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GEOPRIV                                                       M. Thomson
Internet-Draft                                                    Andrew
Expires: July 5, 2006                                       January 2006


    Geodetic Shapes for the Representation of Uncertainty in PIDF-LO
                 draft-thomson-geopriv-geo-shape-00.txt

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Copyright Notice

   Copyright (C) The Internet Society (2006).

Abstract

   This document defines a set of shapes for the representation of
   uncertainty for PIDF-LO geodetic location information.  This includes
   a GML profile and a schema that defines additional geometries.
   Further recommendations are made to restrict the use of geographic
   Coordinate Reference Systems (CRS) and units of measure restrictions
   that improve interoperability.






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Table of Contents

   1.  Introduction . . . . . . . . . . . . . . . . . . . . . . . . .  3
   2.  Conventions used in this document  . . . . . . . . . . . . . .  4
   3.  Overview . . . . . . . . . . . . . . . . . . . . . . . . . . .  5
     3.1.  About Location Information . . . . . . . . . . . . . . . .  5
       3.1.1.  Coordinate Reference Systems . . . . . . . . . . . . .  5
       3.1.2.  Uncertainty  . . . . . . . . . . . . . . . . . . . . .  5
       3.1.3.  Confidence . . . . . . . . . . . . . . . . . . . . . .  6
   4.  General Information  . . . . . . . . . . . . . . . . . . . . .  8
     4.1.  GML Version and Profile  . . . . . . . . . . . . . . . . .  8
     4.2.  Coordinate Reference Systems . . . . . . . . . . . . . . .  8
     4.3.  Units of Measure . . . . . . . . . . . . . . . . . . . . .  8
     4.4.  Lines and Distances  . . . . . . . . . . . . . . . . . . .  9
   5.  Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
     5.1.  Point  . . . . . . . . . . . . . . . . . . . . . . . . . . 10
     5.2.  Polygon  . . . . . . . . . . . . . . . . . . . . . . . . . 10
       5.2.1.  Polygon Upward Normal  . . . . . . . . . . . . . . . . 12
     5.3.  Circle . . . . . . . . . . . . . . . . . . . . . . . . . . 12
     5.4.  Ellipse  . . . . . . . . . . . . . . . . . . . . . . . . . 13
     5.5.  Arc Band . . . . . . . . . . . . . . . . . . . . . . . . . 14
     5.6.  Sphere . . . . . . . . . . . . . . . . . . . . . . . . . . 16
     5.7.  Ellipsoid  . . . . . . . . . . . . . . . . . . . . . . . . 17
     5.8.  Prism  . . . . . . . . . . . . . . . . . . . . . . . . . . 18
   6.  Application Schema . . . . . . . . . . . . . . . . . . . . . . 19
   7.  GML Profile Schema . . . . . . . . . . . . . . . . . . . . . . 22
     7.1.  geometryPrimitives.xsd . . . . . . . . . . . . . . . . . . 22
     7.2.  geometryBasic2d.xsd  . . . . . . . . . . . . . . . . . . . 26
     7.3.  geometryBasic0d1d.xsd  . . . . . . . . . . . . . . . . . . 28
     7.4.  measures.xsd . . . . . . . . . . . . . . . . . . . . . . . 31
     7.5.  gmlBase.xsd  . . . . . . . . . . . . . . . . . . . . . . . 32
     7.6.  basicTypes.xsd . . . . . . . . . . . . . . . . . . . . . . 33
   8.  Security Considerations  . . . . . . . . . . . . . . . . . . . 34
   9.  IANA Considerations  . . . . . . . . . . . . . . . . . . . . . 35
     9.1.  URN Sub-Namespace Registration for
           urn:ietf:params:xml:ns:pidf:geopriv10:geoShape . . . . . . 35
     9.2.  XML Schema Registration  . . . . . . . . . . . . . . . . . 35
   10. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . 37
   11. References . . . . . . . . . . . . . . . . . . . . . . . . . . 38
     11.1. Normative References . . . . . . . . . . . . . . . . . . . 38
     11.2. Informative References . . . . . . . . . . . . . . . . . . 38
   Appendix A.  Calculating the Upward Normal of a Polygon  . . . . . 40
   Appendix B.  Open Issues . . . . . . . . . . . . . . . . . . . . . 41
     B.1.  Shape Names  . . . . . . . . . . . . . . . . . . . . . . . 41
     B.2.  MLP Aggregate Shape Types  . . . . . . . . . . . . . . . . 41
     B.3.  Moving Targets . . . . . . . . . . . . . . . . . . . . . . 41
   Author's Address . . . . . . . . . . . . . . . . . . . . . . . . . 42
   Intellectual Property and Copyright Statements . . . . . . . . . . 43



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1.  Introduction

   This document defines how geodetic location information is specified
   in a PIDF-LO [RFC4119] document.

   PIDF-LO [RFC4119] specifies that the feature schema from version 3.0
   of GML be supported by all implementations.  However, this is not
   practical for a number of reasons.

   The feature schema, and the schema that it relies upon, includes a
   sizable proportion of the GML data types.  This includes parts of the
   geometry and temporal schema that are rarely applicable in the domain
   where PIDF-LO is used.  This means that implementations are required
   to support portions of the GML specification that are not and, in
   some cases, cannot be used.

   GML is structured to be used within an application schema.  An
   application schema being a schema constructed for a particular
   application that both limits GML to what is applicable and provides
   application-specific types.  PIDF-LO does not define such a schema.
   As a result this increases the complexity of implementation and
   decreases the usability of GML within PIDF-LO.  If PIDF-LO is to be
   usable in the internet domain, it requires that such a schema is
   defined.

   This document defines an application schema and profile for using GML
   within PIDF-LO.  This includes a small subset of GML geometry that is
   expanded by a new schema that defines additional geometries.

   These geometries, or shapes, are designed to provide a simple
   representation of shapes that are in common usage.  This includes
   shapes that are commonly found in wireless location technologies as
   well as shapes that are suited to geodetic representations of civic
   features, such as buildings and residental allotments.  These shapes
   enable easy translation from location information in other forms into
   the PIDF-LO form.

   This document also updates the PIDF-LO specification to state that
   the geometry specified in this document is the only requirement for
   geodetic shapes.











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2.  Conventions used in this document

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
   document are to be interpreted as described in [RFC2119].

   This document uses geodesy and mathematics terminology.  While this
   has been limited as far as is practical, some degree of familiarity
   with these disciplines and their terminology is helpful.  In
   particular, terminology following the definitions in GML 3.1.0
   [OGC.GML-3.1.0] is used.

   When referring to XML element, attribute and type definitions by
   name, this document uses namespace prefixes to distinguish between
   elements in different namespaces.  The "gml:" prefix refers to
   elements from the "http://www.opengis.net/gml" namespace [OGC.GML-
   3.1.0]; the "gs:" prefix refers to elements from the
   "urn:ietf:params:xml:ns:pidf:geopriv10:geoShape" namespace.

































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3.  Overview

   PIDF-LO serves as a document for the representation of Location
   Information (LI).  This LI identifies the spatial location of a
   Target; the Target being a generic entity that is likely to be either
   a person or a Device.  LI is a component of the Target's presence
   information.

   The LI that forms the core of a PIDF-LO document originates in the
   Location Generator (LG).  Depending on the specific circumstances,
   particularly the type of access network, the LG can use any number of
   methods to determine LI.  The range of technologies available for
   determining LI are numerous and range from user-provided LI, to
   automatic methods such as wire mapping, radio timing, and GPS.

