voronoi_vertex_ring_c2.h

很多二维 三维几何计算算法 C++ 类库

// Copyright (c) 2003,2004,2005,2006  INRIA Sophia-Antipolis (France) and
// Notre Dame University (U.S.A.).  All rights reserved.
//
// This file is part of CGAL (www.cgal.org); you may redistribute it under
// the terms of the Q Public License version 1.0.
// See the file LICENSE.QPL distributed with CGAL.
//
// Licensees holding a valid commercial license may use this file in
// accordance with the commercial license agreement provided with the software.
//
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
//
// $URL: svn+ssh://scm.gforge.inria.fr/svn/cgal/branches/CGAL-3.3-branch/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2/Voronoi_vertex_ring_C2.h $
// $Id: Voronoi_vertex_ring_C2.h 37157 2007-03-16 10:49:14Z afabri $
// 
//
// Author(s)     : Menelaos Karavelas <[e-mail]>




#ifndef CGAL_SEGMENT_DELAUNAY_GRAPH_2_VORONOI_VERTEX_RING_C2_H
#define CGAL_SEGMENT_DELAUNAY_GRAPH_2_VORONOI_VERTEX_RING_C2_H


#include <CGAL/Segment_Delaunay_graph_2/Basic_predicates_C2.h>
#include <CGAL/Segment_Delaunay_graph_2/Are_same_points_C2.h>
#include <CGAL/Segment_Delaunay_graph_2/Are_same_segments_C2.h>


CGAL_BEGIN_NAMESPACE

CGAL_SEGMENT_DELAUNAY_GRAPH_2_BEGIN_NAMESPACE


template<class K>
class Voronoi_vertex_ring_C2
  : public Basic_predicates_C2<K>
{
public:
  typedef Basic_predicates_C2<K> Base;

  typedef enum {PPP = 0, PPS, PSS, SSS} vertex_t;
  struct PPP_Type {};
  struct PPS_Type {};
  struct PSS_Type {};
  struct SSS_Type {};

  typedef typename Base::Point_2             Point_2;
  typedef typename Base::Segment_2           Segment_2;
  typedef typename Base::Line_2              Line_2;
  typedef typename Base::Site_2              Site_2;
  typedef typename Base::FT                  FT;
  typedef typename Base::RT                  RT;

  typedef typename Base::Sqrt_1              Sqrt_1;
  typedef typename Base::Sqrt_2              Sqrt_2;
  typedef typename Base::Sqrt_3              Sqrt_3;

  typedef typename Base::Homogeneous_point_2 Homogeneous_point_2;

  typedef typename Base::Orientation         Orientation;
  typedef typename Base::Comparison_result   Comparison_result;
  typedef typename Base::Oriented_side       Oriented_side;
  typedef typename Base::Sign                Sign;

private:
  typedef Are_same_points_C2<K>     Are_same_points_2;
  typedef Are_same_segments_C2<K>   Are_same_segments_2;

  typedef typename K::Intersections_tag ITag;

  Are_same_points_2    same_points;
  Are_same_segments_2  same_segments;

private:
  //--------------------------------------------------------------------------

  void
  compute_ppp(const Site_2& sp, const Site_2& sq, const Site_2& sr)
  {
    CGAL_precondition( sp.is_point() && sq.is_point() &&
		       sr.is_point() );

    Point_2 p = sp.point(), q = sq.point(), r = sr.point();

    v_type = PPP;

    RT np = CGAL::square(p.x()) + CGAL::square(p.y());
    RT nq = CGAL::square(q.x()) + CGAL::square(q.y());
    RT nr = CGAL::square(r.x()) + CGAL::square(r.y());

    ux_ppp = 
      np * (q.y() - r.y()) + nq * (r.y() - p.y()) + nr * (p.y() - q.y());
    uy_ppp =
      -(np * (q.x() - r.x()) + nq * (r.x() - p.x()) + nr * (p.x() - q.x()));
    uz_ppp = RT(2) * ( (q.x() * r.y() - r.x() * q.y()) +
		       (r.x() * p.y() - p.x() * r.y()) +
		       (p.x() * q.y() - q.x() * p.y()) );
  }

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

  void
  compute_pss(const Site_2& p, const Site_2& q, const Site_2& r)
  {
    CGAL_precondition( p.is_point() && q.is_segment() &&
		       r.is_segment() );

    v_type = PSS;

    bool pq =
      same_points(p, q.source_site()) || same_points(p, q.target_site());
    bool pr =
      same_points(p, r.source_site()) || same_points(p, r.target_site());

