lsst::sphgeom::Interval< Derived, Scalar > Class Template Reference

Interval represents a closed interval of the real numbers by its upper and lower bounds. More...

#include <Interval.h>

Public Member Functions
	Interval ()
	This constructor creates an empty interval. More...
	Interval (Scalar x)
	This constructor creates a closed interval containing only x. More...
	Interval (Scalar x, Scalar y)
	This constructor creates an interval from the given endpoints. More...
bool	operator== (Interval const &i) const
	Two closed intervals are equal if their endpoints are the same, or both are empty. More...
bool	operator!= (Interval const &i) const
bool	operator== (Scalar x) const
	A closed interval is equal to a point x if both endpoints equal x. More...
bool	operator!= (Scalar x) const
Scalar	getA () const
	getA returns the lower endpoint of this interval. More...
Scalar	getB () const
	getB returns the upper endpoint of this interval. More...
bool	isEmpty () const
	isEmpty returns true if this interval does not contain any points. More...
Scalar	getCenter () const
	getCenter returns the center of this interval. More...
Scalar	getSize () const
	getSize returns the size (length, width) of this interval. More...
Interval &	dilateBy (Scalar x)
	For positive x, dilateBy morphologically dilates this interval by [-x,x], which is equivalent to the taking the Minkowski sum with [-x,x]. More...
Interval &	erodeBy (Scalar x)
Derived	dilatedBy (Scalar x) const
Derived	erodedBy (Scalar x) const
bool	contains (Scalar x) const
bool	contains (Interval const &x) const
bool	isDisjointFrom (Scalar x) const
bool	isDisjointFrom (Interval const &x) const
bool	intersects (Scalar x) const
bool	intersects (Interval const &x) const
bool	isWithin (Scalar x) const
bool	isWithin (Interval const &x) const
Relationship	relate (Scalar x) const
Relationship	relate (Interval const &x) const
Interval &	clipTo (Scalar x)
Interval &	clipTo (Interval const &x)
Derived	clippedTo (Scalar x) const
Derived	clippedTo (Interval const &x) const
Interval &	expandTo (Scalar x)
Interval &	expandTo (Interval const &x)
Derived	expandedTo (Scalar x) const
Derived	expandedTo (Interval const &x) const

Detailed Description

template<typename Derived, typename Scalar>
class lsst::sphgeom::Interval< Derived, Scalar >

Interval represents a closed interval of the real numbers by its upper and lower bounds.

It is parameterized by the Scalar type, which must be constructible from a double.

An interval with identical upper and lower bounds contains a single point, and is equal to that scalar bound.

An interval with an upper bound less than its lower bound is empty (contains no points), as are intervals with NaN as either bound.

Definition at line 48 of file Interval.h.

Constructor & Destructor Documentation

Interval() [1/3]

template<typename Derived, typename Scalar>

lsst::sphgeom::Interval< Derived, Scalar >::Interval ( )

inline

This constructor creates an empty interval.

Definition at line 51 of file Interval.h.

: _a(1.0), _b(0.0) {}

Interval() [2/3]

template<typename Derived, typename Scalar>

lsst::sphgeom::Interval< Derived, Scalar >::Interval ( Scalar  x )

inlineexplicit

This constructor creates a closed interval containing only x.

Definition at line 54 of file Interval.h.

: _a(x), _b(x) {}

Interval() [3/3]

template<typename Derived, typename Scalar>

lsst::sphgeom::Interval< Derived, Scalar >::Interval ( Scalar  x, Scalar  y  )

inline

This constructor creates an interval from the given endpoints.

Definition at line 57 of file Interval.h.

: _a(x), _b(y) {}

Member Function Documentation

clippedTo() [1/2]

template<typename Derived, typename Scalar>

Derived lsst::sphgeom::Interval< Derived, Scalar >::clippedTo ( Scalar  x ) const

inline

clippedTo returns the intersection of this interval and x.

Definition at line 183 of file Interval.h.

{ return Interval(*this).clipTo(x); }

clippedTo() [2/2]

template<typename Derived, typename Scalar>

Derived lsst::sphgeom::Interval< Derived, Scalar >::clippedTo ( Interval< Derived, Scalar > const &  x ) const

inline

clippedTo returns the intersection of this interval and x.

