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

  Program:   Visualization Toolkit
  Module:    vtkHexahedron.cxx
  Language:  C++
  Date:      $Date$
  Version:   $Revision$


Copyright (c) 1993-2001 Ken Martin, Will Schroeder, Bill Lorensen 
All rights reserved.

Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:

 * Redistributions of source code must retain the above copyright notice,
   this list of conditions and the following disclaimer.

 * Redistributions in binary form must reproduce the above copyright notice,
   this list of conditions and the following disclaimer in the documentation
   and/or other materials provided with the distribution.

 * Neither name of Ken Martin, Will Schroeder, or Bill Lorensen nor the names
   of any contributors may be used to endorse or promote products derived
   from this software without specific prior written permission.

 * Modified source versions must be plainly marked as such, and must not be
   misrepresented as being the original software.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ``AS IS''
AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHORS OR CONTRIBUTORS BE LIABLE FOR
ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

=========================================================================*/
#include "vtkHexahedron.h"
#include "vtkMath.h"
#include "vtkLine.h"
#include "vtkQuad.h"
#include "vtkCellArray.h"
#include "vtkPointLocator.h"

// Construct the hexahedron with eight points.
vtkHexahedron::vtkHexahedron()
{
  int i;
  
  this->Points->SetNumberOfPoints(8);
  this->PointIds->SetNumberOfIds(8);

  for (i = 0; i < 8; i++)
    {
    this->Points->SetPoint(i, 0.0, 0.0, 0.0);
    }
  for (i = 0; i < 8; i++)
    {
    this->PointIds->SetId(i,0);
    }
  this->Line = vtkLine::New();
  this->Quad = vtkQuad::New();
}

vtkHexahedron::~vtkHexahedron()
{
  this->Line->Delete();
  this->Quad->Delete();
}

vtkCell *vtkHexahedron::MakeObject()
{
  vtkCell *cell = vtkHexahedron::New();
  cell->DeepCopy(this);
  return cell;
}

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

int vtkHexahedron::EvaluatePosition(float x[3], float* closestPoint,
                                   int& subId, float pcoords[3], 
                                   float& dist2, float *weights)
{
  int iteration, converged;
  float  params[3];
  float  fcol[3], rcol[3], scol[3], tcol[3];
  int i, j;
  float  d, *pt;
  float derivs[24];

  //
  //  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_HEXAHEDRON_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<8; i++)
      {
      pt = this->Points->GetPoint(i);
      for (j=0; j<3; j++)
        {
        fcol[j] += pt[j] * weights[i];
        rcol[j] += pt[j] * derivs[i];
        scol[j] += pt[j] * derivs[i+8];
        tcol[j] += pt[j] * derivs[i+16];
        }
      }

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

    //
    //  compute determinants and generate improvements
    //
    if ( (d=vtkMath::Determinant3x3(rcol,scol,tcol)) == 0.0 )
      {
      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_HEXADRON_CONVERGED) &&
    ((fabs(pcoords[1]-params[1])) < VTK_HEXADRON_CONVERGED) &&
    ((fabs(pcoords[2]-params[2])) < VTK_HEXADRON_CONVERGED) )
      {
      converged = 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
    {
    float pc[3], w[8];
    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, (float *)w);
      dist2 = vtkMath::Distance2BetweenPoints(closestPoint,x);
      }
    return 0;
    }
}
//
// Compute iso-parametrix interpolation functions
//
void vtkHexahedron::InterpolationFunctions(float pcoords[3], float sf[8])
{
  double rm, sm, tm;

  rm = 1. - pcoords[0];
  sm = 1. - pcoords[1];
  tm = 1. - pcoords[2];

  sf[0] = rm*sm*tm;
  sf[1] = pcoords[0]*sm*tm;
  sf[2] = pcoords[0]*pcoords[1]*tm;
  sf[3] = rm*pcoords[1]*tm;
  sf[4] = rm*sm*pcoords[2];
  sf[5] = pcoords[0]*sm*pcoords[2];
  sf[6] = pcoords[0]*pcoords[1]*pcoords[2];
  sf[7] = rm*pcoords[1]*pcoords[2];
}

void vtkHexahedron::InterpolationDerivs(float pcoords[3], float derivs[24])
{
  double rm, sm, tm;

  rm = 1. - pcoords[0];
  sm = 1. - pcoords[1];
  tm = 1. - pcoords[2];

