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

  Program:   Visualization Toolkit
  Module:    vtkUnstructuredGridLinearRayIntegrator.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.

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

/*
 * Copyright 2004 Sandia Corporation.
 * Under the terms of Contract DE-AC04-94AL85000, there is a non-exclusive
 * license for use of this work by or on behalf of the
 * U.S. Government. Redistribution and use in source and binary forms, with
 * or without modification, are permitted provided that this Notice and any
 * statement of authorship are reproduced on all copies.
 */

#include "vtkUnstructuredGridLinearRayIntegrator.h"

#include "vtkColorTransferFunction.h"
#include "vtkDoubleArray.h"
#include "vtkMath.h"
#include "vtkObjectFactory.h"
#include "vtkPiecewiseFunction.h"
#include "vtkVolume.h"
#include "vtkVolumeProperty.h"

#include <algorithm>
#include <set>
#include <vector>

#include <cmath>

#ifndef M_SQRTPI
#define M_SQRTPI 1.77245385090551602792981
#endif
#ifndef M_2_SQRTPI
#define M_2_SQRTPI 1.12837916709551257390
#endif
#ifndef M_1_SQRTPI
#define M_1_SQRTPI (0.5 * M_2_SQRTPI)
#endif

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

// VTK's native classes for defining transfer functions is actually slow to
// access, so we have to cache it somehow.  This class is straightforward
// copy of the transfer function.
class vtkLinearRayIntegratorTransferFunction
{
public:
  vtkLinearRayIntegratorTransferFunction();
  ~vtkLinearRayIntegratorTransferFunction();

  void GetTransferFunction(vtkColorTransferFunction* color, vtkPiecewiseFunction* opacity,
    double unit_distance, double scalar_range[2]);
  void GetTransferFunction(vtkPiecewiseFunction* intensity, vtkPiecewiseFunction* opacity,
    double unit_distance, double scalar_range[2]);

  inline void GetColor(double x, double c[4]);

  struct acolor
  {
    double c[4];
  };
  double* ControlPoints;
  int NumControlPoints;
  acolor* Colors;

private:
  vtkLinearRayIntegratorTransferFunction(const vtkLinearRayIntegratorTransferFunction&) = delete;
  void operator=(const vtkLinearRayIntegratorTransferFunction&) = delete;
};

vtkLinearRayIntegratorTransferFunction::vtkLinearRayIntegratorTransferFunction()
{
  this->ControlPoints = nullptr;
  this->Colors = nullptr;

  this->NumControlPoints = 0;
}

vtkLinearRayIntegratorTransferFunction::~vtkLinearRayIntegratorTransferFunction()
{
  delete[] this->ControlPoints;
  delete[] this->Colors;
}

static const double huebends[6] = { 1.0 / 6.0, 1.0 / 3.0, 0.5, 2.0 / 3.0, 5.0 / 6.0, 1.0 };

void vtkLinearRayIntegratorTransferFunction::GetTransferFunction(vtkColorTransferFunction* color,
  vtkPiecewiseFunction* opacity, double unit_distance, double scalar_range[2])
{
  std::set<double> cpset;

  double* function_range = color->GetRange();
  double* function = color->GetDataPointer();
  while (true)
  {
    cpset.insert(function[0]);
    if (function[0] == function_range[1])
      break;
    function += 4;
  }

  if (color->GetColorSpace() != VTK_CTF_RGB)
  {
    // If we are in an HSV color space, we must insert control points
    // in places where the RGB bends.
    double rgb[3], hsv[3];
    double hue1, hue2;
    double x1, x2;
    std::set<double>::iterator i = cpset.begin();
    x1 = *i;
    color->GetColor(x1, rgb);
    vtkMath::RGBToHSV(rgb, hsv);
    hue1 = hsv[0];
    for (++i; i != cpset.end(); ++i)
    {
      x2 = *i;
      color->GetColor(x2, rgb);
      vtkMath::RGBToHSV(rgb, hsv);
      hue2 = hsv[0];

