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

  Program:   Visualization Toolkit
  Module:    $RCSfile: vtkTetra.cxx,v $

  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.

=========================================================================*/
#include "vtkTetra.h"

#include "vtkCellArray.h"
#include "vtkCellData.h"
#include "vtkLine.h"
#include "vtkMath.h"
#include "vtkObjectFactory.h"
#include "vtkPointData.h"
#include "vtkPointLocator.h"
#include "vtkTriangle.h"
#include "vtkUnstructuredGrid.h"

vtkCxxRevisionMacro(vtkTetra, "$Revision: 1.4 $");
vtkStandardNewMacro(vtkTetra);

//----------------------------------------------------------------------------
// Construct the tetra with four points.
vtkTetra::vtkTetra()
{
  int i;
  
  this->Points->SetNumberOfPoints(4);
  this->PointIds->SetNumberOfIds(4);
  for (i = 0; i < 4; i++)
    {
    this->Points->SetPoint(i, 0.0, 0.0, 0.0);
    }
  for (i = 0; i < 4; i++)
    {
    this->PointIds->SetId(i,0);
    }
  this->Line = vtkLine::New();
  this->Triangle = vtkTriangle::New();
}

//----------------------------------------------------------------------------
vtkTetra::~vtkTetra()
{
  this->Triangle->Delete();
  this->Line->Delete();
}

//----------------------------------------------------------------------------
int vtkTetra::EvaluatePosition(double x[3], double* closestPoint,
                              int& subId, double pcoords[3], 
                              double& minDist2, double *weights)
{
  double pt1[3], pt2[3], pt3[3], pt4[3];
  int i;
  double rhs[3], c1[3], c2[3], c3[3];
  double det, p4;

  subId = 0;
  pcoords[0] = pcoords[1] = pcoords[2] = 0.0;

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

  for (i=0; i<3; i++)
    {  
    rhs[i] = x[i] - pt4[i];
    c1[i] = pt1[i] - pt4[i];
    c2[i] = pt2[i] - pt4[i];
    c3[i] = pt3[i] - pt4[i];
    }

  if ( (det = vtkMath::Determinant3x3(c1,c2,c3)) == 0.0 )
    {
    return -1;
    }

  pcoords[0] = vtkMath::Determinant3x3 (rhs,c2,c3) / det;
  pcoords[1] = vtkMath::Determinant3x3 (c1,rhs,c3) / det;
  pcoords[2] = vtkMath::Determinant3x3 (c1,c2,rhs) / det;
  p4 = 1.0 - pcoords[0] - pcoords[1] - pcoords[2];

  weights[0] = p4;
  weights[1] = pcoords[0];
  weights[2] = pcoords[1];
  weights[3] = pcoords[2];

  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 && p4 >= -0.001 && p4 <= 1.001 )
    {
    if (closestPoint)
      {
      closestPoint[0] = x[0]; 
      closestPoint[1] = x[1]; 
      closestPoint[2] = x[2];
      minDist2 = 0.0; //inside tetra
      }
    return 1; 
    }
  else
    { //could easily be sped up using parametric localization - next release
    double dist2, w[3], closest[3], pc[3];
    int sub;
    vtkTriangle *triangle;

    if (closestPoint)
      {
      for (minDist2=VTK_DOUBLE_MAX,i=0; i<4; i++)
        {
        triangle = (vtkTriangle *) this->GetFace (i);
        triangle->EvaluatePosition(x,closest,sub,pc,dist2,(double *)w);
        
        if ( dist2 < minDist2 )
          {
          closestPoint[0] = closest[0]; 
          closestPoint[1] = closest[1]; 
          closestPoint[2] = closest[2];
          minDist2 = dist2;
          }
        }
      }
    return 0;
    }
}

//----------------------------------------------------------------------------
void vtkTetra::EvaluateLocation(int& vtkNotUsed(subId), double pcoords[3], 
                                double x[3], double *weights)
{
  double u4;
  double pt1[3], pt2[3], pt3[3], pt4[3];
  int i;