   PIDF-LO is designed to be consumed in a wide range of applications.
   In some cases the information is presented to a user, maybe in a
   graphical representation, as a way of identifying the location of the
   Target.  Other applications use LI as input to assist in providing a
   service.

3.1.  About Location Information

   Two forms of LI are defined for use in PIDF-LO.  Geodetic information
   consists of coordinates that identify a location in a particular
   coordinate reference system; and civic addresses [I-D.ietf-geopriv-
   revised-civic-lo] that identify a location based on civic norms
   (countries, cities, streets, etc...).  This document is concerned
   with geodetic LI only.

   The remainder of this section introduces location concepts that
   affect how geodetic LI is represented and interpreted.

3.1.1.  Coordinate Reference Systems

   A coordinate reference system (CRS) specifies how coordinates are
   interpreted.  For use within GML, only the two- and three-dimensional
   WGS84 coordinate reference systems (latitude, longitude, and perhaps
   altitude) are mandatory, see Section 4.2.  Therefore, the shapes
   defined in this document assume one or both of these CRSs and may not
   be applicable to other coordinate reference systems.

3.1.2.  Uncertainty

   Under ideal circumstances LI would describe a point in space
   unambiguously.  However, in reality, location determination methods
   are imprecise for a large number of reasons.




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   Uncertainty can be quantified in measurement in a number of ways,
   usually depending on the method that is used to determine LI.  An
   area or volume is the most common way of representing uncertainty.
   For example, an ellipsoid is common for representing uncertainty in
   GPS measurements; polygons may be used when LI is converted from a
   civic address form; or a circle or ellipse is often used to describe
   the coverage area of a radio antenna.

   Even if location determination results in a single point, uncertainty
   may be specified as a distance from that point.  This form of
   uncertainty indicates the furthest distance from the given point that
   the actual Target is expected to be located.  This still effectively
   defines a circular area, or spherical volume, in which the Target
   could be located.

   This document assumes that any method for determining location is
   subject to uncertainty.  The absence of uncertainty does not indicate
   that there is none, or that the measurement was infinitely precise;
   instead, the absence of uncertainty data indicates that the value of
   uncertainty could not be (or was not) provided.

3.1.3.  Confidence

   Confidence is also used in some cases to express the innate
   variability of location determination.  Variability in determining
   location cannot always be addressed by uncertainty.  Confidence is a
   statistical measure indicating the probability that the given region
   of uncertainty actually covers the target.

   Confidence is typically affected by variation in measurement
   parameters.  However, confidence can also account for the chance of
   human error in the form of data entry errors or exceptional software
   faults.  Likewise, confidence can cover the probability of
   intentional modification of LI (location fraud) beyond the capability
   of providers or protocol to prevent.

   The application of confidence is controversial.  Location
   determination methods do not often directly provide this sort of
   information, and likewise many applications do not use the value in
   any way.  In most cases the confidence cannot be used to make a
   decision.  For instance, one such decision that uses confidence is
   whether or not the LI can be used; in most cases an application
   relies on application and designers being willing to take any LI,
   regardless of the probability of accuracy.

   Because uncertainty is difficult to manage, this document does not
   include a parameter for converying confidence.  Individual
   applications MAY recommend a target level of confidence, but this



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   information is not considered to be required for the core geographic
   format.

















































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4.  General Information

4.1.  GML Version and Profile

   This document is based on the version 3.1.1 schema of GML [OGC.GML-
   3.1.0].  This document updates RFC 4119 [RFC4119].

   This document restricts the required set of GML.  A profile schema is
   included in Section 7.  This profile follows the guidelines of
   [OGC.GML-3.1.0], it is a copy of the GML schema with portions
   removed.  GML compliant implementations MAY use the full GML schema
   or the "geometryPrimitives.xsd" schema in place of this profile, as
   identified by
   "urn:opengis:specification:gml:schema-xsd:geometryPrimitives:3.1.1".

   The GML profile defined in Section 7 removes all unused parts of GML
   from the schema definition.  In particular, this includes cross
   references using XLink [W3C.REC-xlink-20010627].  The "gml:id"
   attribute is retained so that geometry objects MAY still be the
   target of a reference.

4.2.  Coordinate Reference Systems

   Implementations are REQUIRED to support the following coordinate
   reference systems based on WGS 84 [NIMA.TR8350.2-3e].  These are
   identified using the European Petroleum Survey Group (EPSG) Geodetic
   Parameter Dataset, as formalized by the Open Geospatial Consortium
   (OGC):

   3D: WGS 84 (latitude, longitude, altitude), as identified by the URN
      "urn:ogc:def:crs:EPSG::4979".

   2D: WGS 84 (latitude, longitude), as identified by the URN
      "urn:ogc:def:crs:EPSG::4326".

   The most recent version of the EPSG Geodetic Parameter Dataset SHOULD
   be used.  A CRS MUST be specified using the above URN notation only,
   implementations do not need to support user-defined CRSs.

   Implementations MUST specify the CRS using the "srsName" attribute on
   the outermost geometry element.  The CRS MUST NOT be respecified or
   changed for any sub-elements.

4.3.  Units of Measure

   GML permits a range of units of measure for all parameters.  This
   document restricts this set to a single length unit and two angle
   units.



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   Length measures MUST be specified using metres, which is identified
   using the URN "urn:ogc:def:uom:EPSG::9001".

   Angular measures MUST use either degrees or radians.  Measures in
   degrees MUST be identified by the URN "urn:ogc:def:uom:EPSG::9102".
   Measures in radians MUST be identified by the URN
   "urn:ogc:def:uom:EPSG::9101".

   The units of measure MUST be specified on the element that contains
   the value.

4.4.  Lines and Distances

   In this documents, it is assumed that all lines and measurements are
   formed by straight lines.  When joining two points, linear
   interpolation is used, that is, the shortest path in space.  Likewise
   for distances, the distance is the length of the shortest path in
   space.

   Implementations MAY use geodesic interpolation between points and for
   distance measurement.  A geodesic is a line that follows the surface
   of a geoid or ellipsoid, which in this context is usually the WGS 84
   ellipsoid.  Geodesic interpolation can produce a small difference
   from straight line interpolation, which for use in uncertainty is
   acceptable provided that this variation is constrained to
   approximately 2% of the total distance.  The error between a geodesic
   and a straight line reaches 2% of the distance of the line at
   approximately 250km for WGS84.























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5.  Geometry

   This document defines a set of geometry that is appropriate for the
   encoding of the sorts of LI described in Section 3.1.  This section
   describes how geometries can be represented using the application
   schema defined in Section 6.  Pre-existing GML geometries,
   "gml:Point" and "gml:Polygon" are also described with examples.

   This section clarifies the usage of the zero dimensional Point
   (Section 5.1).  The following two dimensional shapes are either
   clarified or defined: Polygon (Section 5.2), Circle (Section 5.3),
   Ellipse (Section 5.4) and Arc Band (Section 5.5).  The following
   three dimensional shapes are defined: Sphere (Section 5.6), Ellipsoid
   (Section 5.7) and Prism (Section 5.8).

   A description of the Point, Circle, Ellipse, Sphere, Ellipsoid,
   Polygon and Arc Band, including descriptions of their parameters and
   explanatory diagrams, can be found in [3GPP.TS23032].

