Geospatial and temporal reference

1. Geospatial and temporal reference ONTOBRAS-2013 The industrial application of ontology: Driven by a foundational ontology A case study illustrating: (radical) refactoring

2. Topics • Theme recapitulation • Project background • The context • What is a reference frame? • From ‘at rest’ to speed • Summary • Questions

3. Theme recapitulation Themes to bear in mind

4. Themes to bear in mind • Refactoring • Rational reconstruction

5. Background

6. Aim • To review the current practices and artefacts used for the information modelling of the Geospatial and Temporal References (G&TR) in the surface ship community and investigate the ways in which the use of ontologies can help to improve them

7. Motivation for the Project • No clear picture of the underlying objects • Algorithms seemed to have significant ad hoc elements • There seemed to be underlying patterns but they had not been made explicit • The result is systems that do not work as well together as required

8. The context

9. Frame of reference – some definitions • Merriam Webster • an arbitrary set of axes with reference to which the position or motion of something is described or physical laws are formulated • http://www.merriam-webster.com/dictionary/frame%20of%20reference • BRITANNICA • reference frame, also called frame of reference, in dynamics, system of graduated lines symbolically attached to a body that serve to describe the position of points relative to the body. ... The reference frames used in dynamics are known as coordinate systems with axes (lines) emanating from a point known as the origin • http://www.britannica.com/EBchecked/topic/495116/reference-frame • Wiki • In physics, a frame of reference (or reference frame) may refer to a coordinate system used to represent and measure properties of objects such as their position and orientation. It may also refer to a set of axes used for such representation • Alternatively, in relativity, the phrase can be used to refer to the relationship between a moving observer and the phenomenon or phenomena under observation. In this context, the phrase often becomes "observational frame of reference" (or "observational reference frame"). The context may itself include a coordinate system used to represent the observer and phenomenon or phenomena • http://en.wikipedia.org/wiki/Frame_of_reference • DEF STAN 21-66 Issue 1 - Ministry of Defence - Defence Standard 21-66 - Common References Standard - Issue 1 Publication Date 16 April 2010 • 6.2.1 Definitions of Reference Frames and Coordinate Systems • 6.2.1.1 A reference frame is a fixed relationship between reality and a mathematical representation of it. It is usually defined by first specifying the mathematical representation of particular physical entities, such as the positions of certain physical components in a platform used as markers, or the centre of the Earth. The positions of other physical entities are then specified with respect to them, for example, by measuring the distances or angles between them • 6.2.1.2 A coordinate system is a systematic labelling of every point of the mathematical representation with a unique list of n numbers, where n is a fixed positive integer called the dimension • 6.2.3.2 The definition of each reference frame consists of the identification of a number of physical datums, the definition of an initial coordinate system based on measurements from those datums, and then the definition of any additional coordinate systems by means of mathematical transformations

10. ISO/IEC 18026:2009 Information technology — Spatial Reference Model (SRM) 0.1 Purpose Spatial information processing requires a robust capability to describe geometric properties such as position, direction and distance.

11. A reference frame • A standard mathematical definition (Cartesian coordinate system) • X, Y and Z Axes • Meeting at a reference point • Enabling the identification of points within the reference frame • What is this? • Hypothesis 1 • A reference frame == an ordered triple of three axes • Hypothesis 1a • A reference frame == an ordered triple of three axes + the set of points these identify

12. A physical (ship) reference frame

13. Physical establishment of reference planes • The first major alignment step is the establishment of reference planes. A position can only be described by relating it to a known reference point. ... • Reference planes are established during the initial construction of the ship and are used as required during alignment of the combat system. Reference planes consist of the center-line reference plane (CRP), the ship base plane (SBP), the master reference plane (MRP), ... • CENTER-LINE REFERENCE PLANE — The center-line reference plane (CRP) is the first plane established. It is the plane containing the ship’s center line and is perpendicular to the SBP. The CRP is the reference used to establish the train zero alignment of all of the combat system equipment. • SHIPBASE PLANE — The shipbase plane (SBP), the basic plane of origin, is perpendicular to the CRP and includes the base line of the ship, but is not necessarily parallel to the keel • MASTER REFERENCE PLANE — The master reference plane (MRP) is a plane within the ship parallel to the SBP. On most ships, the MRP is represented by a master level plate that has been accurately leveled to the SBP and aligned in bearing to the CRP.The MRP is used as the machining reference to establish the foundations of the combat system equipment. After initial construction alignment, the MRP is only used as a reference plane following major damage or modernization http://www.tpub.com/gunners/242.htm