      // Are we crossing the 0/1 boundary?
      if ((color->GetColorSpace() == VTK_CTF_HSV && color->GetHSVWrap()) &&
        ((hue1 - hue2 > 0.5) || (hue2 - hue1 > 0.5)))
      {
        // Yes, we are crossing the boundary.
        if (hue1 > hue2)
        {
          int j;
          for (j = 0; huebends[j] <= hue2; j++)
          {
            double interp = (1 - hue1 + huebends[j]) / (1 - hue1 + hue2);
            cpset.insert((x2 - x1) * interp + x1);
          }
          while (huebends[j] < hue1)
            j++;
          for (; j < 6; j++)
          {
            double interp = (huebends[j] - hue1) / (1 - hue1 + hue2);
            cpset.insert((x2 - x1) * interp + x1);
          }
        }
        else
        {
          int j;
          for (j = 0; huebends[j] <= hue1; j++)
          {
            double interp = (hue1 - huebends[j]) / (1 - hue2 + hue1);
            cpset.insert((x2 - x1) * interp + x1);
          }
          while (huebends[j] < hue2)
            j++;
          for (; j < 6; j++)
          {
            double interp = (1 - huebends[j] + hue1) / (1 - hue2 + hue1);
            cpset.insert((x2 - x1) * interp + x1);
          }
        }
      }
      else
      {
        // No, we are not crossing the boundary.
        int j = 0;
        double minh, maxh;
        if (hue1 < hue2)
        {
          minh = hue1;
          maxh = hue2;
        }
        else
        {
          minh = hue2;
          maxh = hue1;
        }
        while (huebends[j] < minh)
          j++;
        for (j = 0; huebends[j] < maxh; j++)
        {
          double interp = (huebends[j] - hue1) / (hue2 - hue1);
          cpset.insert((x2 - x1) * interp + x1);
        }
      }

      x1 = x2;
      hue1 = hue2;
    }
  }

  function_range = opacity->GetRange();
  function = opacity->GetDataPointer();
  while (true)
  {
    cpset.insert(function[0]);
    if (function[0] == function_range[0])
      break;
    function += 2;
  }

  // Add the scalar at the beginning and end of the range so the interpolation
  // is correct there.
  cpset.insert(scalar_range[0]);
  cpset.insert(scalar_range[1]);
  // Make extra sure there are at least two entries in cpset.
  if (cpset.size() < 2)
  {
    cpset.insert(0.0);
    cpset.insert(1.0);
  }

  // Now record control points and colors.
  delete[] this->ControlPoints;
  delete[] this->Colors;
  this->NumControlPoints = static_cast<int>(cpset.size());
  this->ControlPoints = new double[this->NumControlPoints];
  this->Colors = new acolor[this->NumControlPoints];

  std::copy(cpset.begin(), cpset.end(), this->ControlPoints);
  for (int i = 0; i < this->NumControlPoints; i++)
  {
    color->GetColor(this->ControlPoints[i], this->Colors[i].c);
    this->Colors[i].c[3] = (opacity->GetValue(this->ControlPoints[i]) / unit_distance);
  }
}

void vtkLinearRayIntegratorTransferFunction::GetTransferFunction(vtkPiecewiseFunction* intensity,
  vtkPiecewiseFunction* opacity, double unit_distance, double scalar_range[2])
{
  std::set<double> cpset;

  double* function_range = intensity->GetRange();
  double* function = intensity->GetDataPointer();
  while (true)
  {
    cpset.insert(function[0]);
    if (function[0] == function_range[1])
      break;
    function += 2;
  }

  function_range = opacity->GetRange();
  function = opacity->GetDataPointer();
  while (true)
  {
    cpset.insert(function[0]);
    if (function[0] == function_range[0])
      break;
    function += 2;
  }

  // Add the scalar at the beginning and end of the range so the interpolation
  // is correct there.
  cpset.insert(scalar_range[0]);
  cpset.insert(scalar_range[1]);
  // Make extra sure there are at least two entries in cpset.
  if (cpset.size() < 2)
  {
    cpset.insert(0.0);
    cpset.insert(1.0);
  }

