kernel_ftc3.h

很多二维 三维几何计算算法 C++ 类库

CGAL_KERNEL_MEDIUM_INLINE
typename Equal_to<FT>::result_type
equal_directionC3(const FT &dx1, const FT &dy1, const FT &dz1,
                  const FT &dx2, const FT &dy2, const FT &dz2)
{
  return sign_of_determinant2x2(dx1, dy1, dx2, dy2) == ZERO
      && sign_of_determinant2x2(dx1, dz1, dx2, dz2) == ZERO
      && sign_of_determinant2x2(dy1, dz1, dy2, dz2) == ZERO
      && CGAL_NTS sign(dx1) == CGAL_NTS sign(dx2)
      && CGAL_NTS sign(dy1) == CGAL_NTS sign(dy2)
      && CGAL_NTS sign(dz1) == CGAL_NTS sign(dz2);
}

template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
typename Equal_to<FT>::result_type
equal_planeC3(const FT &ha, const FT &hb, const FT &hc, const FT &hd,
              const FT &pa, const FT &pb, const FT &pc, const FT &pd)
{
    typedef typename Sgn<FT>::result_type  Sg;

    if (!equal_directionC3(ha, hb, hc, pa, pb, pc))
	return false; // Not parallel.

    Sg s1a = CGAL_NTS sign(ha);
    if (s1a != ZERO)
        return s1a == CGAL_NTS sign(pa)
            && sign_of_determinant2x2(pa, pd, ha, hd) == ZERO;
    Sg s1b = CGAL_NTS sign(hb);
    if (s1b != ZERO)
        return s1b == CGAL_NTS sign(pb)
            && sign_of_determinant2x2(pb, pd, hb, hd) == ZERO;
    return CGAL_NTS sign(pc) == CGAL_NTS sign(hc)
        && sign_of_determinant2x2(pc, pd, hc, hd) == ZERO;
}

template <class FT >
CGAL_KERNEL_LARGE_INLINE
typename Same_uncertainty_nt<Oriented_side, FT>::type
side_of_oriented_planeC3(const FT &a,  const FT &b,  const FT &c, const FT &d,
                         const FT &px, const FT &py, const FT &pz)
{
  return enum_cast<Oriented_side>(CGAL_NTS sign(a*px + b*py + c*pz +d));
}

template <class FT >
CGAL_KERNEL_LARGE_INLINE
typename Same_uncertainty_nt<Oriented_side, FT>::type
side_of_oriented_sphereC3(const FT &px, const FT &py, const FT &pz,
                          const FT &qx, const FT &qy, const FT &qz,
                          const FT &rx, const FT &ry, const FT &rz,
                          const FT &sx, const FT &sy, const FT &sz,
                          const FT &tx, const FT &ty, const FT &tz)
{
  FT ptx = px - tx;
  FT pty = py - ty;
  FT ptz = pz - tz;
  FT pt2 = CGAL_NTS square(ptx) + CGAL_NTS square(pty) + CGAL_NTS square(ptz);
  FT qtx = qx - tx;
  FT qty = qy - ty;
  FT qtz = qz - tz;
  FT qt2 = CGAL_NTS square(qtx) + CGAL_NTS square(qty) + CGAL_NTS square(qtz);
  FT rtx = rx - tx;
  FT rty = ry - ty;
  FT rtz = rz - tz;
  FT rt2 = CGAL_NTS square(rtx) + CGAL_NTS square(rty) + CGAL_NTS square(rtz);
  FT stx = sx - tx;
  FT sty = sy - ty;
  FT stz = sz - tz;
  FT st2 = CGAL_NTS square(stx) + CGAL_NTS square(sty) + CGAL_NTS square(stz);
  return enum_cast<Oriented_side>(sign_of_determinant4x4(ptx,pty,ptz,pt2,
                                                         rtx,rty,rtz,rt2,
                                                         qtx,qty,qtz,qt2,
                                                         stx,sty,stz,st2));
}

