mirror of https://github.com/CGAL/cgal
code polishing; added constructive version of the predicate; added versions for different algebraic structures
This commit is contained in:
Menelaos Karavelas
parent
c6fc1d29a8
commit
ae7a08424b
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@ -57,6 +57,37 @@ public:
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s3.point());
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}
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inline
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Sign sqrt_ext_sign(const FT& A, const FT& B,
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const FT& Exp, const FT& Eyp, const FT& Erp,
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const FT& Exy2, const FT& Exr, const FT& Eyr,
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const FT dx, const FT& dy,
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const Field_with_sqrt_tag&) const
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{
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FT G = CGAL::square(Exp) + CGAL::square(Eyp) - CGAL::square(Erp);
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return CGAL::sign(A + B * CGAL::sqrt(G));
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}
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inline
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Sign sqrt_ext_sign(const FT& A, const FT& B,
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const FT& Exp, const FT& Eyp, const FT& Erp,
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const FT& Exy2, const FT& Exr, const FT& Eyr,
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const FT dx, const FT& dy,
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const Integral_domain_without_division_tag&) const
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{
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Sign sA = CGAL::sign(A);
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Sign sB = CGAL::sign(B);
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if ( sA == CGAL::ZERO ) { return sB; }
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if ( sB == CGAL::ZERO ) { return sA; }
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if ( sA == sB ) { return sA; }
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Sign s = CGAL::sign(CGAL::square(Exy2 * Exr - Erp * dy)
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+ CGAL::square(Exy2 * Eyr + Erp * dx)
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- CGAL::square(B));
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return sA * s;
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}
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Orientation predicate(const Site_2& s1, const Site_2& s2,
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const Site_2& s3, const Site_2& p1,
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const Site_2& p2) const
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@ -97,17 +128,147 @@ public:
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FT Exy2 = 2 * det2x2_by_formula(xl, yl, xm, ym);
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#if 0
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FT A = (Exp * Exr + Eyp * Eyr) * Exy2 + (Eyp * dx - Exp * dy) * Erp;
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FT B = Exy * Exy2 - Exp * dx - Eyp * dy;
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FT C = CGAL::square(Exp) + CGAL::square(Eyp) - CGAL::square(Erp);
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return sign_a_plus_b_x_sqrt_c(A, B, C);
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#else
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Sign sA = CGAL::sign((Exp * Exr + Eyp * Eyr) * Exy2
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+ (Eyp * dx - Exp * dy) * Erp);
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return sqrt_ext_sign(A, B, Exp, Eyp, Erp,
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Exy2, Exr, Eyr, dx, dy, Method_tag());
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}
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FT B = Exy * Exy2 - Exp * dx - Eyp * dy;
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Orientation operator()(const Site_2& s1, const Site_2& s2,
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const Site_2& s3, const Site_2& p1,
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const Site_2& p2) const
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{
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Orientation o = predicate(s1, s2, s3, p1, p2);
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#ifndef NDEBUG
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Orientation o_old = Base::operator()(s1, s2, s3, p1, p2);
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CGAL_assertion( o == o_old );
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#endif
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return o;
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}
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};
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//--------------------------------------------------------------------
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template<class K, class MTag>
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class Constructive_orientation8_C2
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{
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public:
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typedef K Kernel;
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typedef MTag Method_tag;
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typedef typename K::Site_2 Site_2;
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typedef typename K::Point_2 Point_2;
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typedef typename K::Orientation Orientation;
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typedef typename K::FT FT;
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typedef Orientation result_type;
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typedef Arity_tag<3> Arity;
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typedef Site_2 argument_type;
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private:
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FT s1x, s1y;
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FT xj, xk, yj, yk, rj, rk, pj, pk, Exp, Eyp, Erp, Exy, Exr, Eyr, A1;
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FT xl_, yl_, ca1, ca2, ca3, cb1, cb2, cb3;
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public:
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Constructive_orientation8_C2(const Site_2& s1, const Site_2& s2,
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const Site_2& s3)
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{
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s1x = s1.x();
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s1y = s1.y();
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xj = s2.x() - s1.x();
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xk = s3.x() - s1.x();
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yj = s2.y() - s1.y();
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yk = s3.y() - s1.y();
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rj = s2.weight() - s1.weight();
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rk = s3.weight() - s1.weight();
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pj = CGAL::square(xj) + CGAL::square(yj) - CGAL::square(rj);
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pk = CGAL::square(xk) + CGAL::square(yk) - CGAL::square(rk);
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Exp = det2x2_by_formula(xj, pj, xk, pk);
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Eyp = det2x2_by_formula(yj, pj, yk, pk);
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Erp = det2x2_by_formula(rj, pj, rk, pk);
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Exy = det2x2_by_formula(xj, yj, xk, yk);
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Exr = det2x2_by_formula(xj, rj, xk, rk);
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Eyr = det2x2_by_formula(yj, rj, yk, rk);
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A1 = Exp * Exr + Eyp * Eyr;
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}
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Constructive_orientation8_C2(const Site_2& s1, const Site_2& s2,
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const Site_2& s3, const Site_2& p1)
