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interval.h
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interval.h
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// Compatiblity layer with ibex for the simple interval library from Luc JAULIN, with minor modifications from Fabrice LE BARS and Jeremy NICOLA.
#ifndef INTERVAL_H
#define INTERVAL_H
#ifdef _MSC_VER
// Disable some Visual Studio warnings.
# ifndef CRT_SECURE_NO_DEPRECATE
# define CRT_SECURE_NO_DEPRECATE
# endif // CRT_SECURE_NO_DEPRECATE
# ifndef _CRT_SECURE_NO_WARNINGS
# define _CRT_SECURE_NO_WARNINGS
# endif // _CRT_SECURE_NO_WARNINGS
//# ifndef _CRT_NONSTDC_NO_WARNINGS
//# define _CRT_NONSTDC_NO_WARNINGS
//# endif // _CRT_NONSTDC_NO_WARNINGS
#endif // _MSC_VER
#include "iboolean.h"
#include <vector>
#include <iomanip>
#include <algorithm>
//#include <limits> // For std::numeric_limits<double>.
// Some macros may need to be undefined for ibex...
#pragma push_macro("boolean")
#pragma push_macro("ERROR")
#pragma push_macro("MAX")
#pragma push_macro("MIN")
#pragma push_macro("max")
#pragma push_macro("min")
#ifndef PREVENT_MACROS_UNDEF_IBEX
#ifdef min
#undef min
#endif // min
#ifdef max
#undef max
#endif // max
#ifdef MIN
#undef MIN
#endif // MIN
#ifdef MAX
#undef MAX
#endif // MAX
#ifdef ERROR
#undef ERROR
#endif // ERROR
#ifdef boolean
#undef boolean
#endif // boolean
#endif // !PREVENT_MACROS_UNDEF_IBEX
#ifdef _MSC_VER
// Disable some Visual Studio warnings that happen sometimes in ibex.
#pragma warning(disable : 4018)
#pragma warning(disable : 4065)
#pragma warning(disable : 4068)
#pragma warning(disable : 4100)
#pragma warning(disable : 4101)
#pragma warning(disable : 4127)
#pragma warning(disable : 4189)
#pragma warning(disable : 4244)
#pragma warning(disable : 4245)
#pragma warning(disable : 4250)
#pragma warning(disable : 4267)
#pragma warning(disable : 4290)
#pragma warning(disable : 4458)
#pragma warning(disable : 4459)
#pragma warning(disable : 4505)
#pragma warning(disable : 4512)
#pragma warning(disable : 4702)
#pragma warning(disable : 4715)
#pragma warning(disable : 4805)
#pragma warning(disable : 4996)
#endif // _MSC_VER
#ifdef __GNUC__
// Disable some GCC warnings that happen sometimes in ibex.
#pragma GCC diagnostic ignored "-Wunused-parameter"
#pragma GCC diagnostic ignored "-Wunused-variable"
#pragma GCC diagnostic ignored "-Wunknown-pragmas"
#if (((__GNUC__ == 4) && (__GNUC_MINOR__ >= 6)) || (__GNUC__ > 4))
#pragma GCC diagnostic push
#else
#pragma GCC diagnostic ignored "-Wpragmas"
#endif // (((__GNUC__ == 4) && (__GNUC_MINOR__ >= 6)) || (__GNUC__ > 4))
#endif // __GNUC__
#include "ibex.h"
#ifdef __GNUC__
// Restore the GCC warnings previously disabled for ibex.
#if (((__GNUC__ == 4) && (__GNUC_MINOR__ >= 6)) || (__GNUC__ > 4))
#pragma GCC diagnostic pop
#else
#pragma GCC diagnostic warning "-Wpragmas"
#pragma GCC diagnostic warning "-Wunknown-pragmas"
#pragma GCC diagnostic warning "-Wunused-variable"
#pragma GCC diagnostic warning "-Wunused-parameter"
#endif // (((__GNUC__ == 4) && (__GNUC_MINOR__ >= 6)) || (__GNUC__ > 4))
#endif // __GNUC__
#ifdef _MSC_VER
// Restore the Visual Studio warnings previously disabled for ibex.