Definition at line 185 of file Interval.h.

                                                {
        return Interval(*this).clipTo(x);
    }

clipTo() [1/2]

template<typename Derived, typename Scalar>

Interval& lsst::sphgeom::Interval< Derived, Scalar >::clipTo ( Scalar  x )

inline

clipTo shrinks this interval until all its points are in x.

Definition at line 159 of file Interval.h.

                                {
        if (x != x) {
            _a = x;
            _b = x;
        } else {
            _a = std::max(_a, x);
            _b = std::min(_b, x);
        }
        return *this;
    }

clipTo() [2/2]

template<typename Derived, typename Scalar>

Interval& lsst::sphgeom::Interval< Derived, Scalar >::clipTo ( Interval< Derived, Scalar > const &  x )

inline

clipTo shrinks this interval until all its points are in x.

Definition at line 170 of file Interval.h.

                                          {
        if (x.isEmpty()) {
            *this = x;
        } else if (!isEmpty()) {
            _a = std::max(_a, x._a);
            _b = std::min(_b, x._b);
        }
        return *this;
    }

contains() [1/2]

template<typename Derived, typename Scalar>

bool lsst::sphgeom::Interval< Derived, Scalar >::contains ( Scalar  x ) const

inline

contains returns true if the intersection of this interval and x is equal to x.

Definition at line 98 of file Interval.h.

                                  {
        return (_a <= x && x <= _b) || x != x;
    }

contains() [2/2]

template<typename Derived, typename Scalar>

bool lsst::sphgeom::Interval< Derived, Scalar >::contains ( Interval< Derived, Scalar > const &  x ) const

inline

contains returns true if the intersection of this interval and x is equal to x.

Definition at line 102 of file Interval.h.

                                            {
        if (x.isEmpty()) {
            return true;
        } else if (isEmpty()) {
            return false;
        }
        return _a <= x._a && _b >= x._b;
    }

dilateBy()

template<typename Derived, typename Scalar>

Interval& lsst::sphgeom::Interval< Derived, Scalar >::dilateBy ( Scalar  x )

inline

For positive x, dilateBy morphologically dilates this interval by [-x,x], which is equivalent to the taking the Minkowski sum with [-x,x].

For negative x, it morphologically erodes this interval by [x,-x]. If x is zero or NaN, or this interval is empty, there is no effect.

Definition at line 230 of file Interval.h.

                                  {
        if (x == x && !isEmpty()) {
            _a = _a - x;
            _b = _b + x;
        }
        return *this;
    }

dilatedBy()

template<typename Derived, typename Scalar>

Derived lsst::sphgeom::Interval< Derived, Scalar >::dilatedBy ( Scalar  x ) const

inline

Definition at line 239 of file Interval.h.

{ return Interval(*this).dilateBy(x); }

erodeBy()

template<typename Derived, typename Scalar>

Interval& lsst::sphgeom::Interval< Derived, Scalar >::erodeBy ( Scalar  x )

inline

Definition at line 238 of file Interval.h.

{ return dilateBy(-x); }

erodedBy()

template<typename Derived, typename Scalar>

Derived lsst::sphgeom::Interval< Derived, Scalar >::erodedBy ( Scalar  x ) const

inline

Definition at line 240 of file Interval.h.

{ return Interval(*this).erodeBy(x); }

expandedTo() [1/2]

template<typename Derived, typename Scalar>

Derived lsst::sphgeom::Interval< Derived, Scalar >::expandedTo ( Scalar  x ) const

inline

expandedTo returns the smallest interval containing the union of this interval and x.

Definition at line 218 of file Interval.h.

{ return Interval(*this).expandTo(x); }

expandedTo() [2/2]

template<typename Derived, typename Scalar>

Derived lsst::sphgeom::Interval< Derived, Scalar >::expandedTo ( Interval< Derived, Scalar > const &  x ) const

inline

expandedTo returns the smallest interval containing the union of this interval and x.

Definition at line 220 of file Interval.h.

