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

  Program:   Visualization Toolkit
  Module:    vtkBox.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 "vtkBox.h"
#include "vtkBoundingBox.h"
#include "vtkMath.h"
#include "vtkObjectFactory.h"
#include "vtkPlane.h"

#include <algorithm> // for sorting
#include <cassert>
#include <limits> // for IntersectWithInfiniteLine
#include <vector> // for IntersectWithPlane

vtkStandardNewMacro(vtkBox);

// Construct the box centered at the origin and each side length 1.0.
//------------------------------------------------------------------------------
vtkBox::vtkBox()
{
  this->BBox = new vtkBoundingBox;
}

//------------------------------------------------------------------------------
// Destroy the bounding box
vtkBox::~vtkBox()
{
  delete this->BBox;
}

//------------------------------------------------------------------------------
// Set the bounds in various ways
void vtkBox::SetBounds(double xMin, double xMax, double yMin, double yMax, double zMin, double zMax)
{
  const double* minP = this->BBox->GetMinPoint();
  const double* maxP = this->BBox->GetMaxPoint();
  if ((minP[0] == xMin) && (maxP[0] == xMax) && (minP[1] == yMin) && (maxP[1] == yMax) &&
    (minP[2] == zMin) && (maxP[2] == zMax))
  {
    return;
  }
  this->BBox->SetBounds(xMin, xMax, yMin, yMax, zMin, zMax);
  this->Modified();
}

//------------------------------------------------------------------------------
void vtkBox::SetBounds(const double bounds[6])
{
  this->SetBounds(bounds[0], bounds[1], bounds[2], bounds[3], bounds[4], bounds[5]);
}

//------------------------------------------------------------------------------
void vtkBox::SetXMin(double x, double y, double z)
{
  vtkDebugMacro(<< this->GetClassName() << " (" << this << "): setting XMin to (" << x << "," << y
                << "," << z << ")");
  const double* p = this->BBox->GetMinPoint();
  if ((p[0] == x) && (p[1] == y) && (p[2] == z))
  {
    return;
  }
  this->BBox->SetMinPoint(x, y, z);
  this->Modified();
}

//------------------------------------------------------------------------------
void vtkBox::SetXMax(double x, double y, double z)
{
  vtkDebugMacro(<< this->GetClassName() << " (" << this << "): setting XMax to (" << x << "," << y
                << "," << z << ")");
  const double* p = this->BBox->GetMaxPoint();
  if ((p[0] == x) && (p[1] == y) && (p[2] == z))
  {
    return;
  }
  this->BBox->SetMaxPoint(x, y, z);
  this->Modified();
}

//------------------------------------------------------------------------------
void vtkBox::GetBounds(
  double& xMin, double& xMax, double& yMin, double& yMax, double& zMin, double& zMax)
{
  this->BBox->GetBounds(xMin, xMax, yMin, yMax, zMin, zMax);
}

//------------------------------------------------------------------------------
void vtkBox::GetBounds(double bounds[6])
{
  this->BBox->GetBounds(bounds);
}

//------------------------------------------------------------------------------
double* vtkBox::GetBounds()
{
  this->BBox->GetBounds(this->Bounds);
  return this->Bounds;
}

//------------------------------------------------------------------------------
void vtkBox::AddBounds(const double bounds[6])
{
  vtkBoundingBox bbox(*(this->BBox));
  this->BBox->AddBounds(bounds);
  // If the unioned bounding has changed called modified
  if ((*this->BBox) != bbox)
  {
    this->Modified();
  }
}

//------------------------------------------------------------------------------
// Evaluate box equation. This differs from the similar vtkPlanes
// (with six planes) because of the "rounded" nature of the corners.
double vtkBox::EvaluateFunction(double x[3])
{
  double diff, dist, minDistance = (-VTK_DOUBLE_MAX), t, distance = 0.0;
  int inside = 1;
  const double* minP = this->BBox->GetMinPoint();
  const double* maxP = this->BBox->GetMaxPoint();

  for (int i = 0; i < 3; i++)
  {
    diff = this->BBox->GetLength(i);
    if (diff != 0.0)
    {
      t = (x[i] - minP[i]) / diff;
      if (t < 0.0)
      {
        inside = 0;
        dist = minP[i] - x[i];
      }
      else if (t > 1.0)
      {
        inside = 0;
        dist = x[i] - maxP[i];
      }
      else
      { // want negative distance, we are inside
        if (t <= 0.5)
        {
          dist = minP[i] - x[i];
        }
        else
        {
          dist = x[i] - maxP[i];
        }
        if (dist > minDistance) // remember, it's negative
        {
          minDistance = dist;
        }
      } // if inside
    }
    else
    {
      dist = fabs(x[i] - minP[i]);
      if (dist > 0.0)
      {
        inside = 0;
      }
    }
    if (dist > 0.0)
    {
      distance += dist * dist;
    }
  } // for all coordinate directions

  distance = sqrt(distance);
  if (inside)
  {
    return minDistance;
  }
  else
  {
    return distance;
  }
}