#pragma warning(default : 4996)
#pragma warning(default : 4805)
#pragma warning(default : 4715)
#pragma warning(default : 4702)
#pragma warning(default : 4512)
#pragma warning(default : 4505)
#pragma warning(default : 4459)
#pragma warning(default : 4458)
#pragma warning(default : 4290)
#pragma warning(default : 4267)
#pragma warning(default : 4250)
#pragma warning(default : 4245)
#pragma warning(default : 4244)
#pragma warning(default : 4189)
#pragma warning(default : 4127)
#pragma warning(default : 4101)
#pragma warning(default : 4100)
#pragma warning(default : 4068)
#pragma warning(default : 4065)
#pragma warning(default : 4018)
#endif // _MSC_VER
// Restore the macros previously undefined for ibex...
#pragma pop_macro("min")
#pragma pop_macro("max")
#pragma pop_macro("MIN")
#pragma pop_macro("MAX")
#pragma pop_macro("ERROR")
#pragma pop_macro("boolean")
#ifdef _MSC_VER
#ifndef UNREFERENCED_PARAMETER
#define UNREFERENCED_PARAMETER(P) (P)
#endif // !UNREFERENCED_PARAMETER
#endif // _MSC_VER
#ifdef __GNUC__
#undef UNREFERENCED_PARAMETER
#define UNREFERENCED_PARAMETER(P) (void)(P)
#endif // __GNUC__
#ifdef __BORLANDC__
#undef UNREFERENCED_PARAMETER
#define UNREFERENCED_PARAMETER(P)
#endif // __BORLANDC__
// To avoid Visual Studio 2013 warning about overflow in floating-point constant arithmetic
// each time INFINITY or NAN is used.
#if (_MSC_VER >= 1800)
#pragma warning(disable : 4056)
#endif // (_MSC_VER >= 1800)
// To avoid Visual Studio warnings that would happen for any project using ibex.
#ifdef _MSC_VER
#pragma warning(disable : 4505)
#pragma warning(disable : 4512)
#endif // _MSC_VER
// To avoid Visual Studio warnings that would happen for any project using interval.
#ifdef _MSC_VER
#pragma warning(disable : 4996)
#endif // _MSC_VER
// The definition of M_PI and M_PI_2 is not in C++ standard, although it is often provided by compilers...
#ifndef M_PI
#define M_PI 3.14159265358979323846
#endif // !M_PI
#ifndef M_PI_2
#define M_PI_2 1.57079632679489661923
#endif // !M_PI_2
#ifndef INFINITY
#define INFINITY HUGE_VAL
#endif // !INFINITY
#if defined(_MSC_VER) || defined(__BORLANDC__)
// Used to define NAN (Not A Number).
#ifndef NAN
extern const unsigned long nan[2];
extern const double nan_double;
//#define NAN (std::numeric_limits<double>::quiet_NaN())
#define NAN nan_double
#define NAN_CONSTS_NEEDED
#endif // !NAN
#endif // defined(_MSC_VER) || defined(__BORLANDC__)
// Infinity is denoted by oo.
#ifndef oo
//#define oo 1.0/0.0
//#define oo 1000000000.0
//#define oo INFINITY
//#define oo (std::numeric_limits<double>::infinity())
#define oo POS_INFINITY
#endif // !oo
// Try to transform the default interval constructor so that it returns an empty interval instead of [-oo,oo]...
//inline ibex::Interval empty_default_interval() { return ibex::Interval(ibex::Interval::EMPTY_SET); }
//#define interval() ibex::Interval(ibex::Interval::EMPTY_SET)
class interval_empty_default : public ibex::Interval
{
public:
//----------------------------------------------------------------------
// Constructors/destructors
//----------------------------------------------------------------------
interval_empty_default() : ibex::Interval(ibex::Interval::EMPTY_SET) { }
interval_empty_default(const ibex::Interval& _i) : ibex::Interval(_i) { }
interval_empty_default(double a, double b) : ibex::Interval(a, b) { }
interval_empty_default(double a) : ibex::Interval(a) { }
//----------------------------------------------------------------------
// Operators
//----------------------------------------------------------------------
// Needed because of errors : overloads have similar conversions...
