A 1d interval with low and high values. More...

#include <DRange1d.h>

Public Member Functions
	DRange1d ()
	constructor for a NULL range. More...

	DRange1d (double low, double high)
	Constructor from explicit low and high. More...

	DRange1d (DRange1dCR source)
	copy constructor. More...

void	InitNull ()
	Set this range to the {NullRange}. More...

bool	IsNull () const
	Test if the range is exactly the same as the null ranges returned by NullRange (). More...

bool	IsEmpty () const
	Test if the range has {low > high}, i.e. there are no x for which {low &le x && x &le high}. More...

bool	IsEmptyOrSinglePoint () const
	Test if the range has {high >= low}, i.e. is empty or just one point. More...

bool	IsSinglePoint () const
	Test if the range is a single point. More...

bool	IsSinglePoint (double value) const
	Test if the range is a particular single point. More...

bool	IsPositiveLength () const
	Test if the range has {high > low}, i.e. has a non-empty set of points with properly sorted lower and upper limit. More...

bool	IsInfinitePositive () const
	Test if the range has the largest possible {high}. More...

bool	IsInfiniteNegative () const
	Test if the range has the most negative possible {low}. More...

bool	IsDoublyInfinite () const
	Test if the range has the most negative {low} and most positive {high}. More...

bool	GetLowHigh (double &a, double &b) const
	Get the low and high limits (unchecked). More...

double	Low () const
	Get the low limit (unchecked). More...

double	High () const
	Get the low limit (unchecked). More...

double	Length () const
	Return {MAX(0, high - low)} The DRange1::NullRange returns 0. More...

bool	Contains (double a) const
	Test if the range contains a given value. More...

void	Extend (double valueA)
	Extend to include a value. More...

void	Extend (double valueA, double valueB)
	Extend to include 2 values. More...

void	Extend (double *values, size_t count)
	Extend to include an array of values. More...

void	Extend (bvector< double > &values)
	Extend to include an array of values. More...

void	Extend (DRange1dCR other)
	Extend to include (union) another (possibly null!!) range. More...

void	ExtendBySignedShift (double tol)
	If non empty, shift endpoints by (-tol, +tol). More...

void	IntersectInPlace (DRange1dCR other)
	Restrict to overlap with another (possibly null!!) range. More...

bool	StrictlyNonEmptyFractionalIntersection (DRange1dCR rangeB, DRange1dR fractionalIntersection)
	Compute intersection of the instance with rangeB. More...

bool	IsSubsetOf (DRange1dCR other) const
	Test if the instance range is a (possibly complete, possibly empty) subset of {other} range. More...

bool	HasNonEmptyIntersectionWith (DRange1dCR other) const
	Test if the instance range is a (possibly complete, but not empty) subset of {other} range. More...

bool	HasPositiveLengthIntersectionWith (DRange1dCR other) const
	Test if the instance range has a positive-length (more than single point) intersection with {other}. More...

bool	IsContainedIn (DRange1dCR other) const
	Test if the instnace range is a (possibly complete) subset of {other} range. More...

double	MaxAbs (double defaultValeForNullRange=0.0) const
	return the largest coordinate (absolute value) in the range. More...

bool	IsEqualInterval (DRange1dCR other) const
	Test if equal intervals in point set sense. More...

bool	IsEqualLowHigh (DRange1dCR other) const
	Direct equality test for low and high parts. More...

bool	IsSameMinMax (DRange1dCR other, double absTol) const
	test for toleranced equality of (min max of) low and high. More...

bool	IsSameLowHigh (DRange1dCR other, double relTol) const
	test for toleranced equality of low to low and high to high More...

bool	FractionToDouble (double fraction, double &x, double defaultReturnX=0.0) const
	map fractional coordinate to real. Returns false if null range. More...

bool	DoubleToFraction (double x, double &fraction, double defaultReturnX=0.0) const
	map real to fraction. Returns false if null range or single point. More...

double	GetTolerance (double absTol=1.0e-14, double localRelTol=1.0e-14, double globalRelTol=0.0)
	return a tolerance computed as {absTol + localRelTol * Extent() + globalRelTol * MaxAbs ()} More...

bool	UpdateRay1dIntersection (double x0, double dxds, double xA, double xB)
	Update a bounding interval of a line based on the variation of that line within one dimension. More...

