240 lines
7.6 KiB
C++
Executable File
240 lines
7.6 KiB
C++
Executable File
// Copyright (c) 2000,2001
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// Utrecht University (The Netherlands),
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// ETH Zurich (Switzerland),
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// INRIA Sophia-Antipolis (France),
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// Max-Planck-Institute Saarbruecken (Germany),
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// and Tel-Aviv University (Israel). All rights reserved.
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//
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// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
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// modify it under the terms of the GNU Lesser General Public License as
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// published by the Free Software Foundation; either version 3 of the License,
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// or (at your option) any later version.
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//
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// Licensees holding a valid commercial license may use this file in
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// accordance with the commercial license agreement provided with the software.
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//
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// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
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// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
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//
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// $URL$
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// $Id$
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// SPDX-License-Identifier: LGPL-3.0+
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//
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// Author(s) : Michael Seel
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#ifndef CGAL_HYPERPLANECD_H
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#define CGAL_HYPERPLANECD_H
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#include <CGAL/basic.h>
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namespace CGAL {
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#define PointCd PointCd2
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template <class FT, class LA>
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std::istream& operator>>(std::istream&, HyperplaneCd<FT,LA>&);
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template <class FT, class LA>
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std::ostream& operator<<(std::ostream&, const HyperplaneCd<FT,LA>&);
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template <class _FT, class _LA>
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class HyperplaneCd : public Handle_for< Tuple_d<_FT,_LA> > {
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typedef Tuple_d<_FT,_LA> Tuple;
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typedef Handle_for<Tuple> Base;
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typedef HyperplaneCd<_FT,_LA> Self;
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using Base::ptr;
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const typename _LA::Vector& vector_rep() const { return ptr()->v; }
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_FT& entry(int i) { return ptr()->v[i]; }
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const _FT& entry(int i) const { return ptr()->v[i]; }
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void invert_rep() { ptr()->invert(); }
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public:
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typedef _FT RT;
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typedef _FT FT;
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typedef _LA LA;
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typedef typename Tuple::const_iterator Coefficient_const_iterator;
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HyperplaneCd(int d = 0) : Base( Tuple(d+1) ) {}
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template <class InputIterator>
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HyperplaneCd(int d, InputIterator first, InputIterator last, const FT& D)
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: Base( Tuple(d+1,first,last,D) ) {}
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template <class InputIterator>
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HyperplaneCd(int d, InputIterator first, InputIterator last)
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: Base( Tuple(d+1,first,last) ) {}
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template <class ForwardIterator>
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void
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construct_from_points(ForwardIterator first, ForwardIterator last,
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const PointCd<FT,LA>& o, Oriented_side side)
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{
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// inline due to template parameter
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TUPLE_DIM_CHECK(first,last,hyperplane::construction);
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CGAL_assertion_msg((first->dimension()==o.dimension()),
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"hyperplane::construction: dimensions disagree.");
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int d = first->dimension(); // we are in $d$ - dimensional space
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int m = static_cast<int>(std::distance(first,last)); // |P| has $m$ points
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typename LA::Matrix A(m,d + 1);
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for (int i = 0; i < m; i++) { /* define $i$-th equation */
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for (int j = 0; j < d; j++)
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A(i,j) = first->cartesian(j); // $j$ - th coord of $i$-th point
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A(i,d) = 1;
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++first;
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}
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typename LA::Matrix spanning_vecs; // columns span solution
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int dim = LA::homogeneous_linear_solver(A,spanning_vecs);
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CGAL_assertion_msg(dim != 0,
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"HyperplaneCd::constructor: set P is full dimensional.");
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if (side == ON_ORIENTED_BOUNDARY)
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{ ptr()->v = spanning_vecs.column(0); return; }
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FT sum = 0; int j;
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for (j = 0; j < dim; j++) {
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for (int i = 0; i < d; i++)
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sum += spanning_vecs(i,j)*o.cartesian(i);
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sum += spanning_vecs(d,j);
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if (sum != FT(0)) break;
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}
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CGAL_assertion_msg(j != dim,
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"HyperplaneCd::constructor: cannot use o to determine side.");
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ptr()->v = spanning_vecs.column(j);
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if ( ( CGAL_NTS sign(sum) > 0 && side == ON_NEGATIVE_SIDE ) ||
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( CGAL_NTS sign(sum) < 0 && side == ON_POSITIVE_SIDE ) )
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invert_rep();
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}
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template <class ForwardIterator>
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HyperplaneCd(ForwardIterator first, ForwardIterator last,
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const PointCd<FT,LA>& o,
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Oriented_side side = ON_ORIENTED_BOUNDARY)
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: Base( Tuple(o.dimension()+1) )
