This is an IVOA Working Draft for review by IVOA members and other interested parties. It is a draft document and may be updated, replaced, or obsoleted by other documents at any time. It is inappropriate to use IVOA Working Drafts as reference materials or to cite them as other than “work in progress”.

A list of current IVOA Recommendations and other technical documents can be found at http://www.ivoa.net/Documents/.

Acknowledgements

I gladly acknowledge helpful discussions with Jim Gray, Wil O’Mullane, Alex Szalay, Jim Cant, and Markus Demleitner.

Contents

1 Scope and Basic Principles 2

2 Definition of STC-S as Derived from STC-X 3

3 How to Apply the Derivation: Query Example 4

4 A few Conventions and Restrictions 5

5 Formal Definition 6

5.1 Time Sub-phrase 6

5.2 Space Sub-phrase 7

5.3 Spectral Sub-phrase 9

5.4 Redshift Sub-phrase 9

Appendix A: Examples 11

A.1 Simple Examples 11

A.2 Simple and Compound Regions 11

A.3 STC-S and STC-X Serializations 12

Changes from Previous Versions 16

References 16

1 Scope and Basic Principles

The STC metadata design for the Virtual Observatory has been implemented in XML Schema. For documentation, see: http://www.ivoa.net/Documents/latest/STC.html. For further clarification, see: http://www.ivoa.net/Documents/latest/STC-Model.html. That design is complete and self-consistent, but may seem bewilderingly complex to the novice user; and, anyway, XML certainly does not lend itself to easy human readability.

There is an obvious need for a syntax that allows humans to specify and interpret STC metadata objects in a way that is as intuitive as possible without being sloppy – essentially a minimalist approach. This is especially true for queries and resource descriptions. A linear string representation provides a standard serialization that will achieve that purpose; we refer to it as STC-S.

The STC-S syntax is derived from the STC-X serialization. This derivation process is defined in the next section and illustrated in the one following.

By necessity, there will be restrictions compared to the XML serialization of the STC model (STC-X); these are enumerated in Section 4.

The last section of this standard provides a formal definition of the STC-S syntax.

2 Definition of STC-S as Derived from STC-X

This standard specifies how a complete STCDescription (AstroCoordSystem, AstrCoords, and AstroCoordArea) element from STC-X can be represented by a single phrase consisting of one or more sub-phrases, with each sub-phrase specifying the STC information for one coordinate frame. Each sub-phrase starts with the type of the CoordArea element assuming the additional role of Frame Identifier. If there is no CoordArea element, the Coord element type fulfills this role. It is followed by the associated coordinate frame specification (ReferenceFrame, ReferencePosition, etc.), the remaining CoordArea elements, and the Coords elements. Since the Frame Identifiers are unique, no additional punctuation or parenthesizing is required.

The syntax in this document is based on a simple recipe that explains how to derive it from an STC-X instance:

Write out all elements and values of the STC element from an XML document, separated by whitespace, and ordered by coordinate frame
Within each coordinate frame, start with the identification of the CoordArea element, immediately followed by the CoordFrame, then the CoordArea elements, and finally the Coords elements; if there is no CoordArea element, start with the identification of the Coords element instead
Allow omission of all words in the resulting sentence that does not change the information content (with the adoption of some common defaults)

As will become apparent, this second rule leads to very considerable economy (and thereby transparency) in what otherwise would be a very verbose construct.

One should note that this definition allows transforming STC-X (XML) into STC-S and vice versa. A transformation and a subsequent inverse transformation are not guaranteed to produce a result that is identical to the original, but it should be equivalent.

STC-S will be case-insensitive except for strings expressing units.

