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

  Program:   Visualization Toolkit
  Module:    vtkQuadraticLinearQuad.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.

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

//Thanks to Soeren Gebbert  who developed this class and
//integrated it into VTK 5.0.

#include "vtkQuadraticLinearQuad.h"

#include "vtkObjectFactory.h"
#include "vtkDoubleArray.h"
#include "vtkMath.h"
#include "vtkQuad.h"
#include "vtkLine.h"
#include "vtkQuadraticEdge.h"
#include "vtkPoints.h"

vtkStandardNewMacro (vtkQuadraticLinearQuad);

//----------------------------------------------------------------------------
// Construct the quadratic linear quad with six points.
vtkQuadraticLinearQuad::vtkQuadraticLinearQuad ()
{
  this->Edge = vtkQuadraticEdge::New();
  this->LinEdge = vtkLine::New ();
  this->Quad = vtkQuad::New ();
  this->Scalars = vtkDoubleArray::New ();
  this->Scalars->SetNumberOfTuples (4); // vertices of a linear quad
  this->Points->SetNumberOfPoints (6);
  this->PointIds->SetNumberOfIds (6);
  for (int i = 0; i < 6; i++)
    {
    this->Points->SetPoint(i, 0.0, 0.0, 0.0);
    this->PointIds->SetId(i,0);
    }
}

//----------------------------------------------------------------------------
vtkQuadraticLinearQuad::~vtkQuadraticLinearQuad ()
{
  this->Edge->Delete();
  this->LinEdge->Delete();
  this->Quad->Delete();
  this->Scalars->Delete();
}

//----------------------------------------------------------------------------
static int LinearQuads[2][4] = { {0, 4, 5, 3}, {4, 1, 2, 5} };

static int LinearQuadEdges[4][3] = { {0, 1, 4}, {1, 2,-1},
                                     {2, 3, 5}, {3, 0,-1}};

//----------------------------------------------------------------------------
int *vtkQuadraticLinearQuad::GetEdgeArray(int edgeId)
{
  return LinearQuadEdges[edgeId];
}

//----------------------------------------------------------------------------
vtkCell *vtkQuadraticLinearQuad::GetEdge(int edgeId)
{
  edgeId = (edgeId < 0 ? 0 : (edgeId > 3 ? 3 : edgeId));

  // We have 2 linear edges
  if (edgeId == 1 || edgeId == 3)
    {
    this->LinEdge->PointIds->SetId(0,this->PointIds->GetId(LinearQuadEdges[edgeId][0]));
    this->LinEdge->PointIds->SetId(1,this->PointIds->GetId(LinearQuadEdges[edgeId][1]));

    this->LinEdge->Points->SetPoint(0,this->Points->GetPoint(LinearQuadEdges[edgeId][0]));
    this->LinEdge->Points->SetPoint(1,this->Points->GetPoint(LinearQuadEdges[edgeId][1]));

    return this->LinEdge;
    }
  // and two quadratic edges
  else // (edgeId == 0 || edgeId == 2)
    {
    this->Edge->PointIds->SetId(0,this->PointIds->GetId(LinearQuadEdges[edgeId][0]));
    this->Edge->PointIds->SetId(1,this->PointIds->GetId(LinearQuadEdges[edgeId][1]));
    this->Edge->PointIds->SetId(2,this->PointIds->GetId(LinearQuadEdges[edgeId][2]));

    this->Edge->Points->SetPoint(0,this->Points->GetPoint(LinearQuadEdges[edgeId][0]));
    this->Edge->Points->SetPoint(1,this->Points->GetPoint(LinearQuadEdges[edgeId][1]));
    this->Edge->Points->SetPoint(2,this->Points->GetPoint(LinearQuadEdges[edgeId][2]));

    return this->Edge;
    }


}

//----------------------------------------------------------------------------
int vtkQuadraticLinearQuad::EvaluatePosition (double *x,
                                              double *closestPoint,
                                              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];

  // two linear quads are used
  for (minDist2 = VTK_DOUBLE_MAX, i = 0; i < 2; 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;
      }
    else if ( subId == 1 )
      {
      pcoords[0] = 0.5 + (pcoords[0]/2.0);
      }
    pcoords[2] = 0.0;
    if(closestPoint!=0)
      {
      // Compute both closestPoint and weights
      this->EvaluateLocation(subId,pcoords,closestPoint,weights);
      }
    else
      {
      // Compute weigths only
      this->InterpolationFunctions(pcoords,weights);
      }
    }

  return returnStatus;
}

//----------------------------------------------------------------------------
void vtkQuadraticLinearQuad::EvaluateLocation(int& vtkNotUsed(subId),
                                              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<6; i++)
    {
    this->Points->GetPoint(i, pt);
    for (j=0; j<3; j++)
      {
      x[j] += pt[j] * weights[i];
      }
    }
}

