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Spatial Data Models
Spatial Data Models L. Bian, University at Buffalo, State University of New York, Amherst, NY, USA & 2009 Elsevier Ltd. All rights reserved.
Glossary Bona Fide Boundary Genuine discontinuities in the world, such as the boundary between a lake and land. Fiat Boundary Boundary that does not exist physically, but can be precisely placed in space, such as an administrative boundary. Field Spatial phenomenon that is spatially extended, and its attributes and processes continuously vary across space. Object-Orientation A computing paradigm that represents phenomena as objects. Objects have identification, properties, and behavior, and they can be organized into a hierarchy of classes. Spatial Data Model A model to discretize a space into discrete geometric units, such as points, lines, polygons, or grid cells. Spatial Object Spatial phenomenon that has discrete boundaries, properties, and processes, and can be mobile or movable. Spatial Region Spatial phenomenon that has not only the characteristics of a spatial object but is also a part of a continuous field.
Introduction Spatial data models are a formal representation of space. Because the computing environment is finite and discrete, a geographic space must be partitioned into a finite number of discrete pieces to accommodate the computing environment. Spatial data models describe the design of the discretization and the relationship between the discretized pieces. Spatial data models are one of the most fundamental concepts in geographic information systems (GIS). They appear in every GIS textbook, GIS software packages, academic research, and professional applications. Three types of information are associated with a spatial data model, location, attributes, and topology. A location is represented by a pair of coordinates in east and north directions. Attributes describe properties of partitioned pieces. Topology, on the other hand, records the spatial relationship between these pieces. Two GIS data models – the vector data model and the raster data model – are commonly used. These are two fundamentally different data models, representing two different ways of partitioning the space.
Vector models partition the space according to the form and function of spatial features, and represent them as geometric forms such as points, lines, and polygons. The implementation of a vector model explicitly records the coordinates of points, turning points of lines, and outlines of polygons. Each point, line, or polygon can have multiple attributes. Because of a clear identification of the spatial features, the vector data model can explicitly represent topology between them, such as which polygonal features are on either side of a line feature or which point features are at either end of a line. Vector data models are advantageous for phenomena that require a clear identification of spatial features, the spatial relationships between them, and a rich set of attributes associated with each. This is especially true for those spatial features that are perceived to be homogeneous and stable. Raster models partition the space into a matrix of regular cells. Because of the regular geometry (shape and size) of raster models, the coordinates of a cell are implicitly referenced by its row and column positions. Attribute data are explicitly represented as a single value for each cell. The adjacency between cells in the four cardinal and the four diagonal directions is clear. Topology between spatial features, which is usually formed by aggregates of cells, is not recorded because single cells, instead of spatial features, are the basic unit of the raster model. Raster models are advantageous for phenomena that are heterogeneous and dynamic. The explicit adjacency between cells is particularly effective for supporting localized simulations that often query information about areas adjacent to a local cell.
Spatial Data Models for Human Geography Human geography is concerned with the spatial differentiation and organization of human activities and with human use of the physical environment. Modeling and analysis in human geography attempt to represent and analyze these activities and the environments. In a generic sense, a model is a representation of certain aspect of reality. Spatial data models represent the spatial aspect of the real world in an abstract way. Unlike those models that directly describe human activities and the human use of environment, spatial data models focus rather on the spatial representation of these activities, such as geometry and topology. Spatial data models are often implemented in spatial databases that provide tools to
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manipulate the data. These tools are mostly for basic spatial operations, but not for the actual modeling and analysis. The spatial databases are built as generic tools. There is no information in them to describe what phenomena that these data models should represent. The separation of the spatial data models from the phenomena that they represent allows the spatial databases to be flexible in order to support a wide range of applications. This separation, in the mean time, makes it critical for users to choose data models appropriate for intended modeling and analysis. There is always more than one spatial data model that can be used to represent the same phenomenon. The choice of the model can have significant impact on the modeling and analysis and the subsequent outcome. An appropriate choice depends on many factors, but the foremost is how a phenomenon is perceived and how it subsequently should be represented.
Spatial Representation Levels of Representation Three levels of abstraction are involved in the representation of space, conceptual models, spatial data models, and spatial data structures. Conceptual models describe the perceived space. Their purpose is to identify essential spatial components and the relationships between them. For example, a population can be conceptualized as either individuals at various locations, subpopulations within administrative regions, or population density varying continuously in space. With the components identified, the relationships refer to those between locations, between regions, and within a continuous space. The second level of the abstraction, the spatial data model, formalizes the perceived spatial components and relationships in terms of basic geometry (e.g., points, lines, polygons, and grids) and topology. In turn, the spatial data models guide the implementation of these components and relationships at the third level, spatial data structures. This level is concerned with how to implement various data models in a computer. Similar multiple levels of abstraction have been proposed for spatial representation. These include the conceptualization, function, and implementation levels, and the scientific, logical, and physical models. The three levels of abstraction represent three distinct viewpoints, that of an observer of the world, a software specifier, and a software implementer. Object and Field Views In perceiving the space (the conceptual model), the object–field dichotomy has offered a profound framework for the conceptual representation of spatial phenomena. With the object view, the reality is perceived as
independent objects littered in space (hereafter referred to as ‘spatial objects’). In contrast, the field view perceives the reality as a continuous plane with variations at an infinite number of locations. The identification of spatial objects in contrast with the identification of fields has been discussed as two opposing conceptualizations of space. In spatial investigations, certain phenomena are easily perceived as discrete spatial objects and others as continuous fields. A continuous phenomenon can be divided indefinitely without changing its essential nature, while a discrete phenomenon most likely cannot be divided without altering its identity. For example, the water in a bucket may be continually halved and yet remain water, but half a bucket is no longer a bucket. The object and field views are not exclusive. A phenomenon can be conceptualized as either a spatial object or a field depending on the spatial scale of the observation, the purpose of an investigation, and convention. The two conceptualizations can coexist as well. In addition to easily recognizable spatial objects and fields, spatial regions have received substantial attention in the literature. This is because spatial regions have dual qualities. They appear to be discrete as spatial objects, but are not quite as independent because they are always parts of a continuous field. The characteristics of spatial objects, spatial regions, and fields have been actively discussed in the geographic information science literature. The two spatial data models, vector and raster, are not directly paired with spatial objects and fields, respectively, or spatial regions. It is most important to first understand the characteristics of spatial phenomena and, based on this understanding, select the most appropriate data models for the intended modeling and analysis. The discussion below summarizes the characteristics of spatial objects, spatial regions, and fields.