3 How to Apply the Derivation: Query Example

The procedure of deriving the STC-S serialization from its STC-X counterpart is illustrated by using the Query example from Appendix B.5 of the STC Recommendation, version 1.33. The first two steps from the previous section yield the “verbose verson”, the third step transforms it into the “economy version” which is the STC-S product:

Verbose version	Economy version	Comments
TimeInterval TimeFrame Name Time TimeScale TT BARYCENTER StartTime ISOTime 1900-01-01T00:00:00	StartTime TT BARYCENTER 1900-01-01	StartTime indicates that we are talking about time and a TimeInterval, TT is uniquely a TimeScale, and the format implies ISOTime
Region SpaceFrame Name Equatorial ICRS BARYCENTER SPHERICAL coord_naxes=2 Circle unit=deg Center 148.9 69.1 Radius 2.0 Position2D unit=deg Name RA,Dec Resolution2 0.0001 0.0001 Resolution2 0.0003 0.0003 Size2 0.5 0.5 Size2 0.67 0.67 PixSize2 0.00005 0.00005 PixSize2 0.00015 0.00015	Circle ICRS BARYCENTER 148.9 69.1 2.0 Resolution 0.0001 0.0001 0.0003 0.0003 Size 0.5 0.5 0.67 0.67 PixSize 0.00005 0.00005 0.00015 0.00015	Circle uniquely implies a SpaceFrame and a Region, and the order of its parameters is fixed; ICRS implies spherical 2-D coordinates; and the two pairs of numbers for Resolution, Size, and PixSize implies upper and lower limits
SpectralInterval SpectralFrame Name Wavelength BARYCENTER Spectral unit=Angstrom LoLimit 4000 HiLimit 7000 Spectral unit=Angstrom Name Lambda Resolution 300 Resolution 600	SpectralInterval BARYCENTER 4000 7000 unit Angstrom Resolution 300 600	SpectralInterval implies a SpectralFrame; its unit implies Wavelength

If the reference positions and time scale do not matter, and one does not care about the Resolutions, Sizes, and PixSizes, the sum-total becomes simply:

StartTime TT BARYCENTER 1900-01-01
Circle ICRS BARYCENTER 148.9 69.1 2.0
Resolution 0.0001 0.0001 0.0003 0.0003 Size 0.5 0.5 0.67 0.67
PixSize 0.00005 0.00005 0.00015 0.00015
SpectralInterval BARYCENTER Angstrom 4000 7000 Resolution 300 600

It may be of interest to note that, had there also been a stop time (say, 2000-01-01) and one did not care about resolutions, sizes, and pixel sizes, the phrase could simply have been composed as follows:

TimeInterval TT BARYCENTER 1900-01-01 2000-01-01
Circle ICRS BARYCENTER 148.9 69.1 2.0
SpectralInterval BARYCENTER Angstrom 4000 7000

4 A few Conventions and Restrictions

A missing required element, if its value or name is not implied by anything else in the phrase, should be interpreted as UNKNOWN or nil; i.e., “don’t care” in the context of a query. nil means “unspecified”, i.e., a missing element in STC-X.

Default units (“deg”, “m”, “s”, “m/s”, “Hz”) may be omitted.

To conform with common abuse, “J2000” and “FK5” will both be interpreted as “FK5 J2000”; “B1950” and “FK4” will be interpreted as “FK4 B1950”.

The STC-S serialization is primarily intended to make simple cases easy to express; it will be restricted to those easy cases and will not support:

Generic coordinate axes (i.e., only Time, Space, Spectral, and Redshift are supported)
Custom coordinate reference frames and custom reference positions
Spatial frames with offset positions
Error, resolution, sizes in 2 or 3 dimensions other than the 2 or 3 element vectors
Relocatable frames
Planetary reference frames
Sectors and Convex Hulls
For ellipses: position angle references other than ‘X’ and units other than “deg”
Geodetic reference spheroids other than IAU 1976

5 Formal Definition

We shall refer to an STC-S expression as a phrase. A phrase is a linear concatenation of one or more sub-phrases. Each sub-phrase pertains to a particular coordinate frame and they shall be concatenated in the following order:

Time Space Spectrum Redshift

A sub-phrase is a linear concatenation of one, two, or three sub-phrase components in the order:

CoordinateFrame CoordinateArea Coordinates

A sub-phrase component is a linear concatenation of one or more words, the first of which is the sub-phrase component identifier. However, the CoordinateArea identifier (or, if CoordinateArea is absent, the Coordinates identifier) is moved in front of the CoordinateFrame sub-phrase component and serves as the sub-phrase identifier.

Words are the names of elements or attributes, or their values

Sub-phrase component identifiers are unique within each sub-phrase and sub-phrase identifiers are unique within each phrase. Words, components, and sub-phrases are separated by whitespace.

Optionally, compound sub-phrases may be recognized for compound Regions. Under those rules the CoordinateArea operational identifier (Union, Intersection, Not, or Difference) precedes the CoordinateFrame component which, in turn, is followed by two or more (if applicable) CoordinateArea components; any CoordinateArea identifier may be preceded by the negation operator Not. The arguments for the compound region operators must be enclosed in parentheses. For Union and Intersection the argument may contain two or more elements; for Difference it must contain exactly two; and for Not it must contain only one. The enclosure in parentheses is merely intended to allow nesting and avoid ambiguities.

5.1 Time Sub-phrase

TimeInterval [fillfactor <fill>] [<timescale>] [<refpos>]
[<start> <stop> ...]
[Time <time>] [unit <unit>] [Error <error> [<error>]]
[Resolution <resln> [<resln>]] [Size <size> [<size>]]
[PixSize <pixsiz> [<pixsiz>]]

StartTime [fillfactor <fill>] [<timescale>] [<refpos>] <start>
[Time <time>] [unit <unit>] [Error <error> [<error>]]
[Resolution <resln> [<resln>]] [Size <size> [<size>]]
[PixSize <pixsiz> [<pixsiz>]]

StopTime [fillfactor <fill>] [<timescale>] [<refpos>] <stop>
[Time <time>] [unit <unit>] [Error <error> [<error>]]
[Resolution <resln> [<resln>]] [Size <size> [<size>]]
[PixSize <pixsiz> [<pixsiz>]]

Time [<timescale>] [<refpos>] [<time>]
[unit <unit>] [Error <error> [<error>]]
[Resolution <resln> [<resln>]] [Size <size> [<size>]]
[PixSize <pixsiz> [<pixsiz>]]

Notes:

<timescale> is one of the following: TT, TDT, ET, TAI, IAT, UTC, TEB, TDB, TCG, TCB, LST, nil; the default value is nil.
<refpos> is one of the following: GEOCENTER, BARYCENTER, HELIOCENTER, TOPOCENTER, GALACTIC_CENTER, EMBARYCENTER, MOON, MERCURY, VENUS, MARS, JUPITER, SATURN, URANUS, NEPTUNE, PLUTO, UNKNOWNRefPos; the default value is UNKNOWNRefPos.
<time>, <start>, and <stop> are one of the following:
<ISOstring>, JD <JDvalue>, MJD <MJDvalue>; there is no default.
<unit> only applies to the arguments that follow it and is one of the following: s, d, a, yr, cy; the default value is s.
<error>, <resln>, <size>, and <pixsiz> are doubles; two doubles indicate a range.
[...] indicates that the preceding parameter set may occur more than once, to specify a “support” area that consists of multiple intervals.
<fill> (single interval only) is a number between 0 and 1; the default value is 1.0.

5.2 Space Sub-phrase

PositionInterval [fillfactor <fill>] <frame> [<refpos>] [<flavor>] [<lolimit> <hilimit> ...]
[Position <pos>] [unit <unit>] [Error <error> [<error>]]
[Resolution <resln> [<resln>]] [Size <size> [<size>]]
[PixSize <pixsiz> [<pixsiz>]]
[<Velocity sub-phrase>]

AllSky [fillfactor <fill>] <frame> [<refpos>] [<flavor>]
[Position <pos>] [unit <unit>] [Error <error> [<error>]]
[Resolution <resln> [<resln>]] [Size <size> [<size>]]
[PixSize <pixsiz> [<pixsiz>]]
[<Velocity sub-phrase>]

Circle [fillfactor <fill>] <frame> [<refpos>] [<flavor>] <pos> <radius>
[Position <pos>] [unit <unit>] [Error <error> [<error>]]
[Resolution <resln> [<resln>]] [Size <size> [<size>]]
[PixSize <pixsiz> [<pixsiz>]]
[<Velocity sub-phrase>]

Ellipse [fillfactor <fill>] <frame> [<refpos>] [<flavor>] <pos> <radius> <radius> <posangle>
[Position <pos>] [unit <unit>] [Error <error> [<error>]]
[Resolution <resln> [<resln>]] [Size <size> [<size>]]
[PixSize <pixsiz> [<pixsiz>]]
[<Velocity sub-phrase>]

Box [fillfactor <fill>] <frame> [<refpos>] [<flavor>] <pos> <bsize>
[Position <pos>] [unit <unit>] [Error <error> [<error>]]
[Resolution <resln> [<resln>]] [Size <size> [<size>]]
[PixSize <pixsiz> [<pixsiz>]]
[<Velocity sub-phrase>]

Polygon [fillfactor <fill>] <frame> [<refpos>] [<flavor>] [<pos> ...]
[Position <pos>] [unit <unit>] [Error <error> [<error>]]
[Resolution <resln> [<resln>]] [Size <size> [<size>]]
[PixSize <pixsiz> [<pixsiz>]]
[<Velocity sub-phrase>]

Convex [fillfactor <fill>] <frame> [<refpos>] [<flavor>] [<hspace> ...]
[Position <pos>] [unit <unit>] [Error <error> [<error>]]
[Resolution <resln> [<resln>]] [Size <size> [<size>]]
[PixSize <pixsiz> [<pixsiz>]]
[<Velocity sub-phrase>]

Position <frame> [<refpos>] [<flavor>] [<pos>]
[unit <unit>] [Error <error> [<error>]]
[Resolution <resln> [<resln>]] [Size <size> [<size>]]
[PixSize <pixsiz> [<pixsiz>]]
[<Velocity sub-phrase>]

Notes:

<frame> is one of the following: ICRS, FK5, FK4, J2000, B1950, ECLIPTIC, GALACTIC[_II], SUPER_GALACTIC, GEO_C, GEO_D, UNKNOWNFrame. ECLIPTIC shall be assumed to have an equinox of J2000 with respect to ICRS.
<refpos> is one of the following: GEOCENTER, BARYCENTER, HELIOCENTER, TOPOCENTER, GALACTIC_CENTER, EMBARYCENTER, MOON, MERCURY, VENUS, MARS, JUPITER, SATURN, URANUS, NEPTUNE, PLUTO, UNKNOWNRefPos; the default value is UNKNOWNRefPos.
<flavor> is one of the following:
SPHER2, UNITSPHER, CART1, CART2, CART3, SPHER3; the default value is SPHER2, except for Convex, where the default is UNITSPHER.
<unit> applies to all numerical arguments except <fill> and is one of the following:
deg, arcmin, arcsec, m, mm, km, AU, pc, kpc, Mpc; the default value for spherical coordinates, except GEO, is deg; for GEO: deg deg m; for Cartesian coordinates: m. For multi-dimensional frames one may specify a unit for each axis, such as “deg deg m”.
<pos>, <lolimit>, <hilimit>, <center>, <bsize>, <error>, <resln>, <size>, and <pixsiz> are lists of 1, 2, or 3 doubles, depending on the dimensionality of the space frame; the last four may be pairs of vectors, indicating ranges; if the vector components are identical, their value will be interpreted as a radius.
<hspace> is a list of 4 doubles: a 3-dimensional unit sphere vector, followed by an offset.
<radius> and <posangle> are doubles; position angle reference is ‘Y’ for spherical coordinates, ‘X’ for Cartesian, unit=deg.
[...] indicates that the preceding parameter set may occur more than once, to specify a “support” area that consists of multiple intervals.
<fill> (single interval only) is a number between 0 and 1; the default value is 1.0.
The Velocity sub-phrase:
[VelocityInterval [fillfactor <fill>] <lolimit> <hilimit> ...]
[Velocity <vel>] [unit <unit>] [Error <error> [<error>]]
[Resolution <resln> [<resln>]] [PixSize <pixsiz> [<pixsiz>]]
with m/s as default unit; allowed values are <spatial unit>/<time unit>.

5.3 Spectral Sub-phrase

SpectralInterval [fillfactor <fill>] [<refpos>]
[<lolimit> <hilimit> ...]
[Spectral <spec>] [unit <unit>] [Error <error> [<error>]]
[Resolution <resln> [<resln>]] [Size <size> [<size>]]
[PixSize <pixsiz> [<pixsiz>]]

Spectral [<refpos>] [<spec>] [unit <unit>] [Error <error> [<error>]]
[Resolution <resln> [<resln>]] [Size <size> [<size>]]
[PixSize <pixsiz> [<pixsiz>]]

Notes:

<refpos> is one of the following: GEOCENTER, BARYCENTER, HELIOCENTER, TOPOCENTER, LSR[K], LSRD, GALACTIC_CENTER, LOCAL_GROUP_CENTER, EMBARYCENTER, MOON, MERCURY, VENUS, MARS, JUPITER, SATURN, URANUS, NEPTUNE, PLUTO, UNKNOWNRefPos; the default value is UNKNOWNRefPos.
<unit> applies to all numeric arguments except <fill> and is one of the following:
Hz, MHz, GHz, m, mm, um, nm, Angstrom, eV, keV, MeV;
the default value is Hz.
<spec>, <lolimit>, <hilimit>, <error>, <resln>, <size>, and <pixsiz> are doubles; the last three may be pairs of doubles, indicating ranges.
[...] indicates that the preceding parameter set may occur more than once, to specify a “support” area that consists of multiple intervals.
<fill> (single interval only) is a number between 0 and 1; the default value is 1.0.

5.4 Redshift Sub-phrase

RedshiftInterval [fillfactor <fill>] [<refpos>] <type> [<dopplerdef>]
[<lolimit> <hilimit> ...]
[Redshift <rs>] [unit <unit>] [Error <error> [<error>]]
[Resolution <resln> [<resln>]] [Size <size> [<size>]]
[PixSize <pixsiz> [<pixsiz>]]

Redshift [<refpos>] [<type>] [<dopplerdef>] [<rs>]
[unit <unit>] [Error <error> [<error>]]
[Resolution <resln> [<resln>]] [Size <size> [<size>]]
[PixSize <pixsiz> [<pixsiz>]]

Notes:

<refpos> is one of the following: GEOCENTER, BARYCENTER, HELIOCENTER, TOPOCENTER, LSR[K], LSRD, GALACTIC_CENTER, LOCAL_GROUP_CENTER, EMBARYCENTER, MOON, MERCURY, VENUS, MARS, JUPITER, SATURN, URANUS, NEPTUNE, PLUTO, UNKNOWNRefPos; the default value is UNKNOWNRefPos.
<unit> applies to all numeric arguments except <fill>; the only allowed value is km/s for velocities, and it should be omitted for redshifts.
<type> is VELOCITY or REDSHIFT; there is no default value.
<dopplerdef> is OPTICAL, RADIO, or RELATIVISTIC; the default value is OPTICAL.
<rs>, <lolimit>, <hilimit>, <error>, <resln>, <size>, and <pixsiz> are doubles; the last three may be pairs of doubles, indicating ranges..
[...] indicates that the preceding parameter set may occur more than once, to specify a “support” area that consists of multiple intervals.
<fill> (single interval only) is a number between 0 and 1; the default value is 1.0.

Appendix A: Examples

STC-S allows, within the restrictions listed in Section 4, a simple character string to represent any type of STC metadata information, such as:

— Positions

— Times and time ranges

— Spectral metadata

— Redshift and Doppler velocity information

— Spatial regions – simple or compound

Or any combination of these – and many more.

A.1 Simple Examples

For instance, this string defines a volume in observing coordinate space:

TimeInterval TT GEOCENTER 2011-01-01 2012-03-30 Resolution 0.2
PositionInterval ICRS GEOCENTER 170 -20 190 10 Resolution 0.0001
SpectralInterval GEOCENTER 4.95 5.0 unit GHz Size 0.05

A single point in Time and Space:

Time TDB BARYCENTER MJD 50814.0
Position ICRS BARYCENTER 147.3 69.3

A.2 Simple and Compound Regions

A simple region:

Circle ICRS TOPOCENTER 147.6 69.9 0.4

Two compound regions:

Union ICRS TOPOCENTER
(Polygon 147.8 69.2 147.4 69.2 147.3 69.4 147.9 69.4
Polygon 147.9 69.7 147.6 69.7 147.5 69.9 148.0 69.9)

and:

Union ICRS TOPOCENTER
(Circle 180 10 20
Circle 190 20 20
Intersection
(Circle 120 -10 20
   Difference
    (Circle 130 -10 20
     Circle 125 -10 2
    )
   Not
    (Circle 118 -8 3)
)
)

A.3 STC-S and STC-X Serializations

The following comprehensive example:

TimeInterval TT GEOCENTER 1996-01-01T00:00:00 1996-01-01T00:30:00
Time MJD 50814.0 Error 1.2 Resolution 0.8 PixSize 1024.0

Circle ICRS GEOCENTER 179.0 -11.5 0.5 Position 179.0 -11.5
Error 0.000889 Resolution 0.001778 Size 0.000333 0.000278
PixSize 0.000083 0.000083

Spectral BARYCENTER 1420.4 unit MHz Resolution 10.0

RedshiftInterval BARYCENTER VELOCITY OPTICAL 200.0 2300.0
Redshift 300.0 Resolution 0.7 PixSize 0.3

is the equivalent of this STC-X expression:

<?xml version="1.0" encoding="UTF-8"?>

</TimeFrame>

<ICRS/>

</SpaceFrame>

</BARYCENTER>

</SpectralFrame>

<DopplerDefinition>OPTICAL</DopplerDefinition>

</BARYCENTER>

</RedshiftFrame>

</AstroCoordSystem>

</TimeInstant>

</Time>

<Name>Position</Name>

</Value2>

<Size2>

</Size2>

</PixSize2>

</Position2D>

<Name>Frequency</Name>

</Spectral>

<Name>Doppler velocity</Name>

</Redshift>

</AstroCoords>

</StartTime>

</StopTime>

</TimeInterval>

</Center>

</Circle>

</RedshiftInterval>

</AstroCoordArea>

</CatalogEntryLocation>

The example in Section 3:

was derived from the following STC-X element:

<?xml version="1.0" encoding="UTF-8"?>

<!--

This STC metadata description specifies a query:

Find all images, within 2 degrees from a certain position, that have these
properties:

spatial resolution: between 0.0001 and 0.003 degrees

size: between 30 and 40 arcmins on the side

pixelsize: between 0.00005 and 0.00015 degrees

covering a band of 300 to 600 Angstrom
in the spectral range 4000 to 7000 A

taken since 1900.0

AstroCoordSystem specifies the coordinate system used in this query.

AstroCoordArea specifies where to look in coordinate space

AstroCoords specifies the (ranges of) properties along the coordinates

-->

</TimeFrame>

<Name>Equatorial</Name>

<ICRS/>

</SpaceFrame>

<Name>Wavelength</Name>

</SpectralFrame>

</AstroCoordSystem>

</Resolution2>

</Resolution2>

<Size2>

</Size2>

<Size2>

</Size2>

</PixSize2>

</PixSize2>

</Position2D>

<Name>Lambda</Name>

</Spectral>

</AstroCoords>

</StartTime>

</TimeInterval>

</Center>

</Circle>

</SpectralInterval>

</AstroCoordArea>

</SearchLocation>

Changes from Previous Versions

Note

From V1.00 to V1.10:

Changed the name from LinearSTC to STC-S

From V1.10 to V1.30:

Changed UNKNOWN to UNKNOWNRefPos or UNKNOWNFrame
Added Convex

From V1.30 to V1.32:

Removed default frame for spatial, since the reference frame is required
Allowed optionally compound sub-phrases (for compound Regions)
Corrected typo in order of elements in Redshift
Allow multiple unit specification for multi-dimensional frames
If all elements of 2- or 3-D errors are identical, interpret as a radius

From V1.32 to V1.33

Changed Redshift default to Redshift
Allowed Size in all coordinates (for consistency, not functionality)
Changed syntax for compound Regions

Working Draft V0.10

Modified sectioning; split Section 2 into 2 and 3
Cleaned up out-of-date text in early sections
Added Appendix with examples

References

A. H. Rots, Space-Time Coordinate Metadata for the Virtual Observatory, http://www.ivoa.net/Documents/latest/STC.html

A. H. Rots, STC-X: Space-Time Coordinate (STC) Metadata XML Implementation
http://www.ivoa.net/Documents/latest/STC-X.html

A. H. Rots, STC-Model: Space-Time Coordinate (STC) Metadata Model
http://www.ivoa.net/Documents/latest/STC-Model.html