  // Now record control points and colors.
  delete[] this->ControlPoints;
  delete[] this->Colors;
  this->NumControlPoints = static_cast<int>(cpset.size());
  this->ControlPoints = new double[this->NumControlPoints];
  this->Colors = new acolor[this->NumControlPoints];

  std::copy(cpset.begin(), cpset.end(), this->ControlPoints);
  for (int i = 0; i < this->NumControlPoints; i++)
  {
    // Is setting all the colors to the same value the right thing to do?
    this->Colors[i].c[0] = this->Colors[i].c[1] = this->Colors[i].c[2] =
      intensity->GetValue(this->ControlPoints[i]);
    this->Colors[i].c[3] = (opacity->GetValue(this->ControlPoints[i]) / unit_distance);
  }
}

inline void vtkLinearRayIntegratorTransferFunction::GetColor(double x, double c[4])
{
  int i = 1;
  while ((i < this->NumControlPoints - 1) && (this->ControlPoints[i] < x))
    i++;

  double before = this->ControlPoints[i - 1];
  double after = this->ControlPoints[i];

  double interp = (x - before) / (after - before);

  double* beforec = this->Colors[i - 1].c;
  double* afterc = this->Colors[i].c;
  c[0] = (1 - interp) * beforec[0] + interp * afterc[0];
  c[1] = (1 - interp) * beforec[1] + interp * afterc[1];
  c[2] = (1 - interp) * beforec[2] + interp * afterc[2];
  c[3] = (1 - interp) * beforec[3] + interp * afterc[3];
}

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

vtkStandardNewMacro(vtkUnstructuredGridLinearRayIntegrator);

vtkUnstructuredGridLinearRayIntegrator::vtkUnstructuredGridLinearRayIntegrator()
{
  this->Property = nullptr;
  this->TransferFunctions = nullptr;
  this->NumIndependentComponents = 0;
}

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

vtkUnstructuredGridLinearRayIntegrator::~vtkUnstructuredGridLinearRayIntegrator()
{
  delete[] this->TransferFunctions;
}

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

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

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

void vtkUnstructuredGridLinearRayIntegrator::Initialize(vtkVolume* volume, vtkDataArray* scalars)
{
  vtkVolumeProperty* property = volume->GetProperty();

  if ((property == this->Property) && (this->TransferFunctionsModified > property->GetMTime()))
  {
    // Nothing has changed from the last time Initialize was run.
    return;
  }

  int numcomponents = scalars->GetNumberOfComponents();

  this->Property = property;
  this->TransferFunctionsModified.Modified();

  if (!property->GetIndependentComponents())
  {
    // The scalars actually hold material properties.
    if ((numcomponents != 4) && (numcomponents != 2))
    {
      vtkErrorMacro("Only 2-tuples and 4-tuples allowed for dependent components.");
    }
    return;
  }

  delete[] this->TransferFunctions;

  this->NumIndependentComponents = numcomponents;
  this->TransferFunctions = new vtkLinearRayIntegratorTransferFunction[numcomponents];

  for (int component = 0; component < numcomponents; component++)
  {
    if (property->GetColorChannels(component) == 1)
    {
      this->TransferFunctions[component].GetTransferFunction(
        property->GetGrayTransferFunction(component), property->GetScalarOpacity(component),
        property->GetScalarOpacityUnitDistance(component), scalars->GetRange(component));
    }
    else
    {
      this->TransferFunctions[component].GetTransferFunction(
        property->GetRGBTransferFunction(component), property->GetScalarOpacity(component),
        property->GetScalarOpacityUnitDistance(component), scalars->GetRange(component));
    }
  }
}

