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cgal/Kinetic_data_structures/include/CGAL/Polynomial/internal/Isolating_interval.h

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// Copyright (c) 2005 Stanford University (USA).
// 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 Lesser General Public License as
// published by the Free Software Foundation; version 2.1 of the License.
// See the file LICENSE.LGPL distributed with CGAL.
//
// 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) : Daniel Russel <drussel@alumni.princeton.edu>
#ifndef CGAL_POLYNOMIAL_INTERNAL_ISOLATING_INTERVAL_H
#define CGAL_POLYNOMIAL_INTERNAL_ISOLATING_INTERVAL_H
#include <CGAL/Polynomial/basic.h>
#include <CGAL/Polynomial/internal/interval_arithmetic.h>
#include <iostream>
CGAL_POLYNOMIAL_BEGIN_INTERNAL_NAMESPACE
//! necessary to support filtered_numbers which I don't like
template <class NT, class Functor>
typename Functor::result_type apply(const Functor &f, const NT &a)
{
return f(a);
}
//! necessary to support filtered_numbers which I don't like
template <class NT, class Functor>
typename Functor::result_type apply(const Functor &f, const NT &a,
const NT &b)
{
return f( a, b);
}
//! necessary to support filtered_numbers which I don't like
template <class NT, class Functor, class Data>
typename Functor::result_type apply(const Functor &f, const NT &a,
const NT &b, const Data &da, const Data &db)
{
return f( a, b, da, db);
}
//! Define the interface for a bounding interval By convention the intervals are closed.
/*!
Just remember the bounds.
*/
template <class FT_t>
class Isolating_interval
{
typedef Isolating_interval<FT_t> This;
public:
typedef FT_t NT;
Isolating_interval(): b_(1, -1){}
Isolating_interval(const NT &lbi): b_(lbi, lbi) {
}
Isolating_interval(const NT &lbi, const NT &ubi): b_(lbi, ubi) {
if(0) print(); // make sure it is instantiated
if (lb() > ub()) {
std::cerr << "b_.first=" << lb() << " and b_.second=" << ub() << std::endl;
}
CGAL_Polynomial_assertion(lb() <= ub());
}
typedef enum Endpoint {UPPER, LOWER}
Endpoint;
//! Damn this is awful, but I can't think of another way for Filtered interval
template <class Function>
typename Function::result_type apply_to_endpoint(const Function &f, Endpoint b) const
{
CGAL_Polynomial_assertion(lb() <= ub());
if (b==UPPER) {
return apply(f,ub());
}
else {
return apply(f, lb());
}
}
//! Damn this is awful, but I can't think of another way for Filtered interval
template <class Function>
typename Function::result_type apply_to_midpoint(const Function &f) {
CGAL_Polynomial_assertion(lb() <= ub());
return apply(f,middle());
}
//!
template <class Function>
typename Function::result_type apply_to_interval(const Function &f) const
{
CGAL_Polynomial_assertion(lb() <= ub());
return apply(f, lb(), ub());
}
//! Allow some extra data. This is kind of an evil hack.
template <class Function, class Data>
typename Function::result_type apply_to_interval(const Function &f,
const Data &d0, const Data &d1) const
{
CGAL_Polynomial_assertion(lb() <= ub());
return apply(f, lb(), ub(), d0, d1);
}
This upper_endpoint_interval() const
{
CGAL_Polynomial_assertion(lb() <= ub());
return This(ub());
}
This lower_endpoint_interval() const
{
CGAL_Polynomial_assertion(lb() <= ub());
return This(lb());
}
//! Make the interval singular on bound b.