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

//----------------------------------------------------------------------------
void vtkQuadraticLinearQuad::Contour (double value,
         vtkDataArray * cellScalars,
         vtkIncrementalPointLocator * locator,
         vtkCellArray * verts,
         vtkCellArray * lines,
         vtkCellArray * polys,
         vtkPointData * inPd,
         vtkPointData * outPd,
         vtkCellData * inCd,
         vtkIdType cellId,
         vtkCellData * outCd)
{
  for (int i = 0; i < 2; i++)
    {
    for (int j = 0; j < 4; j++)
      {
      this->Quad->Points->SetPoint(j,this->Points->GetPoint(LinearQuads[i][j]));
      this->Quad->PointIds->SetId(j,this->PointIds->GetId(LinearQuads[i][j]));
      this->Scalars->SetValue(j,cellScalars->GetTuple1(LinearQuads[i][j]));
      }
    this->Quad->Contour (value, this->Scalars, locator, verts, lines, polys,
                         inPd, outPd, inCd, cellId, outCd);
    }
}

//----------------------------------------------------------------------------
// Clip this quadratic quad using scalar value provided. Like contouring,
// except that it cuts the quad to produce other quads and triangles.
void vtkQuadraticLinearQuad::Clip (double value, vtkDataArray * cellScalars,
            vtkIncrementalPointLocator * locator, vtkCellArray * polys,
            vtkPointData * inPd, vtkPointData * outPd,
            vtkCellData * inCd, vtkIdType cellId,
            vtkCellData * outCd, int insideOut)
{
  for (int i = 0; i < 2; 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,this->PointIds->GetId(LinearQuads[i][j]));
      this->Scalars->SetTuple(j,cellScalars->GetTuple(LinearQuads[i][j]));
      }
    this->Quad->Clip (value, this->Scalars, locator, polys, inPd, outPd, inCd,
                      cellId, outCd, insideOut);
    }
}

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

  //intersect the two linear quads
  for (i = 0; i < 2; 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 vtkQuadraticLinearQuad::Triangulate (int vtkNotUsed (index),
  vtkIdList * ptIds, vtkPoints * pts)
{
  pts->Reset();
  ptIds->Reset();

  // Create four linear triangles:
  // Choose the triangulation that minimizes the edge length
  // across the cell.
  double x0[3], x1[3], x2[3], x3[3], x4[3], x5[3];
  this->Points->GetPoint (0, x0);
  this->Points->GetPoint (1, x1);
  this->Points->GetPoint (2, x2);
  this->Points->GetPoint (3, x3);
  this->Points->GetPoint (4, x4);
  this->Points->GetPoint (5, x5);

  if (vtkMath::Distance2BetweenPoints (x0, x5) <=
    vtkMath::Distance2BetweenPoints (x3, x4))
    {
    ptIds->InsertId (0, this->PointIds->GetId (0));
    ptIds->InsertId (1, this->PointIds->GetId (4));
    ptIds->InsertId (2, this->PointIds->GetId (5));
    pts->InsertPoint (0, this->Points->GetPoint (0));
    pts->InsertPoint (1, this->Points->GetPoint (4));
    pts->InsertPoint (2, this->Points->GetPoint (5));

    ptIds->InsertId (3, this->PointIds->GetId (0));
    ptIds->InsertId (4, this->PointIds->GetId (5));
    ptIds->InsertId (5, this->PointIds->GetId (3));
    pts->InsertPoint (3, this->Points->GetPoint (0));
    pts->InsertPoint (4, this->Points->GetPoint (5));
    pts->InsertPoint (5, this->Points->GetPoint (3));
    }
  else
    {
    ptIds->InsertId (0, this->PointIds->GetId (0));
    ptIds->InsertId (1, this->PointIds->GetId (4));
    ptIds->InsertId (2, this->PointIds->GetId (3));
    pts->InsertPoint (0, this->Points->GetPoint (0));
    pts->InsertPoint (1, this->Points->GetPoint (4));
    pts->InsertPoint (2, this->Points->GetPoint (3));

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

  if (vtkMath::Distance2BetweenPoints (x4, x2) <=
    vtkMath::Distance2BetweenPoints (x5, x1))
    {
    ptIds->InsertId (6, this->PointIds->GetId (4));
    ptIds->InsertId (7, this->PointIds->GetId (1));
    ptIds->InsertId (8, this->PointIds->GetId (2));
    pts->InsertPoint (6, this->Points->GetPoint (4));
    pts->InsertPoint (7, this->Points->GetPoint (1));
    pts->InsertPoint (8, this->Points->GetPoint (2));

