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

  Program:   Visualization Toolkit
  Module:    vtkPyramid.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 "vtkPyramid.h"

#include "vtkCellArray.h"
#include "vtkCellData.h"
#include "vtkDoubleArray.h"
#include "vtkIncrementalPointLocator.h"
#include "vtkLine.h"
#include "vtkMath.h"
#include "vtkObjectFactory.h"
#include "vtkPointData.h"
#include "vtkPolygon.h"
#include "vtkQuad.h"
#include "vtkTriangle.h"
#include "vtkUnstructuredGrid.h"

#include <cassert>
#include <vector>

vtkStandardNewMacro(vtkPyramid);

namespace
{
const double VTK_DIVERGED = 1.e6;
const int VTK_MAX_ITERATION = 10;
const double VTK_CONVERGED = 1.e-03;
}

//------------------------------------------------------------------------------
// Marching pyramids (contouring)
//
namespace
{ // required so we don't violate ODR
// Pyramid topology:
//
//   3 __ 2
//   |\  /|
//   |4\/ |
//   | /\ |
//   |/__\|
//   0    1
constexpr vtkIdType edges[vtkPyramid::NumberOfEdges][2] = {
  { 0, 1 }, // 0
  { 1, 2 }, // 1
  { 2, 3 }, // 2
  { 3, 0 }, // 3
  { 0, 4 }, // 4
  { 1, 4 }, // 5
  { 2, 4 }, // 6
  { 3, 4 }, // 7
};
constexpr vtkIdType faces[vtkPyramid::NumberOfFaces][vtkPyramid::MaximumFaceSize + 1] = {
  { 0, 3, 2, 1, -1 },  // 0
  { 0, 1, 4, -1, -1 }, // 1
  { 1, 2, 4, -1, -1 }, // 2
  { 2, 3, 4, -1, -1 }, // 3
  { 3, 0, 4, -1, -1 }, // 4
};
constexpr vtkIdType edgeToAdjacentFaces[vtkPyramid::NumberOfEdges][2] = {
  { 0, 1 }, // 0
  { 0, 2 }, // 1
  { 0, 3 }, // 2
  { 0, 4 }, // 3
  { 1, 4 }, // 4
  { 1, 2 }, // 5
  { 2, 3 }, // 6
  { 3, 4 }, // 7
};
constexpr vtkIdType faceToAdjacentFaces[vtkPyramid::NumberOfFaces][vtkPyramid::MaximumFaceSize] = {
  { 4, 3, 2, 1 },  // 0
  { 0, 2, 4, -1 }, // 1
  { 0, 3, 1, -1 }, // 2
  { 0, 4, 2, -1 }, // 3
  { 0, 1, 3, -1 }, // 4
};
constexpr vtkIdType pointToIncidentEdges[vtkPyramid::NumberOfPoints][vtkPyramid::MaximumValence] = {
  { 0, 4, 3, -1 }, // 0
  { 0, 1, 5, -1 }, // 1
  { 1, 2, 6, -1 }, // 2
  { 2, 3, 7, -1 }, // 3
  { 4, 5, 6, 7 },  // 4
};
constexpr vtkIdType pointToIncidentFaces[vtkPyramid::NumberOfPoints][vtkPyramid::MaximumValence] = {
  { 1, 4, 0, -1 }, // 0
  { 0, 2, 1, -1 }, // 1
  { 0, 3, 2, -1 }, // 2
  { 0, 4, 3, -1 }, // 3
  { 1, 2, 3, 4 },  // 4
};
constexpr vtkIdType pointToOneRingPoints[vtkPyramid::NumberOfPoints][vtkPyramid::MaximumValence] = {
  { 1, 4, 3, -1 }, // 0
  { 0, 2, 4, -1 }, // 1
  { 1, 3, 4, -1 }, // 2
  { 2, 0, 4, -1 }, // 3
  { 0, 1, 2, 3 },  // 4
};
constexpr vtkIdType numberOfPointsInFace[vtkPyramid::NumberOfFaces] = {
  4, // 0
  3, // 1
  3, // 2
  3, // 3
  3  // 4
};
constexpr vtkIdType valenceAtPoint[vtkPyramid::NumberOfPoints] = {
  4, // 0
  3, // 1
  3, // 2
  3, // 3
  3  // 4
};