Identifying Spatial Objects, Regions, and Fields Spatial Objects and Regions Many characteristics have been used as criteria to identify spatial objects and object-like spatial regions. These can be synthesized into five categories, namely, spatial scale, boundary, attributes, process, and mobility. The spatial scale criterion uses human body as the reference scale and human experience as the basis to categorize spatial phenomena into four types. The first type of spatial phenomena includes everyday tabletop objects that are smaller than the human body and can be moved or manipulated. The second type is an extension of the small objects into large-scale space. This category includes phenomena that are larger than the human body, but perceived as objects, such as buildings. The third type
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refers to spatial phenomena in large-scale space, such as an urban landscape, that cannot be experienced completely all at once. These phenomena are perceived as fields. The fourth type is an extension of fields and refers to those large-scale phenomena that are beyond the range of direct human experience, such as space beyond the earth. The spatial scale criterion can be readily used to identify those spatial phenomena that are easily perceived as spatial objects, either small or large. Boundary is another criterion that has been used to identify spatial objects and regions. From an ontological perspective, boundaries are as essential as the internal content to the ontological make up of a spatial object. Both the aforementioned small-space and largespace objects tend to have well-defined boundaries. The boundary criterion has also been used to identify spatial regions extracted from continuous space. With boundaries, these spatial regions tend to be perceived as objects, as if they were small-scale objects. Boundaries for spatial objects or regions have been categorized into three types according to their origin. The first type, bona fide boundaries, includes those corresponding to genuine discontinuities in the world, such as the boundary between a lake and land. The second type is called fiat boundaries. It includes those that do not exist physically, but can be precisely placed in space, often as a reflection of human intention. The most typical example of this type is administrative boundaries. The third type refers to those that do not exist physically, yet can be placed in space, but not precisely. For example, the boundary between ‘Midwest’ and ‘Northeast’ is such an imprecise boundary. With boundaries, spatial objects can be readily identified and spatial regions be perceived as objects. Attributes are a third criterion. From the ontological viewpoint, things are known to the world and distinguished from one another by their unique properties. Spatial objects can be formally described as oi, a1, a2, y, am>, where i is an object and a1 through am are attributes of the object. Because spatial objects are often identified based on their boundaries, the importance of attributes is most evident when identifying spatial regions. These spatial objects and spatial regions are identified by the magnitude and spatial distribution of attribute values. These include, but are not limited to, the magnitude or threshold of attribute values (e.g., pollution zones), the homogeneity or dominance of attribute values (e.g., landuse and land-cover zones), or the spatial association of attribute prototypes (e.g., cities composed of residential, commercial, and industrial areas). Process, the fourth criterion, is interpreted interchangeably with concepts such as activity, operation, and function. Process may change the state of a phenomenon, and all things change. The information about process is essential in the identification of spatial objects and regions. This criterion is particularly important for
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human geography because, by definition, human geography is concerned with human activities. Similar to attribute, the importance of process is more evident in the delineation of spatial regions than that of spatial objects, because the latter can be readily identified by their boundaries. There are plenty of examples of spatial regions that are delineated by various social, economic, legal, political, and cultural processes, such as administrative regions, electoral districts, and traffic generation zones. The magnitude, dominance, and direction of processes are often used to identify spatial objects and spatial regions. Because process can be represented as attribute change, the attribute and process criteria are often paired together. Mobility has often been used as a criterion to identify spatial objects in small space or large space. Because mobility implies the independence of objects from locations, it is a criterion in its own right, although it can be considered as a special case of the process criterion or a spatially explicit attribute criterion. While moving, objects maintain their identity, properties, and behavior. Many spatial objects in human geography studies can be mobile or can be moved. When an object, such as a vehicle, moves, all parts of the object move together, along with its structure and function. Spatial regions can also be mobile, but it is its attributes and process that move, not its parts. A close analogy is the movement of ‘wave’ in a sport stadium. By a sequence of vertical motion of audiences (standing up and sitting down), a wave moves around the stadium, while its parts (audiences) do not change location. This ‘pseudo’ movement of spatial regions has many implications in selecting spatial data models. In summary, spatial objects and spatial regions can be identified through any number or combination of the aforementioned criteria. The genuine spatial objects exist in both small space and large space, have discrete boundaries, properties, and processes, and are mobile (or movable). Spatial regions are extracted out of continuous space, mostly in large space. They have definable, but nonexistent boundaries, and can be mobile. Properties and process are most important for the identification of spatial regions. Both spatial objects and spatial regions can be conceptualized as objects, although spatial regions carry dual qualifications. Fields As opposed to objects, fields are spatially continuous. By this definition, fields are viewed as a mapping between attributes and an indefinite number of spatial locations. The formal model of fields can be expressed as ox, y, z1, z2, y, zm>, where x, y are continuous locations, and the attributes at the location x, y are represented by the set z1 through zm. Fields can be categorized in several types,
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including scalar, vector, and tensor fields. A scalar field presents a scalar value of an attribute for each location (e.g., population count or density). A vector field identifies the direction and magnitude of a phenomenon at a location (e.g., population migration). A tensor field represents strains at multiple directions through a matrix at every location (e.g., direction of population migration). Many researchers have sought to identify the characteristics of fields. Although fundamentally different from objects, fields can also be described using the criteria discussed earlier, namely, spatial scale, boundary, attributes, process, and mobility. Fields are most often in large-scale space. They are spatially extended without a boundary or the boundary is not a concern. Each location in a field is associated with attributes and processes, and these attributes and processes vary continuously across the field. The motion of parts or the entire field is represented through the movement of attributes and process. These characteristics, that is, the large scale, no-boundaries, the continuous change of attributes and processes, and the pseudo-mobility, fundamentally distinguish fields from spatial objects. Spatial regions, as parts of a field and often conceptualized as objects, do not comply fully with the continuous definition of fields or the discrete definition of objects. The dual qualification of spatial regions presents challenges, as well as flexibilities in their representation. Networks are a special, one-dimensional field embedded in a two-dimensional space. It is considered a field because it is continuous, though in a linear form. The variation of its attributes occurs only on the network, not in the intervening spaces. The formal model of fields, ox, y, z1, z2, y, zm> is applicable to networks, where x, y identify an infinite number of locations constrained to this linear field. The attributes represented by z1, z2, y, zm can be any of the types for two-dimensional fields. Linear segments extracted from a network are equivalent to those spatial regions in a two-dimensional field.
