Interval.h File Reference

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Detailed Description

Interval class definition.

Author:

Bart Stander, John C. Hart

Adapted by Hart from Stander's original 1997 ism code.

Todo:

Remove global functions like IExp().

Definition in file Interval.h.

#include <math.h>
#include <stdio.h>
#include "Infinite.h"
#include "libgm/gm.h"
#include "tnt/vec.h"

Include dependency graph for Interval.h:

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Classes
class	Interval
	An interval arithmetic class. More...
Defines
#define	I_NOT(x)   (((x) == I_TRUE) ? I_FALSE : ((x) == I_FALSE)?I_TRUE:I_MAYBE)
	Complement of an I_TRISTATE variable.
Typedefs
typedef Interval< double >	Intervald
	Convenience typedef so we don't always have to type Interval<double>.
Enumerations
enum	I_TRISTATE { I_TRUE = 0, I_FALSE = -1, I_MAYBE = 1 }
	Tristate logic for interval conditions. More...
enum	IDIF_TYPES { INORMAL = 0, ISPLIT, IDIV_BY_ZERO }
	Used to indicate result of division by zero INORMAL - Division resulted in a single interval - normally ISPLIT - Division resulted in two separate intervals IDIV_BY_ZERO - Error since denominator was zero. More...
Functions
template<class Type> IDIF_TYPES	IDinf (Interval< Type > &v, Interval< Type > &v2, const Interval< Type > &x, const Interval< Type > &y)
	Full Interval division In this extended version, divide by zero is allowed.
template<class Type> std::ostream &	operator<< (std::ostream &os, const Interval< Type > &x)
	Basic output stream operator for printing out the value of the Interval.
template<class Type> Interval< Type >	operator+ (const Interval< Type > &a, const Interval< Type > &b)
	Sum of two Intervals.
template<class Type> Interval< Type >	operator+ (const Interval< Type > &a, const Type &b)
	Sum of an Interval and a base Type.
template<class Type> Interval< Type >	operator+ (const Type &a, const Interval< Type > &b)
	Sum of a base Type and an Interval.
template<class Type> Interval< Type >	operator- (const Interval< Type > &a, const Interval< Type > &b)
	Difference of two Intervals.
template<class Type> Interval< Type >	operator- (const Interval< Type > &a, const Type &b)
	Difference of an Interval and a base Type.
template<class Type> Interval< Type >	operator- (const Type &a, const Interval< Type > &b)
	Difference of a base Type and an Interval.
template<class Type> Interval< Type >	operator * (const Interval< Type > &a, const Interval< Type > &b)
	Product of two Intervals.
template<class Type> Interval< Type >	operator * (const Interval< Type > &a, const Type &b)
	Product of an Interval and a base Type.
template<class Type> Interval< Type >	operator * (const Type &a, const Interval< Type > &b)
	Product of a base Type and an Interval.
template<class Type> Interval< Type >	operator/ (const Interval< Type > &a, const Interval< Type > &b)
	Quotient of two Intervals.
template<class Type> Interval< Type >	operator/ (const Interval< Type > &a, const Type &b)
	Quotient of an Interval and a base Type.
template<class Type> Interval< Type >	operator/ (const Type &a, const Interval< Type > &b)
	Quotient of a base Type and an Interval.
template<class Type> I_TRISTATE	operator< (const Interval< Type > &a, const Interval< Type > &b)
	Less-than for two Intervals.
template<class Type> I_TRISTATE	operator< (const Interval< Type > &a, const Type &b)
	Less than for an Interval and a base Type.
template<class Type> I_TRISTATE	operator< (const Type &a, const Interval< Type > &b)
	Less than for a base Type and an Interval.
template<class Type> I_TRISTATE	operator> (const Interval< Type > &a, const Interval< Type > &b)
	Greater-than for two Intervals.
template<class Type> I_TRISTATE	operator> (const Interval< Type > &a, const Type &b)
	Greater-than for an Interval and a base Type.
template<class Type> I_TRISTATE	operator> (const Type &a, const Interval< Type > &b)
	Greater-than for a base Type and an Interval.
template<class Type> I_TRISTATE	operator<= (const Interval< Type > &a, const Interval< Type > &b)
	Less-than-or-equal-to for two Intervals.
template<class Type> I_TRISTATE	operator<= (const Interval< Type > &a, const Type &b)
	Less-than-or-equal-to for an Interval and a base Type.
template<class Type> I_TRISTATE	operator<= (const Type &a, const Interval< Type > &b)
	Less-than-or-equal-to for a base Type and an Interval.
template<class Type> I_TRISTATE	operator>= (const Interval< Type > &a, const Interval< Type > &b)
	Greater-than-or-equal-to for two Intervals.
template<class Type> I_TRISTATE	operator>= (const Interval< Type > &a, const Type &b)
	Greater-than-or-equal-to for an Interval and a base Type.
template<class Type> I_TRISTATE	operator>= (const Type &a, const Interval< Type > &b)
	Greater-than-or-equal-to for a base Type and an Interval.
template<class Type> I_TRISTATE	operator== (const Interval< Type > &a, const Interval< Type > &b)
	Equivalence for two Intervals.
template<class Type> I_TRISTATE	operator== (const Interval< Type > &a, const Type &b)
	Equivalence for an Interval and a base Type.
template<class Type> I_TRISTATE	operator== (const Type &a, const Interval< Type > &b)
	Equivalence for a base Type and an Interval.
template<class Type> I_TRISTATE	operator!= (const Interval< Type > &a, const Interval< Type > &b)
	Non-Equivalence for two Intervals.
template<class Type> I_TRISTATE	operator!= (const Interval< Type > &a, const Type &b)
	Non-equivalence for an Interval and a base Type.
template<class Type> I_TRISTATE	operator!= (const Type &a, const Interval< Type > &b)
	Non-equivalence for a base Type and an Interval.

