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

  Program:   Visualization Toolkit
  Module:    vtkQuadraticTetra.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.

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

#include "vtkObjectFactory.h"
#include "vtkMath.h"
#include "vtkQuadraticEdge.h"
#include "vtkQuadraticTriangle.h"
#include "vtkTetra.h"
#include "vtkDoubleArray.h"
#include "vtkPoints.h"

vtkStandardNewMacro(vtkQuadraticTetra);

//----------------------------------------------------------------------------
// Construct the tetra with ten points.
vtkQuadraticTetra::vtkQuadraticTetra()
{
  this->Edge = vtkQuadraticEdge::New();
  this->Face = vtkQuadraticTriangle::New();
  this->Tetra = vtkTetra::New();
  this->Scalars = vtkDoubleArray::New();
  this->Scalars->SetNumberOfTuples(4);

  this->Points->SetNumberOfPoints(10);
  this->PointIds->SetNumberOfIds(10);
  for (int i = 0; i < 10; i++)
  {
    this->Points->SetPoint(i, 0.0, 0.0, 0.0);
    this->PointIds->SetId(i,0);
  }
}

//----------------------------------------------------------------------------
vtkQuadraticTetra::~vtkQuadraticTetra()
{
  this->Edge->Delete();
  this->Face->Delete();
  this->Tetra->Delete();
  this->Scalars->Delete();
}

//----------------------------------------------------------------------------
//clip each of the four vertices; the remaining octahedron is
//divided into four tetrahedron.
static int LinearTetras[3][8][4] = { { {0,4,6,7}, {4,1,5,8}, {6,5,2,9}, {7,8,9,3},
                                       {6,4,5,8}, {6,5,9,8}, {6,9,7,8}, {6,7,4,8}},
                                     { {0,4,6,7}, {4,1,5,8}, {6,5,2,9}, {7,8,9,3},
                                       {4,8,5,9}, {4,5,6,9}, {4,6,7,9}, {4,7,8,9}},
                                     { {0,4,6,7}, {4,1,5,8}, {6,5,2,9}, {7,8,9,3},
                                       {5,9,6,7}, {5,6,4,7}, {5,4,8,7}, {5,8,9,7}} };

static int TetraFaces[4][6] = { {0,1,3,4,8,7}, {1,2,3,5,9,8},
                                {2,0,3,6,7,9}, {0,2,1,6,5,4} };

static int TetraEdges[6][3] = { {0,1,4}, {1,2,5}, {2,0,6},
                                {0,3,7}, {1,3,8}, {2,3,9} };

//------------------------Tuple1----------------------------------------------------
int *vtkQuadraticTetra::GetEdgeArray(int edgeId)
{
  return TetraEdges[edgeId];
}
//----------------------------------------------------------------------------
int *vtkQuadraticTetra::GetFaceArray(int faceId)
{
  return TetraFaces[faceId];
}

//----------------------------------------------------------------------------
vtkCell *vtkQuadraticTetra::GetEdge(int edgeId)
{
  edgeId = (edgeId < 0 ? 0 : (edgeId > 5 ? 5 : edgeId ));

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

  // load coordinates
  this->Edge->Points->SetPoint(0,this->Points->GetPoint(TetraEdges[edgeId][0]));
  this->Edge->Points->SetPoint(1,this->Points->GetPoint(TetraEdges[edgeId][1]));
  this->Edge->Points->SetPoint(2,this->Points->GetPoint(TetraEdges[edgeId][2]));

  return this->Edge;
}

//----------------------------------------------------------------------------
vtkCell *vtkQuadraticTetra::GetFace(int faceId)
{
  faceId = (faceId < 0 ? 0 : (faceId > 3 ? 3 : faceId ));

  // load point id's and coordinates
  for (int i=0; i< 6; i++)
  {
    this->Face->PointIds->SetId(
      i,this->PointIds->GetId(TetraFaces[faceId][i]));
    this->Face->Points->SetPoint(
      i,this->Points->GetPoint(TetraFaces[faceId][i]));
  }

  return this->Face;
}

//----------------------------------------------------------------------------
namespace
{
  static const double VTK_DIVERGED = 1.e6;
  static const int VTK_TETRA_MAX_ITERATION=20;
  static const double VTK_TETRA_CONVERGED=1.e-05;
}

int vtkQuadraticTetra::EvaluatePosition(const double* x,
                                        double closestPoint[3],
                                        int& subId, double pcoords[3],
                                        double& dist2, double weights[])
{
  double params[3] = {.25, .25, .25};
  double derivs[30];