Static Public Member Functions
static DRange1d	FromLowHigh (double low, double high)
	Return a range with explicit (possibly reversed) low and high. More...

static DRange1d	NullRange ()
	Return a range which satisfies IsNull () More...

static DRange1d	InfiniteRange ()
	Return a complete range (-DBL_MAX to DBL_MAX) More...

static DRange1d	ZeroAndPositiveRange ()
	Return a complete 0 and positive range (0 to DBL_MAX) More...

static DRange1d	ZeroAndNegativeRange ()
	Return a complete 0 and negative range (-DBL_MAX to 0) More...

static DRange1d	From (double value)
	Return a range containing a single value. More...

static DRange1d	From (double valueA, double valueB)
	Return a (sorted) range of 2 values. More...

static DRange1d	From (double valueA, double valueB, double valueC)
	Return a (sorted) range of 3 values. More...

static DRange1d	From (double *values, size_t n)
	Return a (sorted) range of an array of values. More...

static DRange1d	FromAltitudes (bvector< DPoint3d > &points, DPlane3dCR plane)
	Return a (sorted) range of altitudes of points. More...

static DRange1d	FromIntersection (DRange1dCR rangeA, DRange1dCR rangeB)
	return the (possibly null) intersection of two ranges. More...

static DRange1d	FromUnion (DRange1dCR rangeA, DRange1dCR rangeB)
	return the (possibly null) union of two ranges. More...

static void	SortLowInPlace (bvector< DRange1d > &data)
	Sort on low values. More...

static void	SimplifyInPlace (bvector< DRange1d > &data)
	Combine intervals so there are no overlaps. More...

static DRange1d	FromExtent (bvector< DRange1d > &data)
	Return the encompassing single range. More...

static DRange1d	FromIntersection (bvector< DRange1d > &data)
	Return the overall intersection. More...

static void	AppendClips (bvector< DRange1d > &dataA, DRange1dCR clipper, bvector< DRange1d > &dataOut)
	Intersect each range in dataA with clipper. More...

static void	ClipInPlace (bvector< DRange1d > &dataA, DRange1dCR clipper)
	Intersect each range in dataA with clipper. Retain non-empty result parts. More...

static void	IntersectSorted (bvector< DRange1d > &dataA, bvector< DRange1d > &dataB, bvector< DRange1d > &dataOut)
	Intersect intervals in two pre-sorted sets. Output may NOT be the same as either input. More...

static void	UnionSorted (bvector< DRange1d > &dataA, bvector< DRange1d > &dataB, bvector< DRange1d > &dataOut)
	Union of intervals in two pre-sorted sets. Output may NOT be the same as either input. More...

static void	DifferenceSorted (bvector< DRange1d > &dataA, bvector< DRange1d > &dataB, bvector< DRange1d > &dataOut)
	Intersect intervals in two pre-sorted sets. Output may NOT be the same as either input. More...

static bool	IsIncreasing (bvector< DRange1d > &data, bool allowZeroLength=false, bool allowZeroGaps=false)
	Test for increasing relationships, optionally allowing zero length. More...

static double	LengthSum (bvector< DRange1d > &data)
	Sum the interval lengths. More...

Public Attributes
double	low
	low point of box More...

double	high
	high point of box More...

Detailed Description

A 1d interval with low and high values.

Useful typedefs for DRange1d

typdedef struct const &DRange1d DRange1dCR;
typdedef struct &DRange1d DRange1dR;
typdedef struct const *DRange1d DRange1dCP;
typdedef struct *DRange1d DRange1dP;

If you look closely at "names" for special intervals, there are several tricky distinctions:

{high > low} The "usual" interval with a strictly positive length. You can test for this with {IsPositiveLength ()}
{high == low} A single point interval. This has something int it (one point!) and is NOT empty. You can test for this with {IsSinglePoint()}
{high < low} The set of points x with {low < x < high} is empty. You can test for this with {IsEmpty()}
The initialization value NullInterval – this is a unique value. You can test for this with {IsNull()} The NullInterval is empty, but not all empty intervals are equal to the NullInterval if you compare the low and high values!!

Be aware that if the application needs to treat a single point interval as "empty" for its purposes, the use of "empty" will be what the methods call {IsEmptyOrSinglePoint()}

Constructor & Destructor Documentation

DRange1d ( )

constructor for a NULL range.

DRange1d	(	double	low,
		double	high
	)

Constructor from explicit low and high.