    ptIds->InsertId (9, this->PointIds->GetId (4));
    ptIds->InsertId (10, this->PointIds->GetId (2));
    ptIds->InsertId (11, this->PointIds->GetId (5));
    pts->InsertPoint (9, this->Points->GetPoint (4));
    pts->InsertPoint (10, this->Points->GetPoint (2));
    pts->InsertPoint (11, this->Points->GetPoint (5));
    }
  else
    {
    ptIds->InsertId (6, this->PointIds->GetId (4));
    ptIds->InsertId (7, this->PointIds->GetId (1));
    ptIds->InsertId (8, this->PointIds->GetId (5));
    pts->InsertPoint (6, this->Points->GetPoint (4));
    pts->InsertPoint (7, this->Points->GetPoint (1));
    pts->InsertPoint (8, this->Points->GetPoint (5));

    ptIds->InsertId (9, this->PointIds->GetId (1));
    ptIds->InsertId (10, this->PointIds->GetId (2));
    ptIds->InsertId (11, this->PointIds->GetId (5));
    pts->InsertPoint (9, this->Points->GetPoint (1));
    pts->InsertPoint (10, this->Points->GetPoint (2));
    pts->InsertPoint (11, this->Points->GetPoint (5));
    }

  return 1;
}

//----------------------------------------------------------------------------
void vtkQuadraticLinearQuad::Derivatives (int vtkNotUsed (subId),
  double pcoords[3], double *values, int dim, double *derivs)
{
  double x0[3], x1[3], x2[3], deltaX[3], weights[6];
  int i, j;
  double functionDerivs[12];

  this->Points->GetPoint (0, x0);
  this->Points->GetPoint (1, x1);
  this->Points->GetPoint (2, x2);

  this->InterpolationFunctions (pcoords, weights);
  this->InterpolationDerivs (pcoords, functionDerivs);

  for (i = 0; i < 3; i++)
    {
    deltaX[i] = x1[i] - x0[i] - x2[i];
    }
  for (i = 0; i < dim; i++)
    {
    for (j = 0; j < 3; j++)
      {
      if (deltaX[j] != 0)
        {
        derivs[3 * i + j] = (values[2 * i + 1] - values[2 * i]) / deltaX[j];
        }
      else
        {
        derivs[3 * i + j] = 0;
        }
      }
    }
}



//----------------------------------------------------------------------------
// Compute interpolation functions. The first four nodes are the corner
// vertices; the others are mid-edge nodes.
void vtkQuadraticLinearQuad::InterpolationFunctions(double pcoords[3],
                                                    double weights[6])
{
  double x = pcoords[0];
  double y = pcoords[1];

   //corners
  weights[0] = -1.0 *(2.0 *x - 1.0) * (x - 1.0) * (y - 1.0);
  weights[1] = -1.0 *(2.0 *x - 1.0) * (x)     * (y - 1.0);
  weights[2] =       (2.0 *x - 1.0) * (x)     * (y);
  weights[3] =       (2.0 *x - 1.0) * (x - 1.0 ) * (y);

  //Edge middle nodes
  weights[4] =  4.0  * (x) * (1.0  - x) * (1.0  - y);
  weights[5] =  4.0  * (x) * (1.0  - x) * (y);


}

//----------------------------------------------------------------------------
// Derivatives in parametric space.
void vtkQuadraticLinearQuad::InterpolationDerivs(double pcoords[3], double derivs[12])
{
  double x = pcoords[0];
  double y = pcoords[1];

  // Derivatives in the x-direction
  //corners
  derivs[0] = -1.0 * (4.0 * x - 3.0) * (y - 1.0);
  derivs[1] = -1.0 * (4.0 * x - 1.0) * (y - 1.0);
  derivs[2] =        (4.0 * x - 1.0) * (y);
  derivs[3] =        (4.0 * x - 3.0) * (y);
  //Edge middle nodes
  derivs[4] =  4.0 * (1.0 - 2.0 * x) * (1.0 - y);
  derivs[5] =  4.0 * (1.0 - 2.0 * x) * (y);

  // Derivatives in the y-direction
  //corners
  derivs[6] = -1.0 * (2.0 * x - 1.0) * (x - 1.0);
  derivs[7] = -1.0 * (2.0 * x - 1.0) * (x)    ;
  derivs[8] =        (2.0 * x - 1.0) * (x)    ;
  derivs[9] =        (2.0 * x - 1.0) * (x - 1.0);
  //Edge middle nodes
  derivs[10]= -4.0 * (x) * (1.0 - x);
  derivs[11]=  4.0 * (x) * (1.0 - x);

}

//----------------------------------------------------------------------------
static double vtkQLinQuadCellPCoords[18] = { 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, 0.5, 1.0, 0.0 };

double *vtkQuadraticLinearQuad::GetParametricCoords ()
{
  return vtkQLinQuadCellPCoords;
}

//----------------------------------------------------------------------------
void vtkQuadraticLinearQuad::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());
}

