4. Istanbul 2004 
. A QTM-based 
am on a sphere. 
ed by Springer, 
model based on 
ning technology 
OPERATORS FOR CELL TUPLE-BASED 
SPATIOTEMPORAL DATA MODEL 
Ale Raza 
ESRI 
380 New York Street, Redlands, California 92373-8100, USA 
Tel.: +1-909-793-2853 (ext. 2009) 
Fax: +1-909-307-3067 
araza(@esri.com 
Commission IV, WG 1V/1 
KEY WORDS: Spatial, Temporal, Mathematics, Data Structures, Design, Modeling, GIS 
ABSTRACT: 
À spatiotemporal data model consists of attributes or classes, operations, and consistency constraints. Various models have been 
proposed by the geographic information system (GIS) community. These models could not be implemented because of various 
reasons. One of the reasons is that these models lack completeness and remain limited to the classes. This paper discusses the 
dynamic operators for the object-oriented cell tuple-based spatiotemporal data model (CTSTDM). The CTSTDM and its application 
in urban planning were published earlier by the author. Three main classes are defined in CTSTDM (i.e., spatial, attribute, and 
temporal). A spatiotemporal class is the aggregation of spatial and temporal classes. A spatiotemporal class is a super class of three 
classes (i.e., ZeroTCellClass, OneTCellClass, and TwoTCellClass). Operators pertaining to the object of these subclasses are 
elaborated in this paper. Emphasis is given to TwoTCellClass. Two types of operators can be defined as the objects of these classes: 
static and dynamic operators. Static operators do not affect the system's state (e.g., query operators). Dynamic operators change the 
state of the system (e.g., create, update, or delete operators). Unlike atemporal GIS, in a temporal GIS, objects may die or be killed, 
but they remain in the database with a valid time stamp indicating their life span. Therefore, four dynamic operators can be 
distinguished in spatiotemporal databases (i.e., Create, Kill, Reincarnate, and Delete). In spatiotemporal databases, the Kill operation 
is different from the Delete operation, as the latter is merely a purge operation. Updating a spatiotemporal object is a complex 
operation. Therefore, Kill is a protected operation, while the others are public or private. An object-oriented approach and a notion of 
point set topology are employed to design these operators in a systematic manner. Designing these operators in this fashion may 
pave the way to fill the gap between concepts, design, and implementation of a generic and functional temporal GIS. 
1. INTRODUCTION 
A data model consists of data members (classes or attributes), 
member functions (operations), and consistency constraints. 
Many spatiotemporal data models have been proposed in the 
past two decades. One main impediment for the 
implementation of these models has been the lack of 
completeness of these proposed data models. This problem is 
rooted in the inherent complexity of spatiotemporal data 
models. Most models are restricted to the classes or conceptual 
schema—one of the three main components of any data model. 
These classes are the first abstraction level for data modeling. 
The second component is the operation. Operations define the 
behavior of the model and act as an engine to run these models. 
The engines are guided by consistency rules—the third 
component of any data model. 
These three components have been defined by the author in the 
object-oriented CTSTDM. The CTSTDM's classes, some 
operations, and consistency rules have been published (Raza 
and Kainz, 1999; Raza and Kainz, 2000a). The application of 
CTSTDM in urban planning was published later (Raza and 
Kainz, 2002; Raza and Kainz, 2000b). This model has been 
implemented by Jefferson County, Colorado, USA, for keeping 
track of the county's parcels system (Bochner, 2003). 
Three main classes are defined in CTSTDM (spatial, attribute, 
and temporal). A spatiotemporal class is the aggregation of 
spatial and temporal classes. A spatiotemporal class is a super 
class of three classes (i.e., ZeroTCellClass, OneTCellClass. and 
TwoTCellClass). ZTC, OTC, and TTC are the objects of these 
three classes. The spatiotemporal class and TwoTCellClass are 
defined in §2. The spatiotemporal topology is preserved in a 
cell tuple structure. This cell tuple structure is discussed in §3. 
Operations in spatial databases can be categorized as static 
(e.g., calculating area, length, orientation) and dynamic (e.g. 
adding new node, arc, polygon). Normally in atemporal GIS, 
three fundamental dynamic operations arc applied (i.c., insert, 
delete, and update). Unlike atemporal GIS, in spatiotemporal 
databases (TGIS) objects may die or be killed, but they remain 
in the database with a certain time stamp indicating their life 
span. The fundamental dynamic operators are discussed in §4. 
How these operators are applied to TwoTCellClass is discussed 
in §5. The paper is concluded in §6. 
2. SPATIOTEMPORAL CLASSES 
The object of this class is defined in a space at time t. Formally, 
we can define these objects as follows: 
An (open) m-tcell is a topological space homeomorphic to an 
open ball E" of R" (Euclidean n-space). A finite collection k of 
m-tcells is a TemporalCellComplex (TCC) if 
* Different elements of k have disjoint interiors. 
e For each m-tcell in k, the boundary of m is a union of 
elements of &.