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

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

#include "vtkCellData.h"
#include "vtkDoubleArray.h"
#include "vtkMath.h"
#include "vtkObjectFactory.h"
#include "vtkPointData.h"
#include "vtkPoints.h"
#include "vtkQuad.h"
#include "vtkQuadraticEdge.h"

vtkStandardNewMacro(vtkQuadraticQuad);

//------------------------------------------------------------------------------
// Construct the quad with eight points.
vtkQuadraticQuad::vtkQuadraticQuad()
{
  this->Edge = vtkQuadraticEdge::New();
  this->Quad = vtkQuad::New();
  this->PointData = vtkPointData::New();
  this->CellData = vtkCellData::New();
  this->CellScalars = vtkDoubleArray::New();
  this->CellScalars->SetNumberOfTuples(9);
  this->Scalars = vtkDoubleArray::New();
  this->Scalars->SetNumberOfTuples(4);

  // We add a fictitious ninth point in order to process the cell. The ninth
  // point is in the center of the cell.
  this->Points->SetNumberOfPoints(9);
  this->PointIds->SetNumberOfIds(9);
  for (int i = 0; i < 9; i++)
  {
    this->Points->SetPoint(i, 0.0, 0.0, 0.0);
    this->PointIds->SetId(i, 0);
  }
  this->Points->SetNumberOfPoints(8);
  this->PointIds->SetNumberOfIds(8);
}

//------------------------------------------------------------------------------
vtkQuadraticQuad::~vtkQuadraticQuad()
{
  this->Edge->Delete();
  this->Quad->Delete();

  this->Scalars->Delete();
  this->PointData->Delete();
  this->CellData->Delete();
  this->CellScalars->Delete();
}
//------------------------------------------------------------------------------
vtkCell* vtkQuadraticQuad::GetEdge(int edgeId)
{
  edgeId = (edgeId < 0 ? 0 : (edgeId > 3 ? 3 : edgeId));
  int p = (edgeId + 1) % 4;

  // load point id's
  this->Edge->PointIds->SetId(0, this->PointIds->GetId(edgeId));
  this->Edge->PointIds->SetId(1, this->PointIds->GetId(p));
  this->Edge->PointIds->SetId(2, this->PointIds->GetId(edgeId + 4));

  // load coordinates
  this->Edge->Points->SetPoint(0, this->Points->GetPoint(edgeId));
  this->Edge->Points->SetPoint(1, this->Points->GetPoint(p));
  this->Edge->Points->SetPoint(2, this->Points->GetPoint(edgeId + 4));

  return this->Edge;
}

//------------------------------------------------------------------------------

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

void vtkQuadraticQuad::Subdivide(double* weights)
{
  int i, j;
  double pc[3], x[3];

  pc[0] = pc[1] = 0.5;
  vtkQuadraticQuad::InterpolationFunctions(pc, weights);

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

//------------------------------------------------------------------------------
int vtkQuadraticQuad::EvaluatePosition(const double* x, double closestPoint[3], int& subId,
  double pcoords[3], double& minDist2, double weights[])
{
  double pc[3], dist2;
  int ignoreId, i, returnStatus = 0, status;
  double tempWeights[4];
  double closest[3];

  // compute the midquad node
  this->Subdivide(weights);

  // four linear quads are used
  for (minDist2 = VTK_DOUBLE_MAX, i = 0; i < 4; i++)
  {
    this->Quad->Points->SetPoint(0, this->Points->GetPoint(LinearQuads[i][0]));
    this->Quad->Points->SetPoint(1, this->Points->GetPoint(LinearQuads[i][1]));
    this->Quad->Points->SetPoint(2, this->Points->GetPoint(LinearQuads[i][2]));
    this->Quad->Points->SetPoint(3, this->Points->GetPoint(LinearQuads[i][3]));

    status = this->Quad->EvaluatePosition(x, closest, ignoreId, pc, dist2, tempWeights);
    if (status != -1 && dist2 < minDist2)
    {
      returnStatus = status;
      minDist2 = dist2;
      subId = i;
      pcoords[0] = pc[0];
      pcoords[1] = pc[1];
    }
  }