friend interval_empty_default operator*(const interval_empty_default& x1, const interval_empty_default& x2) { return ibex::Interval(x1)*ibex::Interval(x2); }
friend interval_empty_default operator*(const ibex::Interval& x1, const interval_empty_default& x2) { return ibex::Interval(x1)*ibex::Interval(x2); }
friend interval_empty_default operator*(const interval_empty_default& x1, const ibex::Interval& x2) { return ibex::Interval(x1)*ibex::Interval(x2); }
friend interval_empty_default operator*(const double& x1, const interval_empty_default& x2) { return x1*ibex::Interval(x2); }
friend interval_empty_default operator*(const interval_empty_default& x1, const double& x2) { return ibex::Interval(x1)*x2; }
//operator const ibex::Interval&() const { return *this; }
friend std::ostream& operator<<(std::ostream& os, const interval_empty_default& a);
#ifdef QT_VERSION
//friend QDataStream& operator<<(QDataStream& s, const interval_empty_default& i)
//{
// s << i.lb() << i.ub() << i.is_empty();
// return s;
//}
//friend QDataStream& operator>>(QDataStream& s, interval_empty_default& i)
//{
// s >> i.lb() >> i.ub() >> i.is_empty();
// return s;
//}
friend QDebug operator<<(QDebug os, const interval_empty_default& a)
{
if (a.is_empty()) os.nospace() << "EmptyInterval";
else if (a.lb() != a.ub())
{
os.nospace() << "[" << a.lb() << ", " << a.ub() << "] ";
}
else os.nospace() << a.lb();
return os.space();
}
#endif // QT_VERSION
//----------------------------------------------------------------------
// Member functions
//----------------------------------------------------------------------
interval_empty_default& Intersect(const interval_empty_default& Y);
bool IsEmpty(void) const { return is_empty(); }
};
// interval will be noted as before...
#define interval interval_empty_default
//#define interval ibex::Interval
// To be able to use Interval like in ibex... However this might be confusing as ibex::Interval does not
// have the same default constuctor as interval...
//#define Interval interval_empty_default
// In some cases you might need to disable totally the following defines.
// However, most of the time it should be possible to use e.g. #undef isEmpty where appropriate when
// there are conflicts, as well as including this header at last (this happens sometimes with Qt)...
#ifndef DISABLE_DEFINES_OLD_INTERVAL_CLASS_VARIABLES
#define inf lb()
#define sup ub()
#define isEmpty is_empty()
#endif // !DISABLE_DEFINES_OLD_INTERVAL_CLASS_VARIABLES
// Used to define NAI (Not An Interval).
#ifndef NAI
extern const interval nai;
#define NAI nai
#define NAI_CONST_NEEDED
#endif // !NAI
#ifndef DISABLE_USING_NAMESPACE_STD_INTERVAL_H
using namespace std;
#endif // !DISABLE_USING_NAMESPACE_STD_INTERVAL_H
// Include <QDataStream> and <QDebug> before this file to be able to use Qt specific features if you have Qt.
#ifdef QT_VERSION
//class QDataStream;
//class QDebug;
#else
#define qDebug() std::cout
#endif // QT_VERSION
// Deprecated.
typedef double reel;
//----------------------------------------------------------------------
// Useful real-valued functions
//----------------------------------------------------------------------
double Min(std::vector<double>& x);
double Max(std::vector<double>& x);
double Sign(const double x);
double Chi(const double a, const double b, const double c);
double Arccossin(const double x, const double y);
double Arg(const double x, const double y);
double Det(double ux, double uy, double vx, double vy);
double DistanceDirSegment(double mx, double my, double theta, double ax, double ay, double bx, double by);
void DistanceDirSegment(double& d, double& phi, double mx, double my, double theta, double ax, double ay, double bx, double by);
double DistanceDirSegments(double mx, double my, double theta,
std::vector<double> ax, std::vector<double> ay, std::vector<double> bx, std::vector<double> by);
void DistanceDirSegments(double& d, double& phi, double mx, double my, double theta,
std::vector<double> ax, std::vector<double> ay, std::vector<double> bx, std::vector<double> by);
#define DistanceDirCercle DistanceDirCircle
#define DistanceDirCercles DistanceDirCircles
double DistanceDirCircle(double mx, double my, double theta, double cx, double cy, double r);
void DistanceDirCircle(double& d, double& phi, double mx, double my, double theta, double cx, double cy, double r);
double DistanceDirCircles(double mx, double my, double theta, std::vector<double> cx, std::vector<double> cy, std::vector<double> r);
void DistanceDirCircles(double& d, double& phi, double mx, double my, double theta,
std::vector<double> cx, std::vector<double> cy, std::vector<double> r);
double DistanceDirSegmentsOrCircles(double mx, double my, double theta,
