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

  Program:   Visualization Toolkit
  Module:    vtkOpenGLProjectedTetrahedraMapper.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 2003 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 "vtkOpenGLProjectedTetrahedraMapper.h"

#include "vtkCamera.h"
#include "vtkCellArray.h"
#include "vtkCellData.h"
#include "vtkFloatArray.h"
#include "vtkIdTypeArray.h"
#include "vtkMath.h"
#include "vtkMatrix4x4.h"
#include "vtkObjectFactory.h"
#include "vtkPointData.h"
#include "vtkRenderer.h"
#include "vtkRenderWindow.h"
#include "vtkTimerLog.h"
#include "vtkUnsignedCharArray.h"
#include "vtkUnstructuredGrid.h"
#include "vtkVisibilitySort.h"
#include "vtkVolume.h"
#include "vtkVolumeProperty.h"

#include "vtkOpenGL.h"

#include <math.h>
#include <vtkstd/algorithm>

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

// static int tet_faces[4][3] = { {1,2,3}, {2,0,3}, {0,1,3}, {0,2,1} };
static int tet_edges[6][2] = { {0,1}, {1,2}, {2,0}, 
                               {0,3}, {1,3}, {2,3} };

const int SqrtTableSize = 2048;

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

vtkCxxRevisionMacro(vtkOpenGLProjectedTetrahedraMapper, "1.6");
vtkStandardNewMacro(vtkOpenGLProjectedTetrahedraMapper);

vtkOpenGLProjectedTetrahedraMapper::vtkOpenGLProjectedTetrahedraMapper()
{
  this->TransformedPoints = vtkFloatArray::New();
  this->Colors = vtkUnsignedCharArray::New();

  this->LastProperty = NULL;

  this->OpacityTexture = 0;
  this->MaxCellSize = 0;

  this->GaveError = 0;

  this->SqrtTable = new float[SqrtTableSize];
  this->SqrtTableBias = 0.0;
}

vtkOpenGLProjectedTetrahedraMapper::~vtkOpenGLProjectedTetrahedraMapper()
{
  this->ReleaseGraphicsResources(NULL);
  this->TransformedPoints->Delete();
  this->Colors->Delete();

  delete[] this->SqrtTable;
}

void vtkOpenGLProjectedTetrahedraMapper::PrintSelf(ostream &os, vtkIndent indent)
{
  this->Superclass::PrintSelf(os, indent);
  os << indent << "VisibilitySort: " << this->VisibilitySort << endl;

}

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

void vtkOpenGLProjectedTetrahedraMapper::ReleaseGraphicsResources(vtkWindow *win)
{
  if (this->OpacityTexture)
    {
    GLuint texid = this->OpacityTexture;
    glDeleteTextures(1, &texid);
    this->OpacityTexture = 0;
    }
  this->Superclass::ReleaseGraphicsResources(win);
}

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

void vtkOpenGLProjectedTetrahedraMapper::Render(vtkRenderer *renderer,
                                                vtkVolume *volume)
{
  vtkUnstructuredGrid *input = this->GetInput();
  vtkVolumeProperty *property = volume->GetProperty();

  float last_max_cell_size = this->MaxCellSize;

  // Check to see if input changed.
  if (   (this->InputAnalyzedTime < this->MTime)
      || (this->InputAnalyzedTime < input->GetMTime()) )
    {
    this->GaveError = 0;
    float max_cell_size2 = 0;

    vtkCellArray *cells = input->GetCells();
    if (!cells)
      {
      // Apparently, the input has no cells.  Just do nothing.
      return;
      }

    vtkIdType npts, *pts, i;
    cells->InitTraversal();
    for (i = 0; cells->GetNextCell(npts, pts); i++)
      {
      int j;
      if (npts != 4)
        {
        if (!this->GaveError)
          {
          vtkErrorMacro("Encountered non-tetrahedra cell!");
          this->GaveError = 1;
          }
        continue;
        }
      for (j = 0; j < 6; j++)
        {
        double p1[3], p2[3];
        input->GetPoint(pts[tet_edges[j][0]], p1);
        input->GetPoint(pts[tet_edges[j][1]], p2);
        float size2 = (float)vtkMath::Distance2BetweenPoints(p1, p2);
        if (size2 > max_cell_size2) max_cell_size2 = size2;
        }
      }

    this->MaxCellSize = (float)sqrt(max_cell_size2);

