voronoi_vertex_ring_c2.h

很多二维 三维几何计算算法 C++ 类库

    if ( cr == SMALLER ) { return NEGATIVE; }
    return ZERO;
  }

  //--------------------------------------------------------------------------

  Sign incircle(const Line_2& l, PPS_Type) const
  {
    Point_2 pref = p_ref().point();

    Sqrt_1 vx = ux_pps - pref.x() * uz_pps;
    Sqrt_1 vy = uy_pps - pref.y() * uz_pps;

    Sqrt_1 Rs = CGAL::square(vx) + CGAL::square(vy);
    
    RT Ns = CGAL::square(l.a()) + CGAL::square(l.b());

    Sqrt_1 Ls =
      CGAL::square(l.a() * ux_pps + l.b() * uy_pps + l.c() * uz_pps);

    return CGAL::sign(Ls - Rs * Ns);
  }


  //--------------------------------------------------------------------------

  Sign incircle(const Line_2& l, PSS_Type) const
  {
    Sqrt_1 Zero(RT(0), RT(0), ux.a().c());

    Point_2 pref = p_ref().point();

    Sqrt_3 vx = ux - (pref.x() + Zero) * uz;
    Sqrt_3 vy = uy - (pref.y() + Zero) * uz;

    Sqrt_3 Rs = CGAL::square(vx) + CGAL::square(vy);


    Sqrt_1 a = l.a() + Zero;
    Sqrt_1 b = l.b() + Zero;
    Sqrt_1 c = l.c() + Zero;

    Sqrt_1 Ns = CGAL::square(a) + CGAL::square(b);

    Sqrt_3 Ls = CGAL::square(a * ux + b * uy + c * uz);

    return CGAL::sign(Ls - Rs * Ns);
  }


  //--------------------------------------------------------------------------

  Sign incircle(const Line_2& l, SSS_Type) const
  {
    Sqrt_1 Zero(RT(0), RT(0), ux.a().c());

    RT a1, b1, c1;
    compute_supporting_line(p_.supporting_site(), a1, b1, c1);

    Sqrt_1 a = a1 + Zero;
    Sqrt_1 b = b1 + Zero;
    Sqrt_1 c = c1 + Zero;

    Sqrt_1 Ns = CGAL::square(a) + CGAL::square(b);

    Sqrt_1 la = l.a() + Zero;
    Sqrt_1 lb = l.b() + Zero;
    Sqrt_1 lc = l.c() + Zero;

    Sqrt_1 Ns1 = CGAL::square(la) + CGAL::square(lb);

    Sqrt_3 Ls = CGAL::square(a * ux + b * uy + c * uz);

    Sqrt_3 Ls1 =
      CGAL::square(la * ux + lb * uy + lc * uz);

    return CGAL::sign(Ls1 * Ns - Ls * Ns1);
  }

  //--------------------------------------------------------------------------
  //--------------------------------------------------------------------------

  template<class Type>
  Sign incircle_s(const Site_2& t, Type type) const
  {
    CGAL_precondition( t.is_segment() );

    if ( v_type == PPP || v_type == PPS ) {
      if (  p_.is_point() && q_.is_point() &&
	    is_endpoint_of(p_, t) && is_endpoint_of(q_, t)  ) {
	return NEGATIVE;
      }

      if (  p_.is_point() && r_.is_point() &&
	    is_endpoint_of(p_, t) && is_endpoint_of(r_, t)  ){
	return NEGATIVE;
      }

      if (  q_.is_point() && r_.is_point() &&
	    is_endpoint_of(q_, t) && is_endpoint_of(r_, t)  ){
	return NEGATIVE;
      }
    }

    if ( v_type == PSS ) {
      if ( p_.is_segment() &&
	   same_segments(p_.supporting_site(),
			 t.supporting_site()) ) {
	return POSITIVE;
      }
      if ( q_.is_segment() &&
	   same_segments(q_.supporting_site(),
			 t.supporting_site()) ) {
	return POSITIVE;
      }
      if ( r_.is_segment() &&
	   same_segments(r_.supporting_site(),
			 t.supporting_site()) ) {
	return POSITIVE;
      }
    }

    return incircle_s_no_easy(t, type);
  }

  template<class Type>
  Sign incircle_s_no_easy(const Site_2& t, Type type) const
  {
    Sign d1, d2;
    if (  ( p_.is_point() && same_points(p_, t.source_site()) ) ||
	  ( q_.is_point() && same_points(q_, t.source_site()) ) ||
	  ( r_.is_point() && same_points(r_, t.source_site()) )  ) {
      d1 = ZERO;
    } else {
      d1 = incircle_p(t.source_site());
    }
    if ( d1 == NEGATIVE ) { return NEGATIVE; }

    if (  ( p_.is_point() && same_points(p_, t.target_site()) ) ||
	  ( q_.is_point() && same_points(q_, t.target_site()) ) ||
	  ( r_.is_point() && same_points(r_, t.target_site()) )  ) {
      d2 = ZERO;
    } else {
      d2 = incircle_p(t.target_site());
    }
    if ( d2 == NEGATIVE ) { return NEGATIVE; }