std::vector<double> ax, std::vector<double> ay, std::vector<double> bx, std::vector<double> by,
std::vector<double> cx, std::vector<double> cy, std::vector<double> r);
void DistanceDirSegmentsOrCircles(double& d, double& phi, double mx, double my, double theta,
std::vector<double> ax, std::vector<double> ay, std::vector<double> bx, std::vector<double> by,
std::vector<double> cx, std::vector<double> cy, std::vector<double> r);
//----------------------------------------------------------------------
// Interval-valued functions
//----------------------------------------------------------------------
interval Min(const interval& x, const interval& y);
interval Min(const interval& x, const interval& y, const interval& z);
interval Max(const interval& x, const interval& y);
interval Max(const interval& x, const interval& y, const interval& z);
#define Abs ibex::abs
interval Sign(const interval&);
//interval Modulo(const interval& a, double x);
#define Sqr ibex::sqr
#define Sqrt ibex::sqrt
interval InvSqrt(interval& X);
#define Exp ibex::exp
#define Log ibex::log
#define Pow ibex::pow
//interval Pow(const interval& x, int num, int den);
interval PowFrac(const interval& x, int num, int den);
interval PowRoot(const interval& x, int num, int den);
#define Cos ibex::cos
#define Sin ibex::sin
#define Tan ibex::tan
#define Acos ibex::acos
#define Asin ibex::asin
#define Atan ibex::atan
interval Det(interval&, interval&, interval&, interval&);
interval Det(interval& ux, interval& uy, double& vx, double& vy);
interval Step(const interval&);
interval Parabole(const interval&, double, double, double);
interval Inter(const interval&, const interval&);
interval Inter(std::vector<interval> x);
interval Union(const interval&, const interval&);
interval Union(std::vector<interval> x);
interval Inflate(const interval&, double);
//----------------------------------------------------------------------
// Other functions
//----------------------------------------------------------------------
double Inf(const interval&);
double Sup(const interval&);
double Center(const interval&);
double Width(const interval&);
double Volume(const interval&);
double Rad(const interval&);
#define ToReel ToReal
#define Todouble ToReal
double ToReal(const interval&);
bool Disjoint(const interval& a, const interval& b);
bool Subset(const interval& a, const interval& b);
bool SubsetStrict(const interval& a, const interval& b);
iboolean In(const interval&, const interval&);
bool In(double, const interval&);
//----------------------------------------------------------------------
// Contractors
//----------------------------------------------------------------------
#define Cplus Cadd
void Cadd(interval& Z, interval& X, interval& Y, int dir = 0);
void Cadd(interval& Z, double x, interval& Y, int dir = 0);
void Cadd(interval& Z, interval& X, double y, int dir = 0);
//void Cadd(double z, interval& X, interval& Y, int dir = 0);
#define Cmoins Csub
void Csub(interval& Z, interval& X, interval& Y, int dir = 0);
void Csub(interval& Z, double x, interval& Y, int dir = 0);
void Csub(interval& Z, interval& X, double y, int dir = 0);
//void Csub(double z, interval& X, interval& Y, int dir = 0);
#define Cprod Cmul
void Cmul(interval& Z, interval& X, interval& Y, int dir = 0);
void Cmul(interval& Z, double x, interval& Y, int dir = 0);
void Cmul(interval& Z, interval& X, double y, int dir = 0);
//void Cmul(double z, interval& X, interval& Y, int dir = 0);
void Cdiv(interval& Z, interval& X, interval& Y, int dir = 0);
#define Cegal Cequal
void Cequal(interval& Y, interval& X, int dir);
void Cequal(interval& Y, interval& X);
void Cmin(interval& a, interval& b, interval& c, int dir = 0);
void Cmin(interval& a, interval& b, interval& c, interval& d, int dir = 0);
void Cmin(interval& a, interval& b, interval& c, interval& d, interval& e, int dir = 0);
int Cmin(interval& a, std::vector<interval>& x, int dir = 0);
void Cmax(interval& a, interval& b, interval& c, int dir = 0);
void Cabs(interval& Y, interval& X, int dir = 0);
#define Csame_sign Csign
void Csign(interval& Y, interval& X);
void Csign(interval& Y, interval& X, int dir, double a = 0);
void Cchi(interval& F, interval& A, interval& B, interval& C);
void Cgeq(interval& Y, interval& X);
void Cinteger(interval&);
void Cboolean(interval&);
void Csqr(interval& Y, interval& X, int dir = 0);
void Cexp(interval& Y, interval& X, int dir = 0);
void Clog(interval& Y, interval& X, int dir = 0);
void Cpow(interval& Y, interval& X, int n);
void Ccos(interval& Y, interval& X, int dir = 0);
void Csin(interval& Y, interval& X, int dir = 0);
void Ctan(interval& Y, interval& X, int dir = 0);
void Catan(interval& Y, interval& X, int dir = 0);
//CAngle() bStrongAngle?