Spatial Objects, Regions, and Fields in Human Geography Human geography deals with a variety of spatial phenomena. Some of these can be easily thought as spatial objects, some as typical fields, and others as spatial regions extracted out of continuous fields. Using the five criteria discussed above, namely, scale, boundary, attributes, process, and mobility, these spatial phenomena can be categorized into several types of spatial objects, spatial regions, and fields. The identification of these categories helps the appropriate selection of spatial data models in human geography studies. 1. Individuals: These individuals exist in both small- and large-scale space, have clear boundaries, attributes,
and processes. These individuals can be mobile or sedentary. Mobile individuals are independent of spatial locations, while the sedentary individuals are bound to their locations. The most typical examples of mobile individuals are individual humans or vehicles, while the typical examples of sedentary individuals can include individual buildings in a city. The unique identity, attributes, and behavior (including the mobility) of individuals in this category are of great interest in modeling and analysis. These individuals, the mobile and the sedentary, are normally conceptualized as objects. Both types are fundamental subjects of many human geography studies. 2. Masses of individuals: This category is an extension of the category of individuals. As the constituents of the mass, these individuals are identifiable, but are small in size or large in quantity, or both. These constituents can be mobile or sedentary. The most common examples of the masses of mobile individuals include a human population composed of mobile individuals, or a traffic flow composed of individual vehicles. Examples for the masses of sedentary individuals include urban landscape composed of individual buildings. The collective attributes and behavior, the continuous distribution, and the dynamic or sedentary nature of the masses are important in modeling and analysis. Whether a mass is dynamic or sedentary is relative to the time step and duration of a study. 3. Regions of individuals: This category is an extension of the masses of individuals or another extension of the individuals. These are spatial regions extracted from the continua in the masses of individuals. A region can be mobile or sedentary, dependent upon whether the location of the region as a whole is mobile or not, and independent of whether the constituents of the regions are mobile. Electoral districts extracted from the spatial distribution of population and residential areas extracted from an urban landscape are two examples of sedentary regions. Examples of mobile regions include the spread of disease and urban sprawl. The unique identity, attributes, and behavior (or function) of the regions are of great importance in modeling and analysis. Regions are often conceptualized as objects. Whether a region is dynamic or sedentary depends on the temporal scale of a study. 4. Continuous masses: Phenomena of this type are spatially extended, continuous, and spatially varying. The attributes and function of this type of phenomena vary across space, and the mass may be dynamic or sedentary. Land and roads are examples of sedentary masses in two- and one-dimensional space, respectively. Population density and air pollution can be examples of the dynamic masses (note that the population density refers to a continuous surface expressed as a rate, while the population example
Spatial Data Models
used in the masses of individuals refers to a collection of discrete individuals). The continuous form and the dynamic or sedentary nature of the attributes and function of this type are important to modeling and analysis. Both continuous sedentary mass and continuous dynamic mass are typically conceptualized as fields. 5. Regions in mass: This category is an extension of the continuous masses as the regions are extracted out of the continua. Similar to regions of individuals, the constituents of the regions in mass can be mobile or sedentary, but the mobility of these regions depends on the location of the region as a whole. Land-use and land-cover areas extracted from the continuous land and high-accident sections of a road are examples of sedentary regions in mass. The population density of a certain workforce and plumes of air pollution are examples of dynamic regions in mass. Both sedentary and mobile regions are often conceptualized as objects. The unique attributes and behavior (or functions) of these regions are important for modeling and analysis. The five categories discussed above represent a spectrum of spatial continuity with the most typical objects on one end and the most typical fields on the other, converging to spatial regions in the middle. The first three types begin with phenomena that are perceived as spatial objects and then aggregated into spatial regions and fields. The other two types begin with continuous fields and are then discretized into spatial regions. Spatial phenomena in human geography can be placed anywhere along this spectrum of spatial continuity, not necessarily in distinct categories. A same phenomenon may qualify in a number of categories depending on the objective and scale of a study, as well as the convention in a discipline. For example, a population can be perceived as either mobile or sedentary individuals, a mass of mobile or sedentary individuals, regions of individuals, a continuous mass if presented as population density, either dynamic or sedentary, or regions in the mass of population density. The examples used in aforementioned categories focus on ‘things’, such as humans, vehicles, buildings, land, roads, etc. For human geography that deals with human activities, it is often the activities that are perceived as objects, regions, or fields. Examples of the activities may include crime incidents, cases of disease, the flow of information, the transportation of goods, the migration of populations, and the dispersion of pollutants. In these situations, the activities are perceived as the spatial features, and spatial data models are used to register the spatial distribution of these activities. Regardless of things or activities, the same criteria apply in the identification of types of objects, regions, and fields.
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The identification of these spatial objects, spatial regions, and fields helps select the appropriate spatial data models for the intended investigation. The section below examines spatial data models implemented in GIS and their compatibility with the representation of spatial objects, regions, and fields.