//------------------------------------------------------------------------------
// Evaluate box gradient.
void vtkBox::EvaluateGradient(double x[3], double n[3])
{
  int i, loc[3], minAxis = 0;
  double dist, minDist = VTK_DOUBLE_MAX, center[3];
  double inDir[3], outDir[3];
  const double* minP = this->BBox->GetMinPoint();
  const double* maxP = this->BBox->GetMaxPoint();

  // Compute the location of the point with respect to the box.
  // Ultimately the point will lie in one of 27 separate regions around
  // or within the box. The gradient vector is computed differently in
  // each of the regions.
  inDir[0] = inDir[1] = inDir[2] = 0.0;
  outDir[0] = outDir[1] = outDir[2] = 0.0;
  this->BBox->GetCenter(center);
  for (i = 0; i < 3; i++)
  {
    if (x[i] < minP[i])
    {
      loc[i] = 0;
      outDir[i] = -1.0;
    }
    else if (x[i] > maxP[i])
    {
      loc[i] = 2;
      outDir[i] = 1.0;
    }
    else
    {
      loc[i] = 1;
      if (x[i] <= center[i])
      {
        dist = x[i] - minP[i];
        inDir[i] = -1.0;
      }
      else
      {
        dist = maxP[i] - x[i];
        inDir[i] = 1.0;
      }
      if (dist < minDist) // remember, it's negative
      {
        minDist = dist;
        minAxis = i;
      }
    } // if inside
  }   // for all coordinate directions

  int indx = loc[0] + 3 * loc[1] + 9 * loc[2];

  switch (indx)
  {
    // verts - gradient points away from center point
    case 0:
    case 2:
    case 6:
    case 8:
    case 18:
    case 20:
    case 24:
    case 26:
      for (i = 0; i < 3; i++)
      {
        n[i] = x[i] - center[i];
      }
      vtkMath::Normalize(n);
      break;

    // edges - gradient points out from axis of cube
    case 1:
    case 3:
    case 5:
    case 7:
    case 9:
    case 11:
    case 15:
    case 17:
    case 19:
    case 21:
    case 23:
    case 25:
      for (i = 0; i < 3; i++)
      {
        if (outDir[i] != 0.0)
        {
          n[i] = x[i] - center[i];
        }
        else
        {
          n[i] = 0.0;
        }
      }
      vtkMath::Normalize(n);
      break;

    // faces - gradient points perpendicular to face
    case 4:
    case 10:
    case 12:
    case 14:
    case 16:
    case 22:
      for (i = 0; i < 3; i++)
      {
        n[i] = outDir[i];
      }
      break;

    // interior - gradient is perpendicular to closest face
    case 13:
      n[0] = n[1] = n[2] = 0.0;
      n[minAxis] = inDir[minAxis];
      break;
    default:
      assert("check: impossible case." && 0); // reaching this line is a bug.
      break;
  }
}

#define VTK_RIGHT 0
#define VTK_LEFT 1
#define VTK_MIDDLE 2

//------------------------------------------------------------------------------
// Bounding box intersection modified from Graphics Gems Vol I. The method
// returns a non-zero value if the bounding box is hit. Origin[3] starts
// the ray, dir[3] is the vector components of the ray in the x-y-z
// directions, coord[3] is the location of hit, and t is the parametric
// coordinate along line. (Notes: the intersection ray dir[3] is NOT
// normalized.  Valid intersections will only occur between 0<=t<=1.)
char vtkBox::IntersectBox(const double bounds[6], const double origin[3], const double dir[3],
  double coord[3], double& t, const double tolerance)
{
  bool inside = true;
  char quadrant[3];
  int i, whichPlane = 0;
  double maxT[3], candidatePlane[3];