  // r-derivatives
  derivs[0] = -sm*tm;
  derivs[1] = sm*tm;
  derivs[2] = pcoords[1]*tm;
  derivs[3] = -pcoords[1]*tm;
  derivs[4] = -sm*pcoords[2];
  derivs[5] = sm*pcoords[2];
  derivs[6] = pcoords[1]*pcoords[2];
  derivs[7] = -pcoords[1]*pcoords[2];

  // s-derivatives
  derivs[8] = -rm*tm;
  derivs[9] = -pcoords[0]*tm;
  derivs[10] = pcoords[0]*tm;
  derivs[11] = rm*tm;
  derivs[12] = -rm*pcoords[2];
  derivs[13] = -pcoords[0]*pcoords[2];
  derivs[14] = pcoords[0]*pcoords[2];
  derivs[15] = rm*pcoords[2];

  // t-derivatives
  derivs[16] = -rm*sm;
  derivs[17] = -pcoords[0]*sm;
  derivs[18] = -pcoords[0]*pcoords[1];
  derivs[19] = -rm*pcoords[1];
  derivs[20] = rm*sm;
  derivs[21] = pcoords[0]*sm;
  derivs[22] = pcoords[0]*pcoords[1];
  derivs[23] = rm*pcoords[1];
}

void vtkHexahedron::EvaluateLocation(int& vtkNotUsed(subId), float pcoords[3],
                                     float x[3], float *weights)
{
  int i, j;
  float *pt;

  this->InterpolationFunctions(pcoords, weights);

  x[0] = x[1] = x[2] = 0.0;
  for (i=0; i<8; i++)
    {
    pt = this->Points->GetPoint(i);
    for (j=0; j<3; j++)
      {
      x[j] += pt[j] * weights[i];
      }
    }
}

int vtkHexahedron::CellBoundary(int vtkNotUsed(subId), float pcoords[3], 
                                vtkIdList *pts)
{
  float t1=pcoords[0]-pcoords[1];
  float t2=1.0-pcoords[0]-pcoords[1];
  float t3=pcoords[1]-pcoords[2];
  float t4=1.0-pcoords[1]-pcoords[2];
  float t5=pcoords[2]-pcoords[0];
  float t6=1.0-pcoords[2]-pcoords[0];

  pts->SetNumberOfIds(4);

  // compare against six planes in parametric space that divide element
  // into six pieces.
  if ( t3 >= 0.0 && t4 >= 0.0 && t5 < 0.0 && t6 >= 0.0 )
    {
    pts->SetId(0,this->PointIds->GetId(0));
    pts->SetId(1,this->PointIds->GetId(1));
    pts->SetId(2,this->PointIds->GetId(2));
    pts->SetId(3,this->PointIds->GetId(3));
    }

  else if ( t1 >= 0.0 && t2 < 0.0 && t5 < 0.0 && t6 < 0.0 )
    {
    pts->SetId(0,this->PointIds->GetId(1));
    pts->SetId(1,this->PointIds->GetId(2));
    pts->SetId(2,this->PointIds->GetId(6));
    pts->SetId(3,this->PointIds->GetId(5));
    }

  else if ( t1 >= 0.0 && t2 >= 0.0 && t3 < 0.0 && t4 >= 0.0 )
    {
    pts->SetId(0,this->PointIds->GetId(0));
    pts->SetId(1,this->PointIds->GetId(1));
    pts->SetId(2,this->PointIds->GetId(5));
    pts->SetId(3,this->PointIds->GetId(4));
    }