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

  u4 = 1.0 - pcoords[0] - pcoords[1] - pcoords[2];

  for (i=0; i<3; i++)
    {
    x[i] = pt1[i]*pcoords[0] + pt2[i]*pcoords[1] + pt3[i]*pcoords[2] +
           pt4[i]*u4;
    }

  weights[0] = u4;
  weights[1] = pcoords[0];
  weights[2] = pcoords[1];
  weights[3] = pcoords[2];
}

//----------------------------------------------------------------------------
// Returns the set of points that are on the boundary of the tetrahedron that
// are closest parametrically to the point specified. This may include faces,
// edges, or vertices.
int vtkTetra::CellBoundary(int vtkNotUsed(subId), double pcoords[3], 
                           vtkIdList *pts)
{
  double minPCoord = 1.0 - pcoords[0] - pcoords[1] - pcoords[2];
  int i, idx=3;
  
  for ( i=0; i < 3; i++ )
    {
    if ( pcoords[i] < minPCoord )
      {
      minPCoord = pcoords[i];
      idx = i;
      }
    }
  
  pts->SetNumberOfIds(3);
  switch (idx) //find the face closest to the point
    {
    case 0:
      pts->SetId(0,this->PointIds->GetId(0));
      pts->SetId(1,this->PointIds->GetId(2));
      pts->SetId(2,this->PointIds->GetId(3));
      break;
      
    case 1:
      pts->SetId(0,this->PointIds->GetId(0));
      pts->SetId(1,this->PointIds->GetId(1));
      pts->SetId(2,this->PointIds->GetId(3));
      break;
      
    case 2:
      pts->SetId(0,this->PointIds->GetId(0));
      pts->SetId(1,this->PointIds->GetId(1));
      pts->SetId(2,this->PointIds->GetId(2));
      break;
      
    case 3:
      pts->SetId(0,this->PointIds->GetId(1));
      pts->SetId(1,this->PointIds->GetId(2));
      pts->SetId(2,this->PointIds->GetId(3));
      break;
    }

  if ( pcoords[0] < 0.0 || pcoords[1] < 0.0 || pcoords[2] < 0.0 ||
       pcoords[0] > 1.0 || pcoords[1] > 1.0 || pcoords[2] > 1.0 ||
       (1.0 - pcoords[0] - pcoords[1] - pcoords[2]) < 0.0 )
    {
    return 0;
    }
  else
    {
    return 1;
    }
}

//----------------------------------------------------------------------------
// Marching tetrahedron
//
static int edges[6][2] = { {0,1}, {1,2}, {2,0}, 
                           {0,3}, {1,3}, {2,3} };
static int faces[4][3] = { {0,1,3}, {1,2,3}, {2,0,3}, {0,2,1} };

typedef int EDGE_LIST;
typedef struct {
       EDGE_LIST edges[7];
} TRIANGLE_CASES;

static TRIANGLE_CASES triCases[] = { 
  {{-1, -1, -1, -1, -1, -1, -1}},
  {{ 0, 3, 2, -1, -1, -1, -1}},
  {{ 0, 1, 4, -1, -1, -1, -1}},
  {{ 3, 2, 4, 4, 2, 1, -1}},
  {{ 1, 2, 5, -1, -1, -1, -1}},
  {{ 3, 5, 1, 3, 1, 0, -1}},
  {{ 0, 2, 5, 0, 5, 4, -1}},
  {{ 3, 5, 4, -1, -1, -1, -1}},
  {{ 3, 4, 5, -1, -1, -1, -1}},
  {{ 0, 4, 5, 0, 5, 2, -1}},
  {{ 0, 5, 3, 0, 1, 5, -1}},
  {{ 5, 2, 1, -1, -1, -1, -1}},
  {{ 3, 4, 1, 3, 1, 2, -1}},
  {{ 0, 4, 1, -1, -1, -1, -1}},
  {{ 0, 2, 3, -1, -1, -1, -1}},
  {{-1, -1, -1, -1, -1, -1, -1}}
};

