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// ======================================================================
//
// Copyright (c) 1997-2001 The CGAL Consortium
//
// This software and related documentation is part of an INTERNAL release
// of the Computational Geometry Algorithms Library (CGAL). It is not
// intended for general use.
//
// ----------------------------------------------------------------------
//
// release : $CGAL_Revision: CGAL-2.4-I-64 $
// release_date : $CGAL_Date: 2002/03/18 $
//
// file : include/CGAL/Min_annulus_d.h
// package : Min_annulus_d (1.1.3)
// maintainer : Sven Schönherr <sven@inf.ethz.ch>
// chapter : Geometric Optimisation
//
// source : web/Min_annulus_d.aw
// revision : $Revision$
// revision_date : $Date$
//
// author(s) : Sven Schönherr <sven@inf.ethz.ch>
// coordinator : ETH Zürich (Bernd Gärtner <gaertner@inf.ethz.ch>)
//
// implementation: Smallest enclosing annulus in arbitrary dimension
// ======================================================================
#ifndef CGAL_MIN_ANNULUS_D_H
#define CGAL_MIN_ANNULUS_D_H
// includes
// --------
#ifndef CGAL_OPTIMISATION_BASIC_H
# include <CGAL/Optimisation/basic.h>
#endif
#ifndef CGAL_FUNCTION_OBJECTS_H
# include <CGAL/function_objects.h>
#endif
#ifndef CGAL_IDENTITY_H
# include <CGAL/_QP_solver/identity.h>
#endif
#ifndef CGAL_FUNCTION_OBJECTS_ACCESS_BY_INDEX_H
# include <CGAL/_QP_solver/Access_by_index.h>
#endif
#ifndef CGAL_JOIN_RANDOM_ACCESS_ITERATOR_H
# include <CGAL/_QP_solver/Join_random_access_iterator.h>
#endif
#ifndef CGAL_QP_SOLVER_H
# include <CGAL/_QP_solver/QP_solver.h>
#endif
#ifndef CGAL_JOIN_RANDOM_ACCESS_ITERATOR_H
# include <CGAL/_QP_solver/Join_random_access_iterator.h>
#endif
#ifndef CGAL_PARTIAL_EXACT_PRICING_H
# include <CGAL/_QP_solver/Partial_exact_pricing.h>
#endif
#ifndef CGAL_PARTIAL_FILTERED_PRICING_H
# include <CGAL/_QP_solver/Partial_filtered_pricing.h>
#endif
#ifndef CGAL_PROTECT_VECTOR
# include <vector>
# define CGAL_PROTECT_VECTOR
#endif
#ifndef CGAL_PROTECT_IOSTREAM
# include <iostream>
# define CGAL_PROTECT_IOSTREAM
#endif
#ifndef CGAL_PROTECT_FUNCTIONAL_H
# include <functional>
# define CGAL_PROTECT_FUNCTIONAL_H
#endif
CGAL_BEGIN_NAMESPACE
// Class declarations
// ==================
template < class Traits_ >
class Min_annulus_d;
template < class ET_, class NT_, class Point, class PointIterator,
class Access_coord, class Access_dim >
struct LP_rep_min_annulus_d;
template < class NT >
struct LP_rep_row_of_a {
typedef std::vector<NT> argument_type;
typedef typename argument_type::const_iterator result_type;
result_type
operator ( ) ( const argument_type& v) const { return v.begin(); }
};
// Class interfaces
// ================
template < class Traits_ >
class Min_annulus_d {
public:
// self
typedef Traits_ Traits;
typedef Min_annulus_d<Traits> Self;
// types from the traits class
typedef typename Traits::Point_d Point;
typedef typename Traits::Rep_tag Rep_tag;
typedef typename Traits::RT RT;
typedef typename Traits::FT FT;
typedef typename Traits::Access_dimension_d
Access_dimension_d;
typedef typename Traits::Access_coordinates_begin_d
Access_coordinates_begin_d;
typedef typename Traits::Construct_point_d
Construct_point_d;
typedef typename Traits::ET ET;
typedef typename Traits::NT NT;
private:
// LP solver
typedef CGAL::LP_rep_min_annulus_d<
ET, NT, Point, typename std::vector<Point>::const_iterator,
Access_coordinates_begin_d, Access_dimension_d >
LP_rep;
typedef CGAL::QP_solver< LP_rep > Solver;
typedef typename Solver::Pricing_strategy
Pricing_strategy;
// types from the QP solver
typedef typename Solver::Basic_variable_index_iterator