    // Build a sqrt lookup table for measuring distances.  During perspective
    // modes we have to take a lot of square roots, and a table is much faster
    // than calling the sqrt function.
    this->SqrtTableBias = (SqrtTableSize-1)/max_cell_size2;
    for (i = 0; i < SqrtTableSize; i++)
      {
      this->SqrtTable[i] = (float)sqrt(i/this->SqrtTableBias);
      }

    this->InputAnalyzedTime.Modified();
    }

  if (renderer->GetRenderWindow()->CheckAbortStatus() || this->GaveError)
    {
    return;
    }

  // Check to see if we need to rebuild opacity texture.
  if (   !this->OpacityTexture
      || (last_max_cell_size != this->MaxCellSize)
      || (this->LastProperty != property)
      || (this->OpacityTextureTime < property->GetMTime()) )
    {
    if (!this->OpacityTexture)
      {
      GLuint texid;
      glGenTextures(1, &texid);
      this->OpacityTexture = texid;
      }
    glBindTexture(GL_TEXTURE_2D, this->OpacityTexture);

    float unit_distance = property->GetScalarOpacityUnitDistance();

#define TEXRES  258
    float *texture = new float[TEXRES*TEXRES];
    for (int depthi = 0; depthi < TEXRES; depthi++)
      {
      if (renderer->GetRenderWindow()->CheckAbortStatus())
        {
        delete[] texture;
        return;
        }
      float depth = depthi*this->MaxCellSize/(TEXRES);
      for (int attenuationi = 0; attenuationi < TEXRES; attenuationi++)
        {
        float attenuation = (float)attenuationi/(TEXRES);
        float alpha = 1 - (float)exp(-attenuation*depth/unit_distance);
        texture[(depthi*TEXRES + attenuationi)] = alpha;
        }
      }
    glTexImage2D(GL_TEXTURE_2D, 0, GL_INTENSITY, TEXRES, TEXRES, 1, GL_RED,
                 GL_FLOAT, texture);
    delete[] texture;

    glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_LINEAR);
    glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_LINEAR);
    glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, GL_CLAMP);
    glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_T, GL_CLAMP);

    glBindTexture(GL_TEXTURE_2D, 0);

    this->OpacityTextureTime.Modified();
    }
  if (renderer->GetRenderWindow()->CheckAbortStatus())
    {
    return;
    }

  // Check to see if we need to remap colors.
  if (   (this->ColorsMappedTime < this->MTime)
      || (this->ColorsMappedTime < input->GetMTime())
      || (this->LastProperty != property)
      || (this->ColorsMappedTime < property->GetMTime()) )
    {
    vtkDataArray *scalars = this->GetScalars(input, this->ScalarMode,
                                             this->ArrayAccessMode,
                                             this->ArrayId, this->ArrayName,
                                             this->UsingCellColors);
    if (!scalars)
      {
      vtkErrorMacro(<< "Can't use projected tetrahedra without scalars!");
      return;
      }

    vtkProjectedTetrahedraMapper::MapScalarsToColors(this->Colors, property,
                                                     scalars);

    this->ColorsMappedTime.Modified();
    this->LastProperty = property;
    }
  if (renderer->GetRenderWindow()->CheckAbortStatus())
    {
    return;
    }

  this->Timer->StartTimer();

  this->ProjectTetrahedra(renderer, volume);

  this->Timer->StopTimer();
  this->TimeToDraw = this->Timer->GetElapsedTime();
}

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

inline float vtkOpenGLProjectedTetrahedraMapper::GetCorrectedDepth(
                                         float x, float y, float z1, float z2,
                                         const float inverse_projection_mat[16],
                                         int use_linear_depth_correction,
                                         float linear_depth_correction)
{
  if (use_linear_depth_correction)
    {
    float depth = linear_depth_correction*(z1 - z2);
    if (depth < 0) depth = -depth;
    return depth;
    }
  else
    {
    float eye1[3], eye2[3], invw;