//----------------------------------------------------------------------------
void vtkTetra::Contour(double value, vtkDataArray *cellScalars, 
                       vtkPointLocator *locator,
                       vtkCellArray *verts, 
                       vtkCellArray *lines, 
                       vtkCellArray *polys,
                       vtkPointData *inPd, vtkPointData *outPd,
                       vtkCellData *inCd, vtkIdType cellId, vtkCellData *outCd)
{
  static int CASE_MASK[4] = {1,2,4,8};
  TRIANGLE_CASES *triCase;
  EDGE_LIST  *edge;
  int i, j, index, *vert, v1, v2, newCellId;
  vtkIdType pts[3];
  double t, x1[3], x2[3], x[3], deltaScalar;
  vtkIdType offset = verts->GetNumberOfCells() + lines->GetNumberOfCells();

  // Build the case table
  for ( i=0, index = 0; i < 4; i++)
    {
    if (cellScalars->GetComponent(i,0) >= value)
      {
      index |= CASE_MASK[i];
      }
    }

  triCase = triCases + 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)
        {
        v1 = vert[0]; v2 = vert[1];
        }
      else
        {
        v1 = vert[1]; v2 = vert[0];
        deltaScalar = -deltaScalar;
        }

      // linear interpolation across edge
      t = ( deltaScalar == 0.0 ? 0.0 :
            (value - cellScalars->GetComponent(v1,0)) / deltaScalar );

      this->Points->GetPoint(v1, x1);
      this->Points->GetPoint(v2, x2);

      for (j=0; j<3; j++)
        {
        x[j] = x1[j] + t * (x2[j] - x1[j]);
        }
      if ( locator->InsertUniquePoint(x, pts[i]) )
        {
        if ( outPd ) 
          {
          vtkIdType p1 = this->PointIds->GetId(v1);
          vtkIdType p2 = this->PointIds->GetId(v2);
          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 = offset + polys->InsertNextCell(3,pts);
      outCd->CopyData(inCd,cellId,newCellId);
      }
    }
}

//----------------------------------------------------------------------------
int *vtkTetra::GetEdgeArray(int edgeId)
{
  return edges[edgeId];
}

//----------------------------------------------------------------------------
vtkCell *vtkTetra::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 *vtkTetra::GetFaceArray(int faceId)
{
  return faces[faceId];
}

//----------------------------------------------------------------------------
vtkCell *vtkTetra::GetFace(int faceId)
{
  int *verts;

  verts = faces[faceId];

  // load point id's
  this->Triangle->PointIds->SetId(0,this->PointIds->GetId(verts[0]));
  this->Triangle->PointIds->SetId(1,this->PointIds->GetId(verts[1]));
  this->Triangle->PointIds->SetId(2,this->PointIds->GetId(verts[2]));

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

  return this->Triangle;
}

//----------------------------------------------------------------------------
// 
// Intersect triangle faces against line.
//
int vtkTetra::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];
  double tTemp;
  double pc[3], xTemp[3];
  int faceNum;

  t = VTK_DOUBLE_MAX;
  for (faceNum=0; faceNum<4; faceNum++)
    {
    this->Points->GetPoint(faces[faceNum][0], pt1);
    this->Points->GetPoint(faces[faceNum][1], pt2);
    this->Points->GetPoint(faces[faceNum][2], pt3);

    this->Triangle->Points->SetPoint(0,pt1);
    this->Triangle->Points->SetPoint(1,pt2);
    this->Triangle->Points->SetPoint(2,pt3);

    if ( this->Triangle->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] = 0.0; pcoords[1] = pc[1]; pcoords[2] = 0.0;
            break;

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

          case 3:
            pcoords[0] = pc[0]; pcoords[1] = pc[1]; pcoords[2] = pc[2];
            break;
          }
        }
      }
    }
  return intersection;
}

//----------------------------------------------------------------------------
int vtkTetra::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;
}


//----------------------------------------------------------------------------
void vtkTetra::Derivatives(int vtkNotUsed(subId), double vtkNotUsed(pcoords)[3],
                           double *values, int dim, double *derivs)
{
  double *jI[3], j0[3], j1[3], j2[3];
  double functionDerivs[12], 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(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 < 4; i++) //loop over interp. function derivatives
      {
      value = values[dim*i + k];
      sum[0] += functionDerivs[i] * value;
      sum[1] += functionDerivs[4 + i] * value;
      sum[2] += functionDerivs[8 + 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];
      }
    }
}