#define CNorm Cnorm
void Cnorm(interval& N, interval& X, interval& Y);
void Cnorm(interval& N, interval& X, interval& Y, interval& Z, int dir = 0);
#define Cdistance Cdist
void Cdist(interval& R, interval& X1, interval& Y1, interval& X2, interval& Y2);
#define CScal Cscal
void Cscal(interval& s, interval& ux, interval& uy, interval& vx, interval& vy);
void Cscal(interval& s, double& ux, double& uy, interval& vx, interval& vy);
#define CDet Cdet
void Cdet(interval& det, interval& ux, interval& uy, interval& vx, interval& vy, int dir = 0);
void Cdet(interval& det, double& ux, double& uy, interval& vx, interval& vy, int dir = 0);
void Cdet(interval& det, interval& ux, interval& uy, double& vx, double& vy, int dir = 0);
void Cstep(interval& Y, interval& X);
void Cstep(interval& Y, interval& X, int dir, double a = 0);
void Cramp(interval& Y, interval& X, int dir = 0, double a = 0);
void Cheaviside(interval& Y, interval& X, int dir = 0, double a = 0);
void Crect(interval& Z, interval& X, interval& Y, int dir = 0);
void Crect(interval& Y, interval& X, int dir = 0);
void Ctriangle(interval& Y, interval& X, int dir = 0);
void CDistanceDirLine(interval& dist, interval& mx, interval& my, interval& theta,
double& ax, double& ay, double& bx, double& by);
int CDistanceDirSegment(interval& dist, interval& mx, interval& my, interval& theta,
double ax, double ay, double bx, double by, int dir = 0);
void CDistanceDirSegments(interval& distmin, interval& mx, interval& my, interval& theta,
std::vector<double> ax, std::vector<double> ay, std::vector<double> bx, std::vector<double> by);
#define CinRing CPointInRing
void CPointInRing(interval& X, interval& Y, double cx, double cy, interval R);
void CPointInLine(interval& mx, interval& my, double& ax, double& ay, double& bx, double& by);
#define CinSegment CPointInSegment
void CPointInSegment(interval& mx, interval& my, double ax, double ay, double bx, double by);
#define CinSegments CPointInSegments
void CPointInSegments(interval& mx, interval& my, std::vector<double> ax, std::vector<double> ay, std::vector<double> bx, std::vector<double> by);
#define CinCircle CPointInCircle
void CPointInCircle(interval& mx, interval& my, double cx, double cy, double r);
#define CinCircles CPointInCircles
void CPointInCircles(interval& mx, interval& my, std::vector<double> cx, std::vector<double> cy, std::vector<double> r, bool truth = true);
#define CinSegmentsOrCircles CPointInSegmentsOrCircles
void CPointInSegmentsOrCircles(interval& mx, interval& my,
std::vector<double> ax, std::vector<double> ay, std::vector<double> bx, std::vector<double> by,
std::vector<double> cx, std::vector<double> cy, std::vector<double> r);
void CPointOutsideSegment(interval& mx, interval& my, double& ax, double& ay, double& bx, double& by, bool outer);
void CPointOutsideSegments(interval& mx, interval& my,
std::vector<double> ax, std::vector<double> ay, std::vector<double> bx, std::vector<double> by, bool outer);
void CPoseInSegment(interval& mx, interval& my, interval& phi, double& ax, double& ay, double& bx, double& by);
void CPoseInSegments(interval& mx, interval& my, interval& phi,
std::vector<double> ax, std::vector<double> ay, std::vector<double> bx, std::vector<double> by);
void CPoseInCircle(interval& mx, interval& my, interval& phi, double& cx, double& cy, double& r);
void CPoseInCircles(interval& mx, interval& my, interval& phi, std::vector<double> cx, std::vector<double> cy, std::vector<double> r);
void CPoseInSegmentsOrCircles(interval& mx, interval& my, interval& malpha,
std::vector<double> ax, std::vector<double> ay, std::vector<double> bx, std::vector<double> by,
std::vector<double> cx, std::vector<double> cy, std::vector<double> r);
void CPoseTrans(interval& qx, interval& qy, interval& d, interval& px, interval& py, interval& theta); //Go straight
void CPoseRotTrans(interval& qx, interval& qy, interval& beta, interval& phi, interval& d, interval& px, interval& py, interval& alpha);
