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

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

#include "vtkCell.h"
#include "vtkCellArray.h"
#include "vtkCellData.h"
#include "vtkDoubleArray.h"
#include "vtkIncrementalPointLocator.h"
#include "vtkLine.h"
#include "vtkMath.h"
#include "vtkNonLinearCell.h"
#include "vtkObjectFactory.h"
#include "vtkPointData.h"
#include "vtkPoints.h"

vtkStandardNewMacro(vtkCubicLine);

//----------------------------------------------------------------------------
// Construct the line with four points.
vtkCubicLine::vtkCubicLine()
{
  this->Scalars = vtkDoubleArray::New();
  this->Scalars->SetNumberOfTuples(4);
  this->Points->SetNumberOfPoints(4);
  this->PointIds->SetNumberOfIds(4);
  for (int i = 0; i < 4; i++)
  {
    this->Points->SetPoint(i, 0.0, 0.0, 0.0);
    this->PointIds->SetId(i, 0);
  }
  this->Line = vtkLine::New();
}
//----------------------------------------------------------------------------
// Delete the Line
vtkCubicLine::~vtkCubicLine()
{
  this->Line->Delete();
  this->Scalars->Delete();
}

//----------------------------------------------------------------------------
int vtkCubicLine::EvaluatePosition(const double x[3], double closestPoint[3], int& subId,
  double pcoords[3], double& minDist2, double weights[])
{
  double closest[3];
  double pc[3], dist2;
  int ignoreId, i, returnStatus, status;
  double lineWeights[2];

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

  returnStatus = -1;
  weights[0] = 0.0;
  for (minDist2 = VTK_DOUBLE_MAX, i = 0; i < 3; i++)
  {
    if (i == 0)
    {
      this->Line->Points->SetPoint(0, this->Points->GetPoint(0));
      this->Line->Points->SetPoint(1, this->Points->GetPoint(2));
    }
    else if (i == 1)
    {
      this->Line->Points->SetPoint(0, this->Points->GetPoint(2));
      this->Line->Points->SetPoint(1, this->Points->GetPoint(3));
    }
    else
    {
      this->Line->Points->SetPoint(0, this->Points->GetPoint(3));
      this->Line->Points->SetPoint(1, this->Points->GetPoint(1));
    }

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

  // adjust parametric coordinate
  if (returnStatus != -1)
  {
    if (subId == 0) // first part  : -1 <= pcoords <= -1/3
    {
      pcoords[0] = pcoords[0] * (2.0 / 3.0) - 1;
    }
    else if (subId == 1) // second part  : -1/3 <= pcoords <= 1/3
    {
      pcoords[0] = pcoords[0] * (2.0 / 3.0) - (1.0 / 3.0);
    }
    else // third part : 1/3 <= pcoords <= 1
    {
      pcoords[0] = pcoords[0] * (2.0 / 3.0) + (1.0 / 3.0);
    }
    if (closestPoint != nullptr)
    {
      // Compute both closestPoint and weights
      this->EvaluateLocation(subId, pcoords, closestPoint, weights);
    }
    else
    {
      // Compute weights only
      this->InterpolationFunctions(pcoords, weights);
    }
  }

  return returnStatus;
}

//----------------------------------------------------------------------------
void vtkCubicLine::EvaluateLocation(
  int& vtkNotUsed(subId), const double pcoords[3], double x[3], double* weights)
{
  int i;
  double a0[3], a1[3], a2[3], a3[3];
  this->Points->GetPoint(0, a0);
  this->Points->GetPoint(1, a1);
  this->Points->GetPoint(2, a2); // first midside node
  this->Points->GetPoint(3, a3); // second midside node

  this->InterpolationFunctions(pcoords, weights);

  for (i = 0; i < 3; i++)
  {
    x[i] = a0[i] * weights[0] + a1[i] * weights[1] + a2[i] * weights[2] + a3[i] * weights[3];
  }
}

//----------------------------------------------------------------------------
int vtkCubicLine::CellBoundary(int vtkNotUsed(subId), const double pcoords[3], vtkIdList* pts)
{
  pts->SetNumberOfIds(1);

  if (pcoords[0] >= 0.0)
  {
    pts->SetId(0, this->PointIds->GetId(1)); // The edge points IDs are 0 and 1.
    if (pcoords[0] > 1.0)
    {
      return 0;
    }
    else
    {
      return 1;
    }
  }
  else
  {
    pts->SetId(0, this->PointIds->GetId(0));
    if (pcoords[0] < -1.0)
    {
      return 0;
    }
    else
    {
      return 1;
    }
  }
}