//----------------------------------------------------------------------------
// Compute the center of the tetrahedron,
void vtkTetra::TetraCenter(double p1[3], double p2[3], double p3[3],
                           double p4[3], double center[3])
{
  center[0] = (p1[0]+p2[0]+p3[0]+p4[0]) / 4.0;
  center[1] = (p1[1]+p2[1]+p3[1]+p4[1]) / 4.0;
  center[2] = (p1[2]+p2[2]+p3[2]+p4[2]) / 4.0;
}

//----------------------------------------------------------------------------
double vtkTetra::ComputeVolume(double  p1[3], double p2[3], double p3[3], 
                               double p4[3])
{
  return (vtkMath::Determinant3x3(p2[0]-p1[0], p3[0]-p1[0], p4[0]-p1[0],
                                  p2[1]-p1[1], p3[1]-p1[1], p4[1]-p1[1],
                                  p2[2]-p1[2], p3[2]-p1[2], p4[2]-p1[2])/6.0);
}
                               
//----------------------------------------------------------------------------
// Compute the circumcenter (center[3]) and radius squared (method
// return value) of a tetrahedron defined by the four points x1, x2,
// x3, and x4.
double vtkTetra::Circumsphere(double  x1[3], double x2[3], double x3[3], 
                             double x4[3], double center[3])
{
  double n12[3], n13[3], n14[3], x12[3], x13[3], x14[3];
  double *A[3], rhs[3], sum, diff;
  int i;

  //  calculate normals and intersection points of bisecting planes.  
  //
  for (i=0; i<3; i++) 
    {
    n12[i] = x2[i] - x1[i];
    n13[i] = x3[i] - x1[i];
    n14[i] = x4[i] - x1[i];
    x12[i] = (x2[i] + x1[i]) / 2.0;
    x13[i] = (x3[i] + x1[i]) / 2.0;
    x14[i] = (x4[i] + x1[i]) / 2.0;
    }

  //  Compute solutions to the intersection of two bisecting lines
  //  (3-eqns. in 3-unknowns).
  //
  //  form system matrices
  //
  A[0] = n12;
  A[1] = n13;
  A[2] = n14;

  rhs[0] = vtkMath::Dot(n12,x12); 
  rhs[1] = vtkMath::Dot(n13,x13);
  rhs[2] = vtkMath::Dot(n14,x14);

  // Solve system of equations
  //
  if ( vtkMath::SolveLinearSystem(A,rhs,3) == 0 )
    {
    center[0] = center[1] = center[2] = 0.0;
    return VTK_DOUBLE_MAX;
    }
  else
    {
    for (i=0; i<3; i++)
      {
      center[i] = rhs[i];
      }
    }

  //determine average value of radius squared
  for (sum=0, i=0; i<3; i++) 
    {
    diff = x1[i] - rhs[i];
    sum += diff*diff;
    diff = x2[i] - rhs[i];
    sum += diff*diff;
    diff = x3[i] - rhs[i];
    sum += diff*diff;
    diff = x4[i] - rhs[i];
    sum += diff*diff;
    }

  if ( (sum /= 4.0) > VTK_DOUBLE_MAX )
    {
    return VTK_DOUBLE_MAX;
    }
  else
    {
    return sum;
    }
}

//----------------------------------------------------------------------------
// Compute the incenter (center[3]) and radius (method return value) of
// a tetrahedron defined by the four points p1, p2, p3, and p4.
double vtkTetra::Insphere(double  p1[3], double p2[3], double p3[3], 
                          double p4[3], double center[3])
{
  double u[3], v[3], w[3];
  double p[3], q[3], r[3];
  double O1[3],O2[3];
  double y[3], s[3], t;
  
  u[0] = p2[0]-p1[0];
  u[1] = p2[1]-p1[1];
  u[2] = p2[2]-p1[2];
  
  v[0] = p3[0]-p1[0];
  v[1] = p3[1]-p1[1];
  v[2] = p3[2]-p1[2];
  
  w[0] = p4[0]-p1[0];
  w[1] = p4[1]-p1[1];
  w[2] = p4[2]-p1[2];
  
  vtkMath::Cross(u,v,p);
  vtkMath::Normalize(p);
  
  vtkMath::Cross(v,w,q);
  vtkMath::Normalize(q);
  
  vtkMath::Cross(w,u,r);
  vtkMath::Normalize(r);