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

void vtkUnstructuredGridLinearRayIntegrator::Integrate(vtkDoubleArray* intersectionLengths,
  vtkDataArray* nearIntersections, vtkDataArray* farIntersections, float color[4])
{
  int numintersections = intersectionLengths->GetNumberOfTuples();
  if (this->Property->GetIndependentComponents())
  {
    int numscalars = nearIntersections->GetNumberOfComponents();
    double* nearScalars = new double[numscalars];
    double* farScalars = new double[numscalars];
    std::set<double> segments;
    for (vtkIdType i = 0; i < numintersections; i++)
    {
      double total_length = intersectionLengths->GetValue(i);
      nearIntersections->GetTuple(i, nearScalars);
      farIntersections->GetTuple(i, farScalars);

      // Split up segment on control points, because it is nonlinear in
      // these regions.
      segments.erase(segments.begin(), segments.end());
      segments.insert(0.0);
      segments.insert(1.0);
      for (int j = 0; j < numscalars; j++)
      {
        double* cp = this->TransferFunctions[j].ControlPoints;
        vtkIdType numcp = this->TransferFunctions[j].NumControlPoints;
        double minscalar, maxscalar;
        if (nearScalars[j] < farScalars[j])
        {
          minscalar = nearScalars[j];
          maxscalar = farScalars[j];
        }
        else
        {
          minscalar = farScalars[j];
          maxscalar = nearScalars[j];
        }
        for (int k = 0; k < numcp; k++)
        {
          if (cp[k] <= minscalar)
            continue;
          if (cp[k] >= maxscalar)
            break;
          // If we are here, we need to break the segment at the given scalar.
          // Find the fraction between the near and far segment points.
          segments.insert((cp[k] - nearScalars[j]) / (farScalars[j] - nearScalars[j]));
        }
      }

      // Iterate over all the segment pieces (from front to back) and
      // integrate each piece.
      std::set<double>::iterator segi = segments.begin();
      double nearInterpolant = *segi;
      for (++segi; segi != segments.end(); ++segi)
      {
        double farInterpolant = *segi;
        double nearcolor[4] = { 0.0, 0.0, 0.0, 0.0 };
        double farcolor[4] = { 0.0, 0.0, 0.0, 0.0 };
        double length = total_length * (farInterpolant - nearInterpolant);
        // Here we handle the mixing of material properties.  This never
        // seems to be defined very clearly.  I handle this by assuming
        // that each scalar represents a cloud of particles of a certain
        // color and a certain density.  We mix the scalars in the same way
        // as mixing these particles together.  By necessity, the density
        // becomes greater.  The "opacity" parameter is really interpreted
        // as the attenuation coefficient (which is proportional to
        // density) and can therefore easily be greater than one.  The
        // opacity of the resulting color will, however, always be scaled
        // between 0 and 1.
        for (int j = 0; j < numscalars; j++)
        {
          double scalar = (farScalars[j] - nearScalars[j]) * nearInterpolant + nearScalars[j];
          if (j == 0)
          {
            this->TransferFunctions[j].GetColor(scalar, nearcolor);
          }
          else
          {
            double c[4];
            this->TransferFunctions[j].GetColor(scalar, c);
            if (c[3] + nearcolor[3] > 1.0e-8f)
            {
              nearcolor[0] *= nearcolor[3] / (c[3] + nearcolor[3]);
              nearcolor[1] *= nearcolor[3] / (c[3] + nearcolor[3]);
              nearcolor[2] *= nearcolor[3] / (c[3] + nearcolor[3]);
              nearcolor[0] += c[0] * c[3] / (c[3] + nearcolor[3]);
              nearcolor[1] += c[1] * c[3] / (c[3] + nearcolor[3]);
              nearcolor[2] += c[2] * c[3] / (c[3] + nearcolor[3]);
              nearcolor[3] += c[3];
            }
          }

