Lecture 3

A UML Example: A Patient Information Management System

  • The use of mathematical and physical models in object design
  • C++ limitations on object models
  • Ways of organizing knowledge

    Over time we have evolved a number of ways of organizing our knowledge of the world.

    Organizing Principles

    Mathematics as a source of abstraction


    The Spatial Object

    Specializations of SpatialObject

    There are many ways we could consider specializing the concept of a point set.

    Combinations of these dimensions can generate a large spectrum of classes, any of which might arise in applications. A key advantage of the mathematical design approach is that applications are built using mathematical principles and therefore the critical specialization dimensions are known in advance.


    The subclass structure of spatial object

    The order of specialization
    In the IUE, the sub-classes were generated according to the following sequence of specialization dimensions:

    Interestingly, TargetJr has a similar order of specialization One major difference is that TargetJr does not distinguish classes on embedding dimension at all.

    The argument for this specialization is that many operations that make sense in 3-d cannot even be done in 2-d. Additionally, curves, such as the ellipse, can live in both 2-d and 3-d. How do we know whether or not to pay attention to the third coordinate?

    The argument against is that many operations are shared across embedding dimension and it is clumbersome to multiply the number of classes by two. Also there is the headache of continually dealing with incompatible 2-d vectors and 3-d vectors which arise from the location coordinates of spatial objects.

    A Specialization hieararchy for the line segment

    Mathematical specialization and object languages

    An example, the circle and the ellipse

    The topology heierachy

    Another example of specialization on intrinsic dimension is the topology hierarchy.

    The topology elements

    The transform network

    Transform network(cont)
    A coordinate_system is the representation for a mathematical coordinate space. Among other things, it knows about its dimensionality and can know its relation to other coordinate systems.

    The IUE CoordinateSystem Hierarchy

    The IUE Transform Hierarchy

    Which one doesn't belong?

    The first and last sensor types generate a 2-d image. The stereo camera in the middle does not produce a simple image. Instead, there is an epi-polar mapping between the left and right images which induces a 3-d structure.