5.1.  Point

   The point shape type is the simplest form of geodetic LI, which is
   natively supported by GML.  The "gml:Point" element is used when
   there is no known uncertainty.  A point also forms part of a number
   of other geometries.

   A point MAY be specified using either WGS 84 (latitude, longitude) or
   WGS 84 (latitude, longitude, altitude).  This is shown in the
   following examples:

     <gml:Point srsName="urn:ogc:def:crs:EPSG::4326"
                xmlns:gml="http://www.opengis.net/gml">
       <gml:pos>4.5 -36.2</gml:pos>
     </gml:Point>

     <gml:Point srsName="urn:ogc:def:crs:EPSG::4979"
                xmlns:gml="http://www.opengis.net/gml">
       <gml:pos>4.5 -36.2 54</gml:pos>
     </gml:Point>

5.2.  Polygon

   A polygon uses the "gml:Polygon" element.  A polygon is specified by
   a sequence of points.  A polygon requires at least four points, where
   the first and last point MUST be the same.

   Points specified in a polygon MUST be coplanar.  However,
   implementations SHOULD be prepared to accept small variations that



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   might occur depending on whether the the polygon is specified on a
   plane in space, or only relative to the ellipsoid.  To avoid
   implementation complexity, implementations MAY choose to not support
   polygons that include varying altitude.  Therefore, two polygon forms
   are permitted: polygons specified using EPSG 4326, and polygons
   specified using EPSG 4979 with a constant altitude value.

   Interpolation between points is linear, as defined for the
   "gml:LinearRing" element.  Note that this interpolation is different
   for that specified in [3GPP.TS23032], which uses geodesic
   interpolation.  Since geodesic interpolation is non-trivial to
   implement and some error is acceptable in both [3GPP.TS23032] and
   this document, it is RECOMMENDED that implementations minimize this
   error by ensuring that the sides of polygons are as short as
   possible.

   For interoperability with [3GPP.TS23032], the number of points has
   been limited to 16.  Note that because the first and last points must
   be repeated, this limits the number of discrete points to 15.

   The following example shows a polygon that is specified using EPSG
   4326 and the "gml:pos" element.

     <gml:Polygon srsName="urn:ogc:def:crs:EPSG::4979"
                  xmlns:gml="http://www.opengis.net/gml">
       <gml:exterior>
         <gml:LinearRing>
           <gml:pos>42.556844 -73.248157</gml:pos>
           <gml:pos>42.549631 -73.237283</gml:pos>
           <gml:pos>42.539087 -73.240328</gml:pos>
           <gml:pos>42.535756 -73.254242</gml:pos>
           <gml:pos>42.542969 -73.265115</gml:pos>
           <gml:pos>42.553513 -73.262075</gml:pos>
           <gml:pos>42.556844 -73.248157</gml:pos>
         </gml:LinearRing>
       </gml:exterior>
     </gml:Polygon>














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   The following alternative example shows the same polygon with a
   constant altitude included that is specified using EPSG 4979 and the
   "gml:posList" element.

     <gml:Polygon srsName="urn:ogc:def:crs:EPSG::4979"
                  xmlns:gml="http://www.opengis.net/gml">
       <gml:exterior>
         <gml:LinearRing>
           <gml:posList>
             42.556844 -73.248157 36.6
             42.549631 -73.237283 36.6
             42.539087 -73.240328 36.6
             42.535756 -73.254242 36.6
             42.542969 -73.265115 36.6
             42.553513 -73.262075 36.6
             42.556844 -73.248157 36.6
           </gml:posList>
         </gml:LinearRing>
       </gml:exterior>
     </gml:Polygon>

   Note: The "gml:posList" element is interpreted as a list with the
   dimension of the CRS indicating how many values are required for each
   point.

5.2.1.  Polygon Upward Normal

   The upward normal of a polygon determines the orientation of the
   surface.  The upward normal of a polygon is important for the
   definition of the Prism (Section 5.8).

   [OGC.GML-3.1.0] describes the upward normal of a surface as a unit
   vector pointing to the side of the surface from which the exterior
   boundary appears counterclockwise.  It is RECOMMENDED therefore that
   polygons are specified in a counterclockwise direction, so that their
   upward normal corresponds to an actual _up_.

   The upward normal can also be determined using the _Right Hand Rule_.
   Take your right hand and curl the fingers in the predominant
   direction that the polygon is defined; your thumb then points in the
   direction of the upward normal.

   A method for calculating the upward normal of a polygon that is not
   guaranteed to be coplanar is described in Appendix A.

5.3.  Circle

   The circular area is used for coordinates in two-dimensional CRSs to



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   describe uncertainty about a point.  The definition is based on the
   one-dimensional geometry in GML, "gml:CircleByCenterPoint".

   The centre point of a circular area MUST be specified using a two
   dimensional CRS; in three dimensions, the orientation of the circle
   cannot be specified correctly using this representation.  A point
   with uncertainty that is specified in three dimensions SHOULD use the
   Sphere (Section 5.6) shape type.

     <gs:Circle srsName="urn:ogc:def:crs:EPSG::4326"
         xmlns:gs="urn:ietf:params:xml:ns:pidf:geopriv10:geoShape"
         xmlns:gml="http://www.opengis.net/gml">
       <gml:pos>
         42.5463 -73.2512
       </gml:pos>
       <gml:radius uom="urn:ogc:def:uom:EPSG::9001">
         850.24
       </gml:radius>
     </gs:Circle>

5.4.  Ellipse

   An elliptical area describes an ellipse in two dimensional space.
   The ellipse is described by a center point, the length of its semi-
   major and semi-minor axes, and the orientation of the semi-major
   axis.

   Like the circular area (Section 5.3), the ellipse MUST be specified
   using a two dimensional CRS.

     <gs:Ellipse srsName="urn:ogc:def:crs:EPSG::4326"
         xmlns:gs="urn:ietf:params:xml:ns:pidf:geopriv10:geoShape"
         xmlns:gml="http://www.opengis.net/gml">
       <gml:pos>
         42.5463 -73.2512
       </gml:pos>
       <gs:semiMajorAxis uom="urn:ogc:def:uom:EPSG::9001">
         1275
       </gs:semiMajorAxis>
       <gs:semiMinorAxis uom="urn:ogc:def:uom:EPSG::9001">
         670
       </gs:semiMinorAxis>
       <gs:orientation uom="urn:ogc:def:uom:EPSG::9102">
         43.2
       </gs:orientation>
     </gs:Ellipse>

   The "gml:pos" element indicates the position of the center, or



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   origin, of the ellipse.

   The "gs:semiMajorAxis" and "gs:semiMinorAxis" elements are the length
   of the semi-major and semi-minor axes respectively.

   The "gs:orientation" element is the angle by which the semi-major
   axis is rotated from the first axis of the CRS towards the second
   axis.  For WGS 84, the orientation indicates rotation from Northing
   to Easting, which, if specified in degrees, is roughly equivalent to
   a compass bearing (if magnetic north were the same as the WGS north
   pole).

   Note: An ellipse with equal major and minor axes lengths is a circle.

5.5.  Arc Band

   An arc band is a section of a circular area that is constrained to an
   arc between two radii.  The arc band shape is most useful when radio
   timing technologies are used to determine location, based on a single
   wireless transmitter.  These technologies provide a result that is a
   range from the transmitter, which might also be constrained in
   direction.

   An arc band is defined by the center point of the circle, an inner
   and outer radius, a start angle, and an opening angle.

