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ImathBoxAlgo.h

///////////////////////////////////////////////////////////////////////////
//
// Copyright (c) 2002, Industrial Light & Magic, a division of Lucas
// Digital Ltd. LLC
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// its contributors may be used to endorse or promote products derived
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///////////////////////////////////////////////////////////////////////////



#ifndef INCLUDED_IMATHBOXALGO_H
#define INCLUDED_IMATHBOXALGO_H


//---------------------------------------------------------------------------
//
//    This file contains algorithms applied to or in conjunction
//    with bounding boxes (Imath::Box). These algorithms require
//    more headers to compile. The assumption made is that these
//    functions are called much less often than the basic box
//    functions or these functions require more support classes.
//
//    Contains:
//
//    T clip<T>(const T& in, const Box<T>& box)
//
//    Vec3<T> closestPointOnBox(const Vec3<T>&, const Box<Vec3<T>>& )
//
//    Vec3<T> closestPointInBox(const Vec3<T>&, const Box<Vec3<T>>& )
//
//    void transform(Box<Vec3<T>>&, const Matrix44<T>&)
//
//    bool findEntryAndExitPoints(const Line<T> &line,
//                          const Box< Vec3<T> > &box,
//                          Vec3<T> &enterPoint,
//                          Vec3<T> &exitPoint)
//
//    bool intersects(const Box<Vec3<T>> &box, 
//                const Line3<T> &line, 
//                Vec3<T> result)
//
//    bool intersects(const Box<Vec3<T>> &box, const Line3<T> &line)
//
//---------------------------------------------------------------------------

#include <ImathBox.h>
#include <ImathMatrix.h>
#include <ImathLineAlgo.h>
#include <ImathPlane.h>

namespace Imath {


template <class T>
inline T clip(const T& in, const Box<T>& box)
{
    //
    //      Clip a point so that it lies inside the given bbox
    //

    T out;

    for (int i=0; i<(int)box.min.dimensions(); i++)
    {
      if (in[i] < box.min[i]) out[i] = box.min[i];
      else if (in[i] > box.max[i]) out[i] = box.max[i];
      else out[i] = in[i];
    }

    return out;
}


//
// Return p if p is inside the box.
//
 
template <class T>
Vec3<T> 
closestPointInBox(const Vec3<T>& p, const Box< Vec3<T> >& box )
{
    Imath::V3f b;

    if (p.x < box.min.x)
      b.x = box.min.x;
    else if (p.x > box.max.x)
      b.x = box.max.x;
    else
      b.x = p.x;

    if (p.y < box.min.y)
      b.y = box.min.y;
    else if (p.y > box.max.y)
      b.y = box.max.y;
    else
      b.y = p.y;

    if (p.z < box.min.z)
      b.z = box.min.z;
    else if (p.z > box.max.z)
      b.z = box.max.z;
    else
      b.z = p.z;

    return b;
}

template <class T>
Vec3<T> closestPointOnBox(const Vec3<T>& pt, const Box< Vec3<T> >& box )
{
    //
    //      This sucker is specialized to work with a Vec3f and a box
    //      made of Vec3fs. 
    //

    Vec3<T> result;
    
    // trivial cases first
    if (box.isEmpty())
      return pt;
    else if (pt == box.center()) 
    {
      // middle of z side
      result[0] = (box.max[0] + box.min[0])/2.0;
      result[1] = (box.max[1] + box.min[1])/2.0;
      result[2] = box.max[2];
    }
    else 
    {
      // Find the closest point on a unit box (from -1 to 1),
      // then scale up.