    Point_2 pp = p.point();

    if ( pq && pr ) {
      Sqrt_1 One(RT(1), RT(0), RT(0));

      ux = Sqrt_3(pp.x() * One);
      uy = Sqrt_3(pp.y() * One);
      uz = Sqrt_3(One);
      return;
    }

    

    RT a1, b1, c1, a2, b2, c2;
    compute_supporting_line(q.supporting_site(), a1, b1, c1);
    compute_supporting_line(r.supporting_site(), a2, b2, c2);

    RT c1_ = a1 * pp.x() + b1 * pp.y() + c1;
    RT c2_ = a2 * pp.x() + b2 * pp.y() + c2;

    if ( pq ) {
      c1_ = RT(0);
    }

    if ( pr ) {
      c2_ = RT(0);
    }

    Sign sgn_c1_ = CGAL::sign(c1_);
    Sign sgn_c2_ = CGAL::sign(c2_);

    if ( sgn_c1_ == NEGATIVE ) {
      a1 = -a1;  b1 = -b1;  c1_ = -c1_;
    } else if ( sgn_c1_ == ZERO ) {
      CGAL_assertion( pq );
      if ( same_points(p, q.target_site()) ) {
	a1 = -a1;  b1 = -b1;  c1_ = -c1_;
      }
    }

    if ( sgn_c2_ == NEGATIVE ) {
      a2 = -a2;  b2 = -b2;  c2_ = -c2_;
    } else if ( sgn_c2_ == ZERO ) {
      CGAL_assertion( pr );
      if ( same_points(p, r.source_site()) ) {
	a2 = -a2;  b2 = -b2;  c2_ = -c2_;
      }
    }

    if ( pq ) {
      RT J = a1 * c2_;
      RT I = b1 * c2_;

      RT n1 = CGAL::square(a1) + CGAL::square(b1);
      RT n2 = CGAL::square(a2) + CGAL::square(b2);

      RT D1D2 = n1 * n2;

      Sqrt_1 Zero(RT(0), RT(0), D1D2);

      Sqrt_1 vz(-a1 * a2 - b1 * b2, RT(1), D1D2);

      ux = Sqrt_3(J + pp.x() * vz,
		  Zero, Zero, Zero, Zero, Zero);
      uy = Sqrt_3(I + pp.y() * vz,
		  Zero, Zero, Zero, Zero, Zero);
      uz = Sqrt_3(vz, Zero, Zero, Zero, Zero, Zero);
    } else if ( pr ) {
      RT J = a2 * c1_;
      RT I = b2 * c1_;

      RT n1 = CGAL::square(a1) + CGAL::square(b1);
      RT n2 = CGAL::square(a2) + CGAL::square(b2);

      RT D1D2 = n1 * n2;

      Sqrt_1 Zero(RT(0), RT(0), D1D2);

      Sqrt_1 vz(-a1 * a2 - b1 * b2, RT(1), D1D2);

      ux = Sqrt_3(J + pp.x() * vz,
		  Zero, Zero, Zero, Zero, Zero);
      uy = Sqrt_3(I + pp.y() * vz,
		  Zero, Zero, Zero, Zero, Zero);
      uz = Sqrt_3(vz, Zero, Zero, Zero, Zero, Zero);
    } else {
      Line_2 lq(a1, b1, c1_);
      Line_2 lr(a2, b2, c2_);
      compute_pll(pp, lq, lr);
    }
  }


  void
  compute_pll(const Point_2& p, const Line_2& lq, const Line_2& lr)
  {
    RT a1 = lq.a(), b1 = lq.b(), c1_ = lq.c();
    RT a2 = lr.a(), b2 = lr.b(), c2_ = lr.c();

    CGAL_precondition( c1_ >= RT(0) );
    CGAL_precondition( c2_ >= RT(0) );

    RT n1 = CGAL::square(a1) + CGAL::square(b1);
    RT n2 = CGAL::square(a2) + CGAL::square(b2);

    RT I = b1 * c2_ + b2 * c1_;
    RT J = a1 * c2_ + a2 * c1_;
    
    RT c1c2 = RT(2) * c1_ * c2_;
    RT a1a2 = a1 * a2;
    RT b1b2 = b1 * b2;

    RT D1D2 = n1 * n2;

    Sqrt_1 Zero(RT(0), RT(0), D1D2);
    Sqrt_1 One(RT(1), RT(0), D1D2);


    Sign s1, s2;