GIS Data Models for Spatial Objects, Regions, and Fields Object-Oriented Implementation of Data Models Since the 1990s, object orientation has become the computing paradigm and software industry standard. GIS data models have been implemented in the objectorientation environment since the later part of the 1990s. The object-orientation approach consists of a number of basic principles. Of these, the encapsulation and composition principles tend to be considered conceptual, while others are implementation concerns. The encapsulation concept states that each object has an identity, properties, which are represented as attributes, and behavior, which is represented as methods. Attribute values describe the states of the object, whereas methods can change the state. The identity, properties, and behavior are encapsulated within the object. The composition principle states that objects can be organized into a class hierarchy. Objects in a subclass inherit properties and behavior from its superclass, in addition to their own unique properties and behavior. Objects can also be organized in aggregations and associations. An object is an integral part of the aggregated whole or a member of the associated set. Extensive research has been conducted in the design of object-oriented GIS databases. The object-oriented version of spatial data models has adopted the same space partition as in the traditional data models. Geometric primitives, such as points, lines, polygons, their derivatives in the vector data models, and grids in the raster data models are implemented as software objects. These software objects are encapsulated with attributes and functions and are organized into various hierarchies, associations, and aggregates. Despite the identical geometry, the object-oriented vector models differ from their traditional equivalents. In traditional vector models, data are organized based on location, expressed as coordinates of spatial features. Attributes and topology are attached to the location. Any change in the location requires that the coordinates be updated and the attributes and topology be reestablished. This design makes the representation of movement difficult, thus limiting the usefulness of the vector data model, especially for mobile objects and mobile regions. With the object-oriented implementation, spatial features, represented as software objects, are built on
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their identifiers. Location is no longer the basis for organizing spatial data. Instead, it is treated as an attribute, such as the ‘shape’ attribute in ArcGIS. With this treatment, changes in location can be easily implemented by updating the location attribute, while the identity, other spatial and aspatial attributes, and functions of the object remain intact. This change is one of the major improvements of object-oriented vector models over the traditional ones and has significantly increased the usefulness of GIS in many applications. The differences between the traditional version of raster data models and their object-oriented version are less prominent than those for vector data models. Objectoriented implementation of the raster data model not only keeps the same spatial partition as in the traditional one, but also maintains the basic form of array of cells. The cells may be aggregated into different levels of blocks according to the needed generality. Each block can be treated as a software object. Note that it is the entire array of cells or a block of cells, rather than an individual cell, which is implemented as a software object. Occasionally, individual researchers may treat cells as objects in their own in-house object-oriented GIS applications. While technically feasible, the conceptual advantage of this practice (individual cell objects) is, however, subject to debate. Both vector and raster data models can support the representation of the five types of spatial objects, spatial regions, and fields, though to various degrees. The appropriate choice of spatial data models depends on the compatibility between a data model and the conceptual model of phenomena, that is, spatial objects, regions, and fields. Spatial Data Models for Spatial Objects Spatial objects include the category of individuals discussed earlier. The vector representation for spatial objects is rather straightforward. The discrete form and the use of spatial features (points, lines, polygons, or their derivatives) as the basic unit (as opposed to grid cells in rater data models) make vector data models inherently compatible with spatial objects. This allows vector data models to readily support the representation of scale, boundary, attributes, processes, and mobility of spatial objects. Attributes of spatial objects can be internal (geometric, socioeconomic, etc.), background environment, and spatiotemporal. Vector data models can readily support them. The representation of the scale and boundary of spatial objects can be accommodated by internal attributes, such as shape. The mobility of an object can be supported by updating the spatial and temporal attributes, as discussed earlier. The processes of spatial objects may include the actions of individuals, the
interactions between them, and their interactions with the background environment. Because spatial databases mostly support spatially oriented processes, additional tools may be required to support the representation of some of the other spatial and nonspatial processes. For raster data models, a single cell or an assemblage of connected cells may be used to represent a spatial object, depending on its scale and geometry. Because the basic unit of raster data models is a cell, not a spatial feature, the representation of boundary is implicit. For attributes and processes, their representation is, in general, straightforward. Because a raster database does not have the built-in ability to identify a spatial object, for processes that require spatial objects as the basis, additional programming tools are normally needed. It is seldom a challenge for raster data models to support these tools. The mobility of spatial objects, one of the typical processes, can be represented as a sequential change of attribute for a cell or an assemblage of cells along the path of movement. Raster data models are the simplest way to partition a continuous and complex space into a finite number of discrete pieces. Strictly speaking, raster data models are not entirely compatible with spatial objects conceptually, and a square cell does not resemble most spatial features. It is the simple form and regular arrangement of cells that provide raster data models with the flexibility to support the representation of spatial objects. Spatial Data Models for Spatial Regions Spatial regions include two categories, the regions of individuals and regions in mass, as discussed earlier. Spatial regions are most likely to be represented as lines or polygons in vector data models. Because a spatial region can be perceived as a spatial object, as opposed to a field, the vector data models are conceptually compatible with its representation. The vector representation can support the scale, boundary, attributes, and processes associated with spatial regions, as would they for spatial objects. Unlike spatial objects that are independent of their background environment, spatial regions are bound to the field from which they are extracted. To represent their mobility, it is necessary not only to update the location of a mobile region, but also the rest of field needs to be updated in order to fill the ‘hole’ left by the region. Raster representation of spatial regions is similar to that for spatial objects. An assemblage of cells, rather than a single cell, is most likely to be used to spatially approximate a region. Because of the inherent advantages in representing heterogeneous and dynamic phenomena, it is easier for raster data models to represent the mobility of both spatial objects and regions than vector models.
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Because of the dual quality of spatial regions, that is, they are perceived as discrete spatial objects, but are always parts of a continuous field, a number of representation strategies have been proposed to accommodate this dual quality. These strategies use the raster data model for the internal variation of a region, and integrate a vector data model to support the identity of the region. Spatial Data Models for Fields Fields include the categories of masses of individuals and continuous masses. Both vector and raster data models can be conceptually compatible with a field and, thus, able to support the representation of their characteristics. These characteristics include the spatial continuity, the spatial variation of attributes and processes, and the dynamics of these attributes and process. Six data models have been discussed specifically for the representation of fields. These are polygons, triangulated irregular networks (TINs), contours, cell grids, point grids, and irregular points. Of these, polygons, TINs, contours, and irregular points are vector data models, while cell grids and point grids are raster models. Of the four vector models, the polygon and TIN models partition space into contiguous regions with explicit boundaries. They support the representation of those fields that consist of discrete spatial regions. Each individual polygon may be perceived as a spatial object, but collectively, they are parts of a continuous field. The polygon model can readily support the representation of the spatial continuity of a field, and the spatial variation of attributes, processes, and their dynamics, as it would for spatial regions. For fields with a linear form, such as networks consisting of discrete linear spatial regions, the same principles apply. The TIN model can be considered a special kind of polygon model. The delineation of triangles in a TIN is based on the locations of prominent attribute values, such as value peaks, ridges, passes, and valleys. The resultant triangles contain homogeneous values in slope and aspect and linearly varying values in elevation. TINs, however, are not used frequently in human geography. Contours and irregular points, though in a vector form, are intended to represent a continuously varying space, rather than points, linear-shaped spatial objects, and regions. Strictly speaking, the contour lines and irregular points do not partition the space. They present attribute values of a field at sampled locations, either along the contour lines or at certain point locations. If needed, attribute values for the rest of the field may be estimated based on those at the sampled locations. These two models can support the representation of spatial continuity, spatial variation of attributes and processes, and their dynamics through a sampled form.