      // Find the vector from center to the point, then scale
      // to a unit box.
      Vec3<T> vec = pt - box.center();
      T sizeX = box.max[0]-box.min[0];
      T sizeY = box.max[1]-box.min[1];
      T sizeZ = box.max[2]-box.min[2];

      T halfX = sizeX/2.0;
      T halfY = sizeY/2.0;
      T halfZ = sizeZ/2.0;
      if (halfX > 0.0)
          vec[0] /= halfX;
      if (halfY > 0.0)
          vec[1] /= halfY;
      if (halfZ > 0.0)
          vec[2] /= halfZ;

      // Side to snap side that has greatest magnitude in the vector.
      Vec3<T> mag;
      mag[0] = fabs(vec[0]);
      mag[1] = fabs(vec[1]);
      mag[2] = fabs(vec[2]);

      result = mag;

      // Check if beyond corners
      if (result[0] > 1.0)
          result[0] = 1.0;
      if (result[1] > 1.0)
          result[1] = 1.0;
      if (result[2] > 1.0)
          result[2] = 1.0;

      // snap to appropriate side       
      if ((mag[0] > mag[1]) && (mag[0] >  mag[2])) 
        {
          result[0] = 1.0;
      }
      else if ((mag[1] > mag[0]) && (mag[1] >  mag[2])) 
        {
          result[1] = 1.0;
      }
      else if ((mag[2] > mag[0]) && (mag[2] >  mag[1])) 
        {
          result[2] = 1.0;
      }
      else if ((mag[0] == mag[1]) && (mag[0] == mag[2])) 
        {
          // corner
          result = Vec3<T>(1,1,1);
      }
      else if (mag[0] == mag[1]) 
        {
          // edge parallel with z
          result[0] = 1.0;
          result[1] = 1.0;
      }
      else if (mag[0] == mag[2]) 
        {
          // edge parallel with y
          result[0] = 1.0;
          result[2] = 1.0;
      }
      else if (mag[1] == mag[2]) 
        {
          // edge parallel with x
          result[1] = 1.0;
          result[2] = 1.0;
      }

      // Now make everything point the right way
      for (int i=0; i < 3; i++)
        {
          if (vec[i] < 0.0)
            result[i] = -result[i];
        }

      // scale back up and move to center
      result[0] *= halfX;
      result[1] *= halfY;
      result[2] *= halfZ;

      result += box.center();
    }
    return result;
}

template <class S, class T>
Box< Vec3<S> >
transform(const Box< Vec3<S> >& box, const Matrix44<T>& m)
{
    // Transforms Box3f by matrix, enlarging Box3f to contain result.
    // Clever method courtesy of Graphics Gems, pp. 548-550
    //
    // This works for projection matrices as well as simple affine
    // transformations.  Coordinates of the box are rehomogenized if there
    // is a projection matrix

    // a transformed empty box is still empty
    if (box.isEmpty())
      return box;

    // If the last column is close enuf to ( 0 0 0 1 ) then we use the
    // fast, affine version.  The tricky affine method could maybe be
    // extended to deal with the projection case as well, but its not
    // worth it right now.

    if (m[0][3] * m[0][3] + m[1][3] * m[1][3] + m[2][3] * m[2][3]
      + (1.0 - m[3][3]) * (1.0 - m[3][3]) < 0.00001) 
    {
      // Affine version, use the Graphics Gems hack
      int         i, j;
      Box< Vec3<S> >  newBox;

      for (i = 0; i < 3; i++) 
        {
          newBox.min[i] = newBox.max[i] = (S) m[3][i];

          for (j = 0; j < 3; j++) 
            {
            float a, b;

            a = (S) m[j][i] * box.min[j];
            b = (S) m[j][i] * box.max[j];

            if (a < b) 
                {
                newBox.min[i] += a;
                newBox.max[i] += b;
            }
            else 
                {
                newBox.min[i] += b;
                newBox.max[i] += a;
            }
          }
      }

      return newBox;
    }

    // This is a projection matrix.  Do things the naive way.
    Vec3<S> points[8];

    /* Set up the eight points at the corners of the extent */
    points[0][0] = points[1][0] = points[2][0] = points[3][0] = box.min[0];
    points[4][0] = points[5][0] = points[6][0] = points[7][0] = box.max[0];

    points[0][1] = points[1][1] = points[4][1] = points[5][1] = box.min[1];
    points[2][1] = points[3][1] = points[6][1] = points[7][1] = box.max[1];

    points[0][2] = points[2][2] = points[4][2] = points[6][2] = box.min[2];
    points[1][2] = points[3][2] = points[5][2] = points[7][2] = box.max[2];