    // compute sigma
    Sign s_sigma(ZERO);
    s1 = CGAL::sign(b1);
    s2 = CGAL::sign(-b2);
    if ( s1 == ZERO ) {
      s_sigma = s2;
    } else if ( s2 == ZERO ) {
      s_sigma = s1;
    } else if ( s1 == s2 ) {
      s_sigma = s1;
    } else {
      RT e = CGAL::square(b1) * n2 - CGAL::square(b2) * n1;
      s_sigma = Sign(s1 * CGAL::sign(e));
    }

    Sqrt_1 sigma = Zero;
    if ( s_sigma == POSITIVE ) {
      sigma = One;
    } else if ( s_sigma == NEGATIVE ) {
      sigma = -One;
    }

    // compute rho
    Sign s_rho(ZERO);
    s1 = CGAL::sign(a1);
    s2 = CGAL::sign(-a2);
    if ( s1 == ZERO ) {
      s_rho = s2;
    } else if ( s2 == ZERO ) {
      s_rho = s1;
    } else if ( s1 == s2 ) {
      s_rho = s1;
    } else {
      RT e = CGAL::square(a1) * n2 - CGAL::square(a2) * n1;
      s_rho = Sign(s1 * CGAL::sign(e));
    }

    
    Sqrt_1 rho = Zero;
    if ( s_rho == POSITIVE ) {
      rho = One;
    } else if ( s_rho == NEGATIVE ) {
      rho = -One;
    }

    
    Sqrt_1 vz(-a1a2 - b1b2, RT(1), D1D2);

    RT A = a1a2 - b1b2;
    Sqrt_1 u1( c1c2 * A, c1c2, D1D2);
    Sqrt_1 u2(-c1c2 * A, c1c2, D1D2);


    ux = Sqrt_3(J + p.x() * vz, sigma, Zero, Zero, u1, u2);
    uy = Sqrt_3(I + p.y() * vz, Zero, -rho, Zero, u1, u2);
    uz = Sqrt_3(vz, Zero, Zero, Zero, u1, u2);
  }


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


  void
  compute_pps(const Site_2& p, const Site_2& q, const Site_2& r)
  {
    CGAL_precondition( p.is_point() && q.is_point() &&
		       r.is_segment() );

    v_type = PPS;

    RT a, b, c;
    compute_supporting_line(r.supporting_site(), a, b, c);

    Point_2 pp = p.point(), qq = q.point();

    RT c_ = a * pp.x() + b * pp.y() + c;
    RT cq_ = a * qq.x() + b * qq.y() + c;


    if ( same_points(p, r.source_site()) ||
	 same_points(p, r.target_site()) ) {
      c_ = RT(0);
    }
    if ( same_points(q, r.source_site()) ||
	 same_points(q, r.target_site()) ) {
      cq_ = RT(0);
    }

    Sign s = CGAL::sign(c_);

    if ( s == NEGATIVE ) {
      a = -a;  b = -b;  c = -c;  c_ = -c_;  cq_ = -cq_;
    } else if ( s == ZERO ) {
      Sign s1 = CGAL::sign(cq_);

      CGAL_assertion( s1 != ZERO );
      if ( s1 == NEGATIVE ) {
	a = -a;  b = -b;  c = -c;  c_ = -c_;  cq_ = -cq_;
      }
    }

    RT nl = CGAL::square(a) + CGAL::square(b);

    RT x_ = qq.x() - pp.x();
    RT y_ = qq.y() - pp.y();
    RT n_ = CGAL::square(x_) + CGAL::square(y_);


    Comparison_result res = CGAL::compare( c_, cq_ );

    if ( res == EQUAL ) {
      RT e1 = CGAL::square(c_);
      RT J = nl * (a * n_ + RT(4) * c_ * x_) - RT(4) * a * e1;
      RT I = nl * (b * n_ + RT(4) * c_ * y_) - RT(4) * b * e1;
      RT X = RT(8) * nl * c_;

      ux_pps = Sqrt_1(J + pp.x() * X);
      uy_pps = Sqrt_1(I + pp.y() * X);
      uz_pps = Sqrt_1(X);
      return;
    }


    RT e1 = a * x_ + b * y_;
    RT e2 = b * x_ - a * y_;
    RT e3 = n_ * e1;
    RT e4 = RT(2) * c_ * e2;

    RT X = RT(2) * CGAL::square(e1);
    RT I = b * e3 + x_ * e4;
    RT J = a * e3 - y_ * e4;
    RT S = n_ * nl * c_ * cq_;

    ux_pps = Sqrt_1(J + pp.x() * X, RT(-2) * y_, S);
    uy_pps = Sqrt_1(I + pp.y() * X, RT( 2) * x_, S);
    uz_pps = Sqrt_1(X, RT(0), S);
  }