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The dynamics can be supported by updating the attributes of the contours and points. The representation of field can take full advantage of raster data models, including cell grids and point grids. Their simple form, the explicit representation of attributes, the easy representation of spatial variation, and the support for spatial operations allow the grid models to effectively represent the spatial continuity, spatial variation of attributes and processes, and their dynamics. Due to their inability to identify discrete spatial objects and regions, grid models are most appropriate for continuous fields lacking explicit regions. In these fields, individual grid cells are the result of a simple form of spatial partition. Each cell is a part of a continuous field, not any meaningful spatial object or region.
Composite Structures Both raster and vector data models have been implemented in a layered structure. Raster data models are inherently constrained to a single layer. For vector data models, an individual layer is determined by both theme (e.g., land ownership, delivery areas, or electoral districts) and geometry (e.g., points, lines, or polygons). For example, an urban landscape may consist of residential, commercial, industrial areas (polygons), streets (lines), and individual humans (points). In many GIS software packages, this landscape must be prepared in three layers, a polygon, a line, and a point layer, respectively, although all belong to a single theme. It is theoretically and technically feasible to develop a ‘composite’ structure to support the representation of different geometries or themes in a single layer. For the example above, all three types of geometric features can be presented in a single layer to support modeling and analysis. Computing methods, such as object-oriented and component-based modeling, can support the implementation of the composite structure. The theoretical design of such composite structure, on the other hand, has been discussed in the literature only recently. A multigeometry and multitheme ‘object fields’ has been developed for environmental management recently. Vector data of various geometries and themes are integrated with a continuous raster field of a different theme for comprehensive modeling. Furthermore, the nineintersection system is a notable theoretical development to support the complex topology between points, lines, and polygons. The implementation of a composite structure requires sophisticated vector databases. Continued theoretical development in the research community and the technical development from the GIS software industry are critical for advancing this composite structure or any other more advanced spatial data models.
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See also: First Law of Geography.
Further Reading Bian, L. (2007). Object-oriented representation of environmental phenomena – is everything best represented as an object? Annals of the Association of American Geographers 97, 266--280. Burrough, P. A. and Frank, A. U. (eds.) (1996). Geographic Objects with Indeterminate Boundaries. London: Taylor & Francis. Couclelis, H. (1992). People manipulate objects (but cultivate fields): Beyond the raster-vector debate in GIS. In Frank, A. U., Campari, I. & Formentini, U. (eds.) Theories and Methods of Spatio-Temporal Reasoning in Geographic Space, pp 65--77. Berlin: Springer-Verlag. Cova, T. J. and Goodchild, M. F. (2002). Extending geographical representation to include fields of spatial objects. International Journal of Geographical Information Science 16, 509--532. Egenhofer, M. J. and Franzosa, R. (1991). Point-set topological spatial relation. International Journal of Geographical Information Systems 5, 161--174. Goodchild, M. F. (1992). Geographical data modeling. Computers and Geosciences 18, 401--408. Kemp, K. K. (1997). Fields as a framework for integrating GIS and environmental process models. Part 1: Representing spatial continuity. Transactions in GIS 1, 219--234. Martin, D. J. (1999). Spatial representation: The social scientist’s perspective. In Longley, P. A., Goodchild, M. F., Maguire, D. J. & Rhind, D. W. (eds.) Geographical Information Systems, pp 71--80. New York: Wiley.
Mcintosh, J. and Yuan, M. (2005). A framework to enhance semantic flexibility for analysis of distributed phenomena. International Journal of Geographical Information Science 19, 999--1018. Montello, D. R. (2003). Regions in geography: Process and content. In Duckham, M., Goodchild, M. F. & Worboys, M. F. (eds.) Foundations of Geographic Information Science, pp 173--189. London: Taylor & Francis. Peuquet, D. J. (1994). It’s about time: A conceptual framework for the representation of temporal dynamics in geographic information systems. Annals of the Association of American Geographers 84, 441--461. Peuquet, D. J., Smith, B. and Brogaad, B. (1999). The Ontology of Fields, Report of Specialist Meeting Held under the Auspices of the Varenius Project. Santa Barbara, CA: National Center for Geographic Information and Analysis. Smith, B. and Mark, D. M. (1998). Ontology and geographic kinds. In Poiker, T. K. & Chrisman, N. (eds.) Proceedings of International Symposium on Spatial Data Handling (SDH’98), pp 308--320. Vancouver, BC: International Geographical Union. Worboys, M. F. (1994). Object-oriented approaches to geo-referenced information. International Journal of Geographical Information Systems 8, 385--399. Zubin, D. (1989). Untitled. In Mark, D. M., Frank, A. U., Egenhofer, M. J., Freundschuh, S., McGranaghan, M. & White, R. M. (eds.) Languages of Spatial Relations: Report on the Specialist Meeting for NCGIA Research Initiative 2, Technical Report 89–2, pp 13--17. Santa Barbara, CA: National Center for Geographic Information and Analysis.
Glossary Bona Fide Boundary Genuine discontinuities in the world, such as the boundary between a lake and land. Fiat Boundary Boundary that does not exist physically, but can be precisely placed in space, such as an administrative boundary. Field Spatial phenomenon that is spatially extended, and its attributes and processes continuously vary across space. Object-Orientation A computing paradigm that represents phenomena as objects. Objects have identification, properties, and behavior, and they can be organized into a hierarchy of classes. Spatial Data Model A model to discretize a space into discrete geometric units, such as points, lines, polygons, or grid cells. Spatial Object Spatial phenomenon that has discrete boundaries, properties, and processes, and can be mobile or movable. Spatial Region Spatial phenomenon that has not only the characteristics of a spatial object but is also a part of a continuous field.
