/usr/include/CGAL/Min_annulus_d.h is in libcgal-dev 4.2-5ubuntu1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 | // Copyright (c) 1997-2001 ETH Zurich (Switzerland).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
// You can redistribute it and/or modify it under the terms of the GNU
// General Public License as published by the Free Software Foundation,
// either version 3 of the License, or (at your option) any later version.
//
// 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.
//
// $URL$
// $Id$
//
//
// Author(s) : Sven Schoenherr <sven@inf.ethz.ch>
#ifndef CGAL_MIN_ANNULUS_D_H
#define CGAL_MIN_ANNULUS_D_H
// includes
// --------
#include <CGAL/Optimisation/basic.h>
#include <CGAL/function_objects.h>
#include <CGAL/QP_options.h>
#include <CGAL/QP_solver/QP_solver.h>
#include <CGAL/QP_solver/functors.h>
#include <CGAL/QP_solver/QP_full_filtered_pricing.h>
#include <CGAL/QP_solver/QP_full_exact_pricing.h>
#include <boost/iterator/counting_iterator.hpp>
#include <boost/iterator/transform_iterator.hpp>
// here is how it works. We have d+2 variables:
// R (big radius), r (small radius), c (center). The problem is
//
// min R^2 - r^2
// s.t. ||p - c||^2 >= r^2 for all p
// ||p - c||^2 <= R^2 for all p
//
// This looks nonlinear, but we can in fact make the substitutions
// u = R^2 - c^Tc, v = r^2 - c^Tc and get the following equivalent
// linear program:
//
// min u - v
// s.t. p^Tp - 2p^Tc >= v for all p
// p^Tp - 2p^Tc <= u for all p
//
// or
//
// max v - u
// s.t. v + 2p_1c_1 + 2p_2c_2 + ... + 2p_dc_d <= p^Tp for all p
// - u - 2p_1c_1 - 2p_2c_2 - ... - 2p_dc_d <= -p^Tp for all p
//
// When we introduce a dual variable x_p for every constraint in the first
// set and a dual variable y_p for every constraint in the second set,
// we obtain the following dual program:
//
// min \sum_p x_p p^Tp - \sum_p y_p p^Tp
// s.t.
// 2\sum_p x_p p - 2\sum_p y_p p = 0
// \sum_p x_p = 1 (constraint for v)
// - \sum_p y_p = -1 (constraint for u)
// x_p >= 0 for all p
// y_p >= 0 for all p
//
// in the following functors, the ordering of the constraints is as above;
// the indices of the variables are: x_p_j <-> 2 * j, y_p_j <-> 2 * j + 1
// we also make the substitutions x'_p = x_p / h_p^2, y'_p = y_p / h_p^2
// where h_p is the homogenizing coordinate of p, in order to allow
// homogeneous points. This, however, means that the computed annulus is
// not necessarily correct. If P is a set of homogeneous points,
// P = { (p_0,...,p_{d-1}, h_p) },
// then we always get a *feasible* annulus for the point set
// P' = { (p_0*h_p,...,p_{d-1}*h_p, h_p*h_p) }.
// If the type NT is inexact, this annulus might not even be optimal, since
// the objective function involves terms p^Tp that might not be exactly
// computed -> document all this!!!
namespace CGAL {
namespace MA_detail {
// functor for a fixed column of A
template <class NT, class Iterator>
class A_column : public std::unary_function <int, NT>
{
public:
typedef NT result_type;
A_column()
{}
A_column (int j, int d, Iterator it)
: j_ (j), d_ (d), it_ (it), h_p (*(it+d)), nt_0_ (0), nt_2_ (2)
{}
result_type operator() (int i) const
{
if (j_ % 2 == 0) {
// column for x_p
if (i < d_) return *(it_ + i) * h_p * nt_2_;
if (i == d_) return h_p * h_p;
return nt_0_;
} else {
// column for y_p
if (i < d_) return -(*(it_ + i)) * h_p * nt_2_;
if (i == d_+1) return -h_p * h_p;
return nt_0_;
}
}
private:
int j_; // column number
int d_; // dimension
Iterator it_; // the iterator through the column's point
NT h_p; // the homogenizing coordinate of p
NT nt_0_;
NT nt_2_;
};
// functor for matrix A
template <class NT, class Access_coordinate_begin_d,
class Point_iterator >
class A_matrix : public std::unary_function
<int, boost::transform_iterator <A_column
<NT, typename Access_coordinate_begin_d::Coordinate_iterator>,
boost::counting_iterator<int> > >
{
typedef typename MA_detail::A_column
<NT, typename Access_coordinate_begin_d::Coordinate_iterator> A_column;
public:
typedef boost::transform_iterator
<A_column, boost::counting_iterator<int> > result_type;
A_matrix ()
{}
A_matrix (int d,
const Access_coordinate_begin_d& da_coord,
Point_iterator P)
: d_ (d), da_coord_ (da_coord), P_ (P)
{}
result_type operator () (int j) const
{
return result_type
(0, A_column (j, d_, da_coord_ (*(P_+j/2))));
}
private:
int d_; // dimension
Access_coordinate_begin_d da_coord_; // data accessor
Point_iterator P_; // point set P
};
// The functor necessary to realize access to b
template <class NT>
class B_vector : public std::unary_function<int, NT>
{
public:
typedef NT result_type;
B_vector()
{}
B_vector (int d)
: d_ (d), nt_0_ (0), nt_1_ (1)
{}
result_type operator() (int i) const
{
if (i == d_) return nt_1_;
if (i == d_+1) return -nt_1_;
return nt_0_;
}
private:
int d_;
NT nt_0_;
NT nt_1_;
};
}
// 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;
// public types
typedef std::vector<Point> Point_vector;
typedef typename Point_vector::const_iterator
Point_iterator;
private:
// QP solver iterator types