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

  bool check_if_exact(const Site_2& , unsigned int ,
		      const Tag_false&) const
  {
    return true;
  }

  bool check_if_exact(const Site_2& s, unsigned int i,
		      const Tag_true&) const
  {
    return s.is_input(i);
  }

  // determines of the segment s is on the positive halfspace as
  // defined by the supporting line of the segment supp; the line l
  // is supposed to be the supporting line of the segment supp and we
  // pass it so that we do not have to recompute it
  bool
  is_on_positive_halfspace(const Site_2& supp,
			   const Site_2& s, const Line_2& l) const
  {
    CGAL_precondition( supp.is_segment() && s.is_segment() );
    
    if ( same_segments(supp.supporting_site(),
		       s.supporting_site()) ) {
      return false;
    }

    if ( same_points(supp.source_site(), s.source_site()) ||
	 same_points(supp.target_site(), s.source_site()) ) {
      return oriented_side_of_line(l, s.target()) == ON_POSITIVE_SIDE;
    }

    if ( same_points(supp.source_site(), s.target_site()) ||
	 same_points(supp.target_site(), s.target_site()) ) {
      return oriented_side_of_line(l, s.source()) == ON_POSITIVE_SIDE;
    }

    ITag itag;

    if ( !check_if_exact(s, 0, itag) &&
	 same_segments(supp.supporting_site(),
		       s.crossing_site(0)) ) {
      return oriented_side_of_line(l, s.target()) == ON_POSITIVE_SIDE;
    }

    if ( !check_if_exact(s, 1, itag) &&
	 same_segments(supp.supporting_site(),
		       s.crossing_site(1)) ) {
      return oriented_side_of_line(l, s.source()) == ON_POSITIVE_SIDE;
    }

    return Base::is_on_positive_halfspace(l, s.segment());
  }

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

  void
  orient_lines(const Site_2& p, const Site_2& q,
	       const Site_2& r, RT a[], RT b[], RT c[]) const 
  {
    CGAL_precondition( p.is_segment() && q.is_segment() &&
		       r.is_segment() );

    Line_2 l[3];
    l[0] = compute_supporting_line(p.supporting_site());
    l[1] = compute_supporting_line(q.supporting_site());
    l[2] = compute_supporting_line(r.supporting_site());
    
    bool is_oriented[3] = {false, false, false};

    if ( is_on_positive_halfspace(p, q, l[0]) ||
	 is_on_positive_halfspace(p, r, l[0]) ) {
      is_oriented[0] = true;
    } else {
      l[0] = opposite_line(l[0]);
      if ( is_on_positive_halfspace(p, q, l[0]) ||
	   is_on_positive_halfspace(p, r, l[0]) ) {
	is_oriented[0] = true;
      } else {
	l[0] = opposite_line(l[0]);
      }
    }

    if ( is_on_positive_halfspace(q, p, l[1]) ||
	 is_on_positive_halfspace(q, r, l[1]) ) {
      is_oriented[1] = true;
    } else {
       l[1] = opposite_line(l[1]);
      if ( is_on_positive_halfspace(q, p, l[1]) ||
	   is_on_positive_halfspace(q, r, l[1]) ) {
	is_oriented[1] = true;
      } else {
	l[1] = opposite_line(l[1]);
      }
    }

    if ( is_on_positive_halfspace(r, p, l[2]) ||
	 is_on_positive_halfspace(r, q, l[2]) ) {
      is_oriented[2] = true;
    } else {
      l[2] = opposite_line(l[2]);
      if ( is_on_positive_halfspace(r, p, l[2]) ||
	   is_on_positive_halfspace(r, q, l[2]) ) {
	is_oriented[2] = true;
      } else {
	l[2] = opposite_line(l[2]);
      }
    }

    if ( is_oriented[0] && is_oriented[1] && is_oriented[2] ) {
      for (int i = 0; i < 3; i++) {
	a[i] = l[i].a();
	b[i] = l[i].b();
	c[i] = l[i].c();
      }
      return;
    }

    int i_no(-1);
    for (int i = 0; i < 3; i++) {
      if ( !is_oriented[i] ) {
	i_no = i;
	CGAL_assertion( is_oriented[(i+1)%3] && is_oriented[(i+2)%3] );
	break;
      }
    }

    CGAL_assertion( i_no != -1 );

    RT d[3];
    for (int i = 0; i < 3; i++) {
      d[i] = CGAL::square(l[i].a()) + CGAL::square(l[i].b());
    }

    RT z[3];
    for (int i = 0; i < 3; i++) {
      z[i] = l[(i+1)%3].a() * l[(i+2)%3].b()
	- l[(i+2)%3].a() * l[(i+1)%3].b();
    }