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{
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s1x = s1.x();
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s1y = s1.y();
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xj = s2.x() - s1.x();
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xk = s3.x() - s1.x();
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yj = s2.y() - s1.y();
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yk = s3.y() - s1.y();
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rj = s2.weight() - s1.weight();
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rk = s3.weight() - s1.weight();
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pj = CGAL::square(xj) + CGAL::square(yj) - CGAL::square(rj);
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pk = CGAL::square(xk) + CGAL::square(yk) - CGAL::square(rk);
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Exp = det2x2_by_formula(xj, pj, xk, pk);
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Eyp = det2x2_by_formula(yj, pj, yk, pk);
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Erp = det2x2_by_formula(rj, pj, rk, pk);
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Exy = det2x2_by_formula(xj, yj, xk, yk);
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Exr = det2x2_by_formula(xj, rj, xk, rk);
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Eyr = det2x2_by_formula(yj, rj, yk, rk);
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A1 = Exp * Exr + Eyp * Eyr;
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xl_ = p1.x() - s1.x();
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yl_ = p1.y() - s1.y();
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ca1 = 2 * A1 * xl_ - Eyp * Erp;
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ca2 = -2 * A1 * yl_ + Exp * Erp;
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ca3 = (Eyp * xl_ - Exp * yl_) * Erp;
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cb1 = Exp + Exy * xl_;
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cb2 = Eyp - Exy * yl_;
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cb3 = -Exp * xl_ - Eyp * yl_;
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}
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public:
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inline
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Orientation operator()(const Site_2& s1, const Site_2& s2,
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const Site_2& s3) const
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{
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return Kernel().orientation_2_object()(s1.point(), s2.point(),
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s3.point());
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}
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inline
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Sign sqrt_ext_sign(const FT& A, const FT& B, const FT& Exy2,
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const FT dx, const FT& dy,
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const Field_with_sqrt_tag&) const
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{
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FT G = CGAL::square(Exp) + CGAL::square(Eyp) - CGAL::square(Erp);
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return CGAL::sign(A + B * CGAL::sqrt(G));
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}
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inline
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Sign sqrt_ext_sign(const FT& A, const FT& B, const FT& Exy2,
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const FT dx, const FT& dy,
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const Integral_domain_without_division_tag&) const
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{
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Sign sA = CGAL::sign(A);
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Sign sB = CGAL::sign(B);
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if ( sA == CGAL::ZERO ) { return sB; }
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@ -118,17 +279,57 @@ public:
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+ CGAL::square(Exy2 * Eyr + Erp * dx)
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- CGAL::square(B));
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return sA * s;
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#endif
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}
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Orientation operator()(const Site_2& s1, const Site_2& s2,
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const Site_2& s3, const Site_2& p1,
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const Site_2& p2) const
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Orientation predicate(const Site_2& p1, const Site_2& p2) const
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{
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Orientation o = predicate(s1, s2, s3, p1, p2);
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Orientation o_old = Base::operator()(s1, s2, s3, p1, p2);
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// computes the orientation of the Voronoi vertex of s1, s2, s3 and
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// the points p1 and p2
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FT xl = p1.x() - s1x;
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FT xm = p2.x() - s1x;
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CGAL_assertion( o == o_old );
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FT yl = p1.y() - s1y;
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FT ym = p2.y() - s1y;
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FT dx = xl - xm;
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FT dy = yl - ym;
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FT Exy2 = 2 * det2x2_by_formula(xl, yl, xm, ym);
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FT A = A1 * Exy2 + (Eyp * dx - Exp * dy) * Erp;
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FT B = Exy * Exy2 - Exp * dx - Eyp * dy;
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return sqrt_ext_sign(A, B, Exy2, dx, dy, Method_tag());
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}
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Orientation predicate(const Site_2& p2) const
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{
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// computes the orientation of the Voronoi vertex of s1, s2, s3 and
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// the points p1 and p2
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FT xm = p2.x() - s1x;
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FT ym = p2.y() - s1y;
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FT dx = xl_ - xm;
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FT dy = yl_ - ym;
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FT Exy2 = 2 * det2x2_by_formula(xl_, yl_, xm, ym);
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FT A = ca1 * xm + ca2 * ym + ca3;
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FT B = cb1 * xm + cb2 * ym + cb3;
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return sqrt_ext_sign(A, B, Exy2, dx, dy, Method_tag());
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}
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Orientation operator()(const Site_2& p1, const Site_2& p2) const
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{
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Orientation o = predicate(p1, p2);
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return o;
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}
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Orientation operator()(const Site_2& p2) const
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{
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Orientation o = predicate(p2);
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return o;
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}
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@ -136,6 +337,7 @@ public:
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//--------------------------------------------------------------------
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CGAL_APOLLONIUS_GRAPH_2_END_NAMESPACE
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CGAL_END_NAMESPACE
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