1. Introduction
2. Interpreted geometry
3. Classes representing general concepts
4. The container class
5. Subclasses of Transformation
6. Subclasses of Shape

1. Introduction

RDFGeom2d defines a set of RDF classes and properties for two-dimensional geometry derived from the geometric part of SVG. More specifically, RDFGeom2d is a port of the coordinate systems, paths, and basic shapes sections of the SVG specification from "raw" XML to RDF. This allows geometric entities to participate fully in the RDF world: assertions can be made about geometric objects using vocabularies from the many disciplines that involve geometry. The initial application is geography, where it is used in conjunction with the RDFMap vocabulary. A precedent for importing SVG concepts into RDF is the vocabulary developed by Jim Ley.

RDFGeom2d is compliant with the recommendations for RSS 1.0 modules.

Example

Here is a RDFGeom2d file that contains just one line:

<?xml version="1.0" encoding="iso-8859-1"?> 
<rdf:RDF 
  xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
  xmlns:geom2d="http://nurl.org/0/geom2d/1.0/"
>
     <geom2d:Line rdf:nodeID="line001">
        <geom2d:x1>-123.8327</geom2d:x1>
        <geom2d:y1>46.1908</geom2d:y1>
        <geom2d:x2>-123.833</geom2d:x2>
        <geom2d:y2>46.1829</geom2d:y2>
     </geom2d:Line>
</rdf:RDF>

Note that the namespace for RDFGeom2d is http://nurl.org/0/geom2d/1.0/. "nurl" stands for "Not a URL". nurl.org serves as a root for URIs that denote entities - like geographical properties and geometric points - that are not web resources. Of course, in real life, the URI might (or might not) resolve to a web page as well, but this does not affect the intended denotation of the URI when used in RDF.

2. Interpreted geometry

The intent of RDFGeom2d is to support representation of interpreted geometry. That is, an RDFGeom2d resource may serve to denote a geometric entity in some particular context, such as the centerline of a road in a geographic application, or a curve in a photographic image. When interpretations are assigned to RDFGeom2d resources, properties other than those contained in the RDFGeom2d specification will apply. For example,

<?xml version="1.0" encoding="iso-8859-1"?> 
<rdf:RDF 
  xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
  xmlns:geom2d="http://nurl.org/0/geom2d/1.0/"
  xmlns:map="http://nurl.org/0/geography/map/1.0/"
>
     <geom2d:Line rdf:nodeID="line001">
        <map:isCenterLineOf 
            rdf:resource="http://example.org/geography/roads/US/Oregon/Astoria/tenth_street"/>
        <map:srs resource=
            "http://nurl.org/0/geography/SRSCatalog/wgs84"/>
     </geom2d:Line>
</rdf:RDF>

asserts that line001 is the center line of Tenth Street in Astoria Oregon, and that the line is given in WGS84 (latitude/longitude) coordinates. This is a typical situation; most geometric data in computational applications has an intended denotation outside of pure geometry.

As a consequence of interpretation, shapes have identity that goes beyond their geometrical content. In pure geometry there is only one point with x coordinate 1 and y coordinate 2; by interpreting geometry, this rule of identity, but nothing else, is sacrified.

Here is the list of properties and classes making up RDFGeom2d. Note that classes have uppercase names, and properties lowercase.

3. Classes representing general concepts

Class: Shape

Shape is the class of all 2d geometric forms. Group, Path, Rect, Circle, Ellipse, Line, Polyline, Polygon, Point and Box are subclasses of Shape.

Class: Transformation

Transformation is the class of all functions on the plane. Matrix, Translation, Rotation, Scale, SkewX, and SkewY are subclasses of Tranformation.

Property: transform domain=Shape; range=Transformation

Corresponding SVG attribute: transform.
If a Shape has a transform property, the Shape denotes the geometric form obtained by applying the given transformation to its content.

Class: Group

Corresponding SVG element: g.
Group is a container class for Shapes. A group must have an elements property, and often has the transform property.