   The following figure shows a sample arc band, with the center point
   "c", inner radius "r(i)", outer radius "r(o)", start angle "a(s)",
   and opening angle "a(o)" indicated.






















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           ^        ,.__
           |       /     `-.
           | a(s) /         `-.
           |--.  /             `.
           |   `/                \
           |   /__                \
           |  .   `-.              \
           | .       `.             \
           |. \        \             .
        ---c-- a(o) -- |             | -->
           |.  /       '             |
           |  .       /              '
           |    .    /              ;
                  .,'              /
               r(i)`.             /
                     `.          /
                       `.      ,'
                         `.  ,'
                       r(o)`'

   The center point, "gml:pos", MUST be specified in a two dimensional
   CRS.

   The inner radius, "gs:innerRadius", defines the minimum distance from
   the center point.  The outer radius, "gs:outerRadius", defines the
   maximum distance from the center point.

   The start angle, "gs:startAngle", and opening angles,
   "gs:openingAngle", define where the arc begins and ends.  The arc
   covers an arc the size of the opening (or included) angle that begins
   at the start (or offset) angle.




















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   The following example includes an arc band shape.  This arc band
   starts at 266 degrees and has a 120 degree opening; therefore, the
   end of the band is at a 26 degree bearing.

     <gs:ArcBand srsName="urn:ogc:def:crs:EPSG::4326"
         xmlns:gs="urn:ietf:params:xml:ns:pidf:geopriv10:geoShape"
         xmlns:gml="http://www.opengis.net/gml">
       <gml:pos>
         42.5463 -73.2512
       </gml:pos>
       <gs:innerRadius uom="urn:ogc:def:uom:EPSG::9001">
         1661.55
       </gs:innerRadius>
       <gs:outerRadius uom="urn:ogc:def:uom:EPSG::9001">
         2215.4
       </gs:outerRadius>
       <gs:startAngle uom="urn:ogc:def:uom:EPSG::9102">
         266
       </gs:startAngle>
       <gs:openingAngle uom="urn:ogc:def:uom:EPSG::9102">
         120
       </gs:openingAngle>
     </gs:ArcBand>

   Note: An arc band with an inner radius of zero, and equal start and
   opening angles is a circle.

5.6.  Sphere

   The sphere is a volume that provides the same information as a circle
   (Section 5.3) in three dimensions.  The sphere MUST be specified
   using a three dimensional CRS.

   The following example shows a sphere shape, which is identical to the
   circle example, except for the addition of an altitude in the
   provided coordinates.

     <gs:Sphere srsName="urn:ogc:def:crs:EPSG::4979"
         xmlns:gs="urn:ietf:params:xml:ns:pidf:geopriv10:geoShape"
         xmlns:gml="http://www.opengis.net/gml">
       <gml:pos>
         42.5463 -73.2512 26.3
       </gml:pos>
       <gs:radius uom="urn:ogc:def:uom:EPSG::9001">
         850.24
       </gs:radius>
     </gs:Sphere>




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5.7.  Ellipsoid

   The ellipsoid is a volume that is based on the ellipse (Section 5.4)
   shape, with the addition of a third dimension.  A single value,
   vertical uncertainty, is added to the ellipse to form an ellipsoid.

   A full specification of an ellipsoid would include three angles in
   order to be able to orient the ellipsoid in three dimensions.  This
   representation is limited to a single orientation angle, which is the
   same value that is used for the ellipse.  This limits the major and
   minor axes of the base ellipse to a plane that is parallel to the
   surface of the WGS 84 ellipsoid at the given latitude and longitude.
   Implementations MAY also choose to place these axes on the surface of
   the WGS 84 ellipsoid.  The difference between these two
   interpretations are not considered significant.

   The third length measurement, "gs:vertical", indicates the length of
   the third axis of the ellipsoid, which is a line that is always
   perpindicular to the surface of the WGS 84 ellipsoid, that is, it is
   vertical.

   This ellipsoid representation is similar to that described in
   [3GPP.TS23032].

   The following example shows an ellipsoid.

     <gs:Ellipsoid srsName="urn:ogc:def:crs:EPSG::4979"
         xmlns:gs="urn:ietf:params:xml:ns:pidf:geopriv10:geoShape"
         xmlns:gml="http://www.opengis.net/gml">
       <gml:pos>
         42.5463 -73.2512 26.3
       </gml:pos>
       <gs:semiMajorAxis uom="urn:ogc:def:uom:EPSG::9001">
         7.7156
       </gs:semiMajorAxis>
       <gs:semiMinorAxis uom="urn:ogc:def:uom:EPSG::9001">
         3.31
       </gs:semiMinorAxis>
       <gs:verticalAxis uom="urn:ogc:def:uom:EPSG::9001">
         28.7
       </gs:verticalAxis>
       <gs:orientation uom="urn:ogc:def:uom:EPSG::9102">
         142
       </gs:orientation>
     </gs:Ellipsoid>

   Note: An ellipsoid with equal major, minor and vertical axes lengths
   is a sphere.



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5.8.  Prism

   The prism is a volume that is commonly used to represent a shape that
   has a constant cross section along one axis.  For the purposes of
   PIDF-LO, a prism is most useful when representing a building, or
   single floor of a building.

   A prism is defined by its base, which is a two dimensional surface
   specified using a three dimensional CRS, and a height.  The height is
   a scalar value that is projected in the direction of the upward
   normal of the base surface, see Section 5.2.1.

   It is strongly RECOMMENDED that the base shape for a prism is level,
   that is, it exists at the same altitude for all points.
   Implementations MAY reject prisms that have a base that is not at the
   same altitude.

   The following hexagonal prism might be used to represent a floor of a
   building in geodetic form.

     <gs:Prism srsName="urn:ogc:def:crs:EPSG::4979"
         xmlns:gs="urn:ietf:params:xml:ns:pidf:geopriv10:geoShape"
         xmlns:gml="http://www.opengis.net/gml">
       <gs:base>
         <gml:Polygon>
           <gml:exterior>
             <gml:LinearRing>
               <gml:posList>
                 42.556844 -73.248157 36.6
                 42.549631 -73.237283 36.6
                 42.539087 -73.240328 36.6
                 42.535756 -73.254242 36.6
                 42.542969 -73.265115 36.6
                 42.553513 -73.262075 36.6
                 42.556844 -73.248157 36.6
               </gml:posList>
             </gml:LinearRing>
           </gml:exterior>
         </gml:Polygon>
       </gs:base>
       <gs:height uom="urn:ogc:def:uom:EPSG::9001">
         2.4
       </gs:height>
     </gs:Prism>







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6.  Application Schema

   <?xml version="1.0"?>
   <xs:schema
       targetNamespace="urn:ietf:params:xml:ns:pidf:geopriv10:geoShape"
       xmlns:gs="urn:ietf:params:xml:ns:pidf:geopriv10:geoShape"
       xmlns:xs="http://www.w3.org/2001/XMLSchema"
       xmlns:gml="http://www.opengis.net/gml"
       elementFormDefault="qualified"
       attributeFormDefault="unqualified">

     <xs:annotation>
       <xs:appinfo
           source="urn:ietf:params:xml:schema:pidf:geopriv10:geoShape">
         GEOPRIV Geodetic Shapes
       </xs:appinfo>
       <xs:documentation source="http://www.ietf.org/rfc/rfcXXXX.txt">
   <!-- [[NOTE TO RFC-EDITOR: Please replace above URL with URL of
                          published RFC and remove this note.]] -->
         This document defines geodetic shape types for PIDF-LO.
       </xs:documentation>
     </xs:annotation>