    Line_2 l = compute_supporting_line(t.supporting_site());
    Sign sl = incircle(l, type);

    if ( sl == POSITIVE ) { return sl; }

    if ( sl == ZERO && (d1 == ZERO || d2 == ZERO) ) { return ZERO; }

    Oriented_side os1 = oriented_side(l, t.source(), type);
    Oriented_side os2 = oriented_side(l, t.target(), type);

    if ( sl == ZERO ) {
      if (os1 == ON_ORIENTED_BOUNDARY || os2 == ON_ORIENTED_BOUNDARY) {
	return ZERO;
      }
      return ( os1 == os2 ) ? POSITIVE : ZERO;
    }

    return (os1 == os2) ? POSITIVE : NEGATIVE;
  }

  //--------------------------------------------------------------------------

  

  Sign incircle_s(const Site_2& t) const 
  {
    CGAL_precondition( t.is_segment() );

    if ( is_degenerate_Voronoi_circle() ) {
      // case 1: the new segment is not adjacent to the center of the
      //         degenerate Voronoi circle
      if (  !same_points( p_ref(), t.source_site() ) &&
	    !same_points( p_ref(), t.target_site() )  ) {
	return POSITIVE;
      }

      CGAL_assertion( v_type == PSS );

      if ( p_.is_segment() &&
	   same_segments(p_.supporting_site(),
			 t.supporting_site()) ) {
	return ZERO;
      }

      if ( q_.is_segment() &&
	   same_segments(q_.supporting_site(),
			 t.supporting_site()) ) {
	return ZERO;
      }

      if ( r_.is_segment() &&
	   same_segments(r_.supporting_site(),
			 t.supporting_site()) ) {
	return ZERO;
      }

      Site_2 pr;
      Site_2 sp, sq;
      if ( p_.is_point() ) {
	CGAL_assertion( q_.is_segment() && r_.is_segment() );
	pr = p_;
	sp = q_;
	sq = r_;
      } else if ( q_.is_point() ) {
	CGAL_assertion( r_.is_segment() && p_.is_segment() );
	pr = q_;
	sp = r_;
	sq = p_;
      } else {
	CGAL_assertion( p_.is_segment() && q_.is_segment() );
	pr = r_;
	sp = p_;
	sq = q_;
      }

      Point_2 pq = sq.source(), pp = sp.source(), pt = t.source();

      if ( same_points(sp.source_site(), pr) ) { pp = sp.target(); }
      if ( same_points(sq.source_site(), pr) ) { pq = sq.target(); }
      if ( same_points( t.source_site(), pr) ) { pt =  t.target(); }

      Point_2 pr_ = pr.point();

      if ( CGAL::orientation(pr_, pp, pt) == LEFT_TURN &&
	   CGAL::orientation(pr_, pq, pt) == RIGHT_TURN ) {
	return NEGATIVE;
      }
      return ZERO;
    } // if ( is_degenerate_Voronoi_circle() )

    Sign s(ZERO);
    switch ( v_type ) {
    case PPP:
      s = incircle_s(t, PPP_Type());
      break;
    case PPS:
      s = incircle_s(t, PPS_Type());
      break;
    case PSS:
      s = incircle_s(t, PSS_Type());
      break;
    case SSS:
      s = incircle_s(t, SSS_Type());
      break;
    }

    return s;
  }

  Sign incircle_s_no_easy(const Site_2& t) const
  {
    Sign s(ZERO);
    switch ( v_type ) {
    case PPP:
      s = incircle_s_no_easy(t, PPP_Type());
      break;
    case PPS:
      s = incircle_s_no_easy(t, PPS_Type());
      break;
    case PSS:
      s = incircle_s_no_easy(t, PSS_Type());
      break;
    case SSS:
      s = incircle_s_no_easy(t, SSS_Type());
      break;
    }

    return s;
  }

  //--------------------------------------------------------------------------
  //  subpredicates for the incircle test
  //--------------------------------------------------------------------------


public:
  bool is_degenerate_Voronoi_circle() const
  {
    if ( v_type != PSS ) { return false; }

    if ( p_.is_point() ) {
      return ( is_endpoint_of(p_, q_) && is_endpoint_of(p_, r_) );
    } else if ( q_.is_point() ) {
      return ( is_endpoint_of(q_, p_) && is_endpoint_of(q_, r_) );
    } else {
      CGAL_assertion( r_.is_point() );
      return ( is_endpoint_of(r_, p_) && is_endpoint_of(r_, q_) );
    }
  }


  //--------------------------------------------------------------------------

private:

  //--------------------------------------------------------------------------
  //  the reference point (valid if v_type != SSS)
  //--------------------------------------------------------------------------