// LinearLines for the Contour and the Clip Algorithm
//-----------------------------------------------------------------------------
static int LinearLines[3][2] = { { 0, 2 }, { 2, 3 }, { 3, 1 } };

void vtkCubicLine::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 < 3; i++) // for each subdivided line
  {
    for (int j = 0; j < 2; j++) // for each of the four vertices of the line
    {
      this->Line->Points->SetPoint(j, this->Points->GetPoint(LinearLines[i][j]));
      this->Line->PointIds->SetId(j, this->PointIds->GetId(LinearLines[i][j]));
      this->Scalars->SetValue(j, cellScalars->GetTuple1(LinearLines[i][j]));
    }
    this->Line->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 vtkCubicLine::IntersectWithLine(const double p1[3], const double p2[3], double tol, double& t,
  double x[3], double pcoords[3], int& subId)
{

  int subTest, numLines = 3;

  for (subId = 0; subId < numLines; subId++)
  {
    if (subId == 0)
    {
      this->Line->Points->SetPoint(0, this->Points->GetPoint(0));
      this->Line->Points->SetPoint(1, this->Points->GetPoint(2));
    }
    else if (subId == 1)
    {
      this->Line->Points->SetPoint(0, this->Points->GetPoint(2));
      this->Line->Points->SetPoint(1, this->Points->GetPoint(3));
    }
    else
    {
      this->Line->Points->SetPoint(0, this->Points->GetPoint(3));
      this->Line->Points->SetPoint(1, this->Points->GetPoint(1));
    }

    if (this->Line->IntersectWithLine(p1, p2, tol, t, x, pcoords, subTest))
    {
      // adjust parametric coordinate

      if (subId == 0) // first part  : -1 <= pcoords <= -1/3
      {
        pcoords[0] = pcoords[0] * (2.0 / 3.0) - 1;
      }
      else if (subId == 1) // second part  : -1/3 <= pcoords <= 1/3
      {
        pcoords[0] = pcoords[0] * (2.0 / 3.0) - (1.0 / 3.0);
      }
      else // third part : 1/3 <= pcoords <= 1
      {
        pcoords[0] = pcoords[0] * (2.0 / 3.0) + (1.0 / 3.0);
      }

      return 1;
    }
  }

  return 0;
}

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

  // The first line
  ptIds->InsertId(0, this->PointIds->GetId(0));
  pts->InsertPoint(0, this->Points->GetPoint(0));

  ptIds->InsertId(1, this->PointIds->GetId(2));
  pts->InsertPoint(1, this->Points->GetPoint(2));

  // The second line
  ptIds->InsertId(2, this->PointIds->GetId(2));
  pts->InsertPoint(2, this->Points->GetPoint(2));

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

  // The third line
  ptIds->InsertId(4, this->PointIds->GetId(3));
  pts->InsertPoint(4, this->Points->GetPoint(3));

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

//----------------------------------------------------------------------------
void vtkCubicLine::Derivatives(
  int vtkNotUsed(subId), const double pcoords[3], const double* values, int dim, double* derivs)
{
  double v0, v1, v2, v3;             // Local coordinates of Each point.
  double v10[3], lenX;               // Reesentation of local Axis
  double x0[3], x1[3], x2[3], x3[3]; // Points of the model
  double vec20[3], vec30[3];         // Normal and vector of each point.
  double J;                          // Jacobian Matrix
  double JI;                         // Inverse of the Jacobian Matrix
  double funcDerivs[4], sum, dBydx;  // Derivated values

  // Project points of vtkCubicLine into a 1D system
  this->Points->GetPoint(0, x0);
  this->Points->GetPoint(1, x1);
  this->Points->GetPoint(2, x2);
  this->Points->GetPoint(3, x3);

  for (int i = 0; i < 3; i++) // Compute the vector for each point
  {
    v10[i] = x1[i] - x0[i];
    vec20[i] = x2[i] - x0[i];
    vec30[i] = x3[i] - x0[i];
  }

  if ((lenX = vtkMath::Normalize(v10)) <= 0.0) // degenerate
  {
    for (int j = 0; j < dim; j++)
    {
      for (int i = 0; i < 3; i++)
      {
        derivs[j * dim + i] = 0.0;
      }
    }
    return;
  }

  v0 = 0.0; // convert points to 1D (i.e., local system)

  v1 = lenX;

  v2 = vtkMath::Dot(vec20, v10);

  v3 = vtkMath::Dot(vec30, v10);

  this->InterpolationDerivs(pcoords, funcDerivs);

