interval.h File Reference

Definition of the Tinterval type and the associated functions. More...

#include "boolean.h"
#include <stdio.h>

Data Structures
struct	Tinterval
	Defines a interval. More...
Functions
void	NewInterval (double lower, double upper, Tinterval *i)
	Constructor.
void	CopyInterval (Tinterval i_dst, Tinterval i_org)
	Copy constructor.
boolean	CmpIntervals (Tinterval i1, Tinterval i2)
	Compares two intervals.
double	LowerLimit (Tinterval *i)
	Gets the lower limit.
double	UpperLimit (Tinterval *i)
	Gets the uppser limit.
double	IntervalSize (Tinterval *i)
	Gets the uppser limit.
boolean	IsInside (double p, Tinterval *i)
	Checks if a value is inside an interval.
double	IntervalCenter (Tinterval *i)
	Gets the interval center.
void	SetLowerLimit (double c, Tinterval *i)
	Sets a new lower limit.
void	SetUpperLimit (double c, Tinterval *i)
	Sets a new upper limit.
boolean	IntervalInclusion (Tinterval i1, Tinterval i2)
	Checks is a given interval is fully included into another interval.
boolean	Intersect (Tinterval i1, Tinterval i2)
	Checks is a two intervals intersect.
boolean	Intersection (Tinterval i1, Tinterval i2, Tinterval *i_out)
	Computes the intersection of two intervals.
boolean	Union (Tinterval i1, Tinterval i2, Tinterval *i_out)
	Computes the union of two intervals.
boolean	EmptyInterval (Tinterval *i)
	Checks if a given interval is empty.
void	IntervalScale (Tinterval i1, double e, Tinterval i_out)
	Scales an interval.
void	IntervalProduct (Tinterval i1, Tinterval i2, Tinterval *i_out)
	Product of two intervals.
void	IntervalAdd (Tinterval i1, Tinterval i2, Tinterval *i_out)
	Addition of two intervals.
void	IntervalSubstract (Tinterval i1, Tinterval i2, Tinterval *i_out)
	Substraction of two intervals.
void	IntervalInvert (Tinterval i, Tinterval i_out)
	Change of sign of a given interval.
void	IntervalPow (Tinterval i, unsigned int p, Tinterval i_out)
	Power of a given interval by a integer power factor.
boolean	IntervalSqrt (Tinterval i, Tinterval i_out)
	Interval square root.
void	IntervalDivision (Tinterval num, Tinterval den, Tinterval *i_out)
	Interval division.
void	IntervalOffset (Tinterval i, double offset, Tinterval i_out)
	Interval offset.
void	IntervalSinus (Tinterval i, Tinterval i_out)
	Interval sinus.
void	IntervalCosinus (Tinterval i, Tinterval i_out)
	Interval cosinus.
void	IntervalAtan2 (Tinterval is, Tinterval ic, Tinterval *i_out)
	Interval atan2.
void	PrintInterval (FILE f, Tinterval i)
	Prints an interval.
void	DeleteInterval (Tinterval *i)
	Destructor.

Detailed Description

Definition of the Tinterval type and the associated functions.

See also:: Tinterval, interval.c.

Definition in file interval.h.

Function Documentation

void NewInterval	(	double	lower,
		double	upper,
		Tinterval *	i
	)

Defines a new interval with the given limits.

Parameters:

	lower	The lower limit for the new interval.
	upper	The upper limit for the new interval.
	i	The interval to define.

Definition at line 47 of file interval.c.

References Tinterval::lower_limit, and Tinterval::upper_limit.

Referenced by BoxSaddleClipping(), BoxSphereClipping(), Buffer2Box(), ComputeBoundingBox(), ComputeBoundingBox3d(), CropEquation(), CropLinearConstraint(), ErrorDueToVariable(), EvaluateEquationInt(), EvaluateLinearConstraintInt(), EvaluateMonomialInt(), EvaluateVarSetInt(), GenerateEquationsFromBranch(), GenerateJointEquations(), GenerateJointRangeEquations(), GenerateLinkRot(), GetFirstOrderApproximationToEquation(), InitBox(), IntervalCosinus(), IntervalSinus(), LoadLinearConstraint(), NewFixJoint(), NewFreeJoint(), NewPrismaticJoint(), NewRevoluteJoint(), NewSphericalJoint(), NewSphSphJoint(), NewUniversalJoint(), NewVariable(), ReadBox(), RectangleCircleClipping(), RectangleParabolaClipping(), ResetLinearConstraint(), SampleCuikSystemInBox(), SetEquationInfo(), SimplexExpandBounds(), SimplexGetColBounds(), SimplexGetOptimalValue(), SimplexGetRowBounds(), SimplifyLinearConstraint(), and SplitBox().

