OpenGTA/math/obb.cpp

#ifndef GOMEZ_OBB_H
#define GOMEZ_OBB_H

/**
 * Taken from:
 * http://www.gamasutra.com/features/19990702/data_structures_01.htm
 * http://www.gamasutra.com/features/19991018/Gomez_1.htm
 *
 * Both by Miguel Gomez
 */

#include "obb.hpp"
#include "vector.hpp"

namespace GomezMath {

  //check if two oriented bounding boxes overlap
  const bool OBBOverlap (
      //A
      Vector & a,	//extents
      Vector & Pa,	//position
      Vector * A,	//orthonormal basis
      //B
      Vector & b,	//extents
      Vector & Pb,	//position
      Vector * B	//orthonormal basis
      )
  {
    //translation, in parent frame
    Vector v = Pb - Pa;
    //translation, in A's frame
    Vector T (v.dot (A[0]), v.dot (A[1]), v.dot (A[2]));
    //B's basis with respect to A's local frame
    Scalar R[3][3];
    float ra, rb, t;
    long i, k;
    //calculate rotation matrix
    for (i = 0; i < 3; i++)
      for (k = 0; k < 3; k++)
        R[i][k] = A[i].dot (B[k]);
    /*ALGORITHM: Use the separating axis test for all 15 potential 
      separating axes. If a separating axis could not be found, the two 
      boxes overlap. */
    //A's basis vectors
    for (i = 0; i < 3; i++)
    {
      ra = a[i];
      rb =
        b[0] * fabs (R[i][0]) + b[1] * fabs (R[i][1]) + b[2] * fabs (R[i][2]);
      t = fabs (T[i]);
      if (t > ra + rb)
        return false;
    }
    //B's basis vectors
    for (k = 0; k < 3; k++)
    {
      ra =
        a[0] * fabs (R[0][k]) + a[1] * fabs (R[1][k]) + a[2] * fabs (R[2][k]);
      rb = b[k];
      t = fabs (T[0] * R[0][k] + T[1] * R[1][k] + T[2] * R[2][k]);
      if (t > ra + rb)
        return false;
    }
    //9 cross products
    //L = A0 x B0
    ra = a[1] * fabs (R[2][0]) + a[2] * fabs (R[1][0]);
    rb = b[1] * fabs (R[0][2]) + b[2] * fabs (R[0][1]);
    t = fabs (T[2] * R[1][0] - T[1] * R[2][0]);
    if (t > ra + rb)
      return false;
    //L = A0 x B1
    ra = a[1] * fabs (R[2][1]) + a[2] * fabs (R[1][1]);
    rb = b[0] * fabs (R[0][2]) + b[2] * fabs (R[0][0]);
    t = fabs (T[2] * R[1][1] - T[1] * R[2][1]);
    if (t > ra + rb)
      return false;
    //L = A0 x B2
    ra = a[1] * fabs (R[2][2]) + a[2] * fabs (R[1][2]);
    rb = b[0] * fabs (R[0][1]) + b[1] * fabs (R[0][0]);
    t = fabs (T[2] * R[1][2] - T[1] * R[2][2]);
    if (t > ra + rb)
      return false;
    //L = A1 x B0
    ra = a[0] * fabs (R[2][0]) + a[2] * fabs (R[0][0]);
    rb = b[1] * fabs (R[1][2]) + b[2] * fabs (R[1][1]);
    t = fabs (T[0] * R[2][0] - T[2] * R[0][0]);
    if (t > ra + rb)
      return false;
    //L = A1 x B1
    ra = a[0] * fabs (R[2][1]) + a[2] * fabs (R[0][1]);
    rb = b[0] * fabs (R[1][2]) + b[2] * fabs (R[1][0]);
    t = fabs (T[0] * R[2][1] - T[2] * R[0][1]);
    if (t > ra + rb)
      return false;
    //L = A1 x B2
    ra = a[0] * fabs (R[2][2]) + a[2] * fabs (R[0][2]);
    rb = b[0] * fabs (R[1][1]) + b[1] * fabs (R[1][0]);
    t = fabs (T[0] * R[2][2] - T[2] * R[0][2]);
    if (t > ra + rb)
      return false;
    //L = A2 x B0
    ra = a[0] * fabs (R[1][0]) + a[1] * fabs (R[0][0]);
    rb = b[1] * fabs (R[2][2]) + b[2] * fabs (R[2][1]);
    t = fabs (T[1] * R[0][0] - T[0] * R[1][0]);
    if (t > ra + rb)
      return false;
    //L = A2 x B1
    ra = a[0] * fabs (R[1][1]) + a[1] * fabs (R[0][1]);
    rb = b[0] * fabs (R[2][2]) + b[2] * fabs (R[2][0]);
    t = fabs (T[1] * R[0][1] - T[0] * R[1][1]);
    if (t > ra + rb)
      return false;
    //L = A2 x B2
    ra = a[0] * fabs (R[1][2]) + a[1] * fabs (R[0][2]);
    rb = b[0] * fabs (R[2][1]) + b[1] * fabs (R[2][0]);
    t = fabs (T[1] * R[0][2] - T[0] * R[1][2]);
    if (t > ra + rb)
      return false;
    /*no separating axis found,
      the two boxes overlap */
    return true;
  }

}

#endif