     <xs:import namespace="http://www.opengis.net/gml"
                schemaLocation="geometryPrimitives.xsd"/>

     <xs:element name="Circle" type="gs:CircleType"
                 substitutionGroup="gml:_Surface"/>
     <xs:complexType name="CircleType">
       <xs:complexContent>
         <xs:extension base="gml:AbstractSurfaceType">
           <xs:sequence>
             <xs:group ref="gs:centerGroup"/>
             <xs:element name="radius" type="gml:LengthType"/>
           </xs:sequence>
         </xs:extension>
       </xs:complexContent>
     </xs:complexType>

     <xs:element name="Ellipse" type="gs:EllipseType"
                 substitutionGroup="gml:_Surface"/>
     <xs:complexType name="EllipseType">
       <xs:complexContent>
         <xs:extension base="gml:AbstractSurfaceType">
           <xs:sequence>
             <xs:group ref="gs:centerGroup"/>
             <xs:element name="semiMajorAxis" type="gml:LengthType"/>
             <xs:element name="semiMinorAxis" type="gml:LengthType"/>



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             <xs:element name="orientation" type="gml:AngleType"/>
           </xs:sequence>
         </xs:extension>
       </xs:complexContent>
     </xs:complexType>

     <xs:element name="ArcBand" type="gs:ArcBandType"
                 substitutionGroup="gml:_Surface"/>
     <xs:complexType name="ArcBandType">
       <xs:complexContent>
         <xs:extension base="gml:AbstractSurfaceType">
           <xs:sequence>
             <xs:group ref="gs:centerGroup"/>
             <xs:element name="innerRadius" type="gml:LengthType"/>
             <xs:element name="outerRadius" type="gml:LengthType"/>
             <xs:element name="startAngle" type="gml:AngleType"/>
             <xs:element name="openingAngle" type="gml:AngleType"/>
           </xs:sequence>
         </xs:extension>
       </xs:complexContent>
     </xs:complexType>

     <xs:element name="Prism" type="gs:PrismType"
                 substitutionGroup="gml:_Solid"/>
     <xs:complexType name="PrismType">
       <xs:complexContent>
         <xs:extension base="gml:AbstractSolidType">
           <xs:sequence>
             <xs:element name="base" type="gml:SurfacePropertyType"/>
             <xs:element name="height" type="gml:LengthType"/>
           </xs:sequence>
         </xs:extension>
       </xs:complexContent>
     </xs:complexType>

     <xs:element name="Sphere" type="gs:SphereType"
                 substitutionGroup="gml:_Solid"/>
     <xs:complexType name="SphereType">
       <xs:complexContent>
         <xs:extension base="gml:AbstractSolidType">
           <xs:sequence>
             <xs:group ref="gs:centerGroup"/>
             <xs:element name="radius" type="gml:LengthType"/>
           </xs:sequence>
         </xs:extension>
       </xs:complexContent>
     </xs:complexType>




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     <xs:element name="Ellipsoid" type="gs:EllipsoidType"
                 substitutionGroup="gml:_Solid"/>
     <xs:complexType name="EllipsoidType">
       <xs:complexContent>
         <xs:extension base="gml:AbstractSolidType">
           <xs:sequence>
             <xs:group ref="gs:centerGroup"/>
             <xs:element name="semiMajorAxis" type="gml:LengthType"/>
             <xs:element name="semiMinorAxis" type="gml:LengthType"/>
             <xs:element name="verticalAxis" type="gml:LengthType"/>
             <xs:element name="orientation" type="gml:AngleType"/>
           </xs:sequence>
         </xs:extension>
       </xs:complexContent>
     </xs:complexType>

     <xs:group name="centerGroup">
       <xs:choice>
         <xs:element ref="gml:pos"/>
         <xs:element ref="gml:pointProperty"/>
       </xs:choice>
     </xs:group>

   </xs:schema>



























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7.  GML Profile Schema

   This section defines a profile of GML that follows the
   recommendations in Section 22 of [OGC.GML-3.1.0].  The _copy and
   delete_ method has been employed to generate this schema.  The
   profile includes abridged version of the files:
   "geometryPrimitives.xsd", "geometryBasic2d.xsd",
   "geometryBasic0d1d.xsd", "measures.xsd", "gmlBase.xsd", and
   "basicTypes.xsd".  Note that "units.xsd" and "dictionary.xsd" are
   excluded from this profile.

   For the purposes of brevity, all comments and annotations from the
   original GML schema have been removed.  Schematron [ISO.19757-3.2005]
   validation has also been removed.

7.1.  geometryPrimitives.xsd

   The following file is the profile version of
   "geometryPrimitives.xsd".

   <?xml version="1.0"?>
   <schema xmlns="http://www.w3.org/2001/XMLSchema"
           xmlns:gml="http://www.opengis.net/gml"
           targetNamespace="http://www.opengis.net/gml"
           version="3.1.1" elementFormDefault="qualified">

     <include schemaLocation="geometryBasic2d.xsd"/>

     <element name="Curve" type="gml:CurveType"
              substitutionGroup="gml:_Curve"/>
     <complexType name="CurveType">
       <complexContent>
         <extension base="gml:AbstractCurveType">
           <sequence>
             <element ref="gml:segments"/>
           </sequence>
         </extension>
       </complexContent>
     </complexType>

     <element name="_CurveSegment"
              type="gml:AbstractCurveSegmentType" abstract="true"/>
     <complexType name="AbstractCurveSegmentType" abstract="true">
       <sequence/>
       <attribute name="numDerivativesAtStart" type="integer"
                  use="optional" default="0"/>
       <attribute name="numDerivativesAtEnd" type="integer"
    use="optional" default="0"/>



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       <attribute name="numDerivativeInterior" type="integer"
    use="optional" default="0"/>
     </complexType>

     <element name="segments" type="gml:CurveSegmentArrayPropertyType"/>
     <complexType name="CurveSegmentArrayPropertyType">
       <sequence>
         <element ref="gml:_CurveSegment"
                  minOccurs="0" maxOccurs="unbounded"/>
       </sequence>
     </complexType>

     <element name="LineStringSegment" type="gml:LineStringSegmentType"
              substitutionGroup="gml:_CurveSegment"/>
     <complexType name="LineStringSegmentType">
       <complexContent>
         <extension base="gml:AbstractCurveSegmentType">
           <sequence>
             <choice>
               <choice minOccurs="2" maxOccurs="unbounded">
                 <element ref="gml:pos"/>
                 <element ref="gml:pointProperty"/>
               </choice>
               <element ref="gml:posList"/>
             </choice>
           </sequence>
           <attribute name="interpolation"
                      type="gml:CurveInterpolationType" fixed="linear"/>
         </extension>
       </complexContent>
     </complexType>

     <element name="ArcByCenterPoint" type="gml:ArcByCenterPointType"
              substitutionGroup="gml:_CurveSegment"/>
     <complexType name="ArcByCenterPointType">
       <complexContent>
         <extension base="gml:AbstractCurveSegmentType">
           <sequence>
             <choice>
               <element ref="gml:pos"/>
               <element ref="gml:pointProperty"/>
             </choice>
             <element name="radius" type="gml:LengthType"/>
             <element name="startAngle" type="gml:AngleType"
                      minOccurs="0"/>
             <element name="endAngle" type="gml:AngleType"
                      minOccurs="0"/>
           </sequence>



