[Fwd: [Fwd: Part II - Geometry]]

[Ed Shaya]

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