          scalar = (farScalars[j] - nearScalars[j]) * farInterpolant + nearScalars[j];
          if (j == 0)
          {
            this->TransferFunctions[j].GetColor(scalar, farcolor);
          }
          else
          {
            double c[4];
            this->TransferFunctions[j].GetColor(scalar, c);
            if (c[3] + farcolor[3] > 1.0e-8f)
            {
              farcolor[0] *= farcolor[3] / (c[3] + farcolor[3]);
              farcolor[1] *= farcolor[3] / (c[3] + farcolor[3]);
              farcolor[2] *= farcolor[3] / (c[3] + farcolor[3]);
              farcolor[0] += c[0] * c[3] / (c[3] + farcolor[3]);
              farcolor[1] += c[1] * c[3] / (c[3] + farcolor[3]);
              farcolor[2] += c[2] * c[3] / (c[3] + farcolor[3]);
              farcolor[3] += c[3];
            }
          }
        }
        vtkUnstructuredGridLinearRayIntegrator::IntegrateRay(
          length, nearcolor, nearcolor[3], farcolor, farcolor[3], color);

        nearInterpolant = farInterpolant;
      }
    }
    delete[] nearScalars;
    delete[] farScalars;
  }
  else
  {
    double unitdistance = this->Property->GetScalarOpacityUnitDistance();
    if (nearIntersections->GetNumberOfComponents() == 4)
    {
      for (vtkIdType i = 0; i < numintersections; i++)
      {
        double length = intersectionLengths->GetValue(i);
        double* nearcolor = nearIntersections->GetTuple(i);
        double* farcolor = farIntersections->GetTuple(i);
        vtkUnstructuredGridLinearRayIntegrator::IntegrateRay(length, nearcolor,
          nearcolor[3] / unitdistance, farcolor, farcolor[3] / unitdistance, color);
      }
    }
    else // Two components.
    {
      for (vtkIdType i = 0; i < numintersections; i++)
      {
        double length = intersectionLengths->GetValue(i);
        double* nearcolor = nearIntersections->GetTuple(i);
        double* farcolor = farIntersections->GetTuple(i);
        vtkUnstructuredGridLinearRayIntegrator::IntegrateRay(length, nearcolor[0],
          nearcolor[1] / unitdistance, farcolor[0], farcolor[1] / unitdistance, color);
      }
    }
  }
}

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

void vtkUnstructuredGridLinearRayIntegrator::IntegrateRay(double length, double intensity_front,
  double attenuation_front, double intensity_back, double attenuation_back, float color[4])
{
  float Psi =
    vtkUnstructuredGridLinearRayIntegrator::Psi(length, attenuation_front, attenuation_back);
  float zeta = (float)exp(-0.5 * length * (attenuation_front + attenuation_back));
  float alpha = 1 - zeta;

  float newintensity =
    (1 - color[3]) * (intensity_front * (1 - Psi) + intensity_back * (Psi - zeta));
  // Is setting the RGB values the same the right thing to do?
  color[0] += newintensity;
  color[1] += newintensity;
  color[2] += newintensity;
  color[3] += (1 - color[3]) * alpha;
}

void vtkUnstructuredGridLinearRayIntegrator::IntegrateRay(double length,
  const double color_front[3], double attenuation_front, const double color_back[3],
  double attenuation_back, float color[4])
{
  float Psi =
    vtkUnstructuredGridLinearRayIntegrator::Psi(length, attenuation_front, attenuation_back);
  float zeta = (float)exp(-0.5 * length * (attenuation_front + attenuation_back));
  float alpha = 1 - zeta;

  color[0] += (1 - color[3]) * (color_front[0] * (1 - Psi) + color_back[0] * (Psi - zeta));
  color[1] += (1 - color[3]) * (color_front[1] * (1 - Psi) + color_back[1] * (Psi - zeta));
  color[2] += (1 - color[3]) * (color_front[2] * (1 - Psi) + color_back[2] * (Psi - zeta));
  color[3] += (1 - color[3]) * alpha;
}

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

static inline float erf_fitting_function(float u)
{
  return -1.26551223 +
    u *
    (1.00002368 +
      u *
        (0.37409196 +
          u *
            (0.09678418 +
              u *
                (-0.18628806 +
                  u *
                    (0.27886807 +
                      u *
                        (-1.13520398 + u * (1.48851587 + u * (-0.82215223 + u * 0.17087277))))))));
}