Introduction Spatial data models are a formal representation of space. Because the computing environment is finite and discrete, a geographic space must be partitioned into a finite number of discrete pieces to accommodate the computing environment. Spatial data models describe the design of the discretization and the relationship between the discretized pieces. Spatial data models are one of the most fundamental concepts in geographic information systems (GIS). They appear in every GIS textbook, GIS software packages, academic research, and professional applications. Three types of information are associated with a spatial data model, location, attributes, and topology. A location is represented by a pair of coordinates in east and north directions. Attributes describe properties of partitioned pieces. Topology, on the other hand, records the spatial relationship between these pieces. Two GIS data models – the vector data model and the raster data model – are commonly used. These are two fundamentally different data models, representing two different ways of partitioning the space.
Vector models partition the space according to the form and function of spatial features, and represent them as geometric forms such as points, lines, and polygons. The implementation of a vector model explicitly records the coordinates of points, turning points of lines, and outlines of polygons. Each point, line, or polygon can have multiple attributes. Because of a clear identification of the spatial features, the vector data model can explicitly represent topology between them, such as which polygonal features are on either side of a line feature or which point features are at either end of a line. Vector data models are advantageous for phenomena that require a clear identification of spatial features, the spatial relationships between them, and a rich set of attributes associated with each. This is especially true for those spatial features that are perceived to be homogeneous and stable. Raster models partition the space into a matrix of regular cells. Because of the regular geometry (shape and size) of raster models, the coordinates of a cell are implicitly referenced by its row and column positions. Attribute data are explicitly represented as a single value for each cell. The adjacency between cells in the four cardinal and the four diagonal directions is clear. Topology between spatial features, which is usually formed by aggregates of cells, is not recorded because single cells, instead of spatial features, are the basic unit of the raster model. Raster models are advantageous for phenomena that are heterogeneous and dynamic. The explicit adjacency between cells is particularly effective for supporting localized simulations that often query information about areas adjacent to a local cell.
Spatial Data Models for Human Geography Human geography is concerned with the spatial differentiation and organization of human activities and with human use of the physical environment. Modeling and analysis in human geography attempt to represent and analyze these activities and the environments. In a generic sense, a model is a representation of certain aspect of reality. Spatial data models represent the spatial aspect of the real world in an abstract way. Unlike those models that directly describe human activities and the human use of environment, spatial data models focus rather on the spatial representation of these activities, such as geometry and topology. Spatial data models are often implemented in spatial databases that provide tools to
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manipulate the data. These tools are mostly for basic spatial operations, but not for the actual modeling and analysis. The spatial databases are built as generic tools. There is no information in them to describe what phenomena that these data models should represent. The separation of the spatial data models from the phenomena that they represent allows the spatial databases to be flexible in order to support a wide range of applications. This separation, in the mean time, makes it critical for users to choose data models appropriate for intended modeling and analysis. There is always more than one spatial data model that can be used to represent the same phenomenon. The choice of the model can have significant impact on the modeling and analysis and the subsequent outcome. An appropriate choice depends on many factors, but the foremost is how a phenomenon is perceived and how it subsequently should be represented.
Spatial Representation Levels of Representation Three levels of abstraction are involved in the representation of space, conceptual models, spatial data models, and spatial data structures. Conceptual models describe the perceived space. Their purpose is to identify essential spatial components and the relationships between them. For example, a population can be conceptualized as either individuals at various locations, subpopulations within administrative regions, or population density varying continuously in space. With the components identified, the relationships refer to those between locations, between regions, and within a continuous space. The second level of the abstraction, the spatial data model, formalizes the perceived spatial components and relationships in terms of basic geometry (e.g., points, lines, polygons, and grids) and topology. In turn, the spatial data models guide the implementation of these components and relationships at the third level, spatial data structures. This level is concerned with how to implement various data models in a computer. Similar multiple levels of abstraction have been proposed for spatial representation. These include the conceptualization, function, and implementation levels, and the scientific, logical, and physical models. The three levels of abstraction represent three distinct viewpoints, that of an observer of the world, a software specifier, and a software implementer. Object and Field Views In perceiving the space (the conceptual model), the object–field dichotomy has offered a profound framework for the conceptual representation of spatial phenomena. With the object view, the reality is perceived as
independent objects littered in space (hereafter referred to as ‘spatial objects’). In contrast, the field view perceives the reality as a continuous plane with variations at an infinite number of locations. The identification of spatial objects in contrast with the identification of fields has been discussed as two opposing conceptualizations of space. In spatial investigations, certain phenomena are easily perceived as discrete spatial objects and others as continuous fields. A continuous phenomenon can be divided indefinitely without changing its essential nature, while a discrete phenomenon most likely cannot be divided without altering its identity. For example, the water in a bucket may be continually halved and yet remain water, but half a bucket is no longer a bucket. The object and field views are not exclusive. A phenomenon can be conceptualized as either a spatial object or a field depending on the spatial scale of the observation, the purpose of an investigation, and convention. The two conceptualizations can coexist as well. In addition to easily recognizable spatial objects and fields, spatial regions have received substantial attention in the literature. This is because spatial regions have dual qualities. They appear to be discrete as spatial objects, but are not quite as independent because they are always parts of a continuous field. The characteristics of spatial objects, spatial regions, and fields have been actively discussed in the geographic information science literature. The two spatial data models, vector and raster, are not directly paired with spatial objects and fields, respectively, or spatial regions. It is most important to first understand the characteristics of spatial phenomena and, based on this understanding, select the most appropriate data models for the intended modeling and analysis. The discussion below summarizes the characteristics of spatial objects, spatial regions, and fields.