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void CopyInterval	(	Tinterval *	i_dst,
		Tinterval *	i_org
	)

Defines a new interval from another interval.

Parameters:

	i_dst	The interval to create.
	i_org	The interval from where to copy.

Definition at line 59 of file interval.c.

References Tinterval::lower_limit, and Tinterval::upper_limit.

Referenced by BoxSaddleClipping(), CleanLinearConstraint(), CopyBoxSubset(), CopyJoint(), CopyLinearConstraint(), CopyVariable(), CropEquation(), CropLinearConstraint(), GetLinearConstraintError(), NewPrismaticJoint(), NewRevoluteJoint(), NewUniversalJoint(), ReduceRange(), SetBoxInterval(), SetLinearConstraintError(), SetVariableInterval(), SimpleFromOriginal(), and UpdateOriginalFromSimple().

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boolean CmpIntervals	(	Tinterval *	i1,
		Tinterval *	i2
	)

Compares two intervals.

Parameters:

	i1	The first interval.
	i2	The second interval.

Returns:: TRUE if the two given intervals are the same.

Definition at line 72 of file interval.c.

References Tinterval::lower_limit, and Tinterval::upper_limit.

double LowerLimit ( Tinterval * i )

Gets the lower limit of an interval

Parameters:

i

The interval.

Returns:: The lower limit defining the interval.

Definition at line 81 of file interval.c.

References Tinterval::lower_limit.

Referenced by AddEquation2Simplex(), Box2Buffer(), CoordInequalitiesHold(), CropLinearConstraint(), CSRemoveVarsWithCtRange(), EquationFromLinearConstraint(), GetFirstOrderApproximationToEquation(), GetJointMaxCoordinate(), LinearizeCircleEquation(), LinearizeGeneralEquation(), LinearizeParabolaEquation(), LinearizeSaddleEquation(), LinearizeSphereEquation(), main(), NewInPatchJoint(), randomInInterval(), ReduceRange(), SaveLinearConstraint(), SimplexAddNewConstraintRaw(), SimplexExpandBounds(), SimplexGetOptimalValue(), SimplexSetColBounds(), SimplexSetRowBounds(), and SplitBox().

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double UpperLimit ( Tinterval * i )

Gets the upper limit of an interval.

Parameters:

i

The interval.

Returns:: The upper limit defining the interval.

Definition at line 89 of file interval.c.

References Tinterval::upper_limit.

Referenced by AddEquation2Simplex(), Box2Buffer(), CoordInequalitiesHold(), CropLinearConstraint(), EquationFromLinearConstraint(), GetJointMaxCoordinate(), LinearizeCircleEquation(), LinearizeGeneralEquation(), LinearizeParabolaEquation(), LinearizeSaddleEquation(), LinearizeSphereEquation(), main(), randomInInterval(), ReduceRange(), SaveLinearConstraint(), SimplexAddNewConstraintRaw(), SimplexExpandBounds(), SimplexGetOptimalValue(), SimplexSetColBounds(), SimplexSetRowBounds(), and SplitBox().

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double IntervalSize ( Tinterval * i )

Gets the upper limit of an interval.

Parameters:

i

The interval.

Returns:: The upper limit defining the interval.

Definition at line 98 of file interval.c.

References Tinterval::lower_limit, ROUNDNEAR, ROUNDUP, and Tinterval::upper_limit.