typedef int EDGE_LIST;
struct TRIANGLE_CASES_t
{
  EDGE_LIST edges[13];
};
using TRIANGLE_CASES = struct TRIANGLE_CASES_t;
TRIANGLE_CASES triCases[] = {
  { { -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 } }, // 0
  { { 3, 4, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 } },    // 1
  { { 5, 1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 } },    // 2
  { { 5, 1, 4, 1, 3, 4, -1, -1, -1, -1, -1, -1, -1 } },       // 3
  { { 6, 2, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 } },    // 4
  { { 3, 4, 0, 6, 2, 1, -1, -1, -1, -1, -1, -1, -1 } },       // 5
  { { 5, 2, 0, 6, 2, 5, -1, -1, -1, -1, -1, -1, -1 } },       // 6
  { { 2, 3, 4, 2, 4, 6, 4, 5, 6, -1, -1, -1, -1 } },          // 7
  { { 2, 7, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 } },    // 8
  { { 2, 7, 4, 4, 0, 2, -1, -1, -1, -1, -1, -1, -1 } },       // 9
  { { 5, 1, 0, 2, 7, 3, -1, -1, -1, -1, -1, -1, -1 } },       // 10
  { { 5, 7, 4, 1, 7, 5, 2, 7, 1, -1, -1, -1, -1 } },          // 11
  { { 6, 3, 1, 7, 3, 6, -1, -1, -1, -1, -1, -1, -1 } },       // 12
  { { 4, 6, 7, 0, 6, 4, 1, 6, 0, -1, -1, -1, -1 } },          // 13
  { { 7, 5, 6, 3, 5, 7, 0, 5, 3, -1, -1, -1, -1 } },          // 14
  { { 7, 4, 5, 7, 5, 6, -1, -1, -1, -1, -1, -1, -1 } },       // 15
  { { 7, 5, 4, 7, 6, 5, -1, -1, -1, -1, -1, -1, -1 } },       // 16
  { { 5, 0, 3, 6, 5, 3, 7, 6, 3, -1, -1, -1, -1 } },          // 17
  { { 1, 0, 4, 7, 1, 4, 6, 1, 7, -1, -1, -1, -1 } },          // 18
  { { 6, 1, 3, 7, 6, 3, -1, -1, -1, -1, -1, -1, -1 } },       // 19
  { { 7, 5, 4, 7, 1, 5, 7, 2, 1, -1, -1, -1, -1 } },          // 20
  { { 3, 7, 0, 7, 5, 0, 7, 2, 5, 2, 1, 5, -1 } },             // 21
  { { 4, 2, 0, 7, 2, 4, -1, -1, -1, -1, -1, -1, -1 } },       // 22
  { { 7, 2, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 } },    // 23
  { { 2, 4, 3, 5, 4, 2, 6, 5, 2, -1, -1, -1, -1 } },          // 24
  { { 2, 5, 0, 2, 6, 5, -1, -1, -1, -1, -1, -1, -1 } },       // 25
  { { 6, 1, 0, 4, 6, 0, 3, 6, 4, 3, 2, 6, -1 } },             // 26
  { { 2, 6, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 } },    // 27
  { { 1, 4, 3, 1, 5, 4, -1, -1, -1, -1, -1, -1, -1 } },       // 28
  { { 1, 5, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 } },    // 29
  { { 4, 3, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 } },    // 30
  { { -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 } }, // 31
};
}

//------------------------------------------------------------------------------
bool vtkPyramid::GetCentroid(double centroid[3]) const
{
  return vtkPyramid::ComputeCentroid(this->Points, nullptr, centroid);
}

//------------------------------------------------------------------------------
bool vtkPyramid::ComputeCentroid(vtkPoints* points, const vtkIdType* pointIds, double centroid[3])
{
  double p[3];
  centroid[0] = centroid[1] = centroid[2] = 0.0;
  if (!pointIds)
  {
    vtkPolygon::ComputeCentroid(points, numberOfPointsInFace[4], faces[4], centroid);
    points->GetPoint(4, p);
  }
  else
  {
    vtkIdType facePointsIds[4] = { pointIds[faces[4][0]], pointIds[faces[4][1]],
      pointIds[faces[4][2]], pointIds[faces[4][3]] };
    vtkPolygon::ComputeCentroid(points, numberOfPointsInFace[4], facePointsIds, centroid);
    points->GetPoint(pointIds[4], p);
  }
  centroid[0] += 3 * p[0];
  centroid[1] += 3 * p[1];
  centroid[2] += 3 * p[2];
  centroid[0] *= 0.25;
  centroid[1] *= 0.25;
  centroid[2] *= 0.25;
  return true;
}

//------------------------------------------------------------------------------
bool vtkPyramid::IsInsideOut()
{
  double n[3], a[3], b[3];
  vtkPolygon::ComputeNormal(this->Points, numberOfPointsInFace[4], faces[4], n);
  this->Points->GetPoint(0, a);
  this->Points->GetPoint(4, b);
  b[0] -= a[0];
  b[1] -= a[1];
  b[2] -= a[2];
  return vtkMath::Dot(n, b) > 0.0;
}

//------------------------------------------------------------------------------
//
// Construct the pyramid with five points.
//
vtkPyramid::vtkPyramid()
{
  this->Points->SetNumberOfPoints(5);
  this->PointIds->SetNumberOfIds(5);
  for (int i = 0; i < 5; i++)
  {
    this->Points->SetPoint(i, 0.0, 0.0, 0.0);
    this->PointIds->SetId(i, 0);
  }
  this->Line = vtkLine::New();
  this->Triangle = vtkTriangle::New();
  this->Quad = vtkQuad::New();
}

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

//------------------------------------------------------------------------------
int vtkPyramid::EvaluatePosition(const double x[3], double closestPoint[3], int& subId,
  double pcoords[3], double& dist2, double weights[])
{
  subId = 0;

  // Efficient point access
  vtkDoubleArray* pointArray = static_cast<vtkDoubleArray*>(this->Points->GetData());
  const double* pts = pointArray->GetPointer(0);
  const double *pt0, *pt1, *tmp;

  // There are problems searching for the apex point so we check if
  // we are there first before doing the full parametric inversion.
  const double* apexPoint = pts + 12;
  dist2 = vtkMath::Distance2BetweenPoints(apexPoint, x);
  double baseMidpoint[3];
  baseMidpoint[0] = pts[0];
  baseMidpoint[1] = pts[1];
  baseMidpoint[2] = pts[2];
  for (int i = 1; i < 4; i++)
  {
    tmp = pts + 3 * i;
    baseMidpoint[0] += tmp[0];
    baseMidpoint[1] += tmp[1];
    baseMidpoint[2] += tmp[2];
  }
  for (int i = 0; i < 3; i++)
  {
    baseMidpoint[i] /= 4.;
  }

  double length2 = vtkMath::Distance2BetweenPoints(apexPoint, baseMidpoint);
  // we use .001 as the relative tolerance here since that is the same
  // that is used for the interior cell check below but we need to
  // square it here because we're looking at dist2^2.
  if (dist2 == 0. || (length2 != 0. && dist2 / length2 < 1.e-6))
  {
    pcoords[0] = pcoords[1] = 0;
    pcoords[2] = 1;
    vtkPyramid::InterpolationFunctions(pcoords, weights);
    if (closestPoint)
    {
      memcpy(closestPoint, x, 3 * sizeof(double));
      dist2 = 0.;
    }
    return 1;
  }

  double derivs[15];

  // compute a bound on the volume to get a scale for an acceptable determinant
  double longestEdge = 0;
  for (int i = 0; i < 8; i++)
  {
    pt0 = pts + 3 * edges[i][0];
    pt1 = pts + 3 * edges[i][1];
    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
  double params[3] = { 0.3333333, 0.3333333, 0.3333333 };
  pcoords[0] = pcoords[1] = pcoords[2] = params[0];

  //  enter iteration loop
  int converged = 0;
  for (int iteration = 0; !converged && (iteration < VTK_MAX_ITERATION); iteration++)
  {
    //  calculate element interpolation functions and derivatives
    vtkPyramid::InterpolationFunctions(pcoords, weights);
    vtkPyramid::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 < 5; i++)
    {
      for (int j = 0; j < 3; j++)
      {
        const double coord = pts[3 * i + j];
        fcol[j] += coord * weights[i];
        rcol[j] += coord * derivs[i];
        scol[j] += coord * derivs[i + 5];
        tcol[j] += coord * derivs[i + 10];
      }
    }

    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)
    {
      vtkDebugMacro(<< "Determinant incorrect, iteration " << iteration);
      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_CONVERGED) &&
      ((fabs(pcoords[1] - params[1])) < VTK_CONVERGED) &&
      ((fabs(pcoords[2] - params[2])) < VTK_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;
  }

  vtkPyramid::InterpolationFunctions(pcoords, weights);

  // This is correct in that the XY parametric coordinate plane "shrinks"
  // while Z increases and X and Y always are between 0 and 1.
  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 pyramid
    return 1;
  }
  else
  {
    double pc[3], w[5];
    if (closestPoint)
    {
      for (int 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, static_cast<double*>(w));
      dist2 = vtkMath::Distance2BetweenPoints(closestPoint, x);
    }
    return 0;
  }
}

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

  vtkPyramid::InterpolationFunctions(pcoords, weights);

  x[0] = x[1] = x[2] = 0.0;
  for (i = 0; i < 5; i++)
  {
    this->Points->GetPoint(i, pt);
    for (j = 0; j < 3; j++)
    {
      x[j] += pt[j] * weights[i];
    }
  }
}

//------------------------------------------------------------------------------
// Returns the closest face to the point specified. Closeness is measured
// parametrically.
int vtkPyramid::CellBoundary(int vtkNotUsed(subId), const double pcoords[3], vtkIdList* pts)
{
  int i;

  // define 6 planes that separate regions
  static double normals[6][3] = { { 0.0, -0.5547002, 0.8320503 }, { 0.5547002, 0.0, 0.8320503 },
    { 0.0, 0.5547002, 0.8320503 }, { -0.5547002, 0.0, 0.8320503 }, { 0.70710670, -0.70710670, 0.0 },
    { 0.70710670, 0.70710670, 0.0 } };
  static double point[3] = { 0.5, 0.5, 0.3333333 };
  double vals[6];

  // evaluate 6 plane equations
  for (i = 0; i < 6; i++)
  {
    vals[i] = normals[i][0] * (pcoords[0] - point[0]) + normals[i][1] * (pcoords[1] - point[1]) +
      normals[i][2] * (pcoords[2] - point[2]);
  }

  // compare against six planes in parametric space that divide element
  // into five pieces (each corresponding to a face).
  if (vals[4] >= 0.0 && vals[5] <= 0.0 && vals[0] >= 0.0)
  {
    pts->SetNumberOfIds(3); // triangle face
    pts->SetId(0, this->PointIds->GetId(0));
    pts->SetId(1, this->PointIds->GetId(1));
    pts->SetId(2, this->PointIds->GetId(4));
  }

  else if (vals[4] >= 0.0 && vals[5] >= 0.0 && vals[1] >= 0.0)
  {
    pts->SetNumberOfIds(3); // triangle face
    pts->SetId(0, this->PointIds->GetId(1));
    pts->SetId(1, this->PointIds->GetId(2));
    pts->SetId(2, this->PointIds->GetId(4));
  }

  else if (vals[4] <= 0.0 && vals[5] >= 0.0 && vals[2] >= 0.0)
  {
    pts->SetNumberOfIds(3); // triangle face
    pts->SetId(0, this->PointIds->GetId(2));
    pts->SetId(1, this->PointIds->GetId(3));
    pts->SetId(2, this->PointIds->GetId(4));
  }

  else if (vals[4] <= 0.0 && vals[5] <= 0.0 && vals[3] >= 0.0)
  {
    pts->SetNumberOfIds(3); // triangle face
    pts->SetId(0, this->PointIds->GetId(3));
    pts->SetId(1, this->PointIds->GetId(0));
    pts->SetId(2, this->PointIds->GetId(4));
  }

  else
  {
    pts->SetNumberOfIds(4); // quad face
    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));
  }

  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;
  }
}

//------------------------------------------------------------------------------
void vtkPyramid::Contour(double value, vtkDataArray* cellScalars,
  vtkIncrementalPointLocator* locator, vtkCellArray* verts, vtkCellArray* lines,
  vtkCellArray* polys, vtkPointData* inPd, vtkPointData* outPd, vtkCellData* inCd, vtkIdType cellId,
  vtkCellData* outCd)
{
  static const int CASE_MASK[5] = { 1, 2, 4, 8, 16 };
  TRIANGLE_CASES* triCase;
  EDGE_LIST* edge;
  int i, j, index, v1, v2, newCellId;
  const vtkIdType* vert;
  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 < 5; 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
      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);
      if (outCd)
      {
        outCd->CopyData(inCd, cellId, newCellId);
      }
    }
  }
}

//------------------------------------------------------------------------------
// Return the case table for table-based isocontouring (aka marching cubes
// style implementations). A linear 3D cell with N vertices will have 2**N
// cases. The cases list three edges in order to produce one output triangle.
int* vtkPyramid::GetTriangleCases(int caseId)
{
  return triCases[caseId].edges;
}

//------------------------------------------------------------------------------
const vtkIdType* vtkPyramid::GetEdgeToAdjacentFacesArray(vtkIdType edgeId)
{
  assert(edgeId < vtkPyramid::NumberOfEdges && "edgeId too large");
  return edgeToAdjacentFaces[edgeId];
}

//------------------------------------------------------------------------------
const vtkIdType* vtkPyramid::GetFaceToAdjacentFacesArray(vtkIdType faceId)
{
  assert(faceId < vtkPyramid::NumberOfFaces && "faceId too large");
  return faceToAdjacentFaces[faceId];
}

//------------------------------------------------------------------------------
const vtkIdType* vtkPyramid::GetPointToIncidentEdgesArray(vtkIdType pointId)
{
  assert(pointId < vtkPyramid::NumberOfPoints && "pointId too large");
  return pointToIncidentEdges[pointId];
}

//------------------------------------------------------------------------------
const vtkIdType* vtkPyramid::GetPointToIncidentFacesArray(vtkIdType pointId)
{
  assert(pointId < vtkPyramid::NumberOfPoints && "pointId too large");
  return pointToIncidentFaces[pointId];
}

//------------------------------------------------------------------------------
const vtkIdType* vtkPyramid::GetPointToOneRingPointsArray(vtkIdType pointId)
{
  assert(pointId < vtkPyramid::NumberOfPoints && "pointId too large");
  return pointToOneRingPoints[pointId];
}

//------------------------------------------------------------------------------
const vtkIdType* vtkPyramid::GetEdgeArray(vtkIdType edgeId)
{
  assert(edgeId < vtkPyramid::NumberOfEdges && "edgeId too large");
  return edges[edgeId];
}

//------------------------------------------------------------------------------
vtkCell* vtkPyramid::GetEdge(int edgeId)
{
  const vtkIdType* 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;
}

//------------------------------------------------------------------------------
const vtkIdType* vtkPyramid::GetFaceArray(vtkIdType faceId)
{
  assert(faceId < vtkPyramid::NumberOfFaces && "faceId too large");
  return faces[faceId];
}

//------------------------------------------------------------------------------
vtkCell* vtkPyramid::GetFace(int faceId)
{
  const vtkIdType* verts;

  verts = faces[faceId];

  if (verts[3] != -1) // quad cell
  {
    // 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;
  }
  else
  {
    // 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 faces against line.
//
int vtkPyramid::IntersectWithLine(const double p1[3], const 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];
  double tTemp;
  double pc[3], xTemp[3], dist2, weights[5];

  int faceNum;

  t = VTK_DOUBLE_MAX;

  // first intersect the triangle faces
  for (faceNum = 1; faceNum < 5; 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];
        this->EvaluatePosition(x, xTemp, subId, pcoords, dist2, weights);
      }
    }
  }

  // now intersect the quad face
  this->Points->GetPoint(faces[0][0], pt1);
  this->Points->GetPoint(faces[0][1], pt2);
  this->Points->GetPoint(faces[0][2], pt3);
  this->Points->GetPoint(faces[0][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];
      pcoords[0] = pc[0];
      pcoords[1] = pc[1];
      pcoords[2] = 0.0;
    }
  }

  return intersection;
}

//------------------------------------------------------------------------------
int vtkPyramid::Triangulate(int vtkNotUsed(index), vtkIdList* ptIds, vtkPoints* pts)
{
  int p[4], i;
  ptIds->Reset();
  pts->Reset();