Identifying Spatial Objects, Regions, and Fields Spatial Objects and Regions Many characteristics have been used as criteria to identify spatial objects and object-like spatial regions. These can be synthesized into five categories, namely, spatial scale, boundary, attributes, process, and mobility. The spatial scale criterion uses human body as the reference scale and human experience as the basis to categorize spatial phenomena into four types. The first type of spatial phenomena includes everyday tabletop objects that are smaller than the human body and can be moved or manipulated. The second type is an extension of the small objects into large-scale space. This category includes phenomena that are larger than the human body, but perceived as objects, such as buildings. The third type
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refers to spatial phenomena in large-scale space, such as an urban landscape, that cannot be experienced completely all at once. These phenomena are perceived as fields. The fourth type is an extension of fields and refers to those large-scale phenomena that are beyond the range of direct human experience, such as space beyond the earth. The spatial scale criterion can be readily used to identify those spatial phenomena that are easily perceived as spatial objects, either small or large. Boundary is another criterion that has been used to identify spatial objects and regions. From an ontological perspective, boundaries are as essential as the internal content to the ontological make up of a spatial object. Both the aforementioned small-space and largespace objects tend to have well-defined boundaries. The boundary criterion has also been used to identify spatial regions extracted from continuous space. With boundaries, these spatial regions tend to be perceived as objects, as if they were small-scale objects. Boundaries for spatial objects or regions have been categorized into three types according to their origin. The first type, bona fide boundaries, includes those corresponding to genuine discontinuities in the world, such as the boundary between a lake and land. The second type is called fiat boundaries. It includes those that do not exist physically, but can be precisely placed in space, often as a reflection of human intention. The most typical example of this type is administrative boundaries. The third type refers to those that do not exist physically, yet can be placed in space, but not precisely. For example, the boundary between ‘Midwest’ and ‘Northeast’ is such an imprecise boundary. With boundaries, spatial objects can be readily identified and spatial regions be perceived as objects. Attributes are a third criterion. From the ontological viewpoint, things are known to the world and distinguished from one another by their unique properties. Spatial objects can be formally described as oi, a1, a2, y, am>, where i is an object and a1 through am are attributes of the object. Because spatial objects are often identified based on their boundaries, the importance of attributes is most evident when identifying spatial regions. These spatial objects and spatial regions are identified by the magnitude and spatial distribution of attribute values. These include, but are not limited to, the magnitude or threshold of attribute values (e.g., pollution zones), the homogeneity or dominance of attribute values (e.g., landuse and land-cover zones), or the spatial association of attribute prototypes (e.g., cities composed of residential, commercial, and industrial areas). Process, the fourth criterion, is interpreted interchangeably with concepts such as activity, operation, and function. Process may change the state of a phenomenon, and all things change. The information about process is essential in the identification of spatial objects and regions. This criterion is particularly important for
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human geography because, by definition, human geography is concerned with human activities. Similar to attribute, the importance of process is more evident in the delineation of spatial regions than that of spatial objects, because the latter can be readily identified by their boundaries. There are plenty of examples of spatial regions that are delineated by various social, economic, legal, political, and cultural processes, such as administrative regions, electoral districts, and traffic generation zones. The magnitude, dominance, and direction of processes are often used to identify spatial objects and spatial regions. Because process can be represented as attribute change, the attribute and process criteria are often paired together. Mobility has often been used as a criterion to identify spatial objects in small space or large space. Because mobility implies the independence of objects from locations, it is a criterion in its own right, although it can be considered as a special case of the process criterion or a spatially explicit attribute criterion. While moving, objects maintain their identity, properties, and behavior. Many spatial objects in human geography studies can be mobile or can be moved. When an object, such as a vehicle, moves, all parts of the object move together, along with its structure and function. Spatial regions can also be mobile, but it is its attributes and process that move, not its parts. A close analogy is the movement of ‘wave’ in a sport stadium. By a sequence of vertical motion of audiences (standing up and sitting down), a wave moves around the stadium, while its parts (audiences) do not change location. This ‘pseudo’ movement of spatial regions has many implications in selecting spatial data models. In summary, spatial objects and spatial regions can be identified through any number or combination of the aforementioned criteria. The genuine spatial objects exist in both small space and large space, have discrete boundaries, properties, and processes, and are mobile (or movable). Spatial regions are extracted out of continuous space, mostly in large space. They have definable, but nonexistent boundaries, and can be mobile. Properties and process are most important for the identification of spatial regions. Both spatial objects and spatial regions can be conceptualized as objects, although spatial regions carry dual qualifications. Fields As opposed to objects, fields are spatially continuous. By this definition, fields are viewed as a mapping between attributes and an indefinite number of spatial locations. The formal model of fields can be expressed as ox, y, z1, z2, y, zm>, where x, y are continuous locations, and the attributes at the location x, y are represented by the set z1 through zm. Fields can be categorized in several types,
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including scalar, vector, and tensor fields. A scalar field presents a scalar value of an attribute for each location (e.g., population count or density). A vector field identifies the direction and magnitude of a phenomenon at a location (e.g., population migration). A tensor field represents strains at multiple directions through a matrix at every location (e.g., direction of population migration). Many researchers have sought to identify the characteristics of fields. Although fundamentally different from objects, fields can also be described using the criteria discussed earlier, namely, spatial scale, boundary, attributes, process, and mobility. Fields are most often in large-scale space. They are spatially extended without a boundary or the boundary is not a concern. Each location in a field is associated with attributes and processes, and these attributes and processes vary continuously across the field. The motion of parts or the entire field is represented through the movement of attributes and process. These characteristics, that is, the large scale, no-boundaries, the continuous change of attributes and processes, and the pseudo-mobility, fundamentally distinguish fields from spatial objects. Spatial regions, as parts of a field and often conceptualized as objects, do not comply fully with the continuous definition of fields or the discrete definition of objects. The dual qualification of spatial regions presents challenges, as well as flexibilities in their representation. Networks are a special, one-dimensional field embedded in a two-dimensional space. It is considered a field because it is continuous, though in a linear form. The variation of its attributes occurs only on the network, not in the intervening spaces. The formal model of fields, ox, y, z1, z2, y, zm> is applicable to networks, where x, y identify an infinite number of locations constrained to this linear field. The attributes represented by z1, z2, y, zm can be any of the types for two-dimensional fields. Linear segments extracted from a network are equivalent to those spatial regions in a two-dimensional field.