  J = v0 * funcDerivs[0] + v1 * funcDerivs[1] + v2 * funcDerivs[2] + v3 * funcDerivs[3];

  // Compute inverse Jacobian, return if Jacobian is singular

  if (J != 0)
  {
    JI = 1.0 / J;
  }
  else
  {
    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' coordinate system
  for (int j = 0; j < dim; j++)
  {
    sum = 0.0;
    for (int i = 0; i < 4; i++) // loop over interp. function derivatives
    {
      sum += funcDerivs[i] * values[dim * i + j];
    }

    dBydx = sum * JI;

    // Transform into global system (dot product with global axes)
    derivs[3 * j] = dBydx * v10[0];
    derivs[3 * j + 1] = dBydx * v10[1];
    derivs[3 * j + 2] = dBydx * v10[2];
  }
}

//--------------------------------------------------------------------------
// Clip this line using scalar value provided. Like contouring, except
// that it cuts the line to produce other lines.
void vtkCubicLine::Clip(double value, vtkDataArray* cellScalars,
  vtkIncrementalPointLocator* locator, vtkCellArray* lines, vtkPointData* inPd, vtkPointData* outPd,
  vtkCellData* inCd, vtkIdType cellId, vtkCellData* outCd, int insideOut)
{
  for (int i = 0; i < 3; i++) // for each subdivided line
  {
    for (int j = 0; j < 2; j++) // for each of the four vertices of the line
    {
      this->Line->Points->SetPoint(j, this->Points->GetPoint(LinearLines[i][j]));
      this->Line->PointIds->SetId(j, this->PointIds->GetId(LinearLines[i][j]));
      this->Scalars->SetValue(j, cellScalars->GetTuple1(LinearLines[i][j]));
    }
    this->Line->Clip(
      value, this->Scalars, locator, lines, inPd, outPd, inCd, cellId, outCd, insideOut);
  }
}

//----------------------------------------------------------------------------
//
// Compute interpolation functions
//
void vtkCubicLine::InterpolationFunctions(
  const double pcoords[3], double weights[4]) // N2 and N3 are the middle points
{
  // pcoords[0] = t, weights need to be set in accordance with the definition of the standard cubic
  // line finite element
  double t = pcoords[0];

  weights[0] = (9.0 / 16.0) * (1.0 - t) * (t + (1.0 / 3.0)) * (t - (1.0 / 3.0));
  weights[1] = (-9.0 / 16.0) * (1.0 + t) * ((1.0 / 3.0) - t) * (t + (1.0 / 3.0));
  weights[2] = (27.0 / 16.0) * (t - 1.0) * (t + 1.0) * (t - (1.0 / 3.0));
  weights[3] = (-27.0 / 16.0) * (t - 1.0) * (t + 1.0) * (t + (1.0 / 3.0));
}

//----------------------------------------------------------------------------
void vtkCubicLine::InterpolationDerivs(
  const double pcoords[3], double derivs[4]) // N2 and N3 are the middle points
{
  double t = pcoords[0];

  derivs[0] = (1.0 / 16.0) * (1.0 + 18.0 * t - 27.0 * t * t);
  derivs[1] = (1.0 / 16.0) * (-1.0 + 18.0 * t + 27.0 * t * t);
  derivs[2] = (1.0 / 16.0) * (-27.0 - 18.0 * t + 81.0 * t * t);
  derivs[3] = (1.0 / 16.0) * (27.0 - 18.0 * t - 81.0 * t * t);
}

//----------------------------------------------------------------------------
static double vtkCubicLineCellPCoords[12] = { -1.0, 0.0, 0.0, 1.0, 0.0, 0.0, -(1.0 / 3.0), 0.0, 0.0,
  (1.0 / 3.0), 0.0, 0.0 };
double* vtkCubicLine::GetParametricCoords()
{
  return vtkCubicLineCellPCoords;
}

//----------------------------------------------------------------------------
double vtkCubicLine::GetParametricDistance(const double pcoords[3])
{

  double pc;

  pc = pcoords[0];

  if (pc <= -1.0)
  {
    return pc * (-1.0) - 1.0;
  }
  else if (pc >= 1.0)
  {
    return pc - 1.0;
  }

  return pc; // the parametric coordinate lies between -1.0 and 1.0.
}

//----------------------------------------------------------------------------
void vtkCubicLine::PrintSelf(ostream& os, vtkIndent indent)
{
  this->Superclass::PrintSelf(os, indent);
  os << indent << "Line: " << this->Line << endl;
}