typedef MA_detail::A_matrix <NT, Access_coordinates_begin_d,
Point_iterator> A_matrix;
typedef boost::transform_iterator
<A_matrix,
boost::counting_iterator<int> > A_iterator;
typedef MA_detail::B_vector <NT> B_vector;
typedef boost::transform_iterator
<B_vector,
boost::counting_iterator<int> > B_iterator;
typedef CGAL::Const_oneset_iterator<CGAL::Comparison_result> R_iterator;
typedef std::vector<NT> C_vector;
typedef typename C_vector::const_iterator C_iterator;
// Program type
typedef CGAL::Nonnegative_linear_program_from_iterators
<A_iterator, B_iterator, R_iterator, C_iterator> LP;
// Tags
typedef QP_solver_impl::QP_tags <Tag_true, Tag_true> QP_tags;
// Solver types
typedef CGAL::QP_solver <LP, ET, QP_tags > 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<ET> ET_vector;
typedef QP_access_by_index
<typename std::vector<Point>::const_iterator, int> 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 CGAL::Join_input_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_input_iterator_1<
IVCI, Point_by_index >
Inner_support_point_iterator;
typedef CGAL::Join_input_iterator_1<
IVCI, Point_by_index >
Outer_support_point_iterator;
typedef IVCI Inner_support_point_index_iterator;
typedef IVCI Outer_support_point_index_iterator;
typedef typename ET_vector::const_iterator
Coordinate_iterator;
// creation
Min_annulus_d( const Traits& traits = Traits())
: tco( traits), da_coord(tco.access_coordinates_begin_d_object()),
d( -1), solver(0){}
template < class InputIterator >
Min_annulus_d( InputIterator first,
InputIterator last,
const Traits& traits = Traits())
: tco( traits), da_coord(tco.access_coordinates_begin_d_object()),
solver(0) {
set( first, last);
}
~Min_annulus_d() {
if (solver)
delete solver;
}
// access to point set
int ambient_dimension( ) const { return d; }
int number_of_points( ) const { return static_cast<int>(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 {
CGAL_optimisation_assertion_msg(number_of_points() >= 2,
"support_points_begin: not enough points");
return Support_point_iterator(
solver->basic_original_variable_indices_begin(),
CGAL::compose1_1(
Point_by_index( points.begin()),
std::bind2nd( std::divides<int>(), 2)));
}
Support_point_iterator
support_points_end() const {
CGAL_optimisation_assertion_msg(number_of_points() >= 2,
"support_points_begin: not enough points");
return Support_point_iterator(
solver->basic_original_variable_indices_end(),
CGAL::compose1_1(
Point_by_index( points.begin()),
std::bind2nd( std::divides<int>(), 2)));
}
int number_of_inner_support_points() const { return static_cast<int>(inner_indices.size());}
int number_of_outer_support_points() const { return static_cast<int>(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())); }
Inner_support_point_index_iterator
inner_support_points_indices_begin() const
{ return inner_indices.begin(); }
Inner_support_point_index_iterator
inner_support_points_indices_end() const
{ return inner_indices.end(); }
Outer_support_point_index_iterator
outer_support_points_indices_begin() const
{ return outer_indices.begin(); }
Outer_support_point_index_iterator
outer_support_points_indices_end() const
{ return outer_indices.end(); }
// 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);
ET h_p_sqr = da_coord(p)[d] * da_coord(p)[d];
return CGAL::Bounded_side
(CGAL_NTS sign( sqr_d - h_p_sqr * sqr_i_rad_numer)
* CGAL_NTS sign( h_p_sqr * 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);
ET h_p_sqr = da_coord(p)[d] * da_coord(p)[d];
return ( ( h_p_sqr * sqr_i_rad_numer < sqr_d) &&
( sqr_d < h_p_sqr * 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);
ET h_p_sqr = da_coord(p)[d] * da_coord(p)[d];
return (( sqr_d == h_p_sqr * sqr_i_rad_numer) ||
( sqr_d == h_p_sqr * 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);
ET h_p_sqr = da_coord(p)[d] * da_coord(p)[d];
return ( ( sqr_d < h_p_sqr * sqr_i_rad_numer) ||
( h_p_sqr * 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( std::size_t 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
Access_coordinates_begin_d da_coord; // data accessor
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
private:
// squared distance to center * h_p^2 * c_d^2
ET sqr_dist_exact( const Point& p) const
{
ET result(0);
typename Access_coordinates_begin_d::Coordinate_iterator
p_it (da_coord ( p)); // this is p * h_p
ET c_d = center_coords[d];
ET h_p = p_it[d];
for (int i=0; i<d; ++i) {
ET x =
c_d * ET(p_it[i]) - /* this is c_d * p_i * h_p */
h_p * center_coords[i] /* this is h_p * c_i * c_d */ ;
result += x * x;
}
return result;
}
// the function above computes sqr_dist as ||p-c||^2
// (endowed with a factor of c_d^2 * h_p^2)
// but we know that c was computed from (possibly slightly wrong)
// data if NT is inexact; in order to compensate for this, let
// us instead compute sqr_dist as p^Tp - 2c^Tp + c^Tc, where we use
// the (potentially wrong) values of p^Tp and p that went into the
// linear program; this will give us correct containment / on_boundary
// checks also in the inexact-NT case.