14. Physical (ship) reference planes • Hypothesis 2 • A ship reference frame == an ordered triple of planes. • Hypothesis 2a • A ship reference frame == an ordered triple of planes + the set of points they identify From an engineering perspective, planes are easier to operate with than axes. However, both planes and axes give the same result; they identify the same set of points. This kind of arbitrary equivalence raises ontological qualms; does a reference frame consist of axes or planes? Surely an axes-based reference frame is NOT identical to a plane-based reference frame? Furthermore, the ordering of the places in the triples is conventional (and arbitrary). This raises further ontological qualms. Finally, does the reference frame include the set of points?

15. A practical concern Ship Sensors Reference Frames Ships have sensors, and these sensors have positions (centres) some distance away from the CRP and so have their own reference frames; one that are fixed relative to the ship. [Recall: “The MRP is used … to establish the foundations of the combat system equipment.]

16. Frames relatively ‘at rest’ • The ship and its (onboard) sensors are ‘at rest’ with respect to one another • What links them is a consistent distance (over time) between their axes and points • Furthermore, their set of points are equivalent; a point in one reference frame has (at all times) an equivalent (identical?) point in the other • This suggests that • the choice of reference frame may be an arbitrary way of encoding a name for a point • the ship and its (onboard) sensors are in some sense in the same frame of reference

17. A set of ‘equipollent’ reference frames • Leibniz articulated an “equipollence of hypotheses”: in any system of interacting bodies, any hypothesis that any particular body is at rest is equivalent to any other. … • This principle clearly defines (what we would call) a set of reference frames, differing in their arbitrary choices of a resting point or origin, but agreeing on the relative positions of bodies at any moment and their changing relative distances through time DiSalle, Robert, "Space and Time: Inertial Frames", The Stanford Encyclopedia of Philosophy (Winter 2009 Edition), Edward N. Zalta (ed.), URL = <http://plato.stanford.edu/archives/win2009/entries/spacetime-iframes/>.

18. Purpose: identifying points over time • Reference Frames (as axes or planes) are used to name/encode points in space-time • Given the frame and the encoding, there is an algorithm to identify the point • This can be used at different points in time to identify the ‘same’ point • Over time, any two points within the frame remain equidistant time = t2 time = t1

19. Equipollent frames as an equivalence class • Equipollent frames identify the same points; non-equipollent frames identify different points • Consider this example • At a point in time, you and a boy on the train identify the position of the locomotive (as x metres in front) • At a later point in time, for the boy on the train, the locomotive is still in the same position. For you, the locomotive has moved on from that position • So, you must be talking about different positions that happened to coincide at that point in time • For anyone else standing on the train, the locomotive stays in the same position. This illustrates that the identity of the space-time points is invariant across the Leibnitzian “equipollent” frames (and vice-versa) • The Equipollence relation is an equivalence relation that picks out frames with the same set of points

20. What is a reference frame? What is a position?

21. A descriptive approach • We have (at least) two hypotheses • An ordered triple of axes (+ a set of points) • An ordered triple of planes (+ a set of points) • We regard permutations of the axes/planes as different frames of references • An equivalence class of ‘equipollent’ reference frames is then a set of whichever of these hypotheses we choose • All frames within an equipollent equivalence class have the same set of points; frames from different equipollent equivalence classes have a different set of points

22. A revisionary extensional approach • The simplest extensional objects in play are the positions identified by the reference frame • These are space-time lines • The path through time of a point particle • A point at each time, extended through time • (Often called worldlines in the physics literature) • The CRP mark on a ship is an obvious example

23. Positions as an invariant • What equipollency picks out is that the identity of the points/positions is invariant across a variety of difference coordinate systems • The coordinate systems can vary, while the points / positions remain the same • The current structure has no place for these points / positions or the ‘frame’ they occupy • The ‘same’ point from our analysis perspective will be regarded as different points as they are in different frames • For example, the ship CRP ‘point’ will be a ‘different’ point in each reference frame.