#if 0
    invw = 1/(  inverse_projection_mat[ 3]*x
              + inverse_projection_mat[ 7]*y
              + inverse_projection_mat[11]*z1
              + inverse_projection_mat[15] );
    eye1[0] = invw*(  inverse_projection_mat[ 0]*x
                    + inverse_projection_mat[ 4]*y
                    + inverse_projection_mat[ 8]*z1
                    + inverse_projection_mat[12] );
    eye1[1] = invw*(  inverse_projection_mat[ 1]*x
                    + inverse_projection_mat[ 5]*y
                    + inverse_projection_mat[ 9]*z1
                    + inverse_projection_mat[13] );
    eye1[2] = invw*(  inverse_projection_mat[ 2]*x
                    + inverse_projection_mat[ 6]*y
                    + inverse_projection_mat[10]*z1
                    + inverse_projection_mat[14] );

    invw = 1/(  inverse_projection_mat[ 3]*x
              + inverse_projection_mat[ 7]*y
              + inverse_projection_mat[11]*z2
              + inverse_projection_mat[15] );
    eye2[0] = invw*(  inverse_projection_mat[ 0]*x
                    + inverse_projection_mat[ 4]*y
                    + inverse_projection_mat[ 8]*z2
                    + inverse_projection_mat[12] );
    eye2[1] = invw*(  inverse_projection_mat[ 1]*x
                    + inverse_projection_mat[ 5]*y
                    + inverse_projection_mat[ 9]*z2
                    + inverse_projection_mat[13] );
    eye2[2] = invw*(  inverse_projection_mat[ 2]*x
                    + inverse_projection_mat[ 6]*y
                    + inverse_projection_mat[10]*z2
                    + inverse_projection_mat[14] );
#else
    // This code does the same as the commented code above, but also collects
    // common arithmetic between the two matrix x vector operations.  An
    // optimizing compiler may or may not pick up on that.
    float common[4];

    common[0] = (  inverse_projection_mat[ 0]*x
                 + inverse_projection_mat[ 4]*y
                 + inverse_projection_mat[12] );
    common[1] = (  inverse_projection_mat[ 1]*x
                 + inverse_projection_mat[ 5]*y
                 + inverse_projection_mat[13] );
    common[2] = (  inverse_projection_mat[ 2]*x
                 + inverse_projection_mat[ 6]*y
                 + inverse_projection_mat[10]*z1
                 + inverse_projection_mat[14] );
    common[3] = (  inverse_projection_mat[ 3]*x
                 + inverse_projection_mat[ 7]*y
                 + inverse_projection_mat[15] );

    invw = 1/(common[3] + inverse_projection_mat[11]*z1);
    eye1[0] = invw*(common[0] + inverse_projection_mat[ 8]*z1);
    eye1[1] = invw*(common[1] + inverse_projection_mat[ 9]*z1);
    eye1[2] = invw*(common[2] + inverse_projection_mat[10]*z1);

    invw = 1/(common[3] + inverse_projection_mat[11]*z2);
    eye2[0] = invw*(common[0] + inverse_projection_mat[ 8]*z2);
    eye2[1] = invw*(common[1] + inverse_projection_mat[ 9]*z2);
    eye2[2] = invw*(common[2] + inverse_projection_mat[10]*z2);
#endif

    float dist2 = vtkMath::Distance2BetweenPoints(eye1, eye2);
    return this->SqrtTable[(int)(dist2*this->SqrtTableBias)];
    }
}

//-----------------------------------------------------------------------------
void vtkOpenGLProjectedTetrahedraMapper::ProjectTetrahedra(vtkRenderer *renderer,
                                                     vtkVolume *volume)
{
  vtkUnstructuredGrid *input = this->GetInput();

  this->VisibilitySort->SetInput(input);
  this->VisibilitySort->SetDirectionToBackToFront();
  this->VisibilitySort->SetModelTransform(volume->GetMatrix());
  this->VisibilitySort->SetCamera(renderer->GetActiveCamera());
  this->VisibilitySort->SetMaxCellsReturned(1000);

  this->VisibilitySort->InitTraversal();

  if (renderer->GetRenderWindow()->CheckAbortStatus())
    {
    return;
    }

  float projection_mat[16];
  float modelview_mat[16];
  glGetFloatv(GL_PROJECTION_MATRIX, projection_mat);
  glGetFloatv(GL_MODELVIEW_MATRIX, modelview_mat);