Property: elements; domain = Group range = an rdf:Seq of Shapes

5. Subclasses of Tranformation

Class: Matrix

Corresponds to the matrix transform definition in SVG.
A Matrix defines an affine transformation of the plane, given by properties a,b,c,d,e,f:

Property:a domain = Matrix; range = decimal
Property:b domain = Matrix; range = decimal
Property:c domain = Matrix; range = decimal
Property:d domain = Matrix; range = decimal
Property:e domain = Matrix; range = decimal
Property:f domain = Matrix; range = decimal

(decimal is the numerical data type defined by XML Schema dataypes)

Class: Translation

Corresponds to the translate transform definition in SVG.

Property:tx domain =Translation; range = decimal

Property:ty domain = Translation; range = decimal

tx,ty specify the amount translation in x and y.

Class: Scale

Corresponds to the scale transform definition in SVG.

Property:sx domain = Scale; range = decimal

Property:sy domain = Scale; range = decimal

sx,sy specify the scaling in x and y.

Class: Rotation

Corresponds to the rotate transform definition in SVG.

Class: SkewX

Corresponds to the skewX transform definition in SVG.

Class: SkewY

Corresponds to the skewY transform definition in SVG.

Property:angle domain = union of Rotation, SkewX, and SkewY ; range = decimal

angle specifies the angle in degrees of rotation, skew in x, or skew in y when applied to Rotation, SkewX, SkewY, respectively.

Class: Path

Corresponding SVG element:path
A path must have the pathData property, which uses the syntax defined in SVG to define a straight or curved line.

Property: pathData domain = Path; range = string

Corresponding SVG attribute: the d attribute of paths.

Class: Rect

Corresponding SVG element: rect

Property: x range = decimal for the domain Rect

Corresponding SVG attribute: x

Property: y range = decimal for the domain Rect

Corresponding SVG attribute: y

Property: width range = decimal for the domain Rect

Corresponding SVG attribute: width

Property: height range = decimal for the domain Rect

Corresponding SVG attribute: height

Property: rx range = decimal for the domain Rect

Corresponding SVG attribute: rx

Property: ry range = decimal for the domain Rect

Corresponding SVG attribute: ry

Class: Circle

Corresponding SVG element: circle

Property: cx range = decimal for the domain Circle

Corresponding SVG attribute: cx

Property: cy range = decimal for the domain Circle

Corresponding SVG attribute: cy

Property: r range = decimal for the domain Circle

Corresponding SVG attribute: r

Class: Ellipse

Corresponding SVG element: ellipse

Property: cx range = decimal for the domain Ellipse

Corresponding SVG attribute: cx

Property: cy range = decimal for the domain Ellipse

Corresponding SVG attribute: cy

Property: rx range = decimal for the domain Ellipse

Corresponding SVG attribute: rx

Property: ry range = decimal for the domain Ellipse

Corresponding SVG attribute: ry

Class: Line

Corresponding SVG element: line

Property: x1 range = decimal for the domain Line

Corresponding SVG attribute: x1

Property: y1 range = decimal for the domain Line

Corresponding SVG attribute: y1

Property: x2 range = decimal for the domain Line

Corresponding SVG attribute: x2

Property: y2 range = decimal for the domain Line

Corresponding SVG attribute: y2

Class: Polyline

Corresponding SVG element: polyline

Property: points range = rdf:Seq containing values of type Point, for the domain Polyline

Corresponding SVG attribute: points

Polyline example

Class: Polygon

Corresponding SVG element: polygon

Property: points range = rdf:Seq containing values of type Point, for the domain Polygon

Corresponding SVG attribute: points

Property: fillRule; domain = Shape range = one of the strings "nonzero" or "evenodd"

Corresponding SVG attribute: fill-rule

The fillRule property, if present, signifies that the shape to which it appies denotes an area rather than a curve. The rule by which the area is determined is the same as specified by SVG for the fill-rule property.

Polygon example

Class: Point

Property: x; range = decimal for the domain Point

Property: y; range = decimal for the domain Point

Class:Box

Box constitutes an alternate formulation of the SVG rect element, without the option of rounding corners.

Property: xmin; range = decimal for the domain Box

Property: xmax; range = decimal for the domain Box

Property: ymin; range = decimal for the domain Box

Property: ymax; range = decimal for the domain Box

When applied to a box, xmin,ymin (resp. xmax,ymax) specify the minimum (resp. maximum) values of the coordinates of points within the box.