This endpoint_interval(Endpoint b) const
{
CGAL_Polynomial_assertion(lb() <= ub());
if (b==UPPER) {
return This(ub());
}
else {
return This(lb());
}
}
This midpoint_interval() const
{
CGAL_Polynomial_assertion(lb() <= ub());
return This(middle());
}
//! Split in half
This first_half() const
{
CGAL_Polynomial_assertion(lb() <= ub());
return This(lb(), middle());
}
//! Split in half
This second_half() const
{
CGAL_Polynomial_assertion(lb() <= ub());
return This(middle(), ub());
}
//! Return both the first and second half; the midpoint is computed once
std::pair<This,This> split() const
{
CGAL_Polynomial_assertion(lb() <= ub());
NT mid = middle();
return std::pair<This,This>(This(lb(), mid), This(mid, ub()));
}
//! Returns the interval [(a+(a+b)/2)/2,((a+b)/2+b)/2]
This middle_half() const
{
CGAL_Polynomial_assertion(lb() <= ub());
NT mid = middle();
NT mid_left = midpoint(lb(), middle());
NT mid_right = midpoint(middle(), ub());
return This(mid_left, mid_right);
}
std::pair<This,This> split_at(const NT& x) const
{
CGAL_Polynomial_assertion(lb() <= ub());
CGAL_precondition( !is_singular() &&
lower_bound() < x && x < upper_bound() );
return std::pair<This,This>( This(lower_bound(), x),
This(x, upper_bound()) );
}
This split_at_first_half(const NT& x) const
{
CGAL_Polynomial_assertion(lb() <= ub());
CGAL_precondition( !is_singular() &&
lower_bound() < x && x < upper_bound() );
return This(lower_bound(), x);
}
This split_at_second_half(const NT& x) const
{
CGAL_Polynomial_assertion(lb() <= ub());
CGAL_precondition( !is_singular() &&
lower_bound() < x && x < upper_bound() );
return This(x, upper_bound());
}
This interval_around_endpoint(Endpoint b) const
{
CGAL_Polynomial_assertion(lb() <= ub());
NT mid = middle();
if ( b == LOWER ) {
return This(lower_bound()-NT(1), mid);
} // end-if
// b == UPPER
return This(mid, upper_bound()+NT(1));
}
//! See if the interval only contains a point.
bool is_singular() const
{
CGAL_Polynomial_assertion(lb() <= ub());
return lb()==ub();
}
const NT &to_nt() const
{
CGAL_Polynomial_assertion(lb() <= ub());
CGAL_Polynomial_precondition(is_singular());
return lb();
}
/*bool overlaps(const This &o) const {
if (b_.first > o.b_.first && b_.first < o.b_.second) return true;
else if (b_.second > o.b_.first && b_.first < o.b_.second) return true;
else if (o.b_.second > b_.first && b_.first < b_.second) return true;
else if (o.b_.first > b_.first && b_.first < b_.second) return true;
else if (*this==o) return true;
else return false;
}*/
//! Compare this interval to another.
Order order(const This &o) const
{
CGAL_Polynomial_assertion(lb() <= ub());
CGAL_Polynomial_assertion(o.lb() <= o.ub());
if (*this < o) return STRICTLY_BELOW;
else if (o < *this) return STRICTLY_ABOVE;
else if (lb() <= o.lb() && ub() >= o.ub()) return CONTAINS;
else if (o.lb() <= lb() && o.ub() >= ub()) return CONTAINED;
else if (*this == o) return EQUAL;
else if (lb() < o.lb()) return BELOW;
else return ABOVE;
}
//! Cut this at bound b on interval o
/*! i.e. If bd is UPPER, then o is assumed to be below this (but
overlaping) and the new interval goes from o.upper_bound() to
this->upper_bound()
*/
/*This chop(const This &o, Endpoint bd) const {
if (bd== UPPER) {
Polynomial_assertion(lb()== o.lb() && ub() > o.ub());
return This(o.ub(), ub());
} else {
Polynomial_assertion(ub()== o.ub() && lb() < o.lb());
return This(lb(),o.lb());
}
}*/
int number_overlap_intervals(const This &o) const
{
CGAL_Polynomial_assertion(lb() <= ub());
CGAL_Polynomial_assertion(o.lb() <= o.ub());
Order ord= order(o);
switch(ord) {
case CONTAINS:
return 3;
case CONTAINED:
return 1;
case BELOW:
case ABOVE:
return 2;
case STRICTLY_ABOVE:
case STRICTLY_BELOW:
return 1;
default:
return -1;
}
}
// If we have two partially overllaping intervals, then
// *_overlap_interval return the three possible intervals of *this:
// the common interval and the non-common remainders of the two
// intervals.