#if 0
// This function is not used directly.  It is here for reference.
static inline float erf(float x)
{
  /* Compute as described in Numerical Recipes in C++ by Press, et al. */
/*   x = abs(x);        In this application, x should always be >= 0. */
  float u = 1/(1 + 0.5*x);
  float ans = u*exp(-x*x + erf_fitting_function(u));
/*   return (x >= 0 ? 1 - ans : ans - 1);    x should always be >= 0. */
  return 1 - ans;
}
#endif

/* Compute Dawson's integral as described in Numerical Recipes in C++ by
   Press, et al. */
#define H 0.4
static const float dawson_constant0 = 0.852144;
static const float dawson_constant1 = 0.236928;
static const float dawson_constant2 = 0.0183156;
static const float dawson_constant3 = 0.000393669;
static const float dawson_constant4 = 2.35258e-6;
static const float dawson_constant5 = 3.90894e-9;
static inline float dawson(float x)
{
  if (x > 0.2)
  {
    /*  x = abs(x);       In this application, x should always be >= 0. */
    int n0 = 2 * (int)((0.5 / H) * x + 0.5);
    float xp = x - (float)n0 * H;
    float e1 = exp((2 * H) * xp);
    float e2 = e1 * e1;
    float d1 = n0 + 1;
    float d2 = d1 - 2;
    float sum = 0;
    sum = dawson_constant0 * (e1 / d1 + 1 / (d2 * e1));
    d1 += 2;
    d2 -= 2;
    e1 *= e2;
    sum += dawson_constant1 * (e1 / d1 + 1 / (d2 * e1));
    d1 += 2;
    d2 -= 2;
    e1 *= e2;
    sum += dawson_constant2 * (e1 / d1 + 1 / (d2 * e1));
    d1 += 2;
    d2 -= 2;
    e1 *= e2;
    sum += dawson_constant3 * (e1 / d1 + 1 / (d2 * e1));
    d1 += 2;
    d2 -= 2;
    e1 *= e2;
    sum += dawson_constant4 * (e1 / d1 + 1 / (d2 * e1));
    d1 += 2;
    d2 -= 2;
    e1 *= e2;
    sum += dawson_constant5 * (e1 / d1 + 1 / (d2 * e1));
    return M_1_SQRTPI * exp(-xp * xp) * sum;
  }
  else
  {
    float x2 = x * x;
    return x * (1 - (2.0 / 3.0) * x2 * (1 - .4 * x2 * (1 - (2.0 / 7.0) * x2)));
  }
}

#if 0
// This function is not used directly.  It is here for reference.
inline float erfi(float x)
{
  return M_2_SQRTPI*exp(x*x)*dawson(x);
}
#endif

float vtkUnstructuredGridLinearRayIntegrator::Psi(
  float length, float attenuation_front, float attenuation_back)
{
  float difftauD = length * fabs(attenuation_back - attenuation_front);

  if (difftauD < 1.0e-8f)
  {
    // Volume is homogeneous (with respect to attenuation).
    float tauD = length * attenuation_front;
    if (tauD < 1.0e-8f)
    {
      return 1;
    }
    else
    {
      return (1 - (float)exp(-tauD)) / tauD;
    }
  }
  else
  {
    float invsqrt2difftauD = 1 / (float)sqrt(2 * difftauD);
    float frontterm = length * invsqrt2difftauD * attenuation_front;
    float backterm = length * invsqrt2difftauD * attenuation_back;
    if (attenuation_back > attenuation_front)
    {
      float u, Y;
      u = 1 / (1 + 0.5f * frontterm);
      Y = u * (float)exp(erf_fitting_function(u));
      u = 1 / (1 + 0.5f * backterm);
      Y += -u * exp(frontterm * frontterm - backterm * backterm + erf_fitting_function(u));
      Y *= M_SQRTPI * invsqrt2difftauD;
      return Y;
    }
    else
    {
      float expterm = (float)exp(backterm * backterm - frontterm * frontterm);
      return 2 * invsqrt2difftauD * (dawson(frontterm) - expterm * dawson(backterm));
    }
  }
}
