Application of the functional data model and cellular structure theory to continuously time-varying spatial data modeling

摘要

Over the past decade, less work is done in continuously time-varying spatial object modeling. This paper will exploit theoretical approaches for continuously time-varying spatial object modeling. In general, there exist two time views of time parameter and time dimension. In the view of time parameter, spatial objects change over time. In the view of time dimension, space-time is a continuum. Following from these two time views, the functional data model and cellular structure theory are applied to support continuously time-varying spatial object modeling. Accordingly, a time-varying spatial functional data model and a space-time manifold data model are developed. In the time-varying spatial functional data model, a spatio-temporal object is a mapping from time domain to spatial object domain. In the space-time manifold model, a spatio-temporal object is a simplicial complex composed of zero dimensional spatio-temporal simplexes, one dimensional spatio-temporal simplexes, two dimensional spatio-temporal simplexes, three dimensional spatio-temporal simplexes. It is clear that, the time-varying spatial functional data model explicitly shows time-varying semantics of spatial objects while the space-time manifold model is potential to capture spatial-temporal geometric and topological properties.