  O1[0] = p[0]-q[0];
  O1[1] = p[1]-q[1];
  O1[2] = p[2]-q[2];

  O2[0] = q[0]-r[0];
  O2[1] = q[1]-r[1];
  O2[2] = q[2]-r[2];

  vtkMath::Cross(O1,O2,y);
  
  O1[0] = u[0]-w[0];
  O1[1] = u[1]-w[1];
  O1[2] = u[2]-w[2];

  O2[0] = v[0]-w[0];
  O2[1] = v[1]-w[1];
  O2[2] = v[2]-w[2];
  
  vtkMath::Cross(O1,O2,s);
  vtkMath::Normalize(s);
  
  s[0] = -1 * s[0];
  s[1] = -1 * s[1];
  s[2] = -1 * s[2];
  
  O1[0] = s[0]-p[0];
  O1[1] = s[1]-p[1];
  O1[2] = s[2]-p[2];
  
  t = vtkMath::Dot(w,s)/vtkMath::Dot(y,O1);
  center[0] = p1[0] + (t * y[0]);
  center[1] = p1[1] + (t * y[1]);
  center[2] = p1[2] + (t * y[2]);

  return (fabs(t* vtkMath::Dot(y,p)));
}

//----------------------------------------------------------------------------
// Given a 3D point x[3], determine the barycentric coordinates of the point.
// Barycentric coordinates are a natural coordinate system for simplices that
// express a position as a linear combination of the vertices. For a 
// tetrahedron, there are four barycentric coordinates (because there are
// four vertices), and the sum of the coordinates must equal 1. If a 
// point x is inside a simplex, then all four coordinates will be strictly 
// positive.  If three coordinates are zero (so the fourth =1), then the 
// point x is on a vertex. If two coordinates are zero, the point x is on an 
// edge (and so on). In this method, you must specify the vertex coordinates
// x1->x4. Returns 0 if tetrahedron is degenerate.
int vtkTetra::BarycentricCoords(double x[3], double  x1[3], double x2[3], 
                                double x3[3], double x4[3], double bcoords[4])
{
  double *A[4], p[4], a1[4], a2[4], a3[4], a4[4];
  int i;

  // Homogenize the variables; load into arrays.
  //
  a1[0] = x1[0]; a1[1] = x2[0]; a1[2] = x3[0]; a1[3] = x4[0];
  a2[0] = x1[1]; a2[1] = x2[1]; a2[2] = x3[1]; a2[3] = x4[1];
  a3[0] = x1[2]; a3[1] = x2[2]; a3[2] = x3[2]; a3[3] = x4[2];
  a4[0] = 1.0;   a4[1] = 1.0;   a4[2] = 1.0;   a4[3] = 1.0;
  p[0] = x[0]; p[1] = x[1]; p[2] = x[2]; p[3] = 1.0;

  //   Now solve system of equations for barycentric coordinates
  //
  A[0] = a1;
  A[1] = a2;
  A[2] = a3;
  A[3] = a4;

  if ( vtkMath::SolveLinearSystem(A,p,4) )
    {
    for (i=0; i<4; i++)
      {
      bcoords[i] = p[i];
      }
    return 1;
    }
  else
    {
    return 0;
    }
}

//----------------------------------------------------------------------------
//
// Compute iso-parametric interpolation functions
//
void vtkTetra::InterpolationFunctions(double pcoords[3], double sf[4])
{
  sf[0] = 1.0 - pcoords[0] - pcoords[1] - pcoords[2];
  sf[1] = pcoords[0];
  sf[2] = pcoords[1];
  sf[3] = pcoords[2];
}

//----------------------------------------------------------------------------
void vtkTetra::InterpolationDerivs(double derivs[12])
{
  // r-derivatives
  derivs[0] = -1.0;
  derivs[1] = 1.0;
  derivs[2] = 0.0;
  derivs[3] = 0.0;

  // s-derivatives
  derivs[4] = -1.0;
  derivs[5] = 0.0;
  derivs[6] = 1.0;
  derivs[7] = 0.0;