  else if ( t3 < 0.0 && t4 < 0.0 && t5 >= 0.0 && t6 < 0.0 )
    {
    pts->SetId(0,this->PointIds->GetId(4));
    pts->SetId(1,this->PointIds->GetId(5));
    pts->SetId(2,this->PointIds->GetId(6));
    pts->SetId(3,this->PointIds->GetId(7));
    }

  else if ( t1 < 0.0 && t2 >= 0.0 && t5 >= 0.0 && t6 >= 0.0 )
    {
    pts->SetId(0,this->PointIds->GetId(0));
    pts->SetId(1,this->PointIds->GetId(4));
    pts->SetId(2,this->PointIds->GetId(7));
    pts->SetId(3,this->PointIds->GetId(3));
    }

  else // if ( t1 < 0.0 && t2 < 0.0 && t3 >= 0.0 && t6 < 0.0 )
    {
    pts->SetId(0,this->PointIds->GetId(2));
    pts->SetId(1,this->PointIds->GetId(3));
    pts->SetId(2,this->PointIds->GetId(7));
    pts->SetId(3,this->PointIds->GetId(6));
    }


  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;
    }
}

static int edges[12][2] = { {0,1}, {1,2}, {3,2}, {0,3},
                            {4,5}, {5,6}, {7,6}, {4,7},
                            {0,4}, {1,5}, {3,7}, {2,6}};
static int faces[6][4] = { {0,4,7,3}, {1,2,6,5},
                           {0,1,5,4}, {3,7,6,2},
                           {0,3,2,1}, {4,5,6,7} };
//
// Marching cubes case table
//
#include "vtkMarchingCubesCases.h"
#include "vtkObjectFactory.h"



//------------------------------------------------------------------------------
vtkHexahedron* vtkHexahedron::New()
{
  // First try to create the object from the vtkObjectFactory
  vtkObject* ret = vtkObjectFactory::CreateInstance("vtkHexahedron");
  if(ret)
    {
    return (vtkHexahedron*)ret;
    }
  // If the factory was unable to create the object, then create it here.
  return new vtkHexahedron;
}




void vtkHexahedron::Contour(float value, vtkDataArray *cellScalars, 
                            vtkPointLocator *locator,
                            vtkCellArray *vtkNotUsed(verts), 
                            vtkCellArray *vtkNotUsed(lines), 
                            vtkCellArray *polys, 
                            vtkPointData *inPd, vtkPointData *outPd,
                            vtkCellData *inCd, vtkIdType cellId,
                            vtkCellData *outCd)
{
  static int CASE_MASK[8] = {1,2,4,8,16,32,64,128};
  VTK_TRIANGLE_CASES *triCase;
  EDGE_LIST  *edge;
  int i, j, index, *vert;
  int e1, e2, newCellId;
  vtkIdType pts[3];
  float t, x1[3], x2[3], x[3], deltaScalar;

  // Build the case table
  for ( i=0, index = 0; i < 8; i++)
    {
    if (cellScalars->GetComponent(i,0) >= value)
      {
      index |= CASE_MASK[i];
      }
    }

  triCase = VTK_TRIANGLE_CASES::GetCases() + index;
  edge = triCase->edges;

  for ( ; edge[0] > -1; edge += 3 )
    {
    for (i=0; i<3; i++) // insert triangle
      {
      vert = edges[edge[i]];
      // calculate a preferred interpolation direction
      deltaScalar = (cellScalars->GetComponent(vert[1],0) 
                     - cellScalars->GetComponent(vert[0],0));
      if (deltaScalar > 0)
        {
        e1 = vert[0]; e2 = vert[1];
        }
      else
        {
        e1 = vert[1]; e2 = vert[0];
        deltaScalar = -deltaScalar;
        }