  // Get the inverse projection matrix so that we can convert distances in
  // clipping space to distances in world or eye space.
  float inverse_projection_mat[16];
  float linear_depth_correction = 1;
  int use_linear_depth_correction;
  double tmp_mat[16];

  // VTK's matrix functions use doubles.
  vtkstd::copy(projection_mat, projection_mat+16, tmp_mat);
  // VTK and OpenGL store their matrices differently.  Correct.
  vtkMatrix4x4::Transpose(tmp_mat, tmp_mat);
  // Take the inverse.
  vtkMatrix4x4::Invert(tmp_mat, tmp_mat);
  // Restore back to OpenGL form.
  vtkMatrix4x4::Transpose(tmp_mat, tmp_mat);
  // Copy back to float for faster computation.
  vtkstd::copy(tmp_mat, tmp_mat+16, inverse_projection_mat);

  // Check to see if we can just do a linear depth correction from clipping
  // space to eye space.
  use_linear_depth_correction = (   (projection_mat[ 3] == 0.0)
                                 && (projection_mat[ 7] == 0.0)
                                 && (projection_mat[11] == 0.0)
                                 && (projection_mat[15] == 1.0) );
  if (use_linear_depth_correction)
    {
    float pos1[3], *pos2;

    pos1[0] = inverse_projection_mat[8] + inverse_projection_mat[12];
    pos1[1] = inverse_projection_mat[9] + inverse_projection_mat[13];
    pos1[2] = inverse_projection_mat[10] + inverse_projection_mat[14];

    pos2 = inverse_projection_mat + 12;

    linear_depth_correction = sqrt(vtkMath::Distance2BetweenPoints(pos1, pos2));
    }

  // Transform all the points.
  vtkProjectedTetrahedraMapper::TransformPoints(input->GetPoints(),
                                                projection_mat, modelview_mat,
                                                this->TransformedPoints);
  float *points = this->TransformedPoints->GetPointer(0);

  if (renderer->GetRenderWindow()->CheckAbortStatus())
    {
    return;
    }

  glDisable(GL_LIGHTING);
  glDepthMask(GL_FALSE);

  glEnable(GL_TEXTURE_2D);
  glBindTexture(GL_TEXTURE_2D, this->OpacityTexture);
  glTexEnvi(GL_TEXTURE_ENV, GL_TEXTURE_ENV_MODE, GL_MODULATE);

  glShadeModel(GL_SMOOTH);
  glBlendFunc(GL_ONE, GL_ONE_MINUS_SRC_ALPHA);

  // Establish vertex arrays.
  float tet_points[5*3];
  glVertexPointer(3, GL_FLOAT, 0, tet_points);
  glEnableClientState(GL_VERTEX_ARRAY);

  unsigned char tet_colors[5*3];
  glColorPointer(3, GL_UNSIGNED_BYTE, 0, tet_colors);
  glEnableClientState(GL_COLOR_ARRAY);

  float tet_texcoords[5*2];
  glTexCoordPointer(2, GL_FLOAT, 0, tet_texcoords);
  glEnableClientState(GL_TEXTURE_COORD_ARRAY);

  // Since we had to transform the points on the CPU, replace the OpenGL
  // transforms with the identity matrix.
  glMatrixMode(GL_PROJECTION);
  glLoadIdentity();
  glMatrixMode(GL_MODELVIEW);
  glLoadIdentity();

  unsigned char *colors = this->Colors->GetPointer(0);
  vtkIdType *cells = input->GetCells()->GetPointer();
  vtkIdType totalnumcells = input->GetNumberOfCells();
  vtkIdType numcellsrendered = 0;