  // Make sure tolerance is non-zero
  double tol = (tolerance <= 0 ? FLT_EPSILON : tolerance);

  // Make sure bounds are not degenerate (i.e., have positive volume); pad by
  // tolerance if it is.
  double bds[6];
  for (i = 0; i < 3; ++i)
  {
    if ((bounds[2 * i + 1] - bounds[2 * i]) > 0)
    {
      bds[2 * i] = bounds[2 * i];
      bds[2 * i + 1] = bounds[2 * i + 1];
    }
    else
    {
      bds[2 * i] = bounds[2 * i] - tol;
      bds[2 * i + 1] = bounds[2 * i + 1] + tol;
    }
  }

  //  First find closest planes
  //
  for (i = 0; i < 3; i++)
  {
    if (origin[i] < bds[2 * i])
    {
      quadrant[i] = VTK_LEFT;
      candidatePlane[i] = bds[2 * i];
      inside = false;
    }
    else if (origin[i] > bds[2 * i + 1])
    {
      quadrant[i] = VTK_RIGHT;
      candidatePlane[i] = bds[2 * i + 1];
      inside = false;
    }
    else
    {
      quadrant[i] = VTK_MIDDLE;
    }
  }

  //  Check whether origin of ray is inside bbox
  //
  if (inside)
  {
    coord[0] = origin[0];
    coord[1] = origin[1];
    coord[2] = origin[2];
    t = 0;
    return 1;
  }

  //  Calculate parametric distances to plane
  //
  for (i = 0; i < 3; i++)
  {
    if (quadrant[i] != VTK_MIDDLE && dir[i] != 0.0)
    {
      maxT[i] = (candidatePlane[i] - origin[i]) / dir[i];
    }
    else
    {
      maxT[i] = -1.0;
    }
  }

  //  Find the largest parametric value of intersection
  //
  for (i = 0; i < 3; i++)
  {
    if (maxT[whichPlane] < maxT[i])
    {
      whichPlane = i;
    }
  }

  //  Check for valid intersection along line
  //
  if (maxT[whichPlane] > 1.0 || maxT[whichPlane] < 0.0)
  {
    return 0;
  }
  else
  {
    t = maxT[whichPlane];
  }

  //  Intersection point along line is okay.  Check bbox.
  //
  for (i = 0; i < 3; i++)
  {
    if (whichPlane != i)
    {
      coord[i] = origin[i] + maxT[whichPlane] * dir[i];
      if ((coord[i] < bds[2 * i] - tol) || (coord[i] > bds[2 * i + 1] + tol))
      {
        return 0;
      }
    }
    else
    {
      coord[i] = candidatePlane[i];
    }
  }

  return 1;
}
#undef VTK_RIGHT
#undef VTK_LEFT
#undef VTK_MIDDLE

//------------------------------------------------------------------------------
// Bounding box intersection code from David Gobbi.  Go through the
// bounding planes one at a time and compute the parametric coordinate
// of each intersection.
int vtkBox::IntersectWithLine(const double bounds[6], const double p1[3], const double p2[3],
  double& t1, double& t2, double x1[3], double x2[3], int& plane1, int& plane2)
{
  plane1 = -1;
  plane2 = -1;
  t1 = 0.0;
  t2 = 1.0;

  for (int j = 0; j < 3; j++)
  {
    for (int k = 0; k < 2; k++)
    {
      // Compute distances of p1 and p2 from the plane along the plane normal
      int i = 2 * j + k;
      double d1 = (bounds[i] - p1[j]) * (1 - 2 * k);
      double d2 = (bounds[i] - p2[j]) * (1 - 2 * k);

      // If both distances are positive, both points are outside
      if (d1 > 0 && d2 > 0)
      {
        return 0;
      }
      // If one of the distances is positive, the line crosses the plane
      else if (d1 > 0 || d2 > 0)
      {
        // Compute fractional distance "t" of the crossing between p1 & p2
        double t = 0.0;
        if (d1 != 0)
        {
          t = d1 / (d1 - d2);
        }

        // If point p1 was clipped, adjust t1
        if (d1 > 0)
        {
          if (t >= t1)
          {
            t1 = t;
            plane1 = i;
          }
        }
        // else point p2 was clipped, so adjust t2
        else
        {
          if (t <= t2)
          {
            t2 = t;
            plane2 = i;
          }
        }

