Part II - Geometry

[Ed Shaya]

The appendix lost its linefeeds, so I put them back in.

Ed

Astronomy Ontology: Part II - Geometry

Everything in the Geometry ontology is a subclass of GeometricEntity 
which is a direct subclass of owl:Thing.
This helps makes things tidy  at the level below Thing. 

Lets start with geo:Space and its properties:

Space  hasDimensionality [single nonNegativeInteger] # Just the number 
                                         #of Dimensions in the Space
    hasDimension [multiple q:Quantity]   #Can make a list of the 
                                  #Dimensions (presumably orthogonal)

    hasSlice [multiple Space]     #Infinite slice (ie, drop a few 
                                  #dimensions if you like)

    sliceOf [single Space]        #inverse_of_hasSlice

    hasRegion [single Region]     #Any section of the Space

Note that Space will probably be used to define parameter spaces or 
a physical Space (Dimensions of length, width, height say), a subclass 
of this would be astro:Space which refers only to Space of the Universe 
or a simulation of the Universe.

To describe Region we need to work our way up from Shape and Point. 
I made an arbitrary decision that Shape is the boundaryOf Region.  Thus
if we say a Shape Square, this refer to the boundary of a square Region.
If we say Shape Sphere, this refers to the surface of the solid 
Spherical region. 
Here is the class Hierarchy for Shape:

Shape

* Any-D_Shape   \*Dimension of shape depends on min dimensions
                    \*needed to describe it.  Of course, it may be 
		       \*mapped to another space where the dimensionality
                    \*is different.
* Curve         \*Curves can wander around N-dimensional

* One-D_Shape

      o Line

            + Directrix

      o LineSegment

            + Chord

                  # Diameter

            + Diagonal

            + Side

                  # Edge

      o Ray


* Point

      o Center

            + CenterOfMass  \*Well, maybe this and the next
                                \*belong in physics. 
            + CenterOfRotation 

            + GeometricCenter

      o EndPoint

      o FocusPoint

      o Pole

      o Vertex

      o VertexOfParabola
Here I interrupt the list of shapes for brevity, and put the rest of 
the list at the end as an appendix.

All Shapes inherit the following properties:

Shape embeddedIn [single Space | multiple Region]
   similarTo [multiple Space]
   congruentTo [multiple Shape]
   definedBy  [multiple Intersection | mutiple sci:Expression 
			| multiple LineSegment]

LineSegment has a restricted definedBy
LineSegment definedBy  [2 EndPoint]

And now we can look at Region Class

* Region

      o Intersection

            + ast:AscendingNode

            + ast:DescendingNode

      o Union

      o Point  \* Point is both Region and Shape (because it
		 \* does not make too much sense to talk about
		 \* its boundary 


Region hasBoundary [single Shape]
     hasSubClass Intersection ofRegion [multiple Region]
                                  ofShape [multiple Shape]

So, a region is built by defining its boundary or by intersecting 
Regions or Shapes or by the Union of them.  
Perhaps other ways will be added.

One more item before I run out of time.
Angle hasAngularSize [single sci:AngularSize]

Thus there can be a thing AngleA which hasAngularSize 7degpm3
Where 7degpm3 is a q:Quantity/sci:Measurement 
7degpm3 value 7
     units deg
     error 3
                                           
Well, we didn't get to coordinates in this.  Maybe in the next Part.
=================================
Appendix: The rest of the Shapes
Projection

        ParallelProjection

          ObliqueProjection

            CabinetProjection

            CavalierProjection

          OrthographicProjection

            AxonometricProjection

              Isometric

            MultiviewProjection

        PerspectiveProjection

        PlanarProjection

        ProjectionOnto3D_Shape

      Three-D_Shape

        Cone

          CircularCone

        Hyperboloid

        Parabaloid

        Polyhedron

          Octahedron

          Prism

          Pyramid

        Spheroid

          OblateSpheroid

          ProlateSpheroid

          Sphere

        ProjectionOnto3D_Shape

      Two-D_Shape

        CurveOnPlane

          ClosedCurve

            Ellipse

              Circle

                GreatCircle

          ConicSection

            Ellipse

              Circle

                GreatCircle

            Hyperbola

            Parabola

          Harmonograph

            LissajousCurve

        Plane

        Polygon

          ConcavePolygon

          ConvexPolygon

            Hexagon

            Octagon

            Pentagon

            Quadralateral

              Parallelogram

                Rectangle

                  Square

                Rhombus

                  Square

              Trapezoid

            Triangle

              EquilateralTriangle

              IsoscelesTriangle

              RightTriangle

          Face