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Define Documentation

#define I_NOT (  x   )     (((x) == I_TRUE) ? I_FALSE : ((x) == I_FALSE)?I_TRUE:I_MAYBE)

Complement of an I_TRISTATE variable. I_TRUE->I_FALSE I_FALSE->I_TRUE I_MAYBE->I_MAYBE Definition at line 37 of file Interval.h. Referenced by operator!=().

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Typedef Documentation

typedef Interval<double> Intervald

Convenience typedef so we don't always have to type Interval<double>. Definition at line 156 of file Interval.h. Referenced by Wyvill::d2kernel(), Blinn::d2kernel(), Wyvill::dkernel(), Blinn::dkernel(), Implicit::Fx(), Implicit::Fxx(), Implicit::Fxy(), Implicit::Fxz(), Implicit::Fy(), Implicit::Fyx(), Implicit::Fyy(), Implicit::Fyz(), Implicit::Fz(), Implicit::Fzx(), Implicit::Fzy(), Implicit::Fzz(), Sphere::grad(), Segment::grad(), RBF::grad(), Blob::grad(), Blend::grad(), Algebraic::grad(), RBF::gradphi(), Implicit::gradq(), Algebraic::gradq(), Implicit::gradt(), RFunction::h(), AUnion::h(), ASubtraction::h(), AIntersection::h(), Sphere::hess(), RBF::hess(), Blob::hess(), Blend::hess(), Algebraic::hess(), RBF::hessphi(), RFunction::hf(), Blend::hf(), AUnion::hf(), ASubtraction::hf(), AIntersection::hf(), RFunction::hff(), Blend::hff(), AUnion::hff(), ASubtraction::hff(), AIntersection::hff(), RFunction::hfg(), Blend::hfg(), AUnion::hfg(), ASubtraction::hfg(), AIntersection::hfg(), RFunction::hg(), Blend::hg(), AUnion::hg(), ASubtraction::hg(), AIntersection::hg(), RFunction::hgg(), Blend::hgg(), AUnion::hgg(), ASubtraction::hgg(), AIntersection::hgg(), Blend::hr1(), Blend::hr2(), AUnion::indomain(), Wyvill::kernel(), Blinn::kernel(), Segment::m_alrp(), Algebraic::m_alrp(), Segment::m_blrp(), Plane::m_dlrp(), Plane::m_nlrp(), Mover::m_olrp(), Sphere::m_rlrp(), Offset::m_rlrp(), Sphere::m_xlrp(), NewtonDegenerate::NewtonSubdivisionBreak(), Implicit::operator()(), RBFPoint::phi(), RBF::phi(), UnaryOp::proc(), Sum::proc(), Subtraction::proc(), Sphere::proc(), Segment::proc(), RBF::proc(), Plane::proc(), Offset::proc(), Mover::proc(), ImpList::proc(), Implicit::proc(), Difference::proc(), Complement::proc(), Blob::proc(), Blend::proc(), Algebraic::proc(), ADF::proc(), Implicit::procq(), Algebraic::procq(), Sphere::proct(), Segment::proct(), Plane::proct(), Offset::proct(), Mover::proct(), Implicit::proct(), and SearchDegenerate::search().