Referenced by AddEquation2Simplex(), CleanLinearConstraint(), ComputeSplitDimInt(), CropEquation(), CropLinearConstraint(), CSRemoveLCVars(), CSRemoveVarsWithCtRange(), EquationFromLinearConstraint(), EquationFromLinearConstraintProduct(), ErrorDueToVariable(), GenerateJointRangeEquations(), GetBoxDiagonal(), GetBoxMaxDim(), GetBoxMaxSizeVarSet(), GetBoxMinSizeVarSet(), GetBoxSize(), GetBoxVolume(), IntervalAtan2(), IntervalCosinus(), IntervalSinus(), IsPunctualBox(), PrintLinearConstraint(), ReduceBox(), ReduceBoxEquationWise(), ReduceRange(), ReplaceVariableInEquation(), SetSimplexBounds(), SimplexAddNewConstraint(), and SimplexSetRowBounds().

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boolean IsInside	(	double	p,
		Tinterval *	i
	)

Checks if a value is inside an interval.

Parameters:

	p	The value
	i	The interval.

Returns:: TRUE if the point is inside the interval.

Definition at line 228 of file interval.c.

References Tinterval::lower_limit.

Referenced by AddEquation2Simplex(), BoxSaddleClipping(), CropLinearConstraint(), IntervalPow(), PointInBox(), PointInSubBox(), and PointInSystemBox().

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double IntervalCenter ( Tinterval * i )

Computes the interval center, i.e., the average between the upper and the lower limit.

Parameters:

i

The interval.

Returns:: The interval center.

Definition at line 112 of file interval.c.

References INF, Tinterval::lower_limit, and Tinterval::upper_limit.

Referenced by CropEquation(), CSRemoveLCVars(), DistanceToSubBoxCenter(), EquationFromLinearConstraint(), EquationFromLinearConstraintProduct(), ErrorInInequalities(), ErrorInSolution(), EvaluateEqMin(), GenerateJointRangeEquations(), GetBoxCenterDistance(), LinearizeCircleEquation(), LinearizeGeneralEquation(), LinearizeParabolaEquation(), LinearizeSphereEquation(), main(), MoveWorld(), NewRevoluteJoint(), NewUniversalJoint(), PrintLinearConstraint(), ReplaceVariableInEquation(), SampleCuikSystemInBox(), SimplifyCuikSystem(), and UpdateSplitWeight().

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void SetLowerLimit	(	double	c,
		Tinterval *	i
	)

Changes the lower limit for an interval.

Parameters:

	c	The new lower limit.
	i	The interval.

Definition at line 134 of file interval.c.

References Tinterval::lower_limit.

Referenced by ReduceRange().

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void SetUpperLimit	(	double	c,
		Tinterval *	i
	)

Changes the upper limit for an interval.

Parameters:

	c	The new lower limit.
	i	The interval.

Definition at line 139 of file interval.c.

References Tinterval::upper_limit.

Referenced by ReduceRange().

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boolean IntervalInclusion	(	Tinterval *	i1,
		Tinterval *	i2
	)

Checks is a given interval is fully included into another interval.

Parameters:

	i1	The interval to be included.
	i2	The inclusion interval.

Returns:: TRUE if i1 is fully included in i2.

Definition at line 147 of file interval.c.

References Tinterval::lower_limit, and Tinterval::upper_limit.

Referenced by BoxInclusion().

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boolean Intersect	(	Tinterval *	i1,
		Tinterval *	i2
	)

Checks two given intervals have a non-empty intersection.

Parameters:

	i1	The first interval.
	i2	The second interval.

Returns:: TRUE if i1 and i2 intersect.

Definition at line 157 of file interval.c.

References Intersection().

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boolean Intersection	(	Tinterval *	i1,
		Tinterval *	i2,
		Tinterval *	i_out
	)

Computes the intersection of two intervals.

Parameters:

	i1	The first interval.
	i2	The second interval.
	i_out	The output intersection interval, possibly empty.

Returns:: TRUE if i_out is not empty.

Definition at line 170 of file interval.c.

References Tinterval::lower_limit, and Tinterval::upper_limit.

Referenced by BoxesIntersection(), BoxSaddleClipping(), BoxSphereClipping(), CropLinearConstraint(), Intersect(), RectangleCircleClipping(), RectangleParabolaClipping(), SimplifyLinearConstraint(), and UpdateOriginalFromSimple().