  // t-derivatives
  derivs[8] = -1.0;
  derivs[9] = 0.0;
  derivs[10] = 0.0;
  derivs[11] = 1.0;
}

//----------------------------------------------------------------------------
// Given parametric coordinates compute inverse Jacobian transformation
// matrix. Returns 9 elements of 3x3 inverse Jacobian plus interpolation
// function derivatives. Returns 0 if no inverse exists.
int vtkTetra::JacobianInverse(double **inverse, double derivs[12])
{
  int i, j;
  double *m[3], m0[3], m1[3], m2[3];
  double x[3];

  // compute interpolation function derivatives
  this->InterpolationDerivs(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 < 4; j++ )
    {
    this->Points->GetPoint(j, x);
    for ( i=0; i < 3; i++ )
      {
      m0[i] += x[i] * derivs[j];
      m1[i] += x[i] * derivs[4 + j];
      m2[i] += x[i] * derivs[8 + j];
      }
    }

  // now find the inverse
  if ( vtkMath::InvertMatrix(m,inverse,3) == 0 )
    {
#define VTK_MAX_WARNS 3    
    static int numWarns=0;
    if ( numWarns++ < VTK_MAX_WARNS )
      {
      vtkErrorMacro(<<"Jacobian inverse not found");
      vtkErrorMacro(<<"Matrix:" << m[0][0] << " " << m[0][1] << " " << m[0][2]
      << m[1][0] << " " << m[1][1] << " " << m[1][2] 
      << m[2][0] << " " << m[2][1] << " " << m[2][2] );
      return 0;
      }
    }

  return 1;
}

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

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

//----------------------------------------------------------------------------
// The clip table produces either a single tetrahedron or a single wedge as
// output.  The format of the case table is #pts, ptids. Points >= 100 are
// existing vertices; otherwise the number is an edge number requiring that
// an intersection is produced.

// support tetra clipping
typedef int TETRA_EDGE_LIST;
typedef struct {
       TETRA_EDGE_LIST edges[7];
} TETRA_CASES;
 
static TETRA_CASES tetraCases[] = { 
  {{ 0,   0,   0,   0,   0,   0,   0}},   // 0
  {{ 4,   0,   3,   2, 100,   0,   0}},   // 1
  {{ 4,   0,   1,   4, 101,   0,   0}},   // 2
  {{ 6, 101,   1,   4, 100,   2,   3}},   // 3
  {{ 4,   1,   2,   5, 102,   0,   0}},   // 4
  {{ 6, 102,   5,   1, 100,   3,   0}},   // 5
  {{ 6, 102,   2,   5, 101,   0,   4}},   // 6
  {{ 6,   3,   4,   5, 100, 101, 102}},   // 7
  {{ 4,   3,   4,   5, 103,   0,   0}},   // 8
  {{ 6, 103,   4,   5, 100,   0,   2}},   // 9
  {{ 6, 103,   5,   3, 101,   1,   0}},   // 10
  {{ 6, 100, 101, 103,   2,   1,   5}},   // 11
  {{ 6,   2, 102,   1,   3, 103,   4}},   // 12
  {{ 6,   0,   1,   4, 100, 102, 103}},   // 13
  {{ 6,   0,   3,   2, 101, 103, 102}},   // 14
  {{ 4, 100, 101, 102, 103,   0,   0}}    // 15
};

//----------------------------------------------------------------------------
// Clip this tetra using scalar value provided. Like contouring, except that
// it cuts the tetra to produce other 3D cells (note that this method will
// produce a single tetrahedra or a single wedge). The table has been
// carefully designed to insure that face neighbors--after clipping--are
// remain compatible. 
void vtkTetra::Clip(double value, vtkDataArray *cellScalars, 
                    vtkPointLocator *locator, vtkCellArray *tets,
                    vtkPointData *inPD, vtkPointData *outPD,
                    vtkCellData *inCD, vtkIdType cellId, vtkCellData *outCD,
                    int insideOut)
{
  static int CASE_MASK[4] = {1,2,4,8};
  TETRA_CASES *tetraCase;
  TETRA_EDGE_LIST  *edge;
  int i, j, index, *vert, newCellId;
  vtkIdType pts[6];
  int vertexId;
  double t, x1[3], x2[3], x[3];