    Box< Vec3<S> > newBox;
    for (int i = 0; i < 8; i++) 
      newBox.extendBy(points[i] * m);

    return newBox;
}

template <class T>
Box< Vec3<T> >
affineTransform(const Box< Vec3<T> > &bbox, const Matrix44<T> &M)
{
    float       min0, max0, min1, max1, min2, max2, a, b;
    float       min0new, max0new, min1new, max1new, min2new, max2new;

    min0 = bbox.min[0];
    max0 = bbox.max[0];
    min1 = bbox.min[1];
    max1 = bbox.max[1];
    min2 = bbox.min[2];
    max2 = bbox.max[2];

    min0new = max0new = M[3][0];
    a = M[0][0] * min0;
    b = M[0][0] * max0;
    if (a < b) {
        min0new += a;
        max0new += b;
    } else {
        min0new += b;
        max0new += a;
    }
    a = M[1][0] * min1;
    b = M[1][0] * max1;
    if (a < b) {
        min0new += a;
        max0new += b;
    } else {
        min0new += b;
        max0new += a;
    }
    a = M[2][0] * min2;
    b = M[2][0] * max2;
    if (a < b) {
        min0new += a;
        max0new += b;
    } else {
        min0new += b;
        max0new += a;
    }

    min1new = max1new = M[3][1];
    a = M[0][1] * min0;
    b = M[0][1] * max0;
    if (a < b) {
        min1new += a;
        max1new += b;
    } else {
        min1new += b;
        max1new += a;
    }
    a = M[1][1] * min1;
    b = M[1][1] * max1;
    if (a < b) {
        min1new += a;
        max1new += b;
    } else {
        min1new += b;
        max1new += a;
    }
    a = M[2][1] * min2;
    b = M[2][1] * max2;
    if (a < b) {
        min1new += a;
        max1new += b;
    } else {
        min1new += b;
        max1new += a;
    }

    min2new = max2new = M[3][2];
    a = M[0][2] * min0;
    b = M[0][2] * max0;
    if (a < b) {
        min2new += a;
        max2new += b;
    } else {
        min2new += b;
        max2new += a;
    }
    a = M[1][2] * min1;
    b = M[1][2] * max1;
    if (a < b) {
        min2new += a;
        max2new += b;
    } else {
        min2new += b;
        max2new += a;
    }
    a = M[2][2] * min2;
    b = M[2][2] * max2;
    if (a < b) {
        min2new += a;
        max2new += b;
    } else {
        min2new += b;
        max2new += a;
    }

    Box< Vec3<T> > xbbox;

    xbbox.min[0] = min0new;
    xbbox.max[0] = max0new;
    xbbox.min[1] = min1new;
    xbbox.max[1] = max1new;
    xbbox.min[2] = min2new;
    xbbox.max[2] = max2new;

    return xbbox;
}


template <class T>
bool findEntryAndExitPoints(const Line3<T>& line,
                      const Box<Vec3<T> >& box,
                      Vec3<T> &enterPoint,
                      Vec3<T> &exitPoint)
{
    if ( box.isEmpty() ) return false;
    if ( line.distanceTo(box.center()) > box.size().length()/2. ) return false;

    Vec3<T> points[8], inter, bary;
    Plane3<T>     plane;
    int           i, v0, v1, v2;
    bool    front = false, valid, validIntersection = false;

    // set up the eight coords of the corners of the box
    for(i = 0; i < 8; i++) 
    {
      points[i].setValue( i & 01 ? box.min[0] : box.max[0],
                      i & 02 ? box.min[1] : box.max[1],
                      i & 04 ? box.min[2] : box.max[2]);
    }