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boolean Union	(	Tinterval *	i1,
		Tinterval *	i2,
		Tinterval *	i_out
	)

Computes the union of two intervals.

Parameters:

	i1	The first interval.
	i2	The second interval.
	i_out	The output union interval, possibly empty.

Returns:: TRUE if i_out is not empty. The union of two intervals is empty if the two input intervals were empty.

Definition at line 182 of file interval.c.

References FALSE, Tinterval::lower_limit, TRUE, and Tinterval::upper_limit.

Referenced by BoxSphereClipping(), BoxUnion(), RectangleCircleClipping(), and RectangleParabolaClipping().

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boolean EmptyInterval ( Tinterval * i )

Checks if a given interval is empty.

Parameters:

i

The interval to check.

Returns:: TRUE if i is empty.

Definition at line 220 of file interval.c.

References Tinterval::lower_limit, and Tinterval::upper_limit.

Referenced by PrintInterval(), and ReduceRange().

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void IntervalScale	(	Tinterval *	i1,
		double	e,
		Tinterval *	i_out
	)

Product of an interval and a constant.

Parameters:

	i1	The input interval.
	e	The scale factor.
	i_out	The resulting interval.

Definition at line 237 of file interval.c.

References Tinterval::lower_limit, ROUNDDOWN, ROUNDNEAR, ROUNDUP, and Tinterval::upper_limit.

Referenced by BoxSaddleClipping(), CleanLinearConstraint(), ErrorDueToVariable(), GetFirstOrderApproximationToEquation(), RectangleParabolaClipping(), ScaleBox(), and ScaleLinearConstraint().

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void IntervalProduct	(	Tinterval *	i1,
		Tinterval *	i2,
		Tinterval *	i_out
	)

Product of two intervals.

Parameters:

	i1	The first interval.
	i2	The second interval.
	i_out	The resulting interval.

Definition at line 269 of file interval.c.

References Tinterval::lower_limit, ROUNDDOWN, ROUNDNEAR, ROUNDUP, and Tinterval::upper_limit.

Referenced by BoxSaddleClipping(), CropLinearConstraint(), DummifyAndAddEquation(), ErrorDueToVariable(), EvaluateLinearConstraintInt(), EvaluateMonomialInt(), EvaluateVarSetInt(), GetFirstOrderApproximationToEquation(), RectangleParabolaClipping(), SimplexGetOptimalValue(), and SimplifyLinearConstraint().

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void IntervalAdd	(	Tinterval *	i1,
		Tinterval *	i2,
		Tinterval *	i_out
	)

Sum of two intervals.

Parameters:

	i1	The first interval.
	i2	The second interval.
	i_out	The resulting interval.

Definition at line 303 of file interval.c.

References Tinterval::lower_limit, ROUNDDOWN, ROUNDNEAR, ROUNDUP, and Tinterval::upper_limit.

Referenced by AddLinearConstraints(), BoxSphereClipping(), CleanLinearConstraint(), CropLinearConstraint(), ErrorDueToVariable(), EvaluateEquationInt(), EvaluateLinearConstraintInt(), GetFirstOrderApproximationToEquation(), NewInPatchJoint(), RectangleCircleClipping(), SimplexGetOptimalValue(), and UpdateOriginalFromSimple().

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void IntervalSubstract	(	Tinterval *	i1,
		Tinterval *	i2,
		Tinterval *	i_out
	)

Substraction of two intervals.

Parameters:

	i1	The first interval.
	i2	The second interval.
	i_out	The resulting interval.

Definition at line 322 of file interval.c.

References Tinterval::lower_limit, ROUNDDOWN, ROUNDNEAR, ROUNDUP, and Tinterval::upper_limit.

void IntervalInvert	(	Tinterval *	i,
		Tinterval *	i_out
	)

Change of sign of a given interval. Equivalen to scale the interval with -1.

Parameters:

	i	The input interval.
	i_out	The resulting interval.

Definition at line 341 of file interval.c.

References Tinterval::lower_limit, and Tinterval::upper_limit.

Referenced by BoxSphereClipping(), GetFirstOrderApproximationToEquation(), InvertLinearConstraint(), PrintLinearConstraint(), RectangleCircleClipping(), RectangleParabolaClipping(), and UpdateOriginalFromSimple().