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Enumeration Type Documentation

enum I_TRISTATE

Tristate logic for interval conditions. I_TRUE - True for all possible members. I_FALSE - False for all possible members. I_MAYBE - True for some, false for others. Enumeration values: I_TRUE  I_FALSE  I_MAYBE  Definition at line 23 of file Interval.h. Referenced by operator!=(), operator<(), operator<=(), operator==(), operator>(), and operator>=().

enum IDIF_TYPES

Used to indicate result of division by zero INORMAL - Division resulted in a single interval - normally ISPLIT - Division resulted in two separate intervals IDIV_BY_ZERO - Error since denominator was zero. Enumeration values: INORMAL  ISPLIT  IDIV_BY_ZERO  Definition at line 30 of file Interval.h. Referenced by IDinf().

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Function Documentation

template<class Type> IDIF_TYPES IDinf (  Interval< Type > &  v, Interval< Type > &  v2, const Interval< Type > &  x, const Interval< Type > &  y )

Full Interval division In this extended version, divide by zero is allowed. When this happens two semi-infinite intervals result. Parameters: x  Numerator. y  Denominator. v  Quotient. v2  Second part of quotient if a split occurs. Returns: ISPLIT if a split occurs. ()IDIV_BY_0, if that occurs. INORMAL (nothing bad happened). IDinf, interval divide by infinity, was taken from John M. Snyder's Thesis, California Institute of Technology, 1991 Definition at line 174 of file Interval.h. References Interval< Type >::check(), Interval< Type >::contains(), Interval< Type >::high(), IDIF_TYPES, IDIV_BY_ZERO, INORMAL, Interval< Type >::isMixed(), Interval< Type >::isNegative(), ISPLIT, Interval< Type >::isPositive(), and Interval< Type >::low(). Referenced by Newton::GaussSeidelRow().

template<class Type> Interval<Type> operator * (  const Type &  a, const Interval< Type > &  b )

Product of a base Type and an Interval. Definition at line 312 of file Interval.h.

template<class Type> Interval<Type> operator * (  const Interval< Type > &  a, const Type &  b )

Product of an Interval and a base Type. Definition at line 304 of file Interval.h.

template<class Type> Interval<Type> operator * (  const Interval< Type > &  a, const Interval< Type > &  b )

Product of two Intervals. Definition at line 296 of file Interval.h.

template<class Type> I_TRISTATE operator!= (  const Type &  a, const Interval< Type > &  b )

Non-equivalence for a base Type and an Interval. Definition at line 498 of file Interval.h. References I_TRISTATE.

template<class Type> I_TRISTATE operator!= (  const Interval< Type > &  a, const Type &  b )

Non-equivalence for an Interval and a base Type. Definition at line 491 of file Interval.h. References I_TRISTATE.

template<class Type> I_TRISTATE operator!= (  const Interval< Type > &  a, const Interval< Type > &  b )

Non-Equivalence for two Intervals. Returns: I_FALSE only if intervals equal with width zero. I_MAYBE only if intervals overlap. I_TRUE otherwise. Definition at line 484 of file Interval.h. References I_NOT, and I_TRISTATE.

template<class Type> Interval<Type> operator+ (  const Type &  a, const Interval< Type > &  b )

Sum of a base Type and an Interval. Definition at line 264 of file Interval.h.

template<class Type> Interval<Type> operator+ (  const Interval< Type > &  a, const Type &  b )

Sum of an Interval and a base Type. Definition at line 256 of file Interval.h.

template<class Type> Interval<Type> operator+ (  const Interval< Type > &  a, const Interval< Type > &  b )

Sum of two Intervals. Definition at line 248 of file Interval.h.

template<class Type> Interval<Type> operator- (  const Type &  a, const Interval< Type > &  b )

Difference of a base Type and an Interval. Definition at line 288 of file Interval.h.

template<class Type> Interval<Type> operator- (  const Interval< Type > &  a, const Type &  b )

Difference of an Interval and a base Type. Definition at line 280 of file Interval.h.

template<class Type> Interval<Type> operator- (  const Interval< Type > &  a, const Interval< Type > &  b )

Difference of two Intervals. Definition at line 272 of file Interval.h.

template<class Type> Interval<Type> operator/ (  const Type &  a, const Interval< Type > &  b )

Quotient of a base Type and an Interval. Definition at line 336 of file Interval.h.

template<class Type> Interval<Type> operator/ (  const Interval< Type > &  a, const Type &  b )

Quotient of an Interval and a base Type. Definition at line 328 of file Interval.h.

template<class Type> Interval<Type> operator/ (  const Interval< Type > &  a, const Interval< Type > &  b )

Quotient of two Intervals. Definition at line 320 of file Interval.h.