  // adjust parametric coordinates
  if (returnStatus != -1)
  {
    if (subId == 0)
    {
      pcoords[0] /= 2.0;
      pcoords[1] /= 2.0;
    }
    else if (subId == 1)
    {
      pcoords[0] = 0.5 + (pcoords[0] / 2.0);
      pcoords[1] /= 2.0;
    }
    else if (subId == 2)
    {
      pcoords[0] = 0.5 + (pcoords[0] / 2.0);
      pcoords[1] = 0.5 + (pcoords[1] / 2.0);
    }
    else
    {
      pcoords[0] /= 2.0;
      pcoords[1] = 0.5 + (pcoords[1] / 2.0);
    }
    pcoords[2] = 0.0;
    if (closestPoint != nullptr)
    {
      // Compute both closestPoint and weights
      this->EvaluateLocation(subId, pcoords, closestPoint, weights);
    }
    else
    {
      // Compute weights only
      vtkQuadraticQuad::InterpolationFunctions(pcoords, weights);
    }
  }

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

  vtkQuadraticQuad::InterpolationFunctions(pcoords, weights);

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

//------------------------------------------------------------------------------
int vtkQuadraticQuad::CellBoundary(int subId, const double pcoords[3], vtkIdList* pts)
{
  return this->Quad->CellBoundary(subId, pcoords, pts);
}

static double MidPoints[1][3] = { { 0.5, 0.5, 0.0 } };

//------------------------------------------------------------------------------
void vtkQuadraticQuad::InterpolateAttributes(
  vtkPointData* inPd, vtkCellData* inCd, vtkIdType cellId, vtkDataArray* cellScalars)
{
  int numMidPts, i, j;
  double weights[20];
  double x[3];
  double s;

  // Copy point and cell attribute data, first make sure it's empty:
  this->PointData->Initialize();
  this->CellData->Initialize();
  // Make sure to copy ALL arrays. These field data have to be
  // identical to the input field data. Otherwise, CopyData
  // that occurs later may not work because the output field
  // data was initialized (CopyAllocate) with the input field
  // data.
  this->PointData->CopyAllOn();
  this->CellData->CopyAllOn();
  this->PointData->CopyAllocate(inPd, 9);
  this->CellData->CopyAllocate(inCd, 4);

  // copy the point data over into point ids 0->7
  for (i = 0; i < 8; i++)
  {
    this->PointData->CopyData(inPd, this->PointIds->GetId(i), i);
    this->CellScalars->SetValue(i, cellScalars->GetTuple1(i));
  }

  // copy the cell data over to the linear cells
  for (i = 0; i < 4; i++)
  {
    this->CellData->CopyData(inCd, cellId, i);
  }

  // Interpolate new values
  double p[3];
  this->Points->Resize(9);
  this->CellScalars->Resize(9);
  for (numMidPts = 0; numMidPts < 1; numMidPts++)
  {
    vtkQuadraticQuad::InterpolationFunctions(MidPoints[numMidPts], weights);

    x[0] = x[1] = x[2] = 0.0;
    s = 0.0;
    for (i = 0; i < 8; i++)
    {
      this->Points->GetPoint(i, p);
      for (j = 0; j < 3; j++)
      {
        x[j] += p[j] * weights[i];
      }
      s += cellScalars->GetTuple1(i) * weights[i];
    }
    this->Points->SetPoint(8 + numMidPts, x);
    this->CellScalars->SetValue(8 + numMidPts, s);
    this->PointData->InterpolatePoint(inPd, 8 + numMidPts, this->PointIds, weights);
  }
}

//------------------------------------------------------------------------------
void vtkQuadraticQuad::Contour(double value, vtkDataArray* cellScalars,
  vtkIncrementalPointLocator* locator, vtkCellArray* verts, vtkCellArray* lines,
  vtkCellArray* polys, vtkPointData* inPd, vtkPointData* outPd, vtkCellData* inCd, vtkIdType cellId,
  vtkCellData* outCd)
{
  // interpolate point and cell data
  this->InterpolateAttributes(inPd, inCd, cellId, cellScalars);

