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// Copyright (c) 2000,2001 // Utrecht University (The Netherlands), // ETH Zurich (Switzerland), // INRIA Sophia-Antipolis (France), // Max-Planck-Institute Saarbruecken (Germany), // and Tel-Aviv University (Israel). All rights reserved. // // This file is part of CGAL (www.cgal.org) // // $URL: https://github.com/CGAL/cgal/blob/v6.1/Kernel_d/include/CGAL/Kernel_d/function_objectsHd.h $ // $Id: include/CGAL/Kernel_d/function_objectsHd.h b26b07a1242 $ // SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : Michael Seel //--------------------------------------------------------------------- // file generated by notangle from noweb/function_objectsHd.lw // please debug or modify noweb file // coding: K. Mehlhorn, M. Seel //--------------------------------------------------------------------- #ifndef CGAL_FUNCTION_OBJECTSHD_H #define CGAL_FUNCTION_OBJECTSHD_H #include #include namespace CGAL { template class Compute_coordinateHd { typedef typename K::FT FT; typedef typename K::Point_d Point_d; public: typedef FT result_type; result_type operator()(const Point_d& p, int i) const { return p.cartesian(i); } }; template class Point_dimensionHd { typedef typename K::RT RT; typedef typename K::Point_d Point_d; public: typedef int result_type; result_type operator()(const Point_d& p) const { return p.dimension(); } }; template class Less_coordinateHd { typedef typename K::RT RT; typedef typename K::Point_d Point_d; public: typedef bool result_type; result_type operator()(const Point_d& p, const Point_d& q, int i) const { int d = p.dimension(); return p.cartesian(i)*q.homogeneous(d) struct Lift_to_paraboloidHd { typedef typename R::Point_d Point_d; typedef typename R::RT RT; typedef typename R::LA LA; Point_d operator()(const Point_d& p) const { int d = p.dimension(); typename LA::Vector h(d+2); RT D = p.homogeneous(d); RT sum = 0; for (int i = 0; i struct Project_along_d_axisHd { typedef typename R::Point_d Point_d; typedef typename R::RT RT; typedef typename R::LA LA; Point_d operator()(const Point_d& p) const { int d = p.dimension(); return Point_d(d-1, p.homogeneous_begin(),p.homogeneous_end()-2, p.homogeneous(d)); } }; template struct MidpointHd { typedef typename R::Point_d Point_d; Point_d operator()(const Point_d& p, const Point_d& q) const { return Point_d(p + (q-p)/2); } }; template struct Center_of_sphereHd { typedef typename R::Point_d Point_d; typedef typename R::RT RT; typedef typename R::LA LA; template Point_d operator()(Forward_iterator start, Forward_iterator end) const { CGAL_assertion(start!=end); CGAL_USE(end); int d = start->dimension(); typename LA::Matrix M(d); typename LA::Vector b(d); Point_d pd = *start++; RT pdd = pd.homogeneous(d); for (int i = 0; i < d; i++) { // we set up the equation for p_i Point_d pi = *start++; RT pid = pi.homogeneous(d); b[i] = 0; for (int j = 0; j < d; j++) { M(i,j) = RT(2) * pdd * pid * (pi.homogeneous(j)*pdd - pd.homogeneous(j)*pid); b[i] += (pi.homogeneous(j)*pdd - pd.homogeneous(j)*pid) * (pi.homogeneous(j)*pdd + pd.homogeneous(j)*pid); } } RT D; typename LA::Vector x; LA::linear_solver(M,b,x,D); return Point_d(d,x.begin(),x.end(),D); } }; // Center_of_sphereHd template struct Squared_distanceHd { typedef typename R::Point_d Point_d; typedef typename R::Vector_d Vector_d; typedef typename R::FT FT; FT operator()(const Point_d& p, const Point_d& q) const { Vector_d v = p-q; return v.squared_length(); } }; template struct Position_on_lineHd { typedef typename R::Point_d Point_d; typedef typename R::LA LA; typedef typename R::FT FT; typedef typename R::RT RT; bool operator()(const Point_d& p, const Point_d& s, const Point_d& t, FT& l) const { int d = p.dimension(); CGAL_assertion_msg((d==s.dimension())&&(d==t.dimension()&& d>0), "position_along_line: argument dimensions disagree."); CGAL_assertion_msg((s!=t), "Position_on_line_d: line defining points are equal."); RT lnum = (p.homogeneous(0)*s.homogeneous(d) - s.homogeneous(0)*p.homogeneous(d)) * t.homogeneous(d); RT lden = (t.homogeneous(0)*s.homogeneous(d) - s.homogeneous(0)*t.homogeneous(d)) * p.homogeneous(d); RT num(lnum), den(lden), lnum_i, lden_i; for (int i = 1; i < d; i++) { lnum_i = (p.homogeneous(i)*s.homogeneous(d) - s.homogeneous(i)*p.homogeneous(d)) * t.homogeneous(d); lden_i = (t.homogeneous(i)*s.homogeneous(d) - s.homogeneous(i)*t.homogeneous(d)) * p.homogeneous(d); if (lnum*lden_i != lnum_i*lden) return false; if (lden_i != 0) { den = lden_i; num = lnum_i; } } l = R::make_FT(num,den); return true; } }; template struct Barycentric_coordinatesHd { typedef typename R::Point_d Point_d; typedef typename R::LA LA; typedef typename R::RT RT; template OutputIterator operator()(ForwardIterator first, ForwardIterator last, const Point_d& p, OutputIterator result) { TUPLE_DIM_CHECK(first,last,Barycentric_coordinates_d); CGAL_assertion_code( int d = p.dimension(); ) typename R::Affine_rank_d affine_rank; CGAL_assertion(affine_rank(first,last)==d); typename LA::Matrix M(first,last); typename LA::Vector b(p.homogeneous_begin(),p.homogeneous_end()), x; RT D; LA::linear_solver(M,b,x,D); for (int i=0; i< x.dimension(); ++result, ++i) { *result= R::make_FT(x[i],D); } return result; } }; template struct OrientationHd { typedef typename R::Point_d Point_d; typedef typename R::LA LA; template Orientation operator()(ForwardIterator first, ForwardIterator last) { TUPLE_DIM_CHECK(first,last,Orientation_d); int d = static_cast(std::distance(first,last)); // range contains d points of dimension d-1 CGAL_assertion_msg(first->dimension() == d-1, "Orientation_d: needs first->dimension() + 1 many points."); typename LA::Matrix M(d); // quadratic for (int i = 0; i < d; ++first,++i) { for (int j = 0; j < d; ++j) M(i,j) = first->homogeneous(j); } int row_correction = ( (d % 2 == 0) ? -1 : +1 ); // we invert the sign if the row number is even i.e. d is odd return Orientation(row_correction * LA::sign_of_determinant(M)); } }; template struct Side_of_oriented_sphereHd { typedef typename R::Point_d Point_d; typedef typename R::LA LA; typedef typename R::RT RT; template Oriented_side operator()(ForwardIterator first, ForwardIterator last, const Point_d& x) { TUPLE_DIM_CHECK(first,last,Side_of_oriented_sphere_d); int d = static_cast(std::distance(first,last)); // |A| contains |d| points CGAL_assertion_msg((d-1 == first->dimension()), "Side_of_oriented_sphere_d: needs first->dimension()+1 many input points."); typename LA::Matrix M(d + 1); for (int i = 0; i < d; ++first, ++i) { RT Sum = 0; RT hd = first->homogeneous(d-1); M(i,0) = hd*hd; for (int j = 0; j < d; j++) { RT hj = first->homogeneous(j); M(i,j + 1) = hj * hd; Sum += hj*hj; } M(i,d) = Sum; } RT Sum = 0; RT hd = x.homogeneous(d-1); M(d,0) = hd*hd; for (int j = 0; j < d; j++) { RT hj = x.homogeneous(j); M(d,j + 1) = hj * hd; Sum += hj*hj; } M(d,d) = Sum; return CGAL::Sign(- LA::sign_of_determinant(M)); } }; template struct Side_of_bounded_sphereHd { typedef typename R::Point_d Point_d; typedef typename R::LA LA; typedef typename R::RT RT; template Bounded_side operator()(ForwardIterator first, ForwardIterator last, const Point_d& p) { TUPLE_DIM_CHECK(first,last,region_of_sphere); typename R::Orientation_d _orientation; Orientation o = _orientation(first,last); CGAL_assertion_msg((o != 0), "Side_of_bounded_sphere_d: \ A must be full dimensional."); typename R::Side_of_oriented_sphere_d _side_of_oriented_sphere; Oriented_side oside = _side_of_oriented_sphere(first,last,p); if (o == POSITIVE) { switch (oside) { case ON_POSITIVE_SIDE : return ON_BOUNDED_SIDE; case ON_ORIENTED_BOUNDARY: return ON_BOUNDARY; case ON_NEGATIVE_SIDE : return ON_UNBOUNDED_SIDE; } } else { switch (oside) { case ON_POSITIVE_SIDE : return ON_UNBOUNDED_SIDE; case ON_ORIENTED_BOUNDARY: return ON_BOUNDARY; case ON_NEGATIVE_SIDE : return ON_BOUNDED_SIDE; } } return ON_BOUNDARY; // never reached } }; template struct Contained_in_simplexHd { typedef typename R::Point_d Point_d; typedef typename R::LA LA; typedef typename R::RT RT; template bool operator()(ForwardIterator first, ForwardIterator last, const Point_d& p) { TUPLE_DIM_CHECK(first,last,Contained_in_simplex_d); int k = static_cast(std::distance(first,last)); // |A| contains |k| points int d = first->dimension(); CGAL_assertion_code( typename R::Affinely_independent_d check_independence; ) CGAL_assertion_msg(check_independence(first,last), "Contained_in_simplex_d: A not affinely independent."); CGAL_assertion(d==p.dimension()); typename LA::Matrix M(d + 1,k); typename