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void IntervalPow	(	Tinterval *	i,
		unsigned int	p,
		Tinterval *	i_out
	)

Computes

i_out=i_in^p

.

Parameters:

	i	The input interval.
	p	The power.
	i_out	The resulting interval.

Definition at line 352 of file interval.c.

References IsInside(), Tinterval::lower_limit, ROUNDDOWN, ROUNDNEAR, ROUNDUP, and Tinterval::upper_limit.

Referenced by BoxSphereClipping(), DummifyAndAddEquation(), ErrorDueToVariable(), EvaluateVarSetInt(), GetFirstOrderApproximationToEquation(), NewInPatchJoint(), RectangleCircleClipping(), and RectangleParabolaClipping().

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boolean IntervalSqrt	(	Tinterval *	i,
		Tinterval *	i_out
	)

Computes the square root of an interval. Negative parts of the interval are not taken into account. If the whole input interval is negative the result is an empty interval.

Parameters:

	i	The input interval.
	i_out	The resulting interval.

Returns:: TRUE if the output interval is NULL.

Definition at line 386 of file interval.c.

References FALSE, Tinterval::lower_limit, ROUNDDOWN, ROUNDNEAR, ROUNDUP, TRUE, and Tinterval::upper_limit.

Referenced by BoxSphereClipping(), NewInPatchJoint(), RectangleCircleClipping(), and RectangleParabolaClipping().

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void IntervalDivision	(	Tinterval *	num,
		Tinterval *	den,
		Tinterval *	i_out
	)

Divides one interval by another. If the denominator includes the zero, this function triggers an error.

Parameters:

	num	The interval numerator.
	den	The interval denominator.
	i_out	The resulting interval.

Definition at line 412 of file interval.c.

References Error(), Tinterval::lower_limit, ROUNDDOWN, ROUNDNEAR, ROUNDUP, and Tinterval::upper_limit.

Referenced by BoxSaddleClipping(), CropLinearConstraint(), and SimplifyLinearConstraint().

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void IntervalOffset	(	Tinterval *	i,
		double	offset,
		Tinterval *	i_out
	)

Displaces an interval by a constant value.

Parameters:

	i	The input interval.
	offset	The quantity to add to the interval limits.
	i_out	The resulting interval.

Definition at line 448 of file interval.c.

References Tinterval::lower_limit, ROUNDDOWN, ROUNDNEAR, ROUNDUP, and Tinterval::upper_limit.

Referenced by AddCt2LinearConstraint(), AddEquation2Simplex(), ErrorDueToVariable(), EvaluateEqMin(), GetFirstOrderApproximationToEquation(), NewRevoluteJoint(), and NewUniversalJoint().

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void IntervalSinus	(	Tinterval *	i,
		Tinterval *	i_out
	)

Computes the bound of the sinus on a given interval.

Parameters:

	i	The input interval.
	i_out	The resulting interval.

Definition at line 468 of file interval.c.

References IntervalSinus(), IntervalSize(), Tinterval::lower_limit, M_2PI, M_PI_2, NewInterval(), NormalizeAngle(), ROUNDDOWN, ROUNDNEAR, ROUNDUP, and Tinterval::upper_limit.

Referenced by IntervalSinus().

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void IntervalCosinus	(	Tinterval *	i,
		Tinterval *	i_out
	)

Computes the bound of the cosinus on a given interval.

Parameters:

	i	The input interval.
	i_out	The resulting interval.

Definition at line 528 of file interval.c.

References IntervalCosinus(), IntervalSize(), Tinterval::lower_limit, M_2PI, M_PI, NewInterval(), NormalizeAngle(), and Tinterval::upper_limit.

Referenced by GenerateJointRangeEquations(), and IntervalCosinus().

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void IntervalAtan2	(	Tinterval *	is,
		Tinterval *	ic,
		Tinterval *	i_out
	)

Computes the bound of the atan2 on a given sin/cos intervals.

The current implementation is tailored to post-process solution files and in only works for small intervals.

The output in in the range $[-\pi,\pi]$ except for the case where is and ic include (-1,0). In this case the output interval is in the range $[0,2\:\pi]$ .