        // If this happens, there's no line left
        if (t1 > t2)
        {
          // Allow for planes that are coincident or slightly inverted
          if (plane1 < 0 || plane2 < 0 || (plane1 >> 1) != (plane2 >> 1))
          {
            return 0;
          }
        }
      }
    }
  }

  double* x = x1;
  double t = t1;
  int plane = plane1;

  for (int count = 0; count < 2; count++)
  {
    if (x)
    {
      for (int i = 0; i < 3; i++)
      {
        if (plane == 2 * i || plane == 2 * i + 1)
        {
          x[i] = bounds[plane];
        }
        else
        {
          x[i] = p1[i] * (1.0 - t) + p2[i] * t;
          if (x[i] < bounds[2 * i])
          {
            x[i] = bounds[2 * i];
          }
          if (x[i] > bounds[2 * i + 1])
          {
            x[i] = bounds[2 * i + 1];
          }
        }
      }
    }

    x = x2;
    t = t2;
    plane = plane2;
  }

  return 1;
}

//------------------------------------------------------------------------------
bool vtkBox::IntersectWithInfiniteLine(const double bounds[6], const double p1[3],
  const double p2[3], double& t1, double& t2, double x1[3], double x2[3], int& plane1, int& plane2)
{
  plane1 = -1;
  plane2 = -1;
  t1 = -std::numeric_limits<double>::infinity();
  t2 = std::numeric_limits<double>::infinity();

  for (int j = 0; j < 3; j++)
  {
    for (int k = 0; k < 2; k++)
    {
      // Compute distances of p1 and p2 from the plane along the plane normal
      int i = 2 * j + k;
      double t =
        std::abs(bounds[i] - p1[j]) < VTK_DBL_MIN ? 0.0 : (bounds[i] - p1[j]) / (p2[j] - p1[j]);
      double xface = p1[(j + 1) % 3] + t * (p2[(j + 1) % 3] - p1[(j + 1) % 3]),
             yface = p1[(j + 2) % 3] + t * (p2[(j + 2) % 3] - p1[(j + 2) % 3]);
      // if (xface, yface) is inside the current face
      if (xface >= bounds[(2 * j + 2) % 6] && xface <= bounds[(2 * j + 3) % 6] &&
        yface >= bounds[(2 * j + 4) % 6] && yface <= bounds[(2 * j + 5) % 6])
      {
        if (t1 == -std::numeric_limits<double>::infinity())
        {
          t1 = t;
          plane1 = 2 * j + k;
        }
        else if (t >= t1)
        {
          t2 = t;
          plane2 = 2 * j + k;
          break;
        }
        else
        {
          t2 = t1;
          t1 = t;
          plane2 = plane1;
          plane1 = 2 * j + k;
          break;
        }
      }
    }
  }

  if (x1)
  {
    x1[0] = p1[0] + t1 * (p2[0] - p1[0]);
    x1[1] = p1[1] + t1 * (p2[1] - p1[1]);
    x1[2] = p1[2] + t1 * (p2[2] - p1[2]);
  }
  if (x2)
  {
    x2[0] = p1[0] + t2 * (p2[0] - p1[0]);
    x2[1] = p1[1] + t2 * (p2[1] - p1[1]);
    x2[2] = p1[2] + t2 * (p2[2] - p1[2]);
  }

  return t1 != -std::numeric_limits<double>::infinity();
}

//------------------------------------------------------------------------------
vtkTypeBool vtkBox::IntersectWithPlane(double bounds[6], double origin[3], double normal[3])
{
  // Evaluate the eight points. If there is a sign change, then there is an
  // intersection.
  double p[3], d;
  int x, y, z, sign = 1, firstOne = 1;

  for (z = 4; z <= 5; ++z)
  {
    p[2] = bounds[z];
    for (y = 2; y <= 3; ++y)
    {
      p[1] = bounds[y];
      for (x = 0; x <= 1; ++x)
      {
        p[0] = bounds[x];
        d = vtkPlane::Evaluate(normal, origin, p);
        if (firstOne)
        {
          sign = (d >= 0 ? 1 : -1);
          firstOne = 0;
        }
        if (d == 0.0 || (sign > 0 && d < 0.0) || (sign < 0 && d > 0.0))
        {
          return 1;
        }
      } // x
    }   // y
  }     // z

  return 0; // no intersection
}

//------------------------------------------------------------------------------
// Support for IntersectWithPlane
namespace
{
struct IntPoint
{
  int Id;
  double T;
  IntPoint(int id, double t)
    : Id(id)
    , T(t)
  {
  }
};

bool IntPointCompare(const IntPoint& a, const IntPoint& b)
{
  return (a.T < b.T);
}