  // Let's do it!
  for (vtkIdTypeArray *sorted_cell_ids = this->VisibilitySort->GetNextCells();
       sorted_cell_ids != NULL;
       sorted_cell_ids = this->VisibilitySort->GetNextCells())
    {
    this->UpdateProgress((double)numcellsrendered/totalnumcells);
    if (renderer->GetRenderWindow()->CheckAbortStatus())
      {
      break;
      }
    vtkIdType *cell_ids = sorted_cell_ids->GetPointer(0);
    vtkIdType num_cell_ids = sorted_cell_ids->GetNumberOfTuples();
    for (vtkIdType i = 0; i < num_cell_ids; i++)
      {
      vtkIdType cell = cell_ids[i];
      int j;

      // Get the data for the tetrahedra.
      for (j = 0; j < 4; j++)
        {
        // Assuming we only have tetrahedra, each entry in cells has 5
        // components.
        const float *p = points + 3*cells[5*cell + j + 1];
        tet_points[j*3 + 0] = p[0];
        tet_points[j*3 + 1] = p[1];
        tet_points[j*3 + 2] = p[2];

        const unsigned char *c;
        if (this->UsingCellColors)
          {
          c = colors + 4*cell;
          }
        else
          {
          c = colors + 4*cells[5*cell + j + 1];
          }
        tet_colors[j*3 + 0] = c[0];
        tet_colors[j*3 + 1] = c[1];
        tet_colors[j*3 + 2] = c[2];

        tet_texcoords[j*2 + 0] = (float)c[3]/255;
        tet_texcoords[j*2 + 1] = 0;
        }

      // The classic PT algorithm uses face normals to determine the
      // projection class and then do calculations individually.  However,
      // Wylie 2002 shows how to use the intersection of two segments to
      // calculate the depth of the thick part for any case.  Here, we use
      // face normals to determine which segments to use.  One segment
      // should be between two faces that are either both front facing or
      // back facing.  Obviously, we only need to test three faces to find
      // two such faces.  We test the three faces connected to point 0.
      vtkIdType segment1[2];
      vtkIdType segment2[2];

      float v1[2], v2[2], v3[3];
      v1[0] = tet_points[1*3 + 0] - tet_points[0*3 + 0];
      v1[1] = tet_points[1*3 + 1] - tet_points[0*3 + 1];
      v2[0] = tet_points[2*3 + 0] - tet_points[0*3 + 0];
      v2[1] = tet_points[2*3 + 1] - tet_points[0*3 + 1];
      v3[0] = tet_points[3*3 + 0] - tet_points[0*3 + 0];
      v3[1] = tet_points[3*3 + 1] - tet_points[0*3 + 1];

      float face_dir1 = v3[0]*v2[1] - v3[1]*v2[0];
      float face_dir2 = v1[0]*v3[1] - v1[1]*v3[0];
      float face_dir3 = v2[0]*v1[1] - v2[1]*v1[0];

      if (   (face_dir1 * face_dir2 >= 0)
          && (   (face_dir1 != 0)       // Handle a special case where 2 faces
              || (face_dir2 != 0) ) )   // are perpendicular to the view plane.
        {
        segment1[0] = 0;  segment1[1] = 3;
        segment2[0] = 1;  segment2[1] = 2;
        }
      else if (face_dir1 * face_dir3 >= 0)
        {
        segment1[0] = 0;  segment1[1] = 2;
        segment2[0] = 1;  segment2[1] = 3;
        }
      else      // Unless the tet is degenerate, face_dir2*face_dir3 >= 0
        {
        segment1[0] = 0;  segment1[1] = 1;
        segment2[0] = 2;  segment2[1] = 3;
        }