  Site_2 p_ref() const
  {
    CGAL_precondition ( v_type != SSS );

    if ( v_type == PPS ) {
      if ( pps_idx == 0 ) { return p_; }
      if ( pps_idx == 1 ) { return q_; }
      return r_;
    }

    if ( p_.is_point() ) {
      return p_;
    } else if ( q_.is_point() ) {
      return q_;
    } else {
      CGAL_assertion( r_.is_point() );
      return r_;
    }
  }


public:
  //--------------------------------------------------------------------------
  //--------------------------------------------------------------------------
  //                           access methods
  //--------------------------------------------------------------------------
  //--------------------------------------------------------------------------

  inline FT x(Integral_domain_without_division_tag) const {
    return CGAL::to_double(hx()) / CGAL::to_double(hw());
  }
  inline FT y(Integral_domain_without_division_tag) const {
    return CGAL::to_double(hy()) / CGAL::to_double(hw());
  }

  inline FT x(Field_tag) const { return hx() / hw(); }
  inline FT y(Field_tag) const { return hy() / hw(); }

  inline FT x() const {
      typedef Algebraic_structure_traits<FT> AST;
      return x(typename AST::Algebraic_category());
  }
    
  inline FT y() const {
      typedef Algebraic_structure_traits<FT> AST;
      return y(typename AST::Algebraic_category());
  }

  FT hx() const {
    if ( v_type == PPP ) { return ux_ppp; }
    if ( v_type == PPS ) { return to_ft(ux_pps); }
    return to_ft(ux);
  }

  FT hy() const {
    if ( v_type == PPP ) { return uy_ppp; }
    if ( v_type == PPS ) { return to_ft(uy_pps); }
    return to_ft(uy);
  }

  FT hw() const {
    if ( v_type == PPP ) { return uz_ppp; }
    if ( v_type == PPS ) { return to_ft(uz_pps); }
    return to_ft(uz);
  }

  FT squared_radius() const {
    switch (v_type) {
    case PPP:    case PPS:    case PSS:
      {
	Point_2 pref = p_ref().point();
	FT dx2 = CGAL::square(x() - pref.x());
	FT dy2 = CGAL::square(y() - pref.y());
	return dx2 + dy2;
      }
      break;
    case SSS:
      {
	Line_2 l = compute_supporting_line(p_.supporting_site());
	Homogeneous_point_2 q = compute_projection(l, point());

	FT dx2 = CGAL::square(x() - q.x());
	FT dy2 = CGAL::square(y() - q.y());
	return dx2 + dy2;
      }
      break;
    default:
      return FT(0);
    }
  }

  Point_2 point() const {
    if ( is_degenerate_Voronoi_circle() ) {
      return degenerate_point();
    }
    
    return Point_2(x(), y());
  }


  Point_2 degenerate_point() const
  {
    CGAL_precondition( is_degenerate_Voronoi_circle() );
    return p_ref().point();
  }


  typename K::Circle_2 circle() const
  {
    typedef typename K::Circle_2  K_Circle_2;
    return K_Circle_2(point(), squared_radius());
  }

  vertex_t type() const { return v_type; }

public:
  Voronoi_vertex_ring_C2(const Site_2& p,
			 const Site_2& q,
			 const Site_2& r)
    : p_(p), q_(q), r_(r)
  {
    compute_vertex(p, q, r);
  }

  //--------------------------------------------------------------------------

  Sign incircle(const Site_2& t) const 
  {
    Sign s;

    if ( t.is_point() ) {
      s = incircle_p(t);
    } else {
      s = incircle_s(t);
    }

    return s;
  }

  Sign incircle_no_easy(const Site_2& t) const 
  {
    Sign s;

    if ( t.is_point() ) {
      s = incircle_p_no_easy(t);
    } else {
      s = incircle_s_no_easy(t);
    }

    return s;
  }

  //--------------------------------------------------------------------------


  Orientation orientation(const Line_2& l) const 
  {
    Orientation o(COLLINEAR);
    switch ( v_type ) {
    case PPP:
      o = orientation(l, PPP_Type());
      break;
    case PPS:
      o = orientation(l, PPS_Type());
      break;
    case PSS:
      o = orientation(l, PSS_Type());
      break;
    case SSS:
      o = orientation(l, SSS_Type());
      break;
    }

    return o;
  }

  Oriented_side oriented_side(const Line_2& l) const
  {
    Orientation o = orientation(l);

    if ( o == COLLINEAR ) { return ON_ORIENTED_BOUNDARY; }
    return ( o == LEFT_TURN ) ? ON_POSITIVE_SIDE : ON_NEGATIVE_SIDE;
  }

  //--------------------------------------------------------------------------

private:
  const Site_2& p_, q_, r_;

  vertex_t v_type;

  // index that indicates the refence point for the case PPS
  short pps_idx;

  // the case ppp
  RT ux_ppp, uy_ppp, uz_ppp;

  // the case pps
  Sqrt_1 ux_pps, uy_pps, uz_pps;

  // the case pss and sss
  Sqrt_3 ux, uy, uz;
};


CGAL_SEGMENT_DELAUNAY_GRAPH_2_END_NAMESPACE

CGAL_END_NAMESPACE


#endif // CGAL_SEGMENT_DELAUNAY_GRAPH_2_VORONOI_VERTEX_RING_C2_H