      // linear interpolation
      if (deltaScalar == 0.0)
        {
        t = 0.0;
        }
      else
        {
        t = (value - cellScalars->GetComponent(e1,0)) / deltaScalar;
        }

      this->Points->GetPoint(e1, x1);
      this->Points->GetPoint(e2, x2);

      for (j=0; j<3; j++)
        {
        x[j] = x1[j] + t * (x2[j] - x1[j]);
        }
      if ( locator->InsertUniquePoint(x, pts[i]) )
        {
        if ( outPd ) 
          {
          int p1 = this->PointIds->GetId(e1);
          int p2 = this->PointIds->GetId(e2);
          outPd->InterpolateEdge(inPd,pts[i],p1,p2,t);
          }
        }
      }
    // check for degenerate triangle
    if ( pts[0] != pts[1] &&
         pts[0] != pts[2] &&
         pts[1] != pts[2] )
      {
      newCellId = polys->InsertNextCell(3,pts);
      outCd->CopyData(inCd,cellId,newCellId);
      }
    }
}

int *vtkHexahedron::GetEdgeArray(int edgeId)
{
  return edges[edgeId];
}
vtkCell *vtkHexahedron::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 *vtkHexahedron::GetFaceArray(int faceId)
{
  return faces[faceId];
}
vtkCell *vtkHexahedron::GetFace(int faceId)
{
  int *verts, i;

  verts = faces[faceId];

  for (i=0; i<4; i++)
    {
    this->Quad->PointIds->SetId(i,this->PointIds->GetId(verts[i]));
    this->Quad->Points->SetPoint(i,this->Points->GetPoint(verts[i]));
    }

  return this->Quad;
}

// 
// Intersect hexa faces against line. Each hexa face is a quadrilateral.
//
int vtkHexahedron::IntersectWithLine(float p1[3], float p2[3], float tol,
                                    float &t, float x[3], float pcoords[3],
                                    int& subId)
{
  int intersection=0;
  float *pt1, *pt2, *pt3, *pt4;
  float tTemp;
  float pc[3], xTemp[3];
  int faceNum;

  t = VTK_LARGE_FLOAT;
  for (faceNum=0; faceNum<6; faceNum++)
    {
    pt1 = this->Points->GetPoint(faces[faceNum][0]);
    pt2 = this->Points->GetPoint(faces[faceNum][1]);
    pt3 = this->Points->GetPoint(faces[faceNum][2]);
    pt4 = this->Points->GetPoint(faces[faceNum][3]);

    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]; 
        switch (faceNum)
          {
          case 0:
            pcoords[0] = 0.0; pcoords[0] = pc[0]; pcoords[1] = 0.0;
            break;

          case 1:
            pcoords[0] = 1.0; pcoords[0] = pc[0]; pcoords[1] = 0.0;
            break;

          case 2:
            pcoords[0] = pc[0]; pcoords[1] = 0.0; pcoords[2] = pc[1];
            break;

          case 3:
            pcoords[0] = pc[0]; pcoords[1] = 1.0; pcoords[2] = pc[1];
            break;

          case 4:
            pcoords[0] = pc[0]; pcoords[1] = pc[1]; pcoords[2] = 0.0;
            break;

          case 5:
            pcoords[0] = pc[0]; pcoords[1] = pc[1]; pcoords[2] = 1.0;
            break;
          }
        }
      }
    }
  return intersection;
}

int vtkHexahedron::Triangulate(int index, vtkIdList *ptIds, vtkPoints *pts)
{
  int p[4], i;

  ptIds->Reset();
  pts->Reset();