LA::Vector b(p.homogeneous_begin(),p.homogeneous_end()); for (int j = 0; j < k; ++first, ++j) { for (int i = 0; i <= d; ++i) M(i,j) = first->homogeneous(i); } RT D; typename LA::Vector lambda; if ( LA::linear_solver(M,b,lambda,D) ) { int s = CGAL_NTS sign(D); for (int j = 0; j < k; j++) { int t = CGAL_NTS sign(lambda[j]); if (s * t < 0) return false; } return true; } return false; } }; template struct Contained_in_affine_hullHd { typedef typename R::Point_d Point_d; typedef typename R::LA LA; typedef typename R::RT RT; template bool operator()(ForwardIterator first, ForwardIterator last, const Point_d& p) { TUPLE_DIM_CHECK(first,last,Contained_in_affine_hull_d); int k = static_cast(std::distance(first,last)); // |A| contains |k| points int d = first->dimension(); typename LA::Matrix M(d + 1,k); typename LA::Vector b(p.homogeneous_begin(),p.homogeneous_end()); for (int j = 0; j < k; ++first, ++j) for (int i = 0; i <= d; ++i) M(i,j) = first->homogeneous(i); return LA::is_solvable(M,b); } }; template struct Affine_rankHd { typedef typename R::Point_d Point_d; typedef typename R::Vector_d Vector_d; typedef typename R::LA LA; typedef typename R::RT RT; template int operator()(ForwardIterator first, ForwardIterator last) { TUPLE_DIM_CHECK(first,last,Affine_rank_d); int k = static_cast(std::distance(first,last)); // |A| contains |k| points if (k == 0) return -1; if (k == 1) return 0; int d = first->dimension(); typename LA::Matrix M(d,--k); Point_d p0 = *first; ++first; // first points to second for (int j = 0; j < k; ++first, ++j) { Vector_d v = *first - p0; for (int i = 0; i < d; i++) M(i,j) = v.homogeneous(i); } return LA::rank(M); } }; template struct Affinely_independentHd { typedef typename R::Point_d Point_d; typedef typename R::LA LA; typedef typename R::RT RT; template bool operator()(ForwardIterator first, ForwardIterator last) { typename R::Affine_rank_d rank; int n = static_cast(std::distance(first,last)); return rank(first,last) == n-1; } }; template struct Compare_lexicographicallyHd { typedef typename R::Point_d Point_d; typedef typename R::Point_d PointD; //MSVC hack Comparison_result operator()(const Point_d& p1, const Point_d& p2) { return PointD::cmp(p1,p2); } }; template struct Contained_in_linear_hullHd { typedef typename R::LA LA; typedef typename R::RT RT; typedef typename R::Vector_d Vector_d; template bool operator()( ForwardIterator first, ForwardIterator last, const Vector_d& x) { TUPLE_DIM_CHECK(first,last,Contained_in_linear_hull_d); int k = static_cast(std::distance(first,last)); // |A| contains |k| vectors int d = first->dimension(); typename LA::Matrix M(d,k); typename LA::Vector b(d); for (int i = 0; i < d; i++) { b[i] = x.homogeneous(i); for (int j = 0; j < k; j++) M(i,j) = (first+j)->homogeneous(i); } return LA::is_solvable(M,b); } }; template struct Linear_rankHd { typedef typename R::LA LA; typedef typename R::RT RT; template int operator()(ForwardIterator first, ForwardIterator last) { TUPLE_DIM_CHECK(first,last,linear_rank); int k = static_cast(std::distance(first,last)); // k vectors int d = first->dimension(); typename LA::Matrix M(d,k); for (int i = 0; i < d ; i++) for (int j = 0; j < k; j++) M(i,j) = (first + j)->homogeneous(i); return LA::rank(M); } }; template struct Linearly_independentHd { typedef typename R::LA LA; typedef typename R::RT RT; template bool operator()(ForwardIterator first, ForwardIterator last) { typename R::Linear_rank_d rank; return rank(first,last) == static_cast(std::distance(first,last)); } }; template struct Linear_baseHd { typedef typename R::LA LA; typedef typename R::RT RT; typedef typename R::Vector_d Vector_d; template OutputIterator operator()(ForwardIterator first, ForwardIterator last, OutputIterator result) { TUPLE_DIM_CHECK(first,last,linear_base); int k = static_cast(std::distance(first,last)); // k vectors int d = first->dimension(); typename LA::Matrix M(d,k); for (int j = 0; j < k; j++) for (int i = 0; i < d; i++) M(i,j) = (first+j)->homogeneous(i); std::vector indcols; int r = LA::independent_columns(M,indcols); for (int l=0; l < r; l++) { typename LA::Vector v = M.column(indcols[l]); *result++ = Vector_d(d,v.begin(),v.end(),1); } return result; } }; } //namespace CGAL #endif // CGAL_FUNCTION_OBJECTSHD_H