  // compute a bound on the volume to get a scale for an acceptable determinant
  double longestEdge = 0;
  for (int i=0; i<6; i++)
  {
    double pt0[3], pt1[3];
    this->Points->GetPoint(TetraEdges[i][0], pt0);
    this->Points->GetPoint(TetraEdges[i][1], pt1);
    double d2 = vtkMath::Distance2BetweenPoints(pt0, pt1);
    if (longestEdge < d2)
    {
      longestEdge = d2;
    }
  }
  // longestEdge value is already squared
  double volumeBound = pow(longestEdge, 1.5);
  double determinantTolerance = 1e-20 < .00001*volumeBound ? 1e-20 : .00001*volumeBound;

  //  set initial position for Newton's method
  subId = 0;
  pcoords[0] = pcoords[1] = pcoords[2] = 0.25;
  //  enter iteration loop
  int converged = 0;
  for (int iteration=0;!converged && (iteration < VTK_TETRA_MAX_ITERATION); iteration++)
  {
    //  calculate element interpolation functions and derivatives
    this->InterpolationFunctions(pcoords, weights);
    this->InterpolationDerivs(pcoords, derivs);

    //  calculate newton functions
    double fcol[3] = {0, 0, 0}, rcol[3] = {0, 0, 0}, scol[3] = {0, 0, 0}, tcol[3] = {0, 0, 0};
    for (int i=0; i<10; i++)
    {
      double pt[3];
      this->Points->GetPoint(i, pt);
      for (int j=0; j<3; j++)
      {
        fcol[j] += pt[j] * weights[i];
        rcol[j] += pt[j] * derivs[i];
        scol[j] += pt[j] * derivs[i+10];
        tcol[j] += pt[j] * derivs[i+20];
      }
    }

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

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

    pcoords[0] = params[0] - 0.5*vtkMath::Determinant3x3 (fcol,scol,tcol) / d;
    pcoords[1] = params[1] - 0.5*vtkMath::Determinant3x3 (rcol,fcol,tcol) / d;
    pcoords[2] = params[2] - 0.5*vtkMath::Determinant3x3 (rcol,scol,fcol) / d;

    //  check for convergence
    if ( ((fabs(pcoords[0]-params[0])) < VTK_TETRA_CONVERGED) &&
         ((fabs(pcoords[1]-params[1])) < VTK_TETRA_CONVERGED) &&
         ((fabs(pcoords[2]-params[2])) < VTK_TETRA_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 &&
       pcoords[0]+pcoords[1]+pcoords[2] <= 1.001 )
  {
    if (closestPoint)
    {
      closestPoint[0] = x[0]; closestPoint[1] = x[1]; closestPoint[2] = x[2];
      dist2 = 0.0; //inside tetra
    }
    return 1;
  }
  else
  {
    double pc[3], w[10];
    if (closestPoint)
    {
      for (int i=0; i<3; i++) //only approximate, not really true for warped tetra
      {
        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,
                             static_cast<double *>(w));
      dist2 = vtkMath::Distance2BetweenPoints(closestPoint,x);
    }
    return 0;
  }
}

//----------------------------------------------------------------------------
void vtkQuadraticTetra::EvaluateLocation(int& vtkNotUsed(subId),
                                         const 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<10; i++)
  {
    this->Points->GetPoint(i, pt);
    for (j=0; j<3; j++)
    {
      x[j] += pt[j] * weights[i];
    }
  }
}

//----------------------------------------------------------------------------
int vtkQuadraticTetra::CellBoundary(int subId, const double pcoords[3],
                                    vtkIdList *pts)
{
  for ( int i = 0; i < 4; ++ i ) // For each of the four vertices of the tet
  {
    this->Tetra->PointIds->SetId( i, this->PointIds->GetId( i ) );
  }

  return this->Tetra->CellBoundary( subId, pcoords, pts );
}

//----------------------------------------------------------------------------
void vtkQuadraticTetra::Contour(double value, vtkDataArray* cellScalars,
                                vtkIncrementalPointLocator* locator,
                                vtkCellArray *verts, vtkCellArray* lines,
                                vtkCellArray* polys,
                                vtkPointData* inPd, vtkPointData* outPd,
                                vtkCellData* inCd, vtkIdType cellId,
                                vtkCellData* outCd)
{
  // Determine how to tessellate. This will depend on the scalars (to try and minimize
  // artifacts).
  double sDiff0 = fabs(cellScalars->GetTuple1(8) - cellScalars->GetTuple1(6));
  double sDiff1 = fabs(cellScalars->GetTuple1(9) - cellScalars->GetTuple1(4));
  double sDiff2 = fabs(cellScalars->GetTuple1(7) - cellScalars->GetTuple1(5));
  int dir = ( (sDiff0 < sDiff1 ? (sDiff0 < sDiff2 ? 0 : 2) : (sDiff1 < sDiff2 ? 1 : 2)) );