This first_overlap_interval(const This &o) const
{
CGAL_Polynomial_assertion(lb() <= ub());
CGAL_Polynomial_assertion(o.lb() <= o.ub());
Order ord= order(o);
switch(ord) {
case CONTAINS:
return This(lb(), o.lb());
case CONTAINED:
case STRICTLY_ABOVE:
case STRICTLY_BELOW:
return *this;
case BELOW:
return This(lb(), o.lb());
case ABOVE:
return This(lb(), o.ub());
default:
return This();
};
}
This second_overlap_interval(const This &o) const
{
CGAL_Polynomial_assertion(lb() <= ub());
CGAL_Polynomial_assertion(o.lb() <= o.ub());
Order ord= order(o);
switch(ord) {
case CONTAINS:
return This(o.lb(), o.ub());
case BELOW:
return This(o.lb(), ub());
case ABOVE:
return This(o.ub(), ub());
default:
return This();
};
}
This third_overlap_interval(const This &o) const
{
CGAL_Polynomial_assertion(lb() <= ub());
CGAL_Polynomial_assertion(o.lb() <= o.ub());
Order ord= order(o);
switch(ord) {
case CONTAINS:
return This(o.ub(), ub());
default:
return This();
};
}
/*std::pair<This, This> split_with(const This &o) const {
bool I_would_like_to_get_rid_of_this;
CGAL_precondition(0);
Order ord= order(o);
typedef std::pair<This, This> IP;
switch(ord){
case STRICTLY_BELOW:
return IP(*this, endpoint_interval(UPPER));
case STRICTLY_ABOVE:
return IP(endpoint_interval(LOWER, *this));
case BELOW:
return IP(This(lb(), o.lb()), This(ub(), o.ub()));
case CONTAINS:
return IP(This(lb(), o.lb()), This();
}
}*/
//! Split this and o into 3 parts
/*!
this and o must overlap and this must be below or containing o.
Then the three regions created by the 4 endpoints are returned.
*/
/*
void subintervals(const This &o, This &a, This &b, This &c) const {
bool I_would_like_to_get_rid_of_this;
Order ord= order(o);
switch (ord){
case BELOW:
a=This(lb(), o.lb());
b=This(o.lb(), ub());
c=This(ub(), o.ub());
break;
case CONTAINS:
a=This(lb, o.lb());
b=o;
c=This(o.ub(), ub());
break;
case CONTAINED:
a=This(o.lb, lb());
b=*this;
c=This(ub(), o.ub());
break;
case ABOVE:
a=This(o.lb(), lb());
b=This(lb(), o.ub());
c=This(o.ub(), ub());
break;
case STRICTLY_BELOW:
a=*this;
b=This(ub(), o.lb());
c=o;
break;
case STRICTLY_ABOVE:
a=o;
b=This(o.ub(), lb());
c=*this;
break;
default:
CGAL_error();
}
CGAL_postcondition(a.ub()==b.lb());
CGAL_postcondition(b.ub()==c.lb());
}*/
/**/
bool operator<(const This &o) const
{
CGAL_Polynomial_assertion(lb() <= ub());
CGAL_Polynomial_assertion(o.lb() <= o.ub());
if (ub() < o.lb()) return true;
return (ub() == o.lb() && (!is_singular() || !o.is_singular()));
/*
if (ub() == o.lb() && (!is_singular() || !o.is_singular())) return true;
else return false;
*/
}
bool operator>(const This &o) const
{
CGAL_Polynomial_assertion(lb() <= ub());
CGAL_Polynomial_assertion(o.lb() <= o.ub());
return o < *this;
}
bool operator>=(const This &o) const
{
CGAL_Polynomial_assertion(lb() <= ub());
CGAL_Polynomial_assertion(o.lb() <= o.ub());
return *this >0 || *this==o;
}
bool operator<=(const This &o) const
{
CGAL_Polynomial_assertion(lb() <= ub());
CGAL_Polynomial_assertion(o.lb() <= o.ub());
return *this < 0 || *this==o;
}
bool operator==(const This &o) const
{
CGAL_Polynomial_assertion(lb() <= ub());
CGAL_Polynomial_assertion(o.lb() <= o.ub());
return lb()==o.lb() && ub()==o.ub();
}
bool operator!=(const This &o) const
{
CGAL_Polynomial_assertion(lb() <= ub());
CGAL_Polynomial_assertion(o.lb() <= o.ub());
return lb()!=o.lb() || ub()!=o.ub();
}
//! Approximate the width with doubles.