} // anonymous namespace

//------------------------------------------------------------------------------
// Return non-zero and generate polygon of intersection. Return 0 and there
// is no intersection. An ordered list of intersection points is returned in
// xout (ordered in the sense that they form a polygon). Note that the
// number of intersections ranges from [3,6]. The memory layout for xout[18]
// is consistent with the vtkPoints array and is organized as (xyz, xyz, xyz,
// xyz, xyz, xyz).
vtkTypeBool vtkBox::IntersectWithPlane(
  double bounds[6], double origin[3], double normal[3], double xout[18])
{
  // Intersect the twelve edges using a pseudo-contouring approach. Then
  // order the intersections to form a polygon.
  static int edges[12][2] = {
    { 0, 1 },
    { 2, 3 },
    { 4, 5 },
    { 6, 7 },
    { 0, 2 },
    { 1, 3 },
    { 4, 6 },
    { 5, 7 },
    { 0, 4 },
    { 1, 5 },
    { 2, 6 },
    { 3, 7 },
  };

  // Generating scalars is needed for performing intersections. Also populate
  // the box corner vertex coordinates,
  int x, y, z, vertNum, edgeNum, v0, v1;
  double n[3], xints[36], scalars[8], p[8][3];
  double s0, s1, t;

  // Make sure normal is non-zero and a unit vector
  n[0] = normal[0];
  n[1] = normal[1];
  n[2] = normal[2];
  if (vtkMath::Normalize(n) == 0.0)
  {
    return 0;
  }

  for (vertNum = 0, z = 4; z <= 5; ++z)
  {
    for (y = 2; y <= 3; ++y)
    {
      for (x = 0; x <= 1; ++x)
      {
        p[vertNum][0] = bounds[x];
        p[vertNum][1] = bounds[y];
        p[vertNum][2] = bounds[z];
        scalars[vertNum] = vtkPlane::Evaluate(n, origin, p[vertNum]);
        vertNum++;
      } // x
    }   // y
  }     // z

  // Intersect each of the twelve edges.
  int numInts = 0;
  for (edgeNum = 0; edgeNum < 12; ++edgeNum)
  {
    v0 = edges[edgeNum][0];
    v1 = edges[edgeNum][1];
    s0 = scalars[v0];
    s1 = scalars[v1];
    // Check for intersection
    if ((s0 < 0.0 && s1 >= 0.0) || (s0 >= 0.0 && s1 < 0.0))
    {
      t = -s0 / (s1 - s0);
      xints[3 * numInts] = p[v0][0] + t * (p[v1][0] - p[v0][0]);
      xints[3 * numInts + 1] = p[v0][1] + t * (p[v1][1] - p[v0][1]);
      xints[3 * numInts + 2] = p[v0][2] + t * (p[v1][2] - p[v0][2]);
      numInts++;
    }
  }

  // If no intersection or invalid intersection just return
  if (numInts < 3)
  {
    return 0;
  }

  // Now sort the intersection points. We do this sort even for triangles to
  // provide consistent ordering (direction) around the plane normal. Note
  // that anything less than three intesections is considered a
  // non-intersection. Create a local coordinate system (xV, yV, n) with the
  // normal out of the polygon plane.
  int i;
  double center[3], Vx[3], Vy[3], v[3], *xp, *xo, dx, dy;
  center[0] = 0.5 * (bounds[0] + bounds[1]);
  center[1] = 0.5 * (bounds[2] + bounds[3]);
  center[2] = 0.5 * (bounds[4] + bounds[5]);

  Vx[0] = xints[0] - center[0];
  Vx[1] = xints[1] - center[1];
  Vx[2] = xints[2] - center[2];
  vtkMath::Normalize(Vx);
  vtkMath::Cross(n, Vx, Vy);
  vtkMath::Normalize(Vy);