  // contour each linear quad separately
  for (int i = 0; i < 4; i++)
  {
    for (int j = 0; j < 4; j++) // for each of the four vertices of the linear quad
    {
      this->Quad->Points->SetPoint(j, this->Points->GetPoint(LinearQuads[i][j]));
      this->Quad->PointIds->SetId(j, LinearQuads[i][j]);
      this->Scalars->SetValue(j, this->CellScalars->GetValue(LinearQuads[i][j]));
    }

    this->Quad->Contour(value, this->Scalars, locator, verts, lines, polys, this->PointData, outPd,
      this->CellData, i, outCd);
  }
}
//------------------------------------------------------------------------------
// Clip this quadratic quad using scalar value provided. Like contouring,
// except that it cuts the quad to produce other quads and triangles.
void vtkQuadraticQuad::Clip(double value, vtkDataArray* cellScalars,
  vtkIncrementalPointLocator* locator, vtkCellArray* polys, vtkPointData* inPd, vtkPointData* outPd,
  vtkCellData* inCd, vtkIdType cellId, vtkCellData* outCd, int insideOut)
{
  // interpolate point and cell data
  this->InterpolateAttributes(inPd, inCd, cellId, cellScalars);

  // contour each linear quad separately
  for (int i = 0; i < 4; i++)
  {
    for (int j = 0; j < 4; j++) // for each of the four vertices of the linear quad
    {
      this->Quad->Points->SetPoint(j, this->Points->GetPoint(LinearQuads[i][j]));
      this->Quad->PointIds->SetId(j, LinearQuads[i][j]);
      this->Scalars->SetValue(j, this->CellScalars->GetValue(LinearQuads[i][j]));
    }

    this->Quad->Clip(value, this->Scalars, locator, polys, this->PointData, outPd, this->CellData,
      i, outCd, insideOut);
  }
}

//------------------------------------------------------------------------------
// Line-line intersection. Intersection has to occur within [0,1] parametric
// coordinates and with specified tolerance.
int vtkQuadraticQuad::IntersectWithLine(
  const double* p1, const double* p2, double tol, double& t, double* x, double* pcoords, int& subId)
{
  int subTest, i;
  subId = 0;
  double weights[8];

  // first define the midquad point
  this->Subdivide(weights);

  // intersect the four linear quads
  for (i = 0; i < 4; i++)
  {
    this->Quad->Points->SetPoint(0, this->Points->GetPoint(LinearQuads[i][0]));
    this->Quad->Points->SetPoint(1, this->Points->GetPoint(LinearQuads[i][1]));
    this->Quad->Points->SetPoint(2, this->Points->GetPoint(LinearQuads[i][2]));
    this->Quad->Points->SetPoint(3, this->Points->GetPoint(LinearQuads[i][3]));

    if (this->Quad->IntersectWithLine(p1, p2, tol, t, x, pcoords, subTest))
    {
      return 1;
    }
  }

  return 0;
}

//------------------------------------------------------------------------------
int vtkQuadraticQuad::Triangulate(int vtkNotUsed(index), vtkIdList* ptIds, vtkPoints* pts)
{
  pts->Reset();
  ptIds->Reset();

  // Create six linear triangles: one at each corner and two
  // to cover the remaining quadrilateral.

  // First the corner vertices
  ptIds->InsertId(0, this->PointIds->GetId(0));
  ptIds->InsertId(1, this->PointIds->GetId(4));
  ptIds->InsertId(2, this->PointIds->GetId(7));
  pts->InsertPoint(0, this->Points->GetPoint(0));
  pts->InsertPoint(1, this->Points->GetPoint(4));
  pts->InsertPoint(2, this->Points->GetPoint(7));

  ptIds->InsertId(3, this->PointIds->GetId(4));
  ptIds->InsertId(4, this->PointIds->GetId(1));
  ptIds->InsertId(5, this->PointIds->GetId(5));
  pts->InsertPoint(3, this->Points->GetPoint(4));
  pts->InsertPoint(4, this->Points->GetPoint(1));
  pts->InsertPoint(5, this->Points->GetPoint(5));

  ptIds->InsertId(6, this->PointIds->GetId(5));
  ptIds->InsertId(7, this->PointIds->GetId(2));
  ptIds->InsertId(8, this->PointIds->GetId(6));
  pts->InsertPoint(6, this->Points->GetPoint(5));
  pts->InsertPoint(7, this->Points->GetPoint(2));
  pts->InsertPoint(8, this->Points->GetPoint(6));

  ptIds->InsertId(9, this->PointIds->GetId(6));
  ptIds->InsertId(10, this->PointIds->GetId(3));
  ptIds->InsertId(11, this->PointIds->GetId(7));
  pts->InsertPoint(9, this->Points->GetPoint(6));
  pts->InsertPoint(10, this->Points->GetPoint(3));
  pts->InsertPoint(11, this->Points->GetPoint(7));