#define VEC3SUB(Z,X,Y)          \
  (Z)[0] = (X)[0] - (Y)[0];     \
  (Z)[1] = (X)[1] - (Y)[1];     \
  (Z)[2] = (X)[2] - (Y)[2];
#define P1 (tet_points + 3*segment1[0])
#define P2 (tet_points + 3*segment1[1])
#define P3 (tet_points + 3*segment2[0])
#define P4 (tet_points + 3*segment2[1])
#define C1 (tet_colors + 3*segment1[0])
#define C2 (tet_colors + 3*segment1[1])
#define C3 (tet_colors + 3*segment2[0])
#define C4 (tet_colors + 3*segment2[1])
#define T1 (tet_texcoords + 2*segment1[0])
#define T2 (tet_texcoords + 2*segment1[1])
#define T3 (tet_texcoords + 2*segment2[0])
#define T4 (tet_texcoords + 2*segment2[1])
      // Find the intersection of the projection of the two segments in the
      // XY plane.  This algorithm is based on that given in Graphics Gems
      // III, pg. 199-202.
      float A[3], B[3], C[3];
      // We can define the two lines parametrically as:
      //        P1 + alpha(A)
      //        P3 + beta(B)
      // where A = P2 - P1
      // and   B = P4 - P3.
      // alpha and beta are in the range [0,1] within the line segment.
      VEC3SUB(A, P2, P1);
      VEC3SUB(B, P4, P3);
      // The lines intersect when the values of the two parameteric equations
      // are equal.  Setting them equal and moving everything to one side:
      //        0 = C + beta(B) - alpha(A)
      // where C = P3 - P1.
      VEC3SUB(C, P3, P1);
      // When we project the lines to the xy plane (which we do by throwing
      // away the z value), we have two equations and two unkowns.  The
      // following are the solutions for alpha and beta.
      float alpha = (B[1]*C[0]-B[0]*C[1])/(A[0]*B[1]-A[1]*B[0]);
      float beta = (A[1]*C[0]-A[0]*C[1])/(A[0]*B[1]-A[1]*B[0]);

      if ((alpha >= 0) && (alpha <= 1))
        {
        // The two segments intersect.  This corresponds to class 2 in
        // Shirley and Tuchman (or one of the degenerate cases).

        // Make new point at intersection.
        tet_points[3*4 + 0] = P1[0] + alpha*A[0];
        tet_points[3*4 + 1] = P1[1] + alpha*A[1];
        tet_points[3*4 + 2] = P1[2] + alpha*A[2];

        // Find depth at intersection.
        float depth = GetCorrectedDepth(tet_points[3*4 + 0],
                                        tet_points[3*4 + 1],
                                        tet_points[3*4 + 2],
                                        P3[2] + beta*B[2],
                                        inverse_projection_mat,
                                        use_linear_depth_correction,
                                        linear_depth_correction);

        // Find color at intersection.
        tet_colors[3*4 + 0] =
          (unsigned char)(0.5f*(  C1[0] + alpha*(C2[0]-C1[0])
                                + C3[0] +  beta*(C4[0]-C3[0]) ));
        tet_colors[3*4 + 1] =
          (unsigned char)(0.5f*(  C1[1] + alpha*(C2[1]-C1[1])
                                + C3[1] +  beta*(C4[1]-C3[1]) ));
        tet_colors[3*4 + 2] =
          (unsigned char)(0.5f*(  C1[2] + alpha*(C2[2]-C1[2])
                                + C3[2] +  beta*(C4[2]-C3[2]) ));

//         tet_colors[3*0 + 0] = 255;
//         tet_colors[3*0 + 1] = 0;
//         tet_colors[3*0 + 2] = 0;
//         tet_colors[3*1 + 0] = 255;
//         tet_colors[3*1 + 1] = 0;
//         tet_colors[3*1 + 2] = 0;
//         tet_colors[3*2 + 0] = 255;
//         tet_colors[3*2 + 1] = 0;
//         tet_colors[3*2 + 2] = 0;
//         tet_colors[3*3 + 0] = 255;
//         tet_colors[3*3 + 1] = 0;
//         tet_colors[3*3 + 2] = 0;
//         tet_colors[3*4 + 0] = 255;
//         tet_colors[3*4 + 1] = 0;
//         tet_colors[3*4 + 2] = 0;

        // Find the opacity at intersection.
        tet_texcoords[2*4 + 0] = 0.5f*(  T1[0] + alpha*(T2[0]-T1[0])
                                       + T3[0] + alpha*(T4[0]-T3[0]));

        // Record the depth at the intersection.
        tet_texcoords[2*4 + 1] = depth/this->MaxCellSize;