                                                 {
        return Interval(*this).expandTo(x);
    }

expandTo() [1/2]

template<typename Derived, typename Scalar>

Interval& lsst::sphgeom::Interval< Derived, Scalar >::expandTo ( Scalar  x )

inline

expandTo minimally expands this interval to contain x.

Definition at line 192 of file Interval.h.

                                  {
        if (isEmpty()) {
            _a = x;
            _b = x;
        } else if (x < _a) {
            _a = x;
        } else if (x > _b) {
            _b = x;
        }
        return *this;
    }

expandTo() [2/2]

template<typename Derived, typename Scalar>

Interval& lsst::sphgeom::Interval< Derived, Scalar >::expandTo ( Interval< Derived, Scalar > const &  x )

inline

expandTo minimally expands this interval to contain x.

Definition at line 204 of file Interval.h.

                                            {
        if (isEmpty()) {
            *this = x;
        } else if (!x.isEmpty()) {
            _a = std::min(_a, x._a);
            _b = std::max(_b, x._b);
        }
        return *this;
    }

getA()

template<typename Derived, typename Scalar>

Scalar lsst::sphgeom::Interval< Derived, Scalar >::getA ( ) const

inline

getA returns the lower endpoint of this interval.

The return value for empty intervals is arbitrary.

Definition at line 76 of file Interval.h.

{ return _a; }

getB()

template<typename Derived, typename Scalar>

Scalar lsst::sphgeom::Interval< Derived, Scalar >::getB ( ) const

inline

getB returns the upper endpoint of this interval.

The return value for empty intervals is arbitrary.

Definition at line 80 of file Interval.h.

{ return _b; }

getCenter()

template<typename Derived, typename Scalar>

Scalar lsst::sphgeom::Interval< Derived, Scalar >::getCenter ( ) const

inline

getCenter returns the center of this interval.

It is arbitrary for empty intervals.

Definition at line 89 of file Interval.h.

{ return 0.5 * (_a + _b); }

getSize()

template<typename Derived, typename Scalar>

Scalar lsst::sphgeom::Interval< Derived, Scalar >::getSize ( ) const

inline

getSize returns the size (length, width) of this interval.

It is zero for single-point intervals, and NaN or negative for empty intervals.

Definition at line 93 of file Interval.h.

{ return _b - _a; }

intersects() [1/2]

template<typename Derived, typename Scalar>

bool lsst::sphgeom::Interval< Derived, Scalar >::intersects ( Scalar  x ) const

inline

intersects returns true if the intersection of this interval and x is non-empty.

Definition at line 130 of file Interval.h.

{ return _a <= x && x <= _b; }

intersects() [2/2]

template<typename Derived, typename Scalar>

bool lsst::sphgeom::Interval< Derived, Scalar >::intersects ( Interval< Derived, Scalar > const &  x ) const

inline

intersects returns true if the intersection of this interval and x is non-empty.

Definition at line 132 of file Interval.h.

                                              {
        return !isDisjointFrom(x);
    }

isDisjointFrom() [1/2]

template<typename Derived, typename Scalar>

bool lsst::sphgeom::Interval< Derived, Scalar >::isDisjointFrom ( Scalar  x ) const

inline

isDisjointFrom returns true if the intersection of this interval and x is empty.

Definition at line 115 of file Interval.h.

                                        {
        return !intersects(x);
    }

isDisjointFrom() [2/2]

template<typename Derived, typename Scalar>

bool lsst::sphgeom::Interval< Derived, Scalar >::isDisjointFrom ( Interval< Derived, Scalar > const &  x ) const

inline

isDisjointFrom returns true if the intersection of this interval and x is empty.

Definition at line 119 of file Interval.h.

                                                  {
        if (isEmpty() || x.isEmpty()) {
            return true;
        }
        return _a > x._b || _b < x._a;
    }

isEmpty()

template<typename Derived, typename Scalar>

bool lsst::sphgeom::Interval< Derived, Scalar >::isEmpty ( ) const

inline

isEmpty returns true if this interval does not contain any points.

Definition at line 83 of file Interval.h.