  // Create five tetrahedron. Triangulation varies depending upon index. This
  // is necessary to insure compatible voxel triangulations.
  //
  if ( (index % 2) )
    {
    p[0] = 0; p[1] = 1; p[2] = 4; p[3] = 3;
    for ( i=0; i < 4; i++ )
      {
      ptIds->InsertNextId(this->PointIds->GetId(p[i]));
      pts->InsertNextPoint(this->Points->GetPoint(p[i]));
      }

    p[0] = 1; p[1] = 4; p[2] = 6; p[3] = 5;
    for ( i=0; i < 4; i++ )
      {
      ptIds->InsertNextId(this->PointIds->GetId(p[i]));
      pts->InsertNextPoint(this->Points->GetPoint(p[i]));
      }

    p[0] = 1; p[1] = 4; p[2] = 3; p[3] = 6;
    for ( i=0; i < 4; i++ )
      {
      ptIds->InsertNextId(this->PointIds->GetId(p[i]));
      pts->InsertNextPoint(this->Points->GetPoint(p[i]));
      }

    p[0] = 1; p[1] = 3; p[2] = 2; p[3] = 6;
    for ( i=0; i < 4; i++ )
      {
      ptIds->InsertNextId(this->PointIds->GetId(p[i]));
      pts->InsertNextPoint(this->Points->GetPoint(p[i]));
      }

    p[0] = 3; p[1] = 6; p[2] = 7; p[3] = 4;
    for ( i=0; i < 4; i++ )
      {
      ptIds->InsertNextId(this->PointIds->GetId(p[i]));
      pts->InsertNextPoint(this->Points->GetPoint(p[i]));
      }
    }
  else
    {
    p[0] = 2; p[1] = 1; p[2] = 0; p[3] = 5;
    for ( i=0; i < 4; i++ )
      {
      ptIds->InsertNextId(this->PointIds->GetId(p[i]));
      pts->InsertNextPoint(this->Points->GetPoint(p[i]));
      }

    p[0] = 0; p[1] = 2; p[2] = 7; p[3] = 3;
    for ( i=0; i < 4; i++ )
      {
      ptIds->InsertNextId(this->PointIds->GetId(p[i]));
      pts->InsertNextPoint(this->Points->GetPoint(p[i]));
      }

    p[0] = 2; p[1] = 5; p[2] = 7; p[3] = 6;
    for ( i=0; i < 4; i++ )
      {
      ptIds->InsertNextId(this->PointIds->GetId(p[i]));
      pts->InsertNextPoint(this->Points->GetPoint(p[i]));
      }

    p[0] = 0; p[1] = 7; p[2] = 4; p[3] = 5;
    for ( i=0; i < 4; i++ )
      {
      ptIds->InsertNextId(this->PointIds->GetId(p[i]));
      pts->InsertNextPoint(this->Points->GetPoint(p[i]));
      }

    p[0] = 0; p[1] = 2; p[2] = 7; p[3] = 5;
    for ( i=0; i < 4; i++ )
      {
      ptIds->InsertNextId(this->PointIds->GetId(p[i]));
      pts->InsertNextPoint(this->Points->GetPoint(p[i]));
      }
    }

  return 1;
}

//
// Compute derivatives in x-y-z directions. Use chain rule in combination
// with interpolation function derivatives.
//
void vtkHexahedron::Derivatives(int vtkNotUsed(subId), float pcoords[3], 
                                float *values, int dim, float *derivs)
{
  double *jI[3], j0[3], j1[3], j2[3];
  float functionDerivs[24], sum[3];
  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 < 8; i++) //loop over interp. function derivatives
      {
      sum[0] += functionDerivs[i] * values[dim*i + k]; 
      sum[1] += functionDerivs[8 + i] * values[dim*i + k];
      sum[2] += functionDerivs[16 + i] * values[dim*i + k];
      }
    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 vtkHexahedron::JacobianInverse(float pcoords[3], double **inverse,
                                    float derivs[24])
{
  int i, j;
  double *m[3], m0[3], m1[3], m2[3];
  float *x;

  // 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 < 8; j++ )
    {
    x = this->Points->GetPoint(j);
    for ( i=0; i < 3; i++ )
      {
      m0[i] += x[i] * derivs[j];
      m1[i] += x[i] * derivs[8 + j];
      m2[i] += x[i] * derivs[16 + j];
      }
    }

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

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

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