        // Establish the order in which the points should be rendered.
        unsigned char gl_indices[6];
        gl_indices[0] = 4;
        gl_indices[1] = segment1[0];
        gl_indices[2] = segment2[0];
        gl_indices[3] = segment1[1];
        gl_indices[4] = segment2[1];
        gl_indices[5] = segment1[0];

        // Render
        glDrawElements(GL_TRIANGLE_FAN, 6, GL_UNSIGNED_BYTE, gl_indices);
        }
      else
        {
        // The two segments do not intersect.  This corresponds to class 1
        // in Shirley and Tuchman.
        if (alpha <= 0)
          {
          // Flip segment1 so that alpha is >= 1.  P1 and P2 are also
          // flipped as are C1-C2 and T1-T2.  Note that this will
          // invalidate A.  B and beta are unaffected.
          vtkstd::swap(segment1[0], segment1[1]);
          alpha = 1 - alpha;
          }
        // From here on, we can assume P2 is the "thick" point.

        // Find the depth under the thick point.  Use the alpha and beta
        // from intersection to determine location of face under thick
        // point.
        float edgez = P3[2] + beta*B[2];
        float pointz = P1[2];
        float facez = (edgez + (alpha-1)*pointz)/alpha;
        float depth = GetCorrectedDepth(P2[0], P2[1], P2[2], facez,
                                        inverse_projection_mat,
                                        use_linear_depth_correction,
                                        linear_depth_correction);

        // Fix color at thick point.  Average color with color of opposite
        // face.
        for (j = 0; j < 3; j++)
          {
          float edgec = C3[j] + beta*(C4[j]-C3[j]);
          float pointc = C1[j];
          float facec = (edgec + (alpha-1)*pointc)/alpha;
          C2[j] = (unsigned char)(0.5f*(facec + C2[j]));
          }

//         tet_colors[3*segment1[0] + 0] = 0;
//         tet_colors[3*segment1[0] + 1] = 255;
//         tet_colors[3*segment1[0] + 2] = 0;
//         tet_colors[3*segment1[1] + 0] = 0;
//         tet_colors[3*segment1[1] + 1] = 255;
//         tet_colors[3*segment1[1] + 2] = 0;
//         tet_colors[3*segment2[0] + 0] = 0;
//         tet_colors[3*segment2[0] + 1] = 255;
//         tet_colors[3*segment2[0] + 2] = 0;
//         tet_colors[3*segment2[1] + 0] = 0;
//         tet_colors[3*segment2[1] + 1] = 255;
//         tet_colors[3*segment2[1] + 2] = 0;

        // Fix opacity at thick point.  Average opacity with opacity of
        // opposite face.
        float edgea = T3[0] + beta*(T4[0]-T3[0]);
        float pointa = T1[0];
        float facea = (edgea + (alpha-1)*pointa)/alpha;
        T2[0] = 0.5f*(facea + T2[0]);

        // Record thickness at thick point.
        T2[1] = depth/this->MaxCellSize;

        // Establish the order in which the points should be rendered.
        unsigned char gl_indices[5];
        gl_indices[0] = segment1[1];
        gl_indices[1] = segment1[0];
        gl_indices[2] = segment2[0];
        gl_indices[3] = segment2[1];
        gl_indices[4] = segment1[0];

        // Render
        glDrawElements(GL_TRIANGLE_FAN, 5, GL_UNSIGNED_BYTE, gl_indices);
        }
      }
    numcellsrendered += num_cell_ids;
    }

  // Restore OpenGL state.
  glMatrixMode(GL_PROJECTION);
  glLoadMatrixf(projection_mat);
  glMatrixMode(GL_MODELVIEW);
  glLoadMatrixf(modelview_mat);

  glDisableClientState(GL_VERTEX_ARRAY);
  glDisableClientState(GL_COLOR_ARRAY);
  glDisableClientState(GL_TEXTURE_COORD_ARRAY);

  glBlendFunc(GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA);

  glBindTexture(GL_TEXTURE_2D, 0);
  glDisable(GL_TEXTURE_2D);

  glDepthMask(GL_TRUE);
  glEnable(GL_LIGHTING);

  this->UpdateProgress(1.0);
}
