al_Frustum.hpp

#ifndef INCLUDE_AL_FRUSTUM_HPP
#define INCLUDE_AL_FRUSTUM_HPP
 
/*  Allocore --
  Multimedia / virtual environment application class library
 
  Copyright (C) 2009. AlloSphere Research Group, Media Arts & Technology, UCSB.
  Copyright (C) 2012. The Regents of the University of California.
  All rights reserved.
 
  Redistribution and use in source and binary forms, with or without
  modification, are permitted provided that the following conditions are met:
 
    Redistributions of source code must retain the above copyright notice,
    this list of conditions and the following disclaimer.
 
    Redistributions in binary form must reproduce the above copyright
    notice, this list of conditions and the following disclaimer in the
    documentation and/or other materials provided with the distribution.
 
    Neither the name of the University of California nor the names of its
    contributors may be used to endorse or promote products derived from
    this software without specific prior written permission.
 
  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
  AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
  ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
  LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
  CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
  SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
  INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
  CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
  ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
  POSSIBILITY OF SUCH DAMAGE.
 
 
  File description:
  This is a rectangular frustum useful for computer graphics
 
  File author(s):
  Lance Putnam, 2011, putnam.lance@gmail.com
*/
 
#include "al/math/al_Plane.hpp"
#include "al/math/al_Vec.hpp"
 
namespace al {
 
template <class T>
class Frustum;
typedef Frustum<double> Frustumd;  
 
 
template <class T>
class Frustum {
 public:
  enum { TOP = 0, BOTTOM, LEFT, RIGHT, NEARP, FARP };
  enum { OUTSIDE = 0, INTERSECT, INSIDE };
 
  Vec<3, T> ntl, ntr, nbl, nbr, ftl, ftr, fbl, fbr;  
  Plane<T> pl[6];                                    
 
  const Vec<3, T>& corner(int i) const { return (&ntl)[i]; }
 
  const Vec<3, T>& corner(int i0, int i1, int i2) const {
    return corner(i2 << 2 | i1 << 1 | i0);
  }
 
  template <class U>
  Vec<3, T> getPoint(const Vec<3, U>& frac) const {
    return lerp(frac[2],
                lerp(frac[1], lerp(frac[0], corner(0, 0, 0), corner(1, 0, 0)),
                     lerp(frac[0], corner(0, 1, 0), corner(1, 1, 0))),
                lerp(frac[1], lerp(frac[0], corner(0, 0, 1), corner(1, 0, 1)),
                     lerp(frac[0], corner(0, 1, 1), corner(1, 1, 1))));
  }
 
  template <class U>
  Vec<3, T> getPoint(const U& fracx, const U& fracy, const U& fracz) const {
    return getPoint(Vec<3, U>(fracx, fracy, fracz));
  }
 
  int testPoint(const Vec<3, T>& p) const;
 
  int testSphere(const Vec<3, T>& center, float radius) const;
 
 
  int testBox(const Vec<3, T>& xyz, const Vec<3, T>& dim) const;
 
  template <class V>
  void boundingBox(Vec<3, V>& xyz, Vec<3, V>& dim) const;
 
  Vec<3, T> center() const {
    return (ntl + ntr + nbl + nbr + ftl + ftr + fbl + fbr) * 0.125;
  }
 
 
  void computePlanes();
 
 private:
  template <class Tf, class Tv>
  static Tv lerp(Tf f, const Tv& x, const Tv& y) {
    return (y - x) * f + x;
  }
};
 
template <class T>
template <class V>
void Frustum<T>::boundingBox(Vec<3, V>& xyz, Vec<3, V>& dim) const {
  Vec<3, T> vmin = corner(0);
  Vec<3, T> vmax = vmin;
 
  for (int i = 1; i < 8; ++i) {
    Vec<3, T> v = corner(i);
    vmin = min(vmin, v);
    vmax = max(vmax, v);
  }
 
  xyz = vmin;
  dim = vmax - vmin;
}
 
template <class T>
void Frustum<T>::computePlanes() {
  pl[TOP].from3Points(ntr, ntl, ftl);
  pl[BOTTOM].from3Points(nbl, nbr, fbr);
  pl[LEFT].from3Points(ntl, nbl, fbl);
  pl[RIGHT].from3Points(nbr, ntr, fbr);
  pl[NEARP].from3Points(ntl, ntr, nbr);
  pl[FARP].from3Points(ftr, ftl, fbl);
}
 
template <class T>
int Frustum<T>::testPoint(const Vec<3, T>& p) const {
  for (int i = 0; i < 6; ++i) {
    if (pl[i].inNegativeSpace(p)) return OUTSIDE;
  }
  return INSIDE;
}
 
template <class T>
int Frustum<T>::testSphere(const Vec<3, T>& c, float r) const {
  int result = INSIDE;
  for (int i = 0; i < 6; ++i) {
    float distance = pl[i].distance(c);
    if (distance < -r)
      return OUTSIDE;
    else if (distance < r)
      result = INTERSECT;
  }
  return result;
}
 
template <class T>
int Frustum<T>::testBox(const Vec<3, T>& xyz, const Vec<3, T>& dim) const {
  int result = INSIDE;
  for (int i = 0; i < 6; ++i) {
    const Vec3d& plNrm = pl[i].normal();
 
    /*
        The positive vertex is the vertex from the box that is further along
        the normal's direction. The negative vertex is the opposite vertex.
 
        If the p-vertex is on the wrong side of the plane, the box can be
        immediately rejected, as it falls completely outside the frustum. On the
        other hand, if the p-vertex is on the right side of the plane, then
        testing the whereabouts of the n-vertex tells if the box is totally on
        the right side of the plane, or if the box intersects the plane.
    */
    // Is positive vertex outside?
    Vec<3, T> vp = xyz;
    if (plNrm[0] > 0) vp[0] += dim[0];
    if (plNrm[1] > 0) vp[1] += dim[1];
    if (plNrm[2] > 0) vp[2] += dim[2];
    if (pl[i].inNegativeSpace(vp)) return OUTSIDE;
 
    // Is negative vertex outside?
    Vec<3, T> vn = xyz;
    if (plNrm[0] < 0) vn[0] += dim[0];
    if (plNrm[1] < 0) vn[1] += dim[1];
    if (plNrm[2] < 0) vn[2] += dim[2];
    if (pl[i].inNegativeSpace(vn)) result = INTERSECT;
  }
  return result;
}
 
}  // namespace al
 
#endif