template<class Type> I_TRISTATE operator< (  const Type &  a, const Interval< Type > &  b )

Less than for a base Type and an Interval. Definition at line 364 of file Interval.h. References I_TRISTATE.

template<class Type> I_TRISTATE operator< (  const Interval< Type > &  a, const Type &  b )

Less than for an Interval and a base Type. Definition at line 357 of file Interval.h. References I_TRISTATE.

template<class Type> I_TRISTATE operator< (  const Interval< Type > &  a, const Interval< Type > &  b )

Less-than for two Intervals. Returns: I_TRUE only if all of me less than any of a. I_FALSE only if none of me is less than any of a. I_MAYBE otherwise. Definition at line 349 of file Interval.h. References I_FALSE, I_MAYBE, I_TRISTATE, and I_TRUE.

template<class Type> std::ostream& operator<< (  std::ostream &  os, const Interval< Type > &  x )

Basic output stream operator for printing out the value of the Interval. Definition at line 241 of file Interval.h.

template<class Type> I_TRISTATE operator<= (  const Type &  a, const Interval< Type > &  b )

Less-than-or-equal-to for a base Type and an Interval. Definition at line 418 of file Interval.h. References I_TRISTATE.

template<class Type> I_TRISTATE operator<= (  const Interval< Type > &  a, const Type &  b )

Less-than-or-equal-to for an Interval and a base Type. Definition at line 411 of file Interval.h. References I_TRISTATE.

template<class Type> I_TRISTATE operator<= (  const Interval< Type > &  a, const Interval< Type > &  b )

Less-than-or-equal-to for two Intervals. Returns: I_TRUE only if all of me less than or equal to any of a. I_FALSE only if none of me is less than or equal to any of a. I_MAYBE otherwise. Definition at line 403 of file Interval.h. References I_FALSE, I_MAYBE, I_TRISTATE, and I_TRUE.

template<class Type> I_TRISTATE operator== (  const Type &  a, const Interval< Type > &  b )

Equivalence for a base Type and an Interval. Definition at line 472 of file Interval.h. References I_TRISTATE.

template<class Type> I_TRISTATE operator== (  const Interval< Type > &  a, const Type &  b )

Equivalence for an Interval and a base Type. Definition at line 465 of file Interval.h. References I_TRISTATE.

template<class Type> I_TRISTATE operator== (  const Interval< Type > &  a, const Interval< Type > &  b )

Equivalence for two Intervals. Returns: I_TRUE only if intervals equal with width zero. I_MAYBE only if intervals overlap. I_FALSE otherwise. Definition at line 457 of file Interval.h. References I_FALSE, I_MAYBE, I_TRISTATE, I_TRUE, Interval< Type >::low(), Interval< Type >::overlaps(), and Interval< Type >::thin().

template<class Type> I_TRISTATE operator> (  const Type &  a, const Interval< Type > &  b )

Greater-than for a base Type and an Interval. Definition at line 391 of file Interval.h. References I_TRISTATE.

template<class Type> I_TRISTATE operator> (  const Interval< Type > &  a, const Type &  b )

Greater-than for an Interval and a base Type. Definition at line 384 of file Interval.h. References I_TRISTATE.

template<class Type> I_TRISTATE operator> (  const Interval< Type > &  a, const Interval< Type > &  b )

Greater-than for two Intervals. Returns: I_TRUE only if all of me greater than any of a. I_FALSE only if none of me is greater than any of a. I_MAYBE otherwise. Definition at line 376 of file Interval.h. References Interval< Type >::high(), I_FALSE, I_MAYBE, I_TRISTATE, I_TRUE, and Interval< Type >::low().

template<class Type> I_TRISTATE operator>= (  const Type &  a, const Interval< Type > &  b )

Greater-than-or-equal-to for a base Type and an Interval. Definition at line 445 of file Interval.h. References I_TRISTATE.

template<class Type> I_TRISTATE operator>= (  const Interval< Type > &  a, const Type &  b )

Greater-than-or-equal-to for an Interval and a base Type. Definition at line 438 of file Interval.h. References I_TRISTATE.

template<class Type> I_TRISTATE operator>= (  const Interval< Type > &  a, const Interval< Type > &  b )

Greater-than-or-equal-to for two Intervals. Returns: I_TRUE only if all of me greater than or equal to any of a. I_FALSE only if none of me is greater than or equal to any of a. I_MAYBE otherwise. Definition at line 430 of file Interval.h. References Interval< Type >::high(), I_FALSE, I_MAYBE, I_TRISTATE, I_TRUE, and Interval< Type >::low().

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