Continuous Data Types and Computation

 

Kenneth Johnson, University of Sheffield

 

Abstract:

 

 

In the general theory of data types, continuous data such as the real
numbers are modelled by topological algebras. Spatial objects
representing data distributed in space is a common data type, modelled
by topological algebras of functions.

 

An important example of spatial objects is found in computer graphics.
We introduce Constructive Volume Geometry as an algebraic framework
for the representation of and reasoning with graphical objects in
three-dimensional space.
 
 
A general theory of spatial data types is developed aiming to model,
specify, compare and compute over spatial objects using methods
independent of any particular space or data. A completeness problem is
formulated and solved in the case of the real numbers. Computing with
spatial objects requires models of computation for continuous data,
and both abstract and concrete models are discussed.