Basic_variable_index_iterator;
// private types
typedef std::vector<Point> Point_vector;
typedef std::vector<ET> ET_vector;
typedef CGAL::Access_by_index<typename std::vector<Point>::const_iterator>
Point_by_index;
typedef std::binder2nd< std::divides<int> >
Divide;
typedef std::vector<int> Index_vector;
typedef std::vector<NT> NT_vector;
typedef std::vector<NT_vector> NT_matrix;
public:
// public types
typedef typename Point_vector::const_iterator
Point_iterator;
typedef CGAL::Join_random_access_iterator_1<
Basic_variable_index_iterator,
CGAL::Unary_compose_1<Point_by_index,Divide> >
Support_point_iterator;
typedef typename Index_vector::const_iterator IVCI;
typedef CGAL::Join_random_access_iterator_1<
IVCI, Point_by_index >
Inner_support_point_iterator;
typedef CGAL::Join_random_access_iterator_1<
IVCI, Point_by_index >
Outer_support_point_iterator;
typedef typename ET_vector::const_iterator
Coordinate_iterator;
// creation
Min_annulus_d( const Traits& traits = Traits(),
int verbose = 0,
std::ostream& stream = std::cout)
: tco( traits), d( -1), solver( verbose, stream)
{
set_pricing_strategy( NT());
}
template < class InputIterator >
Min_annulus_d( InputIterator first,
InputIterator last,
const Traits& traits = Traits(),
int verbose = 0,
std::ostream& stream = std::cout)
: tco( traits), solver( verbose, stream)
{
set_pricing_strategy( NT());
set( first, last);
}
// access to point set
int ambient_dimension( ) const { return d; }
int number_of_points( ) const { return points.size(); }
Point_iterator points_begin( ) const { return points.begin(); }
Point_iterator points_end ( ) const { return points.end (); }
// access to support points
int
number_of_support_points( ) const
{ return number_of_points() < 2 ? number_of_points()
: solver.number_of_basic_variables(); }
Support_point_iterator
support_points_begin() const
{ return Support_point_iterator(
solver.basic_variables_index_begin(),
CGAL::compose1_1(
Point_by_index( points.begin()),
std::bind2nd( std::divides<int>(), 2)));}
Support_point_iterator
support_points_end() const
{ return Support_point_iterator( number_of_points() < 2
? solver.basic_variables_index_begin()
: solver.basic_variables_index_end(),
CGAL::compose1_1(
Point_by_index( points.begin()),
std::bind2nd( std::divides<int>(), 2)));}
int number_of_inner_support_points() const { return inner_indices.size();}
int number_of_outer_support_points() const { return outer_indices.size();}
Inner_support_point_iterator
inner_support_points_begin() const
{ return Inner_support_point_iterator(
inner_indices.begin(),
Point_by_index( points.begin())); }
Inner_support_point_iterator
inner_support_points_end() const
{ return Inner_support_point_iterator(
inner_indices.end(),
Point_by_index( points.begin())); }
Outer_support_point_iterator
outer_support_points_begin() const
{ return Outer_support_point_iterator(
outer_indices.begin(),
Point_by_index( points.begin())); }
Outer_support_point_iterator
outer_support_points_end() const
{ return Outer_support_point_iterator(
outer_indices.end(),
Point_by_index( points.begin())); }
// access to center (rational representation)
Coordinate_iterator
center_coordinates_begin( ) const { return center_coords.begin(); }
Coordinate_iterator
center_coordinates_end ( ) const { return center_coords.end (); }
// access to squared radii (rational representation)
ET squared_inner_radius_numerator( ) const { return sqr_i_rad_numer; }
ET squared_outer_radius_numerator( ) const { return sqr_o_rad_numer; }
ET squared_radii_denominator ( ) const { return sqr_rad_denom; }
// access to center and squared radii
// NOTE: an implicit conversion from ET to RT must be available!
Point
center( ) const
{ CGAL_optimisation_precondition( ! is_empty());
return tco.construct_point_d_object()( ambient_dimension(),
center_coordinates_begin(),
center_coordinates_end()); }
FT
squared_inner_radius( ) const
{ CGAL_optimisation_precondition( ! is_empty());
return FT( squared_inner_radius_numerator()) /
FT( squared_radii_denominator()); }
FT
squared_outer_radius( ) const
{ CGAL_optimisation_precondition( ! is_empty());
return FT( squared_outer_radius_numerator()) /
FT( squared_radii_denominator()); }
// predicates
CGAL::Bounded_side
bounded_side( const Point& p) const
{ CGAL_optimisation_precondition(
is_empty() || tco.access_dimension_d_object()( p) == d);
ET sqr_d = sqr_dist( p);
return CGAL::Bounded_side(
CGAL::NTS::sign( sqr_d - sqr_i_rad_numer)
* CGAL::NTS::sign( sqr_o_rad_numer - sqr_d)); }
bool
has_on_bounded_side( const Point& p) const
{ CGAL_optimisation_precondition(
is_empty() || tco.access_dimension_d_object()( p) == d);
ET sqr_d = sqr_dist( p);
return ( ( sqr_i_rad_numer < sqr_d) && ( sqr_d < sqr_o_rad_numer)); }
bool
has_on_boundary( const Point& p) const
{ CGAL_optimisation_precondition(
is_empty() || tco.access_dimension_d_object()( p) == d);
ET sqr_d = sqr_dist( p);
return (( sqr_d == sqr_i_rad_numer) || ( sqr_d == sqr_o_rad_numer));}
bool
has_on_unbounded_side( const Point& p) const
{ CGAL_optimisation_precondition(
is_empty() || tco.access_dimension_d_object()( p) == d);
ET sqr_d = sqr_dist( p);
return ( ( sqr_d < sqr_i_rad_numer) || ( sqr_o_rad_numer < sqr_d)); }
bool is_empty ( ) const { return number_of_points() == 0; }
bool is_degenerate( ) const
{ return ! CGAL_NTS is_positive( sqr_o_rad_numer); }
// modifiers
template < class InputIterator >
void
set( InputIterator first, InputIterator last)
{ if ( points.size() > 0) points.erase( points.begin(), points.end());
std::copy( first, last, std::back_inserter( points));
set_dimension();
CGAL_optimisation_precondition_msg( check_dimension(),
"Not all points have the same dimension.");
compute_min_annulus(); }
void
insert( const Point& p)
{ if ( is_empty()) d = tco.access_dimension_d_object()( p);
CGAL_optimisation_precondition(
tco.access_dimension_d_object()( p) == d);
points.push_back( p);
compute_min_annulus(); }
template < class InputIterator >
void
insert( InputIterator first, InputIterator last)
{ CGAL_optimisation_precondition_code( int old_n = points.size());
points.insert( points.end(), first, last);
set_dimension();
CGAL_optimisation_precondition_msg( check_dimension( old_n),
"Not all points have the same dimension.");
compute_min_annulus(); }
void
clear( )
{ points.erase( points.begin(), points.end());
compute_min_annulus(); }
// validity check
bool is_valid( bool verbose = false, int level = 0) const;
// traits class access
const Traits& traits( ) const { return tco; }
private:
Traits tco; // traits class object
Point_vector points; // input points
int d; // dimension of input points
ET_vector center_coords; // center of small.encl.annulus
ET sqr_i_rad_numer; // squared inner radius of
ET sqr_o_rad_numer; // ---"--- outer ----"----
ET sqr_rad_denom; // smallest enclosing annulus
Solver solver; // linear programming solver
Index_vector inner_indices;
Index_vector outer_indices;
NT_matrix a_matrix; // matrix `A' of dual LP
NT_vector b_vector; // vector `b' of dual LP
NT_vector c_vector; // vector `c' of dual LP
typename Solver::Pricing_strategy* // pricing strategy
strategyP; // of the QP solver
// squared distance to center
ET
sqr_dist( const Point& p) const
{ return std::inner_product(
center_coords.begin(), center_coords.end()-1,
tco.access_coordinates_begin_d_object()( p), ET( 0),
std::plus<ET>(),
CGAL::compose1_2(
CGAL::compose2_1( std::multiplies<ET>(),
CGAL::identity<ET>(), CGAL::identity<ET>()),
CGAL::compose2_2( std::minus<ET>(),
CGAL::identity<ET>(),
std::bind2nd( std::multiplies<ET>(),
center_coords.back())))); }
// set dimension of input points
void
set_dimension( )
{ d = ( points.size() == 0 ? -1 :
tco.access_dimension_d_object()( points[ 0])); }
// check dimension of input points
bool
check_dimension( unsigned int offset = 0)
{ return ( std::find_if( points.begin()+offset, points.end(),
CGAL::compose1_1( std::bind2nd(
std::not_equal_to<int>(), d),
tco.access_dimension_d_object()))
== points.end()); }
// compute smallest enclosing annulus
void
compute_min_annulus( )
{
// clear inner and outer support points
inner_indices.erase( inner_indices.begin(), inner_indices.end());
outer_indices.erase( outer_indices.begin(), outer_indices.end());
if ( is_empty()) {
center_coords.resize( 1);
sqr_i_rad_numer = -ET( 1);
sqr_o_rad_numer = -ET( 1);
return;
}
if ( number_of_points() == 1) {
inner_indices.push_back( 0);
outer_indices.push_back( 0);
center_coords.resize( d+1);
std::copy( tco.access_coordinates_begin_d_object()( points[ 0]),
tco.access_coordinates_begin_d_object()( points[ 0])+d,
center_coords.begin());
center_coords[ d] = ET( 1);
sqr_i_rad_numer = ET( 0);
sqr_o_rad_numer = ET( 0);
sqr_rad_denom = ET( 1);
return;
}
// set up and solve dual LP
int i, j;
NT nt_0 = 0, nt_1 = 1, nt_2 = 2;
NT nt_minus_1 = -nt_1, nt_minus_2 = -nt_2;
// vector b
b_vector.resize( d+2);
for ( j = 0; j < d; ++j) b_vector[ j] = nt_0;
b_vector[ d ] = nt_1;
b_vector[ d+1] = nt_minus_1;
// matrix A, vector c
a_matrix.erase( a_matrix.begin(), a_matrix.end());
a_matrix.insert( a_matrix.end(), 2*points.size(), NT_vector( d+2));
c_vector.resize( 2*points.size());
for ( i = 0; i < number_of_points(); ++i) {
typename Traits::Access_coordinates_begin_d::Coordinate_iterator
coord_it = tco.access_coordinates_begin_d_object()( points[i]);
NT sum = 0;
for ( j = 0; j < d; ++j) {
a_matrix[ 2*i ][ j] = nt_2*coord_it[ j];
a_matrix[ 2*i+1][ j] = nt_minus_2*coord_it[ j];
sum += NT( coord_it[ j])*NT( coord_it[ j]);
}
a_matrix[ 2*i ][ d ] = nt_1;
a_matrix[ 2*i+1][ d ] = nt_0;
a_matrix[ 2*i ][ d+1] = nt_0;
a_matrix[ 2*i+1][ d+1] = nt_minus_1;
c_vector[ 2*i ] = sum;
c_vector[ 2*i+1] = -sum;
}
typedef typename LP_rep::A_iterator A_it;
typedef typename LP_rep::D_iterator D_it;
solver.set( 2*points.size(), d+2, d+2,
A_it( a_matrix.begin()), b_vector.begin(),
c_vector.begin(), D_it());
solver.init();
solver.solve();
// compute center and squared radius
ET sqr_sum = 0;
center_coords.resize( ambient_dimension()+1);
for ( i = 0; i < d; ++i) {
center_coords[ i] = -solver.dual_variable( i);
sqr_sum += center_coords[ i] * center_coords[ i];
}
center_coords[ d] = solver.variables_common_denominator();
sqr_i_rad_numer = sqr_sum
- solver.dual_variable( d )*center_coords[ d];
sqr_o_rad_numer = sqr_sum
- solver.dual_variable( d+1)*center_coords[ d];
sqr_rad_denom = center_coords[ d] * center_coords[ d];
// split up support points
for ( i = 0; i < solver.number_of_basic_variables(); ++i) {
int index = solver.basic_variables_index_begin()[ i];
if ( index % 2 == 0) {
inner_indices.push_back( index/2);
} else {
outer_indices.push_back( index/2);
}
}
}
template < class NT >
void set_pricing_strategy( NT)
{ strategyP = new CGAL::Partial_filtered_pricing<LP_rep>;
solver.set_pricing_strategy( *strategyP); }
#ifndef _MSC_VER
void set_pricing_strategy( ET)
{ strategyP = new CGAL::Partial_exact_pricing<LP_rep>;
solver.set_pricing_strategy( *strategyP); }
#endif
};
template < class ET_, class NT_, class Point, class PointIterator,
class Access_coord, class Access_dim >
struct LP_rep_min_annulus_d {
typedef ET_ ET;
typedef NT_ NT;
typedef std::vector<NT> NT_vector;
typedef std::vector<NT_vector> NT_matrix;
typedef CGAL_TYPENAME_MSVC_NULL NT_matrix::const_iterator NTMCI;
typedef CGAL::Join_random_access_iterator_1<
NTMCI, LP_rep_row_of_a<NT> > A_iterator;
typedef typename NT_vector::const_iterator
B_iterator;
typedef typename NT_vector::const_iterator
C_iterator;
typedef A_iterator D_iterator; // dummy
typedef CGAL::Tag_true Is_lp;
};
// Function declarations
// =====================
// I/O operators
template < class Traits_ >
std::ostream&
operator << ( std::ostream& os, const Min_annulus_d<Traits_>& min_annulus);
template < class Traits_ >
std::istream&
operator >> ( std::istream& is, Min_annulus_d<Traits_>& min_annulus);
// ============================================================================
// Class implementation
// ====================
// validity check
template < class Traits_ >
bool
Min_annulus_d<Traits_>::
is_valid( bool verbose, int level) const
{
CGAL_USING_NAMESPACE_STD
CGAL::Verbose_ostream verr( verbose);
verr << "CGAL::Min_annulus_d<Traits>::" << endl;
verr << "is_valid( true, " << level << "):" << endl;
verr << " |P| = " << number_of_points()
<< ", |S| = " << number_of_support_points() << endl;
// containment check (a)
// ---------------------
verr << " (a) containment check..." << flush;
Point_iterator point_it = points_begin();
for ( ; point_it != points_end(); ++point_it) {
if ( has_on_unbounded_side( *point_it))
return CGAL::_optimisation_is_valid_fail( verr,
"annulus does not contain all points");
}
verr << "passed." << endl;
// support set check (b)
// ---------------------
verr << " (b) support set check..." << flush;
// all inner support points on inner boundary?
Inner_support_point_iterator i_pt_it = inner_support_points_begin();
for ( ; i_pt_it != inner_support_points_end(); ++i_pt_it) {
if ( sqr_dist( *i_pt_it) != sqr_i_rad_numer)
return CGAL::_optimisation_is_valid_fail( verr,
"annulus does not have all inner support points on its inner boundary");
}
// all outer support points on outer boundary?
Outer_support_point_iterator o_pt_it = outer_support_points_begin();
for ( ; o_pt_it != outer_support_points_end(); ++o_pt_it) {
if ( sqr_dist( *o_pt_it) != sqr_o_rad_numer)
return CGAL::_optimisation_is_valid_fail( verr,
"annulus does not have all outer support points on its outer boundary");
}
/*
// center strictly in convex hull of support points?
typename Solver::Basic_variable_numerator_iterator
num_it = solver.basic_variables_numerator_begin();
for ( ; num_it != solver.basic_variables_numerator_end(); ++num_it) {
if ( ! ( CGAL::NTS::is_positive( *num_it)
&& *num_it <= solver.variables_common_denominator()))
return CGAL::_optimisation_is_valid_fail( verr,
"center does not lie strictly in convex hull of support points");
}
*/
verr << "passed." << endl;
verr << " object is valid!" << endl;
return( true);
}
// output operator
template < class Traits_ >
std::ostream&
operator << ( std::ostream& os,
const Min_annulus_d<Traits_>& min_annulus)
{
CGAL_USING_NAMESPACE_STD
typedef typename Min_annulus_d<Traits_>::Point Point;
typedef ostream_iterator<Point> Os_it;
typedef typename Traits_::ET ET;
typedef ostream_iterator<ET> Et_it;
switch ( CGAL::get_mode( os)) {
case CGAL::IO::PRETTY:
os << "CGAL::Min_annulus_d( |P| = "
<< min_annulus.number_of_points() << ", |S| = "
<< min_annulus.number_of_inner_support_points() << '+'
<< min_annulus.number_of_outer_support_points() << endl;
os << " P = {" << endl;
os << " ";
copy( min_annulus.points_begin(), min_annulus.points_end(),
Os_it( os, ",\n "));
os << "}" << endl;
os << " S_i = {" << endl;
os << " ";
copy( min_annulus.inner_support_points_begin(),
min_annulus.inner_support_points_end(),
Os_it( os, ",\n "));
os << "}" << endl;
os << " S_o = {" << endl;
os << " ";
copy( min_annulus.outer_support_points_begin(),
min_annulus.outer_support_points_end(),
Os_it( os, ",\n "));
os << "}" << endl;
os << " center = ( ";
copy( min_annulus.center_coordinates_begin(),
min_annulus.center_coordinates_end(),
Et_it( os, " "));
os << ")" << endl;
os << " squared inner radius = "
<< min_annulus.squared_inner_radius_numerator() << " / "
<< min_annulus.squared_radii_denominator() << endl;
os << " squared outer radius = "
<< min_annulus.squared_outer_radius_numerator() << " / "
<< min_annulus.squared_radii_denominator() << endl;
break;
case CGAL::IO::ASCII:
copy( min_annulus.points_begin(), min_annulus.points_end(),
Os_it( os, "\n"));
break;
case CGAL::IO::BINARY:
copy( min_annulus.points_begin(), min_annulus.points_end(),
Os_it( os));
break;
default:
CGAL_optimisation_assertion_msg( false,
"CGAL::get_mode( os) invalid!");
break; }
return( os);
}
// input operator
template < class Traits_ >
std::istream&
operator >> ( std::istream& is, CGAL::Min_annulus_d<Traits_>& min_annulus)
{
CGAL_USING_NAMESPACE_STD
switch ( CGAL::get_mode( is)) {
case CGAL::IO::PRETTY:
cerr << endl;
cerr << "Stream must be in ascii or binary mode" << endl;
break;
case CGAL::IO::ASCII:
case CGAL::IO::BINARY:
typedef typename CGAL::Min_annulus_d<Traits_>::Point Point;
typedef istream_iterator<Point> Is_it;
min_annulus.set( Is_it( is), Is_it());
break;
default:
CGAL_optimisation_assertion_msg( false, "CGAL::IO::mode invalid!");
break; }
return( is);
}
CGAL_END_NAMESPACE
#endif // CGAL_MIN_ANNULUS_D_H
// ===== EOF ==================================================================
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