  for ( int i=0; i < 8; i++) //for each subdivided tetra
  {
    for ( int j=0; j<4; j++) //for each of the four vertices of the tetra
    {
      this->Tetra->Points->SetPoint(j,this->Points->GetPoint(LinearTetras[dir][i][j]));
      this->Tetra->PointIds->SetId(j,this->PointIds->GetId(LinearTetras[dir][i][j]));
      this->Scalars->SetValue(j,cellScalars->GetTuple1(LinearTetras[dir][i][j]));
    }
    this->Tetra->Contour(value, this->Scalars, locator, verts,
                         lines, polys, inPd, outPd, inCd, cellId, outCd);
  }
}

//----------------------------------------------------------------------------
// Line-line intersection. Intersection has to occur within [0,1] parametric
// coordinates and with specified tolerance.
int vtkQuadraticTetra::IntersectWithLine(const double* p1, const double* p2,
                                         double tol, double& t,
                                         double* x, double* pcoords, int& subId)
{
  int intersection=0;
  double tTemp;
  double pc[3], xTemp[3];
  int faceNum;

  t = VTK_DOUBLE_MAX;
  for (faceNum=0; faceNum<4; faceNum++)
  {
    for (int i=0; i<6; i++)
    {
      this->Face->Points->SetPoint(i,this->Points->GetPoint(TetraFaces[faceNum][i]));
    }

    if ( this->Face->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 vtkQuadraticTetra::Triangulate(int vtkNotUsed(index), vtkIdList *ptIds,
                                   vtkPoints *pts)
{
  pts->Reset();
  ptIds->Reset();

  for ( int i=0; i < 8; i++)
  {
    for ( int j=0; j < 4; j++)
    {
      ptIds->InsertId(4*i+j,this->PointIds->GetId(LinearTetras[0][i][j]));
      pts->InsertPoint(4*i+j,this->Points->GetPoint(LinearTetras[0][i][j]));
    }
  }

  return 1;
}

//----------------------------------------------------------------------------
// Given parametric coordinates compute inverse Jacobian transformation
// matrix. Returns 9 elements of 3x3 inverse Jacobian plus interpolation
// function derivatives.
void vtkQuadraticTetra::JacobianInverse(const double pcoords[3], double **inverse,
                                        double derivs[60])
{
  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 < 10; j++ )
  {
    this->Points->GetPoint(j, x);
    for ( i=0; i < 3; i++ )
    {
      m0[i] += x[i] * derivs[j];
      m1[i] += x[i] * derivs[10 + j];
      m2[i] += x[i] * derivs[20 + j];
    }
  }

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

//----------------------------------------------------------------------------
void vtkQuadraticTetra::Derivatives(int vtkNotUsed(subId),
                                    const double pcoords[3], const double *values,
                                    int dim, double *derivs)
{
  double *jI[3], j0[3], j1[3], j2[3];
  double functionDerivs[30], 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 < 10; i++) //loop over interp. function derivatives
    {
      sum[0] += functionDerivs[i] * values[dim*i + k];
      sum[1] += functionDerivs[10 + i] * values[dim*i + k];
      sum[2] += functionDerivs[20 + 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];
    }
  }
}

//----------------------------------------------------------------------------
// Clip this quadratic tetra using the scalar value provided. Like contouring,
// except that it cuts the tetra to produce other tetra.
void vtkQuadraticTetra::Clip(double value, vtkDataArray* cellScalars,
                             vtkIncrementalPointLocator* locator, vtkCellArray* tetras,
                             vtkPointData* inPd, vtkPointData* outPd,
                             vtkCellData* inCd, vtkIdType cellId,
                             vtkCellData* outCd, int insideOut)
{
    // Determine how to tessellate. This will depend on the scalars (to try and minimize
  // artifacts).
  double sDiff0 = fabs(cellScalars->GetTuple1(8) - cellScalars->GetTuple1(6));
  double sDiff1 = fabs(cellScalars->GetTuple1(9) - cellScalars->GetTuple1(4));
  double sDiff2 = fabs(cellScalars->GetTuple1(7) - cellScalars->GetTuple1(5));
  int dir = ( (sDiff0 < sDiff1 ? (sDiff0 < sDiff2 ? 0 : 2) : (sDiff1 < sDiff2 ? 1 : 2)) );

  for ( int i=0; i < 8; i++) //for each subdivided tetra
  {
    for ( int j=0; j<4; j++) //for each of the four vertices of the tetra
    {
      this->Tetra->Points->SetPoint(j,this->Points->GetPoint(LinearTetras[dir][i][j]));
      this->Tetra->PointIds->SetId(j,this->PointIds->GetId(LinearTetras[dir][i][j]));
      this->Scalars->SetValue(j,cellScalars->GetTuple1(LinearTetras[dir][i][j]));
    }
    this->Tetra->Clip(value, this->Scalars, locator, tetras, inPd, outPd,
                      inCd, cellId, outCd, insideOut);
  }
}