DRange1d ( DRange1dCR source )

copy constructor.

Member Function Documentation

static void AppendClips	(	bvector< DRange1d > &	dataA,
		DRange1dCR	clipper,
		bvector< DRange1d > &	dataOut
	)

static

Intersect each range in dataA with clipper.

Append non-empty results to dataOut. Note that if the same array is passed for dataA and dataOut, all input contents will remain. (Use {ClipInPlace} to get compaction)

static void ClipInPlace	(	bvector< DRange1d > &	dataA,
		DRange1dCR	clipper
	)

static

Intersect each range in dataA with clipper. Retain non-empty result parts.

bool Contains ( double a ) const

Test if the range contains a given value.

static void DifferenceSorted	(	bvector< DRange1d > &	dataA,
		bvector< DRange1d > &	dataB,
		bvector< DRange1d > &	dataOut
	)

static

Intersect intervals in two pre-sorted sets. Output may NOT be the same as either input.

bool DoubleToFraction	(	double	x,
		double &	fraction,
		double	defaultReturnX = `0.0`
	)		const

map real to fraction. Returns false if null range or single point.

void Extend ( double valueA )

Extend to include a value.

void Extend	(	double	valueA,
		double	valueB
	)

Extend to include 2 values.

void Extend	(	double *	values,
		size_t	count
	)

Extend to include an array of values.

void Extend ( bvector< double > & values )

Extend to include an array of values.

void Extend ( DRange1dCR other )

Extend to include (union) another (possibly null!!) range.

void ExtendBySignedShift ( double tol )

If non empty, shift endpoints by (-tol, +tol).

No change if empty !!!

bool FractionToDouble	(	double	fraction,
		double &	x,
		double	defaultReturnX = `0.0`
	)		const

map fractional coordinate to real. Returns false if null range.

static DRange1d From ( double value )

static

Return a range containing a single value.

static DRange1d From	(	double	valueA,
		double	valueB
	)

static

Return a (sorted) range of 2 values.

static DRange1d From	(	double	valueA,
		double	valueB,
		double	valueC
	)

static

Return a (sorted) range of 3 values.

static DRange1d From	(	double *	values,
		size_t	n
	)

static

Return a (sorted) range of an array of values.

static DRange1d FromAltitudes	(	bvector< DPoint3d > &	points,
		DPlane3dCR	plane
	)

static

Return a (sorted) range of altitudes of points.

static DRange1d FromExtent ( bvector< DRange1d > & data )

static

Return the encompassing single range.

static DRange1d FromIntersection	(	DRange1dCR	rangeA,
		DRange1dCR	rangeB
	)

static

return the (possibly null) intersection of two ranges.

static DRange1d FromIntersection ( bvector< DRange1d > & data )

static

Return the overall intersection.

static DRange1d FromLowHigh	(	double	low,
		double	high
	)

static

Return a range with explicit (possibly reversed) low and high.

static DRange1d FromUnion	(	DRange1dCR	rangeA,
		DRange1dCR	rangeB
	)

static

return the (possibly null) union of two ranges.

bool GetLowHigh	(	double &	a,
		double &	b
	)		const

Get the low and high limits (unchecked).

Returns: true if {b >= a}, i.e. the interval is single point or postive length. (i.e. any empty interval returns false, with whatever limit data is present)

double GetTolerance	(	double	absTol = `1.0e-14`,
		double	localRelTol = `1.0e-14`,
		double	globalRelTol = `0.0`
	)

return a tolerance computed as {absTol + localRelTol * Extent() + globalRelTol * MaxAbs ()}

bool HasNonEmptyIntersectionWith ( DRange1dCR other ) const

Test if the instance range is a (possibly complete, but not empty) subset of {other} range.

bool HasPositiveLengthIntersectionWith ( DRange1dCR other ) const

Test if the instance range has a positive-length (more than single point) intersection with {other}.

double High ( ) const

Get the low limit (unchecked).

static DRange1d InfiniteRange ( )

static

Return a complete range (-DBL_MAX to DBL_MAX)

void InitNull ( )

Set this range to the {NullRange}.

void IntersectInPlace ( DRange1dCR other )

Restrict to overlap with another (possibly null!!) range.

static void IntersectSorted	(	bvector< DRange1d > &	dataA,
		bvector< DRange1d > &	dataB,
		bvector< DRange1d > &	dataOut
	)

static

Intersect intervals in two pre-sorted sets. Output may NOT be the same as either input.