  // The base of the pyramid must be split into two triangles.  There are two
  // ways to do this (across either diagonal).  Pick the shorter diagonal.
  double base_points[4][3];
  for (i = 0; i < 4; i++)
  {
    this->Points->GetPoint(i, base_points[i]);
  }
  double diagonal1, diagonal2;
  diagonal1 = vtkMath::Distance2BetweenPoints(base_points[0], base_points[2]);
  diagonal2 = vtkMath::Distance2BetweenPoints(base_points[1], base_points[3]);

  if (diagonal1 < diagonal2)
  {
    for (i = 0; i < 4; i++)
    {
      p[0] = 0;
      p[1] = 1;
      p[2] = 2;
      p[3] = 4;
      ptIds->InsertNextId(this->PointIds->GetId(p[i]));
      pts->InsertNextPoint(this->Points->GetPoint(p[i]));
    }
    for (i = 0; i < 4; i++)
    {
      p[0] = 0;
      p[1] = 2;
      p[2] = 3;
      p[3] = 4;
      ptIds->InsertNextId(this->PointIds->GetId(p[i]));
      pts->InsertNextPoint(this->Points->GetPoint(p[i]));
    }
  }
  else
  {
    for (i = 0; i < 4; i++)
    {
      p[0] = 0;
      p[1] = 1;
      p[2] = 3;
      p[3] = 4;
      ptIds->InsertNextId(this->PointIds->GetId(p[i]));
      pts->InsertNextPoint(this->Points->GetPoint(p[i]));
    }
    for (i = 0; i < 4; i++)
    {
      p[0] = 1;
      p[1] = 2;
      p[2] = 3;
      p[3] = 4;
      ptIds->InsertNextId(this->PointIds->GetId(p[i]));
      pts->InsertNextPoint(this->Points->GetPoint(p[i]));
    }
  }

  return !(diagonal1 == diagonal2);
}

//------------------------------------------------------------------------------
void vtkPyramid::Derivatives(
  int subId, const double pcoords[3], const double* values, int dim, double* derivs)
{
  if (pcoords[2] > .999)
  {
    // If we are at the apex of the pyramid we need to do something special.
    // As we approach the apex, the derivatives of the parametric shape
    // functions in x and y go to 0 while the inverse of the Jacobian
    // also goes to 0.  This results in 0/0 but using l'Hopital's rule
    // we could actually compute the value of the limit, if we had a
    // functional expression to compute the gradient.  We're on a computer
    // so we don't but we can cheat and do a linear extrapolation of the
    // derivatives which really ends up as the same thing.
    double pcoords1[3] = { .5, .5, 2. * .998 - pcoords[2] };
    std::vector<double> derivs1(3 * dim);
    this->Derivatives(subId, pcoords1, values, dim, &(derivs1[0]));
    double pcoords2[3] = { .5, .5, .998 };
    std::vector<double> derivs2(3 * dim);
    this->Derivatives(subId, pcoords2, values, dim, &(derivs2[0]));
    for (int i = 0; i < dim * 3; i++)
    {
      derivs[i] = 2. * derivs2[i] - derivs1[i];
    }
    return;
  }

  double functionDerivs[15], sum[3], value;
  int i, j, k;
  double *jI[3], j0[3], j1[3], j2[3];
  // 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 point
  {
    sum[0] = sum[1] = sum[2] = 0.0;
    for (i = 0; i < 5; i++) // loop over interp. function derivatives
    {
      value = values[dim * i + k];
      sum[0] += functionDerivs[i] * value;
      sum[1] += functionDerivs[5 + i] * value;
      sum[2] += functionDerivs[10 + 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 iso-parametric interpolation functions for pyramid
//
void vtkPyramid::InterpolationFunctions(const double pcoords[3], double sf[5])
{
  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] = pcoords[2];
}

//------------------------------------------------------------------------------
void vtkPyramid::InterpolationDerivs(const double pcoords[3], double derivs[15])
{
  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] = 0.0;