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           <attribute name="interpolation"
                      type="gml:CurveInterpolationType"
                      fixed="circularArcCenterPointWithRadius"/>
           <attribute name="numArc" type="integer"
                      use="required" fixed="1"/>
         </extension>
       </complexContent>
     </complexType>

     <element name="CircleByCenterPoint"
              type="gml:CircleByCenterPointType"
              substitutionGroup="gml:ArcByCenterPoint"/>
     <complexType name="CircleByCenterPointType">
       <complexContent>
         <extension base="gml:ArcByCenterPointType"/>
       </complexContent>
     </complexType>

     <element name="Surface" type="gml:SurfaceType"
              substitutionGroup="gml:_Surface"/>
     <complexType name="SurfaceType">
       <complexContent>
         <extension base="gml:AbstractSurfaceType">
           <sequence>
             <element ref="gml:patches"/>
           </sequence>
         </extension>
       </complexContent>
     </complexType>

     <element name="_SurfacePatch" type="gml:AbstractSurfacePatchType"
              abstract="true"/>
     <complexType name="AbstractSurfacePatchType" abstract="true">
       <sequence/>
     </complexType>

     <element name="patches" type="gml:SurfacePatchArrayPropertyType"/>
     <complexType name="SurfacePatchArrayPropertyType">
       <sequence minOccurs="0" maxOccurs="unbounded">
         <element ref="gml:_SurfacePatch"/>
       </sequence>
     </complexType>

     <element name="PolygonPatch" type="gml:PolygonPatchType"
              substitutionGroup="gml:_SurfacePatch"/>
     <complexType name="PolygonPatchType">
       <complexContent>
         <extension base="gml:AbstractSurfacePatchType">



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           <sequence>
             <element ref="gml:exterior" minOccurs="0"/>
           </sequence>
           <attribute name="interpolation"
                      type="gml:SurfaceInterpolationType"
                      fixed="planar"/>
         </extension>
       </complexContent>
     </complexType>

     <element name="Rectangle" type="gml:RectangleType"
              substitutionGroup="gml:_SurfacePatch"/>
     <complexType name="RectangleType">
       <complexContent>
         <extension base="gml:AbstractSurfacePatchType">
           <sequence>
             <element ref="gml:exterior"/>
           </sequence>
           <attribute name="interpolation"
                      type="gml:SurfaceInterpolationType"
                      fixed="planar"/>
         </extension>
       </complexContent>
     </complexType>

     <element name="PolyhedralSurface" type="gml:PolyhedralSurfaceType"
              substitutionGroup="gml:Surface"/>
     <complexType name="PolyhedralSurfaceType">
       <complexContent>
         <restriction base="gml:SurfaceType">
           <sequence>
             <element ref="gml:polygonPatches"/>
           </sequence>
         </restriction>
       </complexContent>
     </complexType>

     <element name="polygonPatches"
              type="gml:PolygonPatchArrayPropertyType"
              substitutionGroup="gml:patches"/>
     <complexType name="PolygonPatchArrayPropertyType">
       <complexContent>
         <restriction base="gml:SurfacePatchArrayPropertyType">
           <sequence minOccurs="0" maxOccurs="unbounded">
             <element ref="gml:PolygonPatch"/>
           </sequence>
         </restriction>
       </complexContent>



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     </complexType>

     <element name="_Solid" type="gml:AbstractSolidType" abstract="true"
              substitutionGroup="gml:_GeometricPrimitive"/>
     <complexType name="AbstractSolidType">
       <complexContent>
         <extension base="gml:AbstractGeometricPrimitiveType"/>
       </complexContent>
     </complexType>

     <element name="Solid" type="gml:SolidType"
              substitutionGroup="gml:_Solid"/>
     <complexType name="SolidType">
       <complexContent>
         <extension base="gml:AbstractSolidType">
           <sequence>
             <element name="exterior" type="gml:SurfacePropertyType"
                      minOccurs="0"/>
           </sequence>
         </extension>
       </complexContent>
     </complexType>

     <simpleType name="CurveInterpolationType">
       <restriction base="string">
         <enumeration value="linear"/>
         <enumeration value="geodesic"/>
         <enumeration value="circularArc3Points"/>
         <enumeration value="circularArcCenterPointWithRadius"/>
       </restriction>
     </simpleType>

     <simpleType name="SurfaceInterpolationType">
       <restriction base="string">
         <enumeration value="planar"/>
       </restriction>
     </simpleType>

   </schema>

7.2.  geometryBasic2d.xsd

   The following file is the profile version of "geometryBasic2d.xsd".

   <?xml version="1.0"?>
   <schema xmlns="http://www.w3.org/2001/XMLSchema"
           xmlns:gml="http://www.opengis.net/gml"
           targetNamespace="http://www.opengis.net/gml"



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           version="3.1.1" elementFormDefault="qualified">

     <include schemaLocation="geometryBasic0d1d.xsd"/>

     <element name="_Surface" type="gml:AbstractSurfaceType"
              abstract="true"
              substitutionGroup="gml:_GeometricPrimitive"/>
     <complexType name="AbstractSurfaceType">
       <complexContent>
         <extension base="gml:AbstractGeometricPrimitiveType"/>
       </complexContent>
     </complexType>

     <element name="surfaceProperty" type="gml:SurfacePropertyType"/>
     <complexType name="SurfacePropertyType">
       <sequence>
         <element ref="gml:_Surface"/>
       </sequence>
     </complexType>

     <element name="Polygon" type="gml:PolygonType"
              substitutionGroup="gml:_Surface"/>
     <complexType name="PolygonType">
       <complexContent>
         <extension base="gml:AbstractSurfaceType">
           <sequence>
             <element ref="gml:exterior" minOccurs="0"/>
           </sequence>
         </extension>
       </complexContent>
     </complexType>

     <element name="_Ring" type="gml:AbstractRingType" abstract="true"
              substitutionGroup="gml:_Geometry"/>
     <complexType name="AbstractRingType" abstract="true">
       <complexContent>
         <extension base="gml:AbstractGeometryType"/>
       </complexContent>
     </complexType>

     <element name="exterior" type="gml:AbstractRingPropertyType"/>
     <complexType name="AbstractRingPropertyType">
       <sequence>
         <element ref="gml:_Ring"/>
       </sequence>
     </complexType>

     <element name="LinearRing" type="gml:LinearRingType"



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              substitutionGroup="gml:_Ring"/>
     <complexType name="LinearRingType">
       <complexContent>
         <extension base="gml:AbstractRingType">
           <sequence>
             <choice>
               <choice minOccurs="4" maxOccurs="16">
                 <element ref="gml:pos"/>
                 <element ref="gml:pointProperty"/>
               </choice>
               <element ref="gml:posList"/>
             </choice>
           </sequence>
         </extension>
       </complexContent>
     </complexType>

   </schema>

7.3.  geometryBasic0d1d.xsd

   The following file is the profile version of "geometryBasic0d1d.xsd".

   <?xml version="1.0"?>
   <schema xmlns="http://www.w3.org/2001/XMLSchema"
           xmlns:gml="http://www.opengis.net/gml"
           targetNamespace="http://www.opengis.net/gml"
           version="3.1.1" elementFormDefault="qualified">

     <include schemaLocation="measures.xsd"/>

     <element name="_Geometry" type="gml:AbstractGeometryType"
              abstract="true" substitutionGroup="gml:_GML"/>
     <complexType name="GeometryPropertyType">
       <sequence>
         <element ref="gml:_Geometry"/>
       </sequence>
     </complexType>

     <complexType name="GeometryArrayPropertyType">
       <sequence>
         <element ref="gml:_Geometry"
                  minOccurs="0" maxOccurs="unbounded"/>
       </sequence>
     </complexType>

     <complexType name="AbstractGeometryType" abstract="true">
       <complexContent>



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         <extension base="gml:AbstractGMLType">
           <attribute name="gid" type="string" use="optional">
           </attribute>
           <attributeGroup ref="gml:SRSReferenceGroup"/>
         </extension>
       </complexContent>
     </complexType>

     <attributeGroup name="SRSReferenceGroup">
       <attribute name="srsName" type="anyURI" use="optional"/>
       <attribute name="srsDimension" type="positiveInteger"
                  use="optional"/>
       <attributeGroup ref="gml:SRSInformationGroup"/>
     </attributeGroup>

     <attributeGroup name="SRSInformationGroup">
       <attribute name="axisLabels" type="gml:NCNameList"
                  use="optional"/>
       <attribute name="uomLabels" type="gml:NCNameList"
                  use="optional">
       </attribute>
     </attributeGroup>

     <element name="_GeometricPrimitive"
              type="gml:AbstractGeometricPrimitiveType" abstract="true"
              substitutionGroup="gml:_Geometry"/>
     <complexType name="AbstractGeometricPrimitiveType" abstract="true">
       <complexContent>
         <extension base="gml:AbstractGeometryType"/>
       </complexContent>
     </complexType>

     <element name="Point" type="gml:PointType"
              substitutionGroup="gml:_GeometricPrimitive"/>
     <complexType name="PointType">
       <complexContent>
         <extension base="gml:AbstractGeometricPrimitiveType">
           <sequence>
             <element ref="gml:pos"/>
           </sequence>
         </extension>
       </complexContent>
     </complexType>

     <element name="pointProperty" type="gml:PointPropertyType"/>
     <complexType name="PointPropertyType">
       <sequence>
         <element ref="gml:Point"/>



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       </sequence>
     </complexType>

     <element name="_Curve" type="gml:AbstractCurveType" abstract="true"
              substitutionGroup="gml:_GeometricPrimitive"/>
     <complexType name="AbstractCurveType" abstract="true">
       <complexContent>
         <extension base="gml:AbstractGeometricPrimitiveType"/>
       </complexContent>
     </complexType>

     <element name="curveProperty" type="gml:CurvePropertyType"/>
     <complexType name="CurvePropertyType">
       <sequence>
         <element ref="gml:_Curve"/>
       </sequence>
     </complexType>

     <element name="LineString" type="gml:LineStringType"
              substitutionGroup="gml:_Curve"/>
     <complexType name="LineStringType">
       <complexContent>
         <extension base="gml:AbstractCurveType">
           <sequence>
             <choice>
               <choice minOccurs="2" maxOccurs="unbounded">
                 <element ref="gml:pos"/>
                 <element ref="gml:pointProperty"/>
               </choice>
               <element ref="gml:posList"/>
             </choice>
           </sequence>
         </extension>
       </complexContent>
     </complexType>

     <element name="pos" type="gml:DirectPositionType"/>
     <complexType name="DirectPositionType">
       <simpleContent>
         <extension base="gml:doubleList"/>
       </simpleContent>
     </complexType>

     <element name="posList" type="gml:DirectPositionListType"/>
     <complexType name="DirectPositionListType">
       <simpleContent>
         <extension base="gml:doubleList">
           <attribute name="count" type="positiveInteger"



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                      use="optional"/>
         </extension>
       </simpleContent>
     </complexType>

     <element name="Envelope" type="gml:EnvelopeType"/>

     <complexType name="EnvelopeType">
       <choice>
         <sequence>
           <element name="lowerCorner" type="gml:DirectPositionType"/>
           <element name="upperCorner" type="gml:DirectPositionType"/>
         </sequence>
         <element ref="gml:pos" minOccurs="2" maxOccurs="2"/>
       </choice>
       <attributeGroup ref="gml:SRSReferenceGroup"/>
     </complexType>

   </schema>

7.4.  measures.xsd

   The following file is the profile version of "measures.xsd".

   <?xml version="1.0"?>
   <schema xmlns="http://www.w3.org/2001/XMLSchema"
           xmlns:gml="http://www.opengis.net/gml"
           targetNamespace="http://www.opengis.net/gml"
           version="3.1.1" elementFormDefault="qualified">

     <include schemaLocation="gmlBase.xsd"/>

     <element name="measure" type="gml:MeasureType"/>
     <complexType name="LengthType">
       <simpleContent>
         <restriction base="gml:MeasureType"/>
       </simpleContent>
     </complexType>

     <element name="angle" type="gml:MeasureType"/>
     <complexType name="AngleType">
       <simpleContent>
         <restriction base="gml:MeasureType"/>
       </simpleContent>
     </complexType>

   </schema>




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7.5.  gmlBase.xsd

   The following file is the profile version of "gmlBase.xsd".

   <?xml version="1.0"?>
   <schema xmlns="http://www.w3.org/2001/XMLSchema"
           xmlns:gml="http://www.opengis.net/gml"
           targetNamespace="http://www.opengis.net/gml"
           version="3.1.1" elementFormDefault="qualified">

     <include schemaLocation="basicTypes.xsd"/>

     <element name="_Object" abstract="true"/>

     <element name="_GML" type="gml:AbstractGMLType" abstract="true"
              substitutionGroup="gml:_Object"/>
     <complexType name="AbstractGMLType" abstract="true">
       <attribute ref="gml:id" use="optional"/>
     </complexType>

     <attribute name="id" type="ID"/>
   </schema>





























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7.6.  basicTypes.xsd

   The following file is the profile version of "basicTypes.xsd".

   <?xml version="1.0"?>
   <schema xmlns="http://www.w3.org/2001/XMLSchema"
           xmlns:gml="http://www.opengis.net/gml"
           targetNamespace="http://www.opengis.net/gml"
           version="3.1.1" elementFormDefault="qualified">

     <simpleType name="SignType">
       <restriction base="string">
         <enumeration value="-"/>
         <enumeration value="+"/>
       </restriction>
     </simpleType>

     <simpleType name="booleanList">
       <list itemType="boolean"/>
     </simpleType>

     <simpleType name="NameList">
       <list itemType="Name"/>
     </simpleType>

     <simpleType name="doubleList">
       <list itemType="double"/>
     </simpleType>

     <simpleType name="integerList">
       <list itemType="integer"/>
     </simpleType>

     <complexType name="MeasureType">
       <simpleContent>
         <extension base="double">
           <attribute name="uom" type="anyURI" use="required"/>
         </extension>
       </simpleContent>
     </complexType>

     <simpleType name="NCNameList">
       <list itemType="NCName"/>
     </simpleType>

   </schema>





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8.  Security Considerations

   It is believed that this document does not have any security
   considerations.  If this information is included within a PIDF-LO
   document, the security considerations of [RFC4119] apply, especially
   those that are related to privacy.













































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9.  IANA Considerations

   This section registers the application schema for geodetic shapes and
   its namespace with IANA.

9.1.  URN Sub-Namespace Registration for
      urn:ietf:params:xml:ns:pidf:geopriv10:geoShape

   This section registers a new XML namespace,
   "urn:ietf:params:xml:ns:pidf:geopriv10:geoShape", as per the
   guidelines in [RFC3688].