    // intersect the 12 triangles.
    for(i = 0; i < 12; i++) 
    {
      switch(i) 
        {
      case  0: v0 = 2; v1 = 1; v2 = 0; break;         // +z
      case  1: v0 = 2; v1 = 3; v2 = 1; break;

      case  2: v0 = 4; v1 = 5; v2 = 6; break;         // -z
      case  3: v0 = 6; v1 = 5; v2 = 7; break;

      case  4: v0 = 0; v1 = 6; v2 = 2; break;         // -x
      case  5: v0 = 0; v1 = 4; v2 = 6; break;

      case  6: v0 = 1; v1 = 3; v2 = 7; break;         // +x
      case  7: v0 = 1; v1 = 7; v2 = 5; break;

      case  8: v0 = 1; v1 = 4; v2 = 0; break;         // -y
      case  9: v0 = 1; v1 = 5; v2 = 4; break;

      case 10: v0 = 2; v1 = 7; v2 = 3; break;         // +y
      case 11: v0 = 2; v1 = 6; v2 = 7; break;
      }
      if((valid=intersect (line, points[v0], points[v1], points[v2],
                             inter, bary, front)) == true) 
        {
          if(front == true) 
            {
            enterPoint = inter;
            validIntersection = valid;
          }
          else 
            {
            exitPoint = inter;
            validIntersection = valid;
          }
      }
    }
    return validIntersection;
}

template<class T>
bool intersects(const Box< Vec3<T> > &box, 
            const Line3<T> &line,
            Vec3<T> &result)
{
    /* 
       Fast Ray-Box Intersection
       by Andrew Woo
       from "Graphics Gems", Academic Press, 1990
    */

    const int right     = 0;
    const int left      = 1;
    const int middle    = 2;

    const Vec3<T> &minB = box.min;
    const Vec3<T> &maxB = box.max;
    const Vec3<T> &origin = line.pos;
    const Vec3<T> &dir = line.dir;

    bool inside = true;
    char quadrant[3];
    int whichPlane;
    float maxT[3];
    float candidatePlane[3];

    /* Find candidate planes; this loop can be avoided if
      rays cast all from the eye(assume perpsective view) */
    for (int i=0; i<3; i++)
    {
      if(origin[i] < minB[i]) 
      {
          quadrant[i] = left;
          candidatePlane[i] = minB[i];
          inside = false;
      }
      else if (origin[i] > maxB[i]) 
      {
          quadrant[i] = right;
          candidatePlane[i] = maxB[i];
          inside = false;
      }
      else  
      {
          quadrant[i] = middle;
      }
    }

    /* Ray origin inside bounding box */
    if ( inside ) 
    {
      result = origin;
      return true;
    }


      /* Calculate T distances to candidate planes */
    for (int i = 0; i < 3; i++)
    {
      if (quadrant[i] != middle && dir[i] !=0.)
      {
          maxT[i] = (candidatePlane[i]-origin[i]) / dir[i];
      }
      else
      {
          maxT[i] = -1.;
      }
    }

    /* Get largest of the maxT's for final choice of intersection */
    whichPlane = 0;

    for (int i = 1; i < 3; i++)
    {
      if (maxT[whichPlane] < maxT[i])
      {
          whichPlane = i;
      }
    }

    /* Check final candidate actually inside box */
    if (maxT[whichPlane] < 0.) return false;

    for (int i = 0; i < 3; i++)
    {
      if (whichPlane != i) 
      {
          result[i] = origin[i] + maxT[whichPlane] *dir[i];

          if ((quadrant[i] == right && result[i] < minB[i]) ||
            (quadrant[i] == left && result[i] > maxB[i]))
          {
            return false;     /* outside box */
          }
      }
      else 
      {
          result[i] = candidatePlane[i];
      }
    }

    return true;
}

template<class T>
bool intersects(const Box< Vec3<T> > &box, const Line3<T> &line)
{
    Vec3<T> ignored;
    return intersects(box,line,ignored);
}


} // namespace Imath

#endif

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