ET sqr_dist( const Point& p) const
{
ET result(0), two(2);
NT pTp(0); // computed over input type, possibly slightly wrong
ET cTc(0);
ET two_pTc(0);
typename Access_coordinates_begin_d::Coordinate_iterator
p_it (da_coord ( p)); // this is p * h_p
NT h_p = p_it[d]; // input type!
for (int i=0; i<d; ++i) {
NT p_i (p_it[i]); // input type!
pTp += p_i * p_i; // p_i^2 * h_p^2
cTc += center_coords[i] * center_coords[i]; // c_i^2 * c_d^2
two_pTc +=
// 2 * c_i * c_d * p_i * h_p^2
2 * center_coords[i] * ET(h_p * p_i);
}
ET c_d = center_coords[d];
result =
ET(pTp) * c_d * c_d +
cTc * ET (h_p * h_p) +
- two_pTc * c_d;
return result;
}
// 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( std::size_t 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( da_coord( points[ 0]),
da_coord( points[ 0])+d+1,
center_coords.begin());
sqr_i_rad_numer = ET( 0);
sqr_o_rad_numer = ET( 0);
sqr_rad_denom = ET( 1);
return;
}
// set up vector c and solve dual LP
// the ordering of the constraints is as above; the ordering
// of the variables is: z_p_j <-> 2 * j, y_p_j <-> 2 * j + 1
c_vector.resize( 2*points.size());
for ( int j = 0; j < number_of_points(); ++j) {
typename Traits::Access_coordinates_begin_d::Coordinate_iterator
coord_it = da_coord( points[j]);
NT sum = 0;
for ( int i = 0; i < d; ++i) {
sum += NT( coord_it[ i])*NT( coord_it[ i]);
}
c_vector[ 2*j ] = sum;
c_vector[ 2*j+1] = -sum;
}
LP lp (2*static_cast<int>(points.size()), d+2,
A_iterator ( boost::counting_iterator<int>(0),
A_matrix (d, da_coord, points.begin())),
B_iterator ( boost::counting_iterator<int>(0),
B_vector (d)),
R_iterator (CGAL::EQUAL),
c_vector.begin());
Quadratic_program_options options;
options.set_pricing_strategy(pricing_strategy(NT()));
delete solver;
solver = new Solver(lp, options);
CGAL_optimisation_assertion(solver->status() == QP_OPTIMAL);
// compute center and squared radius
ET sqr_sum = 0;
center_coords.resize( ambient_dimension()+1);
for ( int 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 ( int i = 0; i < solver->number_of_basic_original_variables(); ++i) {
int index = solver->basic_original_variable_indices_begin()[ i];
if ( index % 2 == 0) {
inner_indices.push_back( index/2);
} else {
outer_indices.push_back( index/2);
}
}
}
template < class NT >
Quadratic_program_pricing_strategy pricing_strategy( NT) {
return QP_PARTIAL_FILTERED_DANTZIG;
}
Quadratic_program_pricing_strategy pricing_strategy( ET) {
return QP_PARTIAL_DANTZIG;
}
};
// 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
{
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) {
ET h_p_sqr = da_coord (*i_pt_it)[d] * da_coord (*i_pt_it)[d];
if ( sqr_dist( *i_pt_it) != h_p_sqr * 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) {
ET h_p_sqr = da_coord (*o_pt_it)[d] * da_coord (*o_pt_it)[d];
if ( sqr_dist( *o_pt_it) != h_p_sqr * 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)
{
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)
{
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);
}
} //namespace CGAL
#endif // CGAL_MIN_ANNULUS_D_H
// ===== EOF ==================================================================
|