      URI: urn:ietf:params:xml:ns:pidf:geopriv10:geoShape

      Registrant Contact: IETF, GEOPRIV working group,
      (geopriv@ietf.org), Martin Thomson (martin.thomson@andrew.com).

      XML:

         BEGIN
           <?xml version="1.0"?>
           <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
             "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
           <html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en">
             <head>
               <title>GEOPRIV GML Application Schema</title>
             </head>
             <body>
               <h1>Namespace for GEOPRIV GML Application Schema</h1>
               <h2>urn:ietf:params:xml:ns:pidf:geopriv10:geoShape</h2>
   [[NOTE TO IANA/RFC-EDITOR: Please update RFC URL and replace XXXX
       with the RFC number for this specification.]]
               <p>See <a href="[[RFC URL]]">RFCXXXX</a>.</p>
             </body>
           </html>
         END

9.2.  XML Schema Registration

   This section registers an XML schema as per the guidelines in
   [RFC3688].

   URI: urn:ietf:params:xml:schema:pidf:geopriv10:geoShape

   Registrant Contact: IETF, GEOPRIV working group, (geopriv@ietf.org),
      Martin Thomson (martin.thomson@andrew.com).





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   Schema: The XML for this schema can be found as the entirety of
      Section 6 of this document.

















































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10.  Acknowledgements

   The author would like to thank Carl Reed and Ron Lake of the OGC for
   their help in understanding geodesy and GML.















































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11.  References

11.1.  Normative References

   [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate
              Requirement Levels", BCP 14, RFC 2119, March 1997.

   [RFC4119]  Peterson, J., "A Presence-based GEOPRIV Location Object
              Format", RFC 4119, December 2005.

   [OGC.GML-3.1.0]
              Cox, S., Daisey, P., Lake, R., Portele, C., and A.
              Whiteside, "Geographic information - Geography Markup
              Language (GML)", OpenGIS 03-105r1, April 2004,
              <http://portal.opengeospatial.org/files/
              ?artifact_id=4700>.

11.2.  Informative References

   [RFC3688]  Mealling, M., "The IETF XML Registry", BCP 81, RFC 3688,
              January 2004.

   [I-D.ietf-geopriv-revised-civic-lo]
              Thomson, M. and J. Winterbottom, "Revised Civic Location
              Format for PIDF-LO",
              draft-ietf-geopriv-revised-civic-lo-01 (work in progress),
              January 2006.

   [W3C.REC-xlink-20010627]
              Maler, E., DeRose, S., and D. Orchard, "XML Linking
              Language (XLink) Version 1.0", W3C REC REC-xlink-20010627,
              June 2001.

   [NIMA.TR8350.2-3e]
              US National Imagery and Mapping Agency, "Department of
              Defense (DoD) World Geodetic System 1984 (WGS 84), Third
              Edition", NIMA TR8350.2, January 2000.

   [EPSG.GN7-2]
              European Petroleum Survey Group, "Coordinate Conversions
              and Transforms including Formulas", EPSG Guidance Note 7,
              part 2 , November 2005,
              <http://www.epsg.org/guides/G7-2.html>.

   [3GPP.TS23032]
              3GPP, "Universal Geographical Area Description (GAD)",
              3GPP TS 23.032 v6.0.0, December 2004.




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   [ISO.19757-3.2005]
              International Organization for Standardization and
              International Electrotechnical Commission, "Document
              Schema Definitions Languages (DSDL): Part 3 - Rule-based
              validation - Schematron", ISO/IEC FDIS 19757-3, 2005.

   [Sunday02]
              Sunday, D., "Fast polygon area and Newell normal
              computation.", Journal of Graphics Tools JGT, 7(2):9-
              13,2002, 2002, <http://www.acm.org/jgt/papers/Sunday02/>.









































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Appendix A.  Calculating the Upward Normal of a Polygon

   For a polygon that is guaranteed to be convex and coplanar, the
   upward normal can be found by finding the vector cross product of
   adjacent edges.

   For more general cases the Newell method of approximation described
   in [Sunday02] may be applied.  In particular, this method can be used
   if the points are only approximately coplanar, and for non-convex
   polygons.

   This method can be condensed to the following set of equations:

      Ux := sum from i=1..n of (y[i] * (z[i+1] - z[i-1]))

      Uy := sum from i=1..n of (z[i] * (x[i+1] - x[i-1]))

      Uz := sum from i=1..n of (x[i] * (y[i+1] - y[i-1]))

   For these formulae, the polygon is made of points (x[1], y[1], z[1])
   through (x[n], y[n], x[n]).  Each array is treated as circular, that
   is, x[0] = x[n] and x[n+1] = x[1].

   Note: This method assumes a cartesian coordinate system, this SHOULD
   NOT be applied to coordinates specified in the WGS 84 (latitude,
   longitude, altitude) CRS.  Coordinates specified in a geographic CRS
   SHOULD be transformed to a cartesian, geocentric CRS (such as EPSG
   4978) before this method is applied, see [EPSG.GN7-2] and
   [NIMA.TR8350.2-3e] for details.






















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Appendix B.  Open Issues

B.1.  Shape Names

   Circle or CircularArea?  Ellipse or EllipticalArea?  Sphere or
   SphericalVolume?  These questions are important to the mathematical
   correctness of this section, even if they don't affect how these are
   interpreted.  The shapes mentioned are not 100% correct based on this
   definition.  To be more correct, these could either be used as
   properties of other shapes where they define a boundary, or they
   could be renamed.

   Also, GML recommends that application schema do not reuse names from
   GML, even if they are in different namespaces.  Obviously, this
   reduces confusion.  This affects the Circle type.

B.2.  MLP Aggregate Shape Types

   Part of the reason for this draft is to provide some hope of
   translation from PIDF-LO to MLP.  However, the following MLP types
   are not explicitly supported: LineString, Box, MultiLineString,
   MultiPoint, MultiPolygon, and LinearRing.  These types are not found
   in [3GPP.TS23032].

   These types can be easily supported by either existing GML types, or
   the inclusion of geometry collections.  This has not been done
   primarily because these shape types are not in common usage (to the
   author's knowledge).  Also, since these types have not been expressly
   prohibited, they can still be provided using GML.

   Should these types be included, by mentioning that they MAY be used
   for those rare cases where they are applicable?  Or should they be
   prohibited?  Keep in mind that the current focus is to enable and
   that nothing is expressly prohibited by this document.

B.3.  Moving Targets

   GML and [3GPP.TS23032] have some provision for moving targets -
   including velocity vectors and even uncertainty for velocity in
   [3GPP.TS23032].

   I currently don't think it worthwhile including this information in
   this document, although I anticipate that there will eventually be a
   need for this.  My current thought is that this would be something
   that is easy to add in a future specification.






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Author's Address

   Martin Thomson
   Andrew
   PO Box U40
   Wollongong University Campus, NSW  2500
   AU

   Phone: +61 2 4221 2915
   Email: martin.thomson@andrew.com
   URI:   http://www.andrew.com/








































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   This document and the information contained herein are provided on an
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   ENGINEERING TASK FORCE DISCLAIM ALL WARRANTIES, EXPRESS OR IMPLIED,
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Copyright Statement

   Copyright (C) The Internet Society (2006).  This document is subject
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Acknowledgment

   Funding for the RFC Editor function is currently provided by the
   Internet Society.




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