template <class FT >
CGAL_KERNEL_MEDIUM_INLINE
typename Same_uncertainty_nt<Bounded_side, FT>::type
side_of_bounded_sphereC3(const FT &px, const FT &py, const FT &pz,
                         const FT &qx, const FT &qy, const FT &qz,
                         const FT &rx, const FT &ry, const FT &rz,
                         const FT &sx, const FT &sy, const FT &sz,
                         const FT &tx, const FT &ty, const FT &tz)
{
  return enum_cast<Bounded_side>( side_of_oriented_sphereC3(px, py, pz,
                                                            qx, qy, qz,
                                                            rx, ry, rz,
                                                            sx, sy, sz,
                                                            tx, ty, tz)
                                * orientationC3(px, py, pz,
                                                qx, qy, qz,
                                                rx, ry, rz,
                                                sx, sy, sz) );
}

template <class FT >
CGAL_KERNEL_MEDIUM_INLINE
typename Same_uncertainty_nt<Bounded_side, FT>::type
side_of_bounded_sphereC3(const FT &px, const FT &py, const FT &pz,
                         const FT &qx, const FT &qy, const FT &qz,
                         const FT &tx, const FT &ty, const FT &tz)
{
  // Returns whether T lies inside or outside the sphere which diameter is PQ.
  return enum_cast<Bounded_side>( CGAL_NTS sign((tx-px)*(qx-tx)
	                                      + (ty-py)*(qy-ty)
	                                      + (tz-pz)*(qz-tz)) );
}

template < class FT >
CGAL_KERNEL_INLINE
typename Compare<FT>::result_type
cmp_dist_to_pointC3(const FT &px, const FT &py, const FT &pz,
                    const FT &qx, const FT &qy, const FT &qz,
                    const FT &rx, const FT &ry, const FT &rz)
{
  return CGAL_NTS compare(squared_distanceC3(px,py,pz,qx,qy,qz),
                          squared_distanceC3(px,py,pz,rx,ry,rz));
}

// Because of the way the filtered predicates generator script works,
// cmp_dist_to_pointC3() must be defined _before_ ths following one.
template <class FT >
CGAL_KERNEL_MEDIUM_INLINE
typename Same_uncertainty_nt<Bounded_side, FT>::type
side_of_bounded_sphereC3(const FT &px, const FT &py, const FT &pz,
                         const FT &qx, const FT &qy, const FT &qz,
                         const FT &sx, const FT &sy, const FT &sz,
                         const FT &tx, const FT &ty, const FT &tz)
{
  // Returns whether T lies inside or outside the sphere which equatorial
  // circle is PQR.

  // This code is inspired by the one of circumcenterC3(3 points).

  FT psx = px-sx;
  FT psy = py-sy;
  FT psz = pz-sz;
  FT ps2 = CGAL_NTS square(psx) + CGAL_NTS square(psy) + CGAL_NTS square(psz);
  FT qsx = qx-sx;
  FT qsy = qy-sy;
  FT qsz = qz-sz;
  FT qs2 = CGAL_NTS square(qsx) + CGAL_NTS square(qsy) + CGAL_NTS square(qsz);
  FT rsx = psy*qsz-psz*qsy;
  FT rsy = psz*qsx-psx*qsz;
  FT rsz = psx*qsy-psy*qsx;
  FT tsx = tx-sx;
  FT tsy = ty-sy;
  FT tsz = tz-sz;

  FT num_x = ps2 * det2x2_by_formula(qsy,qsz,rsy,rsz)
	   - qs2 * det2x2_by_formula(psy,psz,rsy,rsz);
  FT num_y = ps2 * det2x2_by_formula(qsx,qsz,rsx,rsz)
	   - qs2 * det2x2_by_formula(psx,psz,rsx,rsz);
  FT num_z = ps2 * det2x2_by_formula(qsx,qsy,rsx,rsy)
	   - qs2 * det2x2_by_formula(psx,psy,rsx,rsy);

  FT den2  = 2 * det3x3_by_formula(psx,psy,psz,
                                   qsx,qsy,qsz,
                                   rsx,rsy,rsz);