  // Build the case table
  if ( insideOut )
    {    
    for ( i=0, index=0; i < 4; i++)
      {
      if (cellScalars->GetComponent(i,0) <= value)
        {
        index |= CASE_MASK[i];
        }
      }
    }    
  else
    {
    for ( i=0, index=0; i < 4; i++)
      {
      if (cellScalars->GetComponent(i,0) > value)
        {
        index |= CASE_MASK[i];
        }
      }
    }

  // Select the case based on the index and get the list of edges for this case
  tetraCase = tetraCases + index;
  edge = tetraCase->edges;

  // produce the clipped cell
  for (i=1; i<=edge[0]; i++) // insert tetra
    {
    // vertex exists, and need not be interpolated
    if (edge[i] >= 100)
      {
      vertexId = edge[i] - 100;
      this->Points->GetPoint(vertexId, x);
      if ( locator->InsertUniquePoint(x, pts[i-1]) )
        {
        outPD->CopyData(inPD,this->PointIds->GetId(vertexId),pts[i-1]);
        }
      }

    else //new vertex, interpolate
      {
      int v1, v2;
      vert = edges[edge[i]];

      // calculate a preferred interpolation direction
      double deltaScalar = (cellScalars->GetComponent(vert[1],0) 
                           - cellScalars->GetComponent(vert[0],0));
      if (deltaScalar > 0)
        {
        v1 = vert[0]; v2 = vert[1];
        }
      else
        {
        v1 = vert[1]; v2 = vert[0];
        deltaScalar = -deltaScalar;
        }

      // linear interpolation across edge
      t = ( deltaScalar == 0.0 ? 0.0 :
            (value - cellScalars->GetComponent(v1,0)) / deltaScalar );

      this->Points->GetPoint(v1, x1);
      this->Points->GetPoint(v2, x2);
      for (j=0; j<3; j++)
        {
        x[j] = x1[j] + t * (x2[j] - x1[j]);
        }

      if ( locator->InsertUniquePoint(x, pts[i-1]) )
        {
        vtkIdType p1 = this->PointIds->GetId(v1);
        vtkIdType p2 = this->PointIds->GetId(v2);
        outPD->InterpolateEdge(inPD,pts[i-1],p1,p2,t);
        }
      }
    }

  int allDifferent, numUnique=1;
  for (i=0; i<(edge[0]-1); i++)
    {
    for (allDifferent=1, j=i+1; j<edge[0] && allDifferent; j++)
      {
      if (pts[i] == pts[j]) allDifferent = 0;
      }
    if (allDifferent) numUnique++;
    }

  if ( edge[0] == 4 && numUnique == 4 ) // check for degenerate tetra
    {
    newCellId = tets->InsertNextCell(edge[0],pts);
    outCD->CopyData(inCD,cellId,newCellId);
    }
  else if ( edge[0] == 6 && numUnique > 3 ) // check for degenerate wedge
    {
    newCellId = tets->InsertNextCell(edge[0],pts);
    outCD->CopyData(inCD,cellId,newCellId);
    }
}

//----------------------------------------------------------------------------
static double vtkTetraCellPCoords[12] = {0.0,0.0,0.0, 1.0,0.0,0.0,
                                        0.0,1.0,0.0, 0.0,0.0,1.0};

double *vtkTetra::GetParametricCoords()
{
  return vtkTetraCellPCoords;
}

//----------------------------------------------------------------------------
double vtkTetra::GetParametricDistance(double pcoords[3])
{
  int i;
  double pDist, pDistMax=0.0;
  double pc[4];

  pc[0] = pcoords[0];
  pc[1] = pcoords[1];
  pc[2] = pcoords[2];
  pc[3] = 1.0 - pcoords[0] - pcoords[1] - pcoords[2];

  for (i=0; i<4; i++)
    {
    if ( pc[i] < 0.0 ) 
      {
      pDist = -pc[i];
      }
    else if ( pc[i] > 1.0 ) 
      {
      pDist = pc[i] - 1.0;
      }
    else //inside the cell in the parametric direction
      {
      pDist = 0.0;
      }
    if ( pDist > pDistMax )
      {
      pDistMax = pDist;
      }
    }
  
  return pDistMax;
}

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