  // Now the two remaining triangles
  // Choose the triangulation that minimizes the edge length
  // across the cell.
  double x4[3], x5[3], x6[3], x7[3];
  this->Points->GetPoint(4, x4);
  this->Points->GetPoint(5, x5);
  this->Points->GetPoint(6, x6);
  this->Points->GetPoint(7, x7);

  if (vtkMath::Distance2BetweenPoints(x4, x6) <= vtkMath::Distance2BetweenPoints(x5, x7))
  {
    ptIds->InsertId(12, this->PointIds->GetId(4));
    ptIds->InsertId(13, this->PointIds->GetId(6));
    ptIds->InsertId(14, this->PointIds->GetId(7));
    pts->InsertPoint(12, this->Points->GetPoint(4));
    pts->InsertPoint(13, this->Points->GetPoint(6));
    pts->InsertPoint(14, this->Points->GetPoint(7));

    ptIds->InsertId(15, this->PointIds->GetId(4));
    ptIds->InsertId(16, this->PointIds->GetId(5));
    ptIds->InsertId(17, this->PointIds->GetId(6));
    pts->InsertPoint(15, this->Points->GetPoint(4));
    pts->InsertPoint(16, this->Points->GetPoint(5));
    pts->InsertPoint(17, this->Points->GetPoint(6));
  }
  else
  {
    ptIds->InsertId(12, this->PointIds->GetId(5));
    ptIds->InsertId(13, this->PointIds->GetId(6));
    ptIds->InsertId(14, this->PointIds->GetId(7));
    pts->InsertPoint(12, this->Points->GetPoint(5));
    pts->InsertPoint(13, this->Points->GetPoint(6));
    pts->InsertPoint(14, this->Points->GetPoint(7));

    ptIds->InsertId(15, this->PointIds->GetId(5));
    ptIds->InsertId(16, this->PointIds->GetId(7));
    ptIds->InsertId(17, this->PointIds->GetId(4));
    pts->InsertPoint(15, this->Points->GetPoint(5));
    pts->InsertPoint(16, this->Points->GetPoint(7));
    pts->InsertPoint(17, this->Points->GetPoint(4));
  }

  return 1;
}

//------------------------------------------------------------------------------
void vtkQuadraticQuad::Derivatives(
  int vtkNotUsed(subId), const double pcoords[3], const double* values, int dim, double* derivs)
{
  double sum[2], p[3];
  double functionDerivs[16];
  double *J[3], J0[3], J1[3], J2[3];
  double *JI[3], JI0[3], JI1[3], JI2[3];

  vtkQuadraticQuad::InterpolationDerivs(pcoords, functionDerivs);

  // Compute transposed Jacobian and inverse Jacobian
  J[0] = J0;
  J[1] = J1;
  J[2] = J2;
  JI[0] = JI0;
  JI[1] = JI1;
  JI[2] = JI2;
  for (int k = 0; k < 3; k++)
  {
    J0[k] = J1[k] = 0.0;
  }

  for (int i = 0; i < 8; i++)
  {
    this->Points->GetPoint(i, p);
    for (int j = 0; j < 2; j++)
    {
      for (int k = 0; k < 3; k++)
      {
        J[j][k] += p[k] * functionDerivs[j * 8 + i];
      }
    }
  }

  // Compute third row vector in transposed Jacobian and normalize it, so that Jacobian determinant
  // stays the same.
  vtkMath::Cross(J0, J1, J2);
  if (vtkMath::Normalize(J2) == 0.0 || !vtkMath::InvertMatrix(J, JI, 3)) // degenerate
  {
    for (int j = 0; j < dim; j++)
    {
      for (int i = 0; i < 3; i++)
      {
        derivs[j * dim + i] = 0.0;
      }
    }
    return;
  }