  // The following could be simplified a bit.
  return enum_cast<Bounded_side>(
                      cmp_dist_to_pointC3<FT>(num_x,    - num_y,  num_z,
	                                      psx*den2, psy*den2, psz*den2,
	                                      tsx*den2, tsy*den2, tsz*den2) );
}

template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
typename Equal_to<FT>::result_type
has_larger_dist_to_pointC3(const FT &px, const FT &py, const FT &pz,
                           const FT &qx, const FT &qy, const FT &qz,
                           const FT &rx, const FT &ry, const FT &rz)
{
  return cmp_dist_to_pointC3(px,py,pz,qx,qy,qz,rx,ry,rz) == LARGER;
}

template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
typename Equal_to<FT>::result_type
has_smaller_dist_to_pointC3(const FT &px, const FT &py, const FT &pz,
                            const FT &qx, const FT &qy, const FT &qz,
                            const FT &rx, const FT &ry, const FT &rz)
{
  return cmp_dist_to_pointC3(px,py,pz,qx,qy,qz,rx,ry,rz) == SMALLER;
}

template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
typename Compare<FT>::result_type
cmp_signed_dist_to_directionC3( const FT &pa, const FT &pb, const FT &pc,
                                const FT &px, const FT &py, const FT &pz,
                                const FT &qx, const FT &qy, const FT &qz)
{
  return CGAL_NTS compare(scaled_distance_to_directionC3(pa,pb,pc,px,py,pz),
                          scaled_distance_to_directionC3(pa,pb,pc,qx,qy,qz));
}

template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
typename Equal_to<FT>::result_type
has_larger_signed_dist_to_directionC3(
     const FT &pa, const FT &pb, const FT &pc,
     const FT &px, const FT &py, const FT &pz,
     const FT &qx, const FT &qy, const FT &qz)
{
  return cmp_signed_dist_to_directionC3(pa,pb,pc,px,py,pz,qx,qy,qz) == LARGER;
}

template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
typename Equal_to<FT>::result_type
has_smaller_signed_dist_to_directionC3(
     const FT &pa, const FT &pb, const FT &pc,
     const FT &px, const FT &py, const FT &pz,
     const FT &qx, const FT &qy, const FT &qz)
{
  return cmp_signed_dist_to_directionC3(pa,pb,pc,px,py,pz,qx,qy,qz) == SMALLER;
}

template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
typename Compare<FT>::result_type
cmp_signed_dist_to_planeC3(
     const FT &ppx, const FT &ppy, const FT &ppz,
     const FT &pqx, const FT &pqy, const FT &pqz,
     const FT &prx, const FT &pry, const FT &prz,
     const FT &px, const FT &py, const FT &pz,
     const FT &qx, const FT &qy, const FT &qz)
{
  return enum_cast<Comparison_result>(sign_of_determinant3x3<FT>(
	                                   pqx-ppx, pqy-ppy, pqz-ppz,
	                                   prx-ppx, pry-ppy, prz-ppz,
	                                   px-qx,   py-qy,   pz-qz));
}

template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
typename Equal_to<FT>::result_type
has_larger_signed_dist_to_planeC3(
     const FT &ppx, const FT &ppy, const FT &ppz,
     const FT &pqx, const FT &pqy, const FT &pqz,
     const FT &prx, const FT &pry, const FT &prz,
     const FT &px, const FT &py, const FT &pz,
     const FT &qx, const FT &qy, const FT &qz)
{
    return cmp_signed_dist_to_planeC3(ppx, ppy, ppz, pqx, pqy, pqz,
	    prx, pry, prz, px, py, pz, qx, qy, qz) == LARGER;
}

template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
typename Equal_to<FT>::result_type
has_smaller_signed_dist_to_planeC3(
     const FT &ppx, const FT &ppy, const FT &ppz,
     const FT &pqx, const FT &pqy, const FT &pqz,
     const FT &prx, const FT &pry, const FT &prz,
     const FT &px, const FT &py, const FT &pz,
     const FT &qx, const FT &qy, const FT &qz)
{
    return cmp_signed_dist_to_planeC3(ppx, ppy, ppz, pqx, pqy, pqz,
	    prx, pry, prz, px, py, pz, qx, qy, qz) == SMALLER;
}

CGAL_END_NAMESPACE

#endif // CGAL_PREDICATES_KERNEL_FTC3_H