//----------------------------------------------------------------------------
int vtkQuadraticTetra::GetParametricCenter(double pcoords[3])
{
  pcoords[0] = pcoords[1] = pcoords[2] = 0.25;
  return 0;
}

//----------------------------------------------------------------------------
// Compute interpolation functions. First four nodes are the
// tetrahedron corner vertices; the others are mid-edge nodes.
void vtkQuadraticTetra::InterpolationFunctions(const double pcoords[3],
                                               double weights[10])
{
  double r = pcoords[0];
  double s = pcoords[1];
  double t = pcoords[2];
  double u = 1.0 - r - s - t;

  // corners
  weights[0] = u*(2.0*u - 1.0);
  weights[1] = r*(2.0*r - 1.0);
  weights[2] = s*(2.0*s - 1.0);
  weights[3] = t*(2.0*t - 1.0);

  // midedge
  weights[4] = 4.0 * u * r;
  weights[5] = 4.0 * r * s;
  weights[6] = 4.0 * s * u;
  weights[7] = 4.0 * u * t;
  weights[8] = 4.0 * r * t;
  weights[9] = 4.0 * s * t;
}

//----------------------------------------------------------------------------
// Derivatives in parametric space.
void vtkQuadraticTetra::InterpolationDerivs(const double pcoords[3], double derivs[30])
{
  double r = pcoords[0];
  double s = pcoords[1];
  double t = pcoords[2];

  // r-derivatives: dW0/dr to dW9/dr
  derivs[0] = 4.0*(r + s + t) - 3.0;
  derivs[1] = 4.0*r - 1.0;
  derivs[2] = 0.0;
  derivs[3] = 0.0;
  derivs[4] = 4.0 - 8.0*r - 4.0*s - 4.0*t;
  derivs[5] = 4.0*s;
  derivs[6] = -4.0*s;
  derivs[7] = -4.0*t;
  derivs[8] = 4.0*t;
  derivs[9] = 0.0;

  // s-derivatives: dW0/ds to dW9/ds
  derivs[10] = 4.0*(r + s + t) - 3.0;
  derivs[11] = 0.0;
  derivs[12] = 4.0*s - 1.0;
  derivs[13] = 0.0;
  derivs[14] = -4.0*r;
  derivs[15] =  4.0*r;
  derivs[16] = 4.0 - 4.0*r - 8.0*s - 4.0*t;
  derivs[17] = -4.0*t;
  derivs[18] = 0.0;
  derivs[19] =  4.0*t;

  // t-derivatives: dW0/dt to dW9/dt
  derivs[20] = 4.0*(r + s + t) - 3.0;
  derivs[21] = 0.0;
  derivs[22] = 0.0;
  derivs[23] = 4.0*t - 1.0;
  derivs[24] = -4.0*r;
  derivs[25] = 0.0;
  derivs[26] = -4.0*s;
  derivs[27] = 4.0 - 4.0*r - 4.0*s - 8.0*t;
  derivs[28] = 4.0*r;
  derivs[29] = 4.0*s;
}

//----------------------------------------------------------------------------
double vtkQuadraticTetra::GetParametricDistance(const 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;
}

//----------------------------------------------------------------------------
static double vtkQTetraCellPCoords[30] = {
  0.0,0.0,0.0, 1.0,0.0,0.0, 0.0,1.0,0.0,
  0.0,0.0,1.0, 0.5,0.0,0.0, 0.5,0.5,0.0,
  0.0,0.5,0.0, 0.0,0.0,0.5, 0.5,0.0,0.5,
  0.0,0.5,0.5};

double *vtkQuadraticTetra::GetParametricCoords()
{
  return vtkQTetraCellPCoords;
}

//----------------------------------------------------------------------------
void vtkQuadraticTetra::PrintSelf(ostream& os, vtkIndent indent)
{
  this->Superclass::PrintSelf(os,indent);

  os << indent << "Edge:\n";
  this->Edge->PrintSelf(os,indent.GetNextIndent());
  os << indent << "Face:\n";
  this->Face->PrintSelf(os,indent.GetNextIndent());
  os << indent << "Tetra:\n";
  this->Tetra->PrintSelf(os,indent.GetNextIndent());
  os << indent << "Scalars:\n";
  this->Scalars->PrintSelf(os,indent.GetNextIndent());
}