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{ construct_from_points(first,last,o,side); }
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HyperplaneCd(const PointCd<FT,LA>& p, const DirectionCd<FT,LA>& dir)
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: Base( Tuple(p.dimension()+1) )
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{
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int d = p.dimension();
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CGAL_assertion_msg((dir.dimension() == d),
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"HyperplaneCd::constructor: parameter dimensions disagree.");
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FT sum = 0;
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for (int i = 0; i < d; i++) {
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sum += dir.delta(i)*p.cartesian(i);
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entry(i) = dir.delta(i);
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}
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entry(d) = -sum;
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}
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HyperplaneCd(const FT& a, const FT& b, const FT& c) :
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Base( Tuple(a,b,c,MatchHelper()) ) {}
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HyperplaneCd(int a, int b, int c) :
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Base( Tuple(FT(a),FT(b),FT(c),MatchHelper()) ) {}
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HyperplaneCd(const FT& a, const FT& b, const FT& c, const FT& d) :
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Base( Tuple(a,b,c,d) ) {}
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HyperplaneCd(int a, int b, int c, int d) :
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Base( Tuple(FT(a),FT(b),FT(c),FT(d)) ) {}
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HyperplaneCd(const HyperplaneCd<FT,LA>& h) : Base(h) {}
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~HyperplaneCd() {}
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int dimension() const { return ptr()->size()-1; }
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FT operator[](int i) const
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{ CGAL_assertion_msg((0<=i && i<=(dimension())),
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"HyperplaneCd::op[]: index out of range.");
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return entry(i); }
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FT coefficient(int i) const { return entry(i); }
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const typename LA::Vector& coefficient_vector() const
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{ return vector_rep(); }
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Coefficient_const_iterator coefficients_begin() const
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{ return ptr()->begin(); }
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Coefficient_const_iterator coefficients_end() const
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{ return ptr()->end(); }
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inline VectorCd<FT,LA> orthogonal_vector() const;
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DirectionCd<FT,LA> orthogonal_direction() const
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{ return orthogonal_vector().direction(); }
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FT value_at(const PointCd<FT,LA>& p) const
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{ CGAL_assertion_msg((dimension()==p.dimension()),
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"HyperplaneCd::value_at: dimensions disagree.");
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FT res(0);
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for (int i=0; i<dimension(); ++i)
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res += coefficient(i)*p.cartesian(i);
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res += coefficient(dimension());
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return res;
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}
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Oriented_side oriented_side(const PointCd<FT,LA>& p) const
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{
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CGAL_assertion_msg(dimension()==p.dimension(),
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"HyperplaneCd::oriented_side: dimensions do not agree.");
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return CGAL_NTS sign(value_at(p));
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}
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bool has_on(const PointCd<FT,LA>& p) const
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{ return (oriented_side(p) == ON_ORIENTED_BOUNDARY); }
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bool has_on_boundary(const PointCd<FT,LA>& p) const
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{ return (oriented_side(p) == ON_ORIENTED_BOUNDARY); }
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bool has_on_positive_side(const PointCd<FT,LA>& p) const
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{ return (oriented_side(p) == ON_POSITIVE_SIDE); }
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bool has_on_negative_side(const PointCd<FT,LA>& p) const
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{ return (oriented_side(p) == ON_NEGATIVE_SIDE); }
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HyperplaneCd<FT,LA> transform(const Aff_transformationCd<FT,LA>& t) const
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{ Aff_transformationCd<FT,LA> t_inv = t.inverse();
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typename LA::Vector res = LA::transpose(t_inv.matrix())*vector_rep();
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if ( t_inv.is_odd() ) res = -res;
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return HyperplaneCd<FT,LA>(dimension(),res.begin(),res.end()); }
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static Comparison_result weak_cmp(
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const HyperplaneCd<FT,LA>&, const HyperplaneCd<FT,LA>&);
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static Comparison_result strong_cmp(
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const HyperplaneCd<FT,LA>&, const HyperplaneCd<FT,LA>&);
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bool operator==(const HyperplaneCd<FT,LA>& h2) const
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{ if (this->identical(h2)) return true;
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if (dimension()!=h2.dimension()) return false;
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return HyperplaneCd<FT,LA>::strong_cmp(*this,h2) == EQUAL;
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}
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bool operator!=(const HyperplaneCd<FT,LA>& h2) const
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{ return !operator==(h2); }
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friend std::istream& operator>> <>
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(std::istream&, HyperplaneCd<FT,LA>&);
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friend std::ostream& operator<< <>
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(std::ostream&, const HyperplaneCd<FT,LA>&);
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}; // end of class HyperplaneCd
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template <class FT, class LA>
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bool weak_equality(const HyperplaneCd<FT,LA>& h1,
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const HyperplaneCd<FT,LA>& h2)
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/*{\Mfunc test for weak equality. }*/
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{ if (h1.identical(h2)) return true;
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if (h1.dimension()!=h2.dimension()) return false;
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return HyperplaneCd<FT,LA>::weak_cmp(h1,h2) == EQUAL;
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}
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#undef PointCd
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} //namespace CGAL
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#endif // CGAL_HYPERPLANECD_H
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//----------------------- end of file ----------------------------------
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