  // s-derivatives
  derivs[5] = -rm * tm;
  derivs[6] = -pcoords[0] * tm;
  derivs[7] = pcoords[0] * tm;
  derivs[8] = rm * tm;
  derivs[9] = 0.0;

  // t-derivatives
  derivs[10] = -rm * sm;
  derivs[11] = -pcoords[0] * sm;
  derivs[12] = -pcoords[0] * pcoords[1];
  derivs[13] = -rm * pcoords[1];
  derivs[14] = 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.
// Note for pyramid: the inverse Jacobian is undefined at the apex.
int vtkPyramid::JacobianInverse(const double pcoords[3], double** inverse, double derivs[15])
{
  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 < 5; j++)
  {
    this->Points->GetPoint(j, x);
    for (i = 0; i < 3; i++)
    {
      m0[i] += x[i] * derivs[j];
      m1[i] += x[i] * derivs[5 + j];
      m2[i] += x[i] * derivs[10 + j];
    }
  }

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

//------------------------------------------------------------------------------
vtkIdType vtkPyramid::GetPointToOneRingPoints(vtkIdType pointId, const vtkIdType*& pts)
{
  assert(pointId < vtkPyramid::NumberOfPoints && "pointId too large");
  pts = pointToOneRingPoints[pointId];
  return valenceAtPoint[pointId];
}

//------------------------------------------------------------------------------
vtkIdType vtkPyramid::GetPointToIncidentFaces(vtkIdType pointId, const vtkIdType*& faceIds)
{
  assert(pointId < vtkPyramid::NumberOfPoints && "pointId too large");
  faceIds = pointToIncidentFaces[pointId];
  return valenceAtPoint[pointId];
}

//------------------------------------------------------------------------------
vtkIdType vtkPyramid::GetPointToIncidentEdges(vtkIdType pointId, const vtkIdType*& edgeIds)
{
  assert(pointId < vtkPyramid::NumberOfPoints && "pointId too large");
  edgeIds = pointToIncidentEdges[pointId];
  return valenceAtPoint[pointId];
}

//------------------------------------------------------------------------------
vtkIdType vtkPyramid::GetFaceToAdjacentFaces(vtkIdType faceId, const vtkIdType*& faceIds)
{
  assert(faceId < vtkPyramid::NumberOfFaces && "faceId too large");
  faceIds = faceToAdjacentFaces[faceId];
  return numberOfPointsInFace[faceId];
}

//------------------------------------------------------------------------------
void vtkPyramid::GetEdgeToAdjacentFaces(vtkIdType edgeId, const vtkIdType*& pts)
{
  assert(edgeId < vtkPyramid::NumberOfEdges && "edgeId too large");
  pts = edgeToAdjacentFaces[edgeId];
}

//------------------------------------------------------------------------------
void vtkPyramid::GetEdgePoints(vtkIdType edgeId, const vtkIdType*& pts)
{
  assert(edgeId < vtkPyramid::NumberOfEdges && "edgeId too large");
  pts = this->GetEdgeArray(edgeId);
}

//------------------------------------------------------------------------------
vtkIdType vtkPyramid::GetFacePoints(vtkIdType faceId, const vtkIdType*& pts)
{
  assert(faceId < vtkPyramid::NumberOfFaces && "faceId too large");
  pts = this->GetFaceArray(faceId);
  return numberOfPointsInFace[faceId];
}

// The choice of the parametric coord for the top corner of the pyramid
// is not unique and is defined by (a, b, 1.), where a, b in [0., 1.].
// In the current implementation, it is arbitrary defined to (0., 0., 1.).
static double vtkPyramidCellPCoords[15] = {
  0.0, 0.0, 0.0, //
  1.0, 0.0, 0.0, //
  1.0, 1.0, 0.0, //
  0.0, 1.0, 0.0, //
  0.0, 0.0, 1.0  //
};

//------------------------------------------------------------------------------
double* vtkPyramid::GetParametricCoords()
{
  return vtkPyramidCellPCoords;
}

//------------------------------------------------------------------------------
void vtkPyramid::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());
  os << indent << "Quad:\n";
  this->Quad->PrintSelf(os, indent.GetNextIndent());
}