  // Now run around point computing angle [0,360) and then sort.
  std::vector<IntPoint> IntPoints;
  IntPoints.emplace_back(0, 0.0);

  for (i = 1; i < numInts; ++i)
  {
    xp = xints + 3 * i;
    v[0] = xp[0] - center[0];
    v[1] = xp[1] - center[1];
    v[2] = xp[2] - center[2];
    vtkMath::Normalize(v);
    dx = vtkMath::Dot(v, Vx);
    dy = vtkMath::Dot(v, Vy);
    t = atan2(dy, dx);
    t = (t >= 0 ? t : (2.0 * vtkMath::Pi() + t));
    IntPoints.emplace_back(i, t);
  }

  std::sort(IntPoints.begin(), IntPoints.end(), IntPointCompare);

  // Copy result of sort to output, merging coincident points.
  // (Merging points in parametric space.)
  int numOutInts = 0;
  std::vector<IntPoint>::iterator i0 = IntPoints.begin();
  std::vector<IntPoint>::iterator i1 = i0;
  while (i1 != IntPoints.end() && numOutInts < 6)
  {
    i = i0->Id;
    xp = xints + 3 * i;
    xo = xout + 3 * numOutInts;
    xo[0] = xp[0];
    xo[1] = xp[1];
    xo[2] = xp[2];
    ++numOutInts;
    do
    {
      ++i1;
    } while (i1 != IntPoints.end() && (i1->T - i0->T) < 0.001);
    i0 = i1;
  }

  return numOutInts;
}

//------------------------------------------------------------------------------
void vtkBox::PrintSelf(ostream& os, vtkIndent indent)
{
  this->Superclass::PrintSelf(os, indent);
  const double* minP = this->BBox->GetMinPoint();
  const double* maxP = this->BBox->GetMaxPoint();

  os << indent << "XMin: (" << minP[0] << ", " << minP[1] << ", " << minP[2] << ")\n";
  os << indent << "XMax: (" << maxP[0] << ", " << maxP[1] << ", " << maxP[2] << ")\n";
}
//------------------------------------------------------------------------------
void vtkBox::GetXMin(double p[3])
{
  this->BBox->GetMinPoint(p[0], p[1], p[2]);
}

//------------------------------------------------------------------------------
void vtkBox::GetXMin(double& x, double& y, double& z)
{
  this->BBox->GetMinPoint(x, y, z);
}

//------------------------------------------------------------------------------
void vtkBox::GetXMax(double p[3])
{
  this->BBox->GetMaxPoint(p[0], p[1], p[2]);
}

//------------------------------------------------------------------------------
void vtkBox::GetXMax(double& x, double& y, double& z)
{
  this->BBox->GetMaxPoint(x, y, z);
}

vtkTypeBool vtkBox::IsBoxInFrustum(double planes[24], double bounds[6])
{
  // 8 points that define the four quadrants.
  static const double factor[8][3] = { { 0.0, 0.0, 0.0 }, { 1.0, 0.0, 0.0 }, { 0.0, 1.0, 0.0 },
    { 1.0, 1.0, 0.0 }, { 0.0, 0.0, 1.0 }, { 1.0, 0.0, 1.0 }, { 0.0, 0.0, 1.0 }, { 1.0, 1.0, 1.0 } };

  // for each of the points check if it is in the frustum
  double size[3];
  size[0] = bounds[1] - bounds[0];
  size[1] = bounds[3] - bounds[2];
  size[2] = bounds[5] - bounds[4];

  // build and test the 8 points
  bool allNeg[6] = { true, true, true, true, true, true };

  // for each point
  for (int i = 0; i < 8; ++i)
  {
    double pt[3];
    pt[0] = bounds[0] + size[0] * factor[i][0];
    pt[1] = bounds[2] + size[1] * factor[i][1];
    pt[2] = bounds[4] + size[2] * factor[i][2];

    // for each plane
    bool allPos = true;
    for (int pj = 0; pj < 6; ++pj)
    {
      // eval the plane function
      double val = pt[0] * planes[pj * 4] + pt[1] * planes[pj * 4 + 1] +
        pt[2] * planes[pj * 4 + 2] + planes[pj * 4 + 3];
      // watch for all positive and all Negative conditions
      if (val < 0)
      {
        allPos = false;
      }
      else if (val > 0)
      {
        allNeg[pj] = false;
      }
    }

    // if any point is positive in all 6 planes then we are in the frustum
    if (allPos)
    {
      return true;
    }
  }

  // if any plane is negative for all 8 points we are not inside
  // e.g. all 8 points are on the far side of a given plane
  for (int l = 0; l < 6; ++l)
  {
    if (allNeg[l])
    {
      return false;
    }
  }

  // not sure so return true
  return true;
}