bool IsContainedIn ( DRange1dCR other ) const

Test if the instnace range is a (possibly complete) subset of {other} range.

bool IsDoublyInfinite ( ) const

Test if the range has the most negative {low} and most positive {high}.

bool IsEmpty ( ) const

Test if the range has {low > high}, i.e. there are no x for which {low &le x && x &le high}.

bool IsEmptyOrSinglePoint ( ) const

Test if the range has {high >= low}, i.e. is empty or just one point.

bool IsEqualInterval ( DRange1dCR other ) const

Test if equal intervals in point set sense.

Any pair of empty intervals (even if different low and high) are equal.

bool IsEqualLowHigh ( DRange1dCR other ) const

Direct equality test for low and high parts.

static bool IsIncreasing	(	bvector< DRange1d > &	data,
		bool	allowZeroLength = `false`,
		bool	allowZeroGaps = `false`
	)

static

Test for increasing relationships, optionally allowing zero length.

bool IsInfiniteNegative ( ) const

Test if the range has the most negative possible {low}.

bool IsInfinitePositive ( ) const

Test if the range has the largest possible {high}.

bool IsNull ( ) const

Test if the range is exactly the same as the null ranges returned by NullRange ().

bool IsPositiveLength ( ) const

Test if the range has {high > low}, i.e. has a non-empty set of points with properly sorted lower and upper limit.

bool IsSameLowHigh	(	DRange1dCR	other,
		double	relTol
	)		const

test for toleranced equality of low to low and high to high

bool IsSameMinMax	(	DRange1dCR	other,
		double	absTol
	)		const

test for toleranced equality of (min max of) low and high.

bool IsSinglePoint ( ) const

Test if the range is a single point.

bool IsSinglePoint ( double value ) const

Test if the range is a particular single point.

bool IsSubsetOf ( DRange1dCR other ) const

Test if the instance range is a (possibly complete, possibly empty) subset of {other} range.

double Length ( ) const

Return {MAX(0, high - low)} The DRange1::NullRange returns 0.

A single-point interval returns 0. An interval with {high < low} returns 0. Normal case returns {high - low}

static double LengthSum ( bvector< DRange1d > & data )

static

Sum the interval lengths.

double Low ( ) const

Get the low limit (unchecked).

double MaxAbs ( double defaultValeForNullRange = 0.0 ) const

return the largest coordinate (absolute value) in the range.

static DRange1d NullRange ( )

static

Return a range which satisfies IsNull ()

static void SimplifyInPlace ( bvector< DRange1d > & data )

static

Combine intervals so there are no overlaps.

static void SortLowInPlace ( bvector< DRange1d > & data )

static

Sort on low values.

bool StrictlyNonEmptyFractionalIntersection	(	DRange1dCR	rangeB,
		DRange1dR	fractionalIntersection
	)

Compute intersection of the instance with rangeB.

Return the intersection as fractions of the instance.

Returns: true if the fractional intersection is more than single point.

static void UnionSorted	(	bvector< DRange1d > &	dataA,
		bvector< DRange1d > &	dataB,
		bvector< DRange1d > &	dataOut
	)

static

Union of intervals in two pre-sorted sets. Output may NOT be the same as either input.

bool UpdateRay1dIntersection	(	double	x0,
		double	dxds,
		double	xA,
		double	xB
	)

Update a bounding interval of a line based on the variation of that line within one dimension.

The ray parameterized {x = x0+s*dxdx} The instance is an {s} range that is live. This is usually initialized to InfiniteRange before clipping. {xA,xB} is an interval of the {x} space. (xA and xB are not required to be sorted.}

Parameters

[in]	x0	ray start coordinate in this dimension
[in]	dxds	Rate of change of ray in this dimension.
[in]	xA	x limit
[in]	xB	x limit.

Returns: true if interval is nonempty at return.

static DRange1d ZeroAndNegativeRange ( )

static

Return a complete 0 and negative range (-DBL_MAX to 0)

static DRange1d ZeroAndPositiveRange ( )

static

Return a complete 0 and positive range (0 to DBL_MAX)

Member Data Documentation

double high

high point of box

double low

low point of box

The documentation for this struct was generated from the following file:

DRange1d.h

Public Member Functions

Static Public Member Functions

Public Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation