GetParametricCoords()
{
  return vtkHexagonalPrismCellPCoords;
}

//----------------------------------------------------------------------------
void vtkHexagonalPrism::PrintSelf(ostream& os, vtkIndent indent)
{
  this->Superclass::PrintSelf(os,indent);
  
  os << indent << "Line:\n";
  this->Line->PrintSelf(os,indent.GetNextIndent());
  os << indent << "Quad:\n";
  this->Quad->PrintSelf(os,indent.GetNextIndent());
  os << indent << "Polygon:\n";
  this->Polygon->PrintSelf(os,indent.GetNextIndent());
}