  // Loop over "dim" derivative values. For each set of values,
  // compute derivatives
  // in local system and then transform into modelling system.
  // First compute derivatives in local x'-y' coordinate system
  for (int j = 0; j < dim; j++)
  {
    sum[0] = sum[1] = 0.0;
    for (int i = 0; i < 8; i++) // loop over interp. function derivatives
    {
      sum[0] += functionDerivs[i] * values[dim * i + j];
      sum[1] += functionDerivs[8 + i] * values[dim * i + j];
    }
    //    dBydx = sum[0]*JI[0][0] + sum[1]*JI[0][1];
    //    dBydy = sum[0]*JI[1][0] + sum[1]*JI[1][1];

    // Transform into global system (dot product with global axes)
    derivs[3 * j] = sum[0] * JI[0][0] + sum[1] * JI[0][1];
    derivs[3 * j + 1] = sum[0] * JI[1][0] + sum[1] * JI[1][1];
    derivs[3 * j + 2] = sum[0] * JI[2][0] + sum[1] * JI[2][1];
  }
}

//------------------------------------------------------------------------------
// Compute interpolation functions. The first four nodes are the corner
// vertices; the others are mid-edge nodes.
void vtkQuadraticQuad::InterpolationFunctions(const double pcoords[3], double weights[8])
{
  double r = pcoords[0];
  double s = pcoords[1];

  // midedge weights
  weights[4] = 4 * r * (1.0 - r) * (1.0 - s);
  weights[5] = 4 * r * (1.0 - s) * s;
  weights[6] = 4 * r * (1.0 - r) * s;
  weights[7] = 4 * (1.0 - r) * (1.0 - s) * s;

  // corner
  weights[0] = (1.0 - r) * (1.0 - s) - 0.5 * (weights[4] + weights[7]);
  weights[1] = r * (1.0 - s) - 0.5 * (weights[4] + weights[5]);
  weights[2] = r * s - 0.5 * (weights[5] + weights[6]);
  weights[3] = (1.0 - r) * s - 0.5 * (weights[6] + weights[7]);
}

//------------------------------------------------------------------------------
// Derivatives in parametric space.
void vtkQuadraticQuad::InterpolationDerivs(const double pcoords[3], double derivs[16])
{
  // Coordinate conversion
  double r = pcoords[0];
  double s = pcoords[1];

  // Derivatives in the r-direction
  // midedge
  derivs[4] = 4 * (1.0 - s) * (1.0 - 2 * r);
  derivs[5] = 4 * (1.0 - s) * s;
  derivs[6] = 4 * s * (1.0 - 2 * r);
  derivs[7] = -4 * (1.0 - s) * s;
  derivs[0] = -(1.0 - s) - 0.5 * (derivs[4] + derivs[7]);
  derivs[1] = (1.0 - s) - 0.5 * (derivs[4] + derivs[5]);
  derivs[2] = s - 0.5 * (derivs[5] + derivs[6]);
  derivs[3] = -s - 0.5 * (derivs[6] + derivs[7]);

  // Derivatives in the s-direction
  // midedge
  derivs[12] = -4 * r * (1.0 - r);
  derivs[13] = 4 * r * (1.0 - 2 * s);
  derivs[14] = 4 * r * (1.0 - r);
  derivs[15] = 4 * (1.0 - r) * (1.0 - 2 * s);
  derivs[8] = -(1.0 - r) - 0.5 * (derivs[12] + derivs[15]);
  derivs[9] = -r - 0.5 * (derivs[12] + derivs[13]);
  derivs[10] = r - 0.5 * (derivs[13] + derivs[14]);
  derivs[11] = (1.0 - r) - 0.5 * (derivs[14] + derivs[15]);
}

//------------------------------------------------------------------------------
static double vtkQQuadCellPCoords[24] = {
  0.0, 0.0, 0.0, //
  1.0, 0.0, 0.0, //
  1.0, 1.0, 0.0, //
  0.0, 1.0, 0.0, //
  0.5, 0.0, 0.0, //
  1.0, 0.5, 0.0, //
  0.5, 1.0, 0.0, //
  0.0, 0.5, 0.0  //
};
double* vtkQuadraticQuad::GetParametricCoords()
{
  return vtkQQuadCellPCoords;
}

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

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