void CPoseTransInWallsOrCircles(interval& px, interval& py, interval& alpha, interval& d,
std::vector<double> ax, std::vector<double> ay, std::vector<double> bx, std::vector<double> by,
std::vector<double> cx,std::vector<double> cy, std::vector<double> r);
void CPoseTransRotInWallsOrCircles(interval& px, interval& py, interval& alpha, interval& d, interval& psi,
std::vector<double> ax, std::vector<double> ay, std::vector<double> bx, std::vector<double> by,
std::vector<double> cx, std::vector<double> cy, std::vector<double> r);
void CPoseRotTransRotInWallsOrCircles(interval& px, interval& py, interval& alpha, interval& phi, interval& d, interval& psi,
std::vector<double> ax, std::vector<double> ay, std::vector<double> bx, std::vector<double> by,
std::vector<double> cx, std::vector<double> cy, std::vector<double> r);
void CPoseRotTransPointInWallsOrCircles(interval& px, interval& py, interval& alpha, interval& phi, interval& d,
std::vector<double> ax, std::vector<double> ay, std::vector<double> bx, std::vector<double> by,
std::vector<double> cx, std::vector<double> cy, std::vector<double> r);
void CPoseTransPointInWall(interval& px,interval& py, interval& alpha, interval& d,
double ax, double ay, double bx, double by, bool truth = true);
void CPoseTransPointInWalls(interval& px,interval& py, interval& alpha, interval& d0,
std::vector<double>& ax, std::vector<double>& ay, std::vector<double>& bx, std::vector<double>& by, bool truth = true);
void CPoseTransPointInWallsOrCircles(interval& px,interval& py, interval& alpha, interval& d0,
std::vector<double> ax,std::vector<double> ay,std::vector<double> bx,std::vector<double> by,
std::vector<double> cx, std::vector<double> cy, std::vector<double> r, bool truth = true);
void CPoseTowardSegment(interval& mx, interval& my, interval& theta,
double& ax, double& ay, double& bx, double& by, bool truth = true);
#define Ccroisepas Cnocross
void Cnocross(interval& px, interval& py, interval& mx, interval& my, double& ax, double& ay, double& bx, double& by);
#define CPatteCroiseAucunSegment CLegCrossNoSegment
void CLegCrossNoSegment(interval& dist, interval& px, interval& py, interval& theta,
std::vector<double> ax, std::vector<double> ay, std::vector<double> bx, std::vector<double> by);
void CLegOnWalls(interval& dist, interval& px, interval& py, interval& theta,
std::vector<double> ax, std::vector<double> ay, std::vector<double> bx, std::vector<double> by);
void CLegOnWallsOrCircles(interval& dist, interval& px, interval& py, interval& theta,
std::vector<double> ax, std::vector<double> ay, std::vector<double> bx, std::vector<double> by,
std::vector<double> cx, std::vector<double> cy, std::vector<double> r);
void ShowContraction(interval&, interval&, interval&, interval&);
void IntButterfly(interval& Y, interval Yo, interval dY, interval& X, interval Xo, int dir);
void Inter1(interval&, interval&, const interval&, const interval&, const interval&);
void Sucre(interval&, const interval&);
void Cnotin(interval& X, interval& Y, int dir = 0);
void C_q_in(interval& x, int q, std::vector<interval>& y);
//----------------------------------------------------------------------
// Separators
//----------------------------------------------------------------------
void SinRing(interval& X, interval& Y, double cx, double cy, interval R, bool outer = false);
//----------------------------------------------------------------------
// Other
//----------------------------------------------------------------------
void diffI(interval &x0, interval &x1, interval &c0, interval &c1);
iboolean TestDiskExists(const interval& X, const interval& Y, const interval& P1, const interval& P2, const interval& P3);
iboolean TestDiskForall(const interval& X, const interval& Y, const interval& P1, const interval& P2, const interval& P3);
#endif // !INTERVAL_H