24. Worldline reference frames • The set of all the points (worldlines) identified by a traditional reference frame seem to be the ‘essence’ of what an equipollent set of frames are • Equipollent set of frames = worldline reference frames • The frame can be seen as the one of many decompositions of a tranche of space-time into lines, in which the lines • Are points at each time-slice • Completely occupy the tranche • These properties make it ideal for identifying points through time; giving points an identity that is not dependent upon the coordinate reference frame.

25. Worldline based axes and planes • Once the (worldline reference) frame is selected • An origin worldline can be selected • Axes and planes can be ‘constructed’ as collections of the points • As is done in standard point-based geometry • Many (infinite) origins, axes and planes can be selected for any ‘worldline reference frame’ • Origins, axes and planes from one ‘worldline reference frame’ cannot be constructed from points in different frames

26. Timeslices • Typically, coordinates have a time component; e.g. <x, y, z, t> • In an extensional ontology • The ‘t’ in <x, y, z, t> refers to a timeslice • And the point being referred to is an intersection of the worldline named by < x, y, z> and the timeslice referred to by ‘t’

27. Separation of concerns • From a separation of concerns perspective, this separates concerns about identity of points (and being ‘at rest’) from how these are labelled (AKA which coordinate system to use) • And, the coordinate system is dependent upon its worldline reference frame

28. Taxonomising the reference frame space • Examination of the uses of reference frames, enables one to develop a taxonomy of the ways in which they are constructed

29. A position sensor detects an object • The goal is to give the position of the object a name/code that can be used to algorithmically identify the position, given the reference frame • One way to look at this is that one needs to characterise the origin-point position displacement • There are a number of ways to do this; one example is <x, y, z> (at t)

30. Coordinate frame components and dependencies • For a general picture, one needs to handle the various different coordinate frames • A good approach is to separate out the components; identifying their dependencies • For example: irrespective of whether axes or frames are used; there is an origin; this is a worldline selected as the origin (which is also the temporal axis) • The choice of origin constrains the choice of spatial axes and planes; so these are dependent upon it

31. Spherical coordinate systems • In a Cartesian linear decomposition, the displacement is broken down into orthogonal component displacements along the axes/planes • In a polar angular decomposition, the displacement is broken down into two components; a radial component which characterises the length of the displacement and an angular component which characterise the direction of the displacement

32. Measurement scales • Knowing the position is <10, 10, 10> is not enough. One needs to know what unit 10 is measured in. Is it metres or yards? Or kilometres or miles? We need to know the measurement scale • The measurement scale is independent of the reference frame apparatus, but the coordinate systems are dependent upon it

33. From ‘at rest’ to speed An extensional picture of speed speed

34. Need to consider not ‘at rest’ frames • Two objects that are not ‘at rest’ relative to each other will have different ‘worldline reference frames’ • Assume these objects are point particles and one particle is moving at a constant velocity (and so speed) relative to the other • If we say that the object is moving at a constant speed of x kilometres per hour (kph), what does this mean?

35. Speed diagram • We can build up a picture • Take the worldline that intersects the starting point of the particle • Consider all the possible paths the particle could follow if it was travelling at x kph; these have the shape of a double right circular (hyper-)cone • Measure an hour along the origin-worldline • Take a timeslice. This will cut the cone in a circle. The radius of the circle will be x kilometres

36. What is a speed? • Extensionally, the constant speed x kph in the reference frame, starting at the origin, is the cone • The constant speed x kphin the reference frame is the collection of all x kph cones • A line is an x kph line if it is in the collection • Speed is the collection of all the individual constant speed collections • Note: the speed is NOT tied to the measurement scale, x kph == y mph. These are the same thing measured using two different scales

37. Speed dependency map • We developed a dependency map to show the components of speed and how they relate • Reference frame • Speeding object • Distance scale • Temporal scale • Speed measured to scale

38. Summary

39. Ontological lessons learnt • Providing an ontological foundation can lead to radical revisions • Start with worldliness rather than axes (or planes) • Foundation guides the analysis • A foundation often leads to a clearer picture • E.g. • Arbitrary choices between axes and planes (and permutation of these) are revealed as encoding choices rather than different underlying frameworks • The same worldline can be encoded in different ways; same object different encoding • The speed objects are separated from the particular measurements. • Same speed, different measurements • Refactoring – which does not change the final results (the points still have the same encoding), can still be radical

40. Questions