                         {
        return !(_a <= _b); // returns true when _a and/or _b is NaN
    }

isWithin() [1/2]

template<typename Derived, typename Scalar>

bool lsst::sphgeom::Interval< Derived, Scalar >::isWithin ( Scalar  x ) const

inline

isWithin returns true if the intersection of this interval and x is this interval.

Definition at line 140 of file Interval.h.

                                  {
        return (_a == x && _b == x) || isEmpty();
    }

isWithin() [2/2]

template<typename Derived, typename Scalar>

bool lsst::sphgeom::Interval< Derived, Scalar >::isWithin ( Interval< Derived, Scalar > const &  x ) const

inline

isWithin returns true if the intersection of this interval and x is this interval.

Definition at line 144 of file Interval.h.

                                            {
        return x.contains(*this);
    }

operator!=() [1/2]

template<typename Derived, typename Scalar>

bool lsst::sphgeom::Interval< Derived, Scalar >::operator!= ( Interval< Derived, Scalar > const &  i ) const

inline

Definition at line 65 of file Interval.h.

{ return !(*this == i); }

operator!=() [2/2]

template<typename Derived, typename Scalar>

bool lsst::sphgeom::Interval< Derived, Scalar >::operator!= ( Scalar  x ) const

inline

Definition at line 72 of file Interval.h.

{ return !(*this == x); }

operator==() [1/2]

template<typename Derived, typename Scalar>

bool lsst::sphgeom::Interval< Derived, Scalar >::operator== ( Interval< Derived, Scalar > const &  i ) const

inline

Two closed intervals are equal if their endpoints are the same, or both are empty.

Definition at line 61 of file Interval.h.

                                              {
        return (_a == i._a && _b == i._b) || (i.isEmpty() && isEmpty());
    }

operator==() [2/2]

template<typename Derived, typename Scalar>

bool lsst::sphgeom::Interval< Derived, Scalar >::operator== ( Scalar  x ) const

inline

A closed interval is equal to a point x if both endpoints equal x.

Definition at line 68 of file Interval.h.

                                    {
        return (_a == x && _b == x) || (x != x && isEmpty());
    }

relate() [1/2]

template<typename Derived , typename Scalar>

Relationship lsst::sphgeom::Interval< Derived, Scalar >::relate

(

Scalar

x

)

const

relate returns a bitset S describing the spatial relationships between this interval and x. For each relation that holds, the bitwise AND of S and the corresponding Relationship will be non-zero.

Definition at line 249 of file Interval.h.

                                                             {
    if (isEmpty()) {
        if (x != x) {
            return CONTAINS | DISJOINT | WITHIN;
        }
        return DISJOINT | WITHIN;
    }
    if (x != x) {
        return CONTAINS | DISJOINT;
    }
    if (_a == x && _b == x) {
        return CONTAINS | WITHIN;
    }
    if (intersects(x)) {
        return CONTAINS;
    }
    return DISJOINT;
}

relate() [2/2]

template<typename Derived , typename Scalar>

Relationship lsst::sphgeom::Interval< Derived, Scalar >::relate

(

Interval< Derived, Scalar > const &

x

)

const

relate returns a bitset S describing the spatial relationships between this interval and x. For each relation that holds, the bitwise AND of S and the corresponding Relationship will be non-zero.

Definition at line 269 of file Interval.h.

{
    if (isEmpty()) {
        if (x.isEmpty()) {
            return CONTAINS | DISJOINT | WITHIN;
        }
        return DISJOINT | WITHIN;
    }
    if (x.isEmpty()) {
        return CONTAINS | DISJOINT;
    }
    if (_a == x._a && _b == x._b) {
        return CONTAINS | WITHIN;
    }
    if (_a > x._b || _b < x._a) {
        return DISJOINT;
    }
    if (_a <= x._a && _b >= x._b) {
        return CONTAINS;
    }
    if (x._a <= _a && x._b >= _b) {
        return WITHIN;
    }
    return INTERSECTS;
}

---

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

• /j/snowflake/release/lsstsw/stack/Linux64/sphgeom/17.0+14/include/lsst/sphgeom/Interval.h