double approximate_width() const
{
CGAL_Polynomial_assertion(lb() <= ub());
return (std::max)(to_double(ub()) - to_double(lb()), 0.0);
}
double approximate_relative_width() const
{
CGAL_Polynomial_assertion(lb() <= ub());
return approximate_width()/(std::max)(to_double(abs(ub())), to_double(abs(lb())));
}
bool contains(const This &o) {
CGAL_Polynomial_assertion(lb() <= ub());
return lb() <= o.lb() && ub() >= o.ub();
}
bool contains(const NT &o) {
return lb() <= o && ub() >= o;
}
template <class OStream>
void write(OStream &out) const
{
if (is_singular()) {
out << lb();
}
else {
out << "(" << lb() << "..." << ub() << ")";
}
if (0) print();
}
void print() const ;
This operator-() const
{
CGAL_Polynomial_assertion(lb() <= ub());
return This(-ub(), -lb());
}
//! return an interval
std::pair<double, double> double_interval() const
{
CGAL_Polynomial_assertion(lb() <= ub());
std::pair<double, double>
lbi= CGAL_POLYNOMIAL_TO_INTERVAL(lb()),
ubi= CGAL_POLYNOMIAL_TO_INTERVAL(ub());
return std::pair<double, double>(lbi.first, ubi.second);
}
const NT& lower_bound() const
{
CGAL_Polynomial_assertion(lb() <= ub());
// bool not_recommended;
return lb();
}
const NT& upper_bound() const
{
CGAL_Polynomial_assertion(lb() <= ub());
// bool not_recommended;
return ub();
}
void set_upper(const NT& u) {
CGAL_Polynomial_assertion(lb() <= ub());
b_.second = u;
}
void set_lower(const NT& l) {
CGAL_Polynomial_assertion(lb() <= ub());
b_.first = l;
}
/*std::pair<NT, NT> () const {
return std::pair<NT,NT>(b_.first, b_.second);
}*/
//! find the min interval containing both.
/*This operator||(const This &o){
return This((std::min)(lb(), o.lb()), (std::max)(ub(), o.ub()));
}*/
//! Union
This operator||(const This &o) const
{
CGAL_Polynomial_assertion(lb() <= ub());
return This((std::min)(lb(), o.lb()), (std::max)(ub(), o.ub()));
}
NT middle() const
{
CGAL_Polynomial_assertion(lb() <= ub());
return NT(0.5)*(ub()+lb());
}
const std::pair<NT,NT>& to_pair() const {
return b_;
}
protected:
std::pair<NT,NT> b_;
NT midpoint(const NT& a, const NT& b) const
{
return NT(0.5)*(a+b);
}
const NT &lb() const
{
return b_.first;
}
const NT &ub() const
{
return b_.second;
}
/*static NT infinity() {
if (std::numeric_limits<NT>::has_infinity){
return std::numeric_limits<NT>::infinity();
} else if (std::numeric_limits<NT>::is_bounded){
return (std::numeric_limits<NT>::max)();
} else {
return NT(1000000000);
}
}*/
};
template <class NT>
void Isolating_interval<NT>::print() const
{
write(std::cout);
std::cout << std::endl;
}
template <class OStream, class NT>
OStream &operator<<(OStream &out, const Isolating_interval<NT> &ii)
{
ii.write(out);
return out;
}
/*template <class NT>
std::pair<double, double> to_interval(const Isolating_interval<NT> &ii){
return ii.to_interval();
}*/
CGAL_POLYNOMIAL_END_INTERNAL_NAMESPACE
#ifdef CGAL_POLYNOMIAL_USE_CGAL
CGAL_BEGIN_NAMESPACE
template <class NT>
std::pair<double, double> to_interval(const typename CGAL_POLYNOMIAL_NS::internal::Isolating_interval<NT> &ii)
{
return ii.double_interval();
}
CGAL_END_NAMESPACE
#endif
#endif
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