Spatial Objects, Regions, and Fields in Human Geography Human geography deals with a variety of spatial phenomena. Some of these can be easily thought as spatial objects, some as typical fields, and others as spatial regions extracted out of continuous fields. Using the five criteria discussed above, namely, scale, boundary, attributes, process, and mobility, these spatial phenomena can be categorized into several types of spatial objects, spatial regions, and fields. The identification of these categories helps the appropriate selection of spatial data models in human geography studies. 1. Individuals: These individuals exist in both small- and large-scale space, have clear boundaries, attributes,
and processes. These individuals can be mobile or sedentary. Mobile individuals are independent of spatial locations, while the sedentary individuals are bound to their locations. The most typical examples of mobile individuals are individual humans or vehicles, while the typical examples of sedentary individuals can include individual buildings in a city. The unique identity, attributes, and behavior (including the mobility) of individuals in this category are of great interest in modeling and analysis. These individuals, the mobile and the sedentary, are normally conceptualized as objects. Both types are fundamental subjects of many human geography studies. 2. Masses of individuals: This category is an extension of the category of individuals. As the constituents of the mass, these individuals are identifiable, but are small in size or large in quantity, or both. These constituents can be mobile or sedentary. The most common examples of the masses of mobile individuals include a human population composed of mobile individuals, or a traffic flow composed of individual vehicles. Examples for the masses of sedentary individuals include urban landscape composed of individual buildings. The collective attributes and behavior, the continuous distribution, and the dynamic or sedentary nature of the masses are important in modeling and analysis. Whether a mass is dynamic or sedentary is relative to the time step and duration of a study. 3. Regions of individuals: This category is an extension of the masses of individuals or another extension of the individuals. These are spatial regions extracted from the continua in the masses of individuals. A region can be mobile or sedentary, dependent upon whether the location of the region as a whole is mobile or not, and independent of whether the constituents of the regions are mobile. Electoral districts extracted from the spatial distribution of population and residential areas extracted from an urban landscape are two examples of sedentary regions. Examples of mobile regions include the spread of disease and urban sprawl. The unique identity, attributes, and behavior (or function) of the regions are of great importance in modeling and analysis. Regions are often conceptualized as objects. Whether a region is dynamic or sedentary depends on the temporal scale of a study. 4. Continuous masses: Phenomena of this type are spatially extended, continuous, and spatially varying. The attributes and function of this type of phenomena vary across space, and the mass may be dynamic or sedentary. Land and roads are examples of sedentary masses in two- and one-dimensional space, respectively. Population density and air pollution can be examples of the dynamic masses (note that the population density refers to a continuous surface expressed as a rate, while the population example
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used in the masses of individuals refers to a collection of discrete individuals). The continuous form and the dynamic or sedentary nature of the attributes and function of this type are important to modeling and analysis. Both continuous sedentary mass and continuous dynamic mass are typically conceptualized as fields. 5. Regions in mass: This category is an extension of the continuous masses as the regions are extracted out of the continua. Similar to regions of individuals, the constituents of the regions in mass can be mobile or sedentary, but the mobility of these regions depends on the location of the region as a whole. Land-use and land-cover areas extracted from the continuous land and high-accident sections of a road are examples of sedentary regions in mass. The population density of a certain workforce and plumes of air pollution are examples of dynamic regions in mass. Both sedentary and mobile regions are often conceptualized as objects. The unique attributes and behavior (or functions) of these regions are important for modeling and analysis. The five categories discussed above represent a spectrum of spatial continuity with the most typical objects on one end and the most typical fields on the other, converging to spatial regions in the middle. The first three types begin with phenomena that are perceived as spatial objects and then aggregated into spatial regions and fields. The other two types begin with continuous fields and are then discretized into spatial regions. Spatial phenomena in human geography can be placed anywhere along this spectrum of spatial continuity, not necessarily in distinct categories. A same phenomenon may qualify in a number of categories depending on the objective and scale of a study, as well as the convention in a discipline. For example, a population can be perceived as either mobile or sedentary individuals, a mass of mobile or sedentary individuals, regions of individuals, a continuous mass if presented as population density, either dynamic or sedentary, or regions in the mass of population density. The examples used in aforementioned categories focus on ‘things’, such as humans, vehicles, buildings, land, roads, etc. For human geography that deals with human activities, it is often the activities that are perceived as objects, regions, or fields. Examples of the activities may include crime incidents, cases of disease, the flow of information, the transportation of goods, the migration of populations, and the dispersion of pollutants. In these situations, the activities are perceived as the spatial features, and spatial data models are used to register the spatial distribution of these activities. Regardless of things or activities, the same criteria apply in the identification of types of objects, regions, and fields.
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The identification of these spatial objects, spatial regions, and fields helps select the appropriate spatial data models for the intended investigation. The section below examines spatial data models implemented in GIS and their compatibility with the representation of spatial objects, regions, and fields.
GIS Data Models for Spatial Objects, Regions, and Fields Object-Oriented Implementation of Data Models Since the 1990s, object orientation has become the computing paradigm and software industry standard. GIS data models have been implemented in the objectorientation environment since the later part of the 1990s. The object-orientation approach consists of a number of basic principles. Of these, the encapsulation and composition principles tend to be considered conceptual, while others are implementation concerns. The encapsulation concept states that each object has an identity, properties, which are represented as attributes, and behavior, which is represented as methods. Attribute values describe the states of the object, whereas methods can change the state. The identity, properties, and behavior are encapsulated within the object. The composition principle states that objects can be organized into a class hierarchy. Objects in a subclass inherit properties and behavior from its superclass, in addition to their own unique properties and behavior. Objects can also be organized in aggregations and associations. An object is an integral part of the aggregated whole or a member of the associated set. Extensive research has been conducted in the design of object-oriented GIS databases. The object-oriented version of spatial data models has adopted the same space partition as in the traditional data models. Geometric primitives, such as points, lines, polygons, their derivatives in the vector data models, and grids in the raster data models are implemented as software objects. These software objects are encapsulated with attributes and functions and are organized into various hierarchies, associations, and aggregates. Despite the identical geometry, the object-oriented vector models differ from their traditional equivalents. In traditional vector models, data are organized based on location, expressed as coordinates of spatial features. Attributes and topology are attached to the location. Any change in the location requires that the coordinates be updated and the attributes and topology be reestablished. This design makes the representation of movement difficult, thus limiting the usefulness of the vector data model, especially for mobile objects and mobile regions. With the object-oriented implementation, spatial features, represented as software objects, are built on
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their identifiers. Location is no longer the basis for organizing spatial data. Instead, it is treated as an attribute, such as the ‘shape’ attribute in ArcGIS. With this treatment, changes in location can be easily implemented by updating the location attribute, while the identity, other spatial and aspatial attributes, and functions of the object remain intact. This change is one of the major improvements of object-oriented vector models over the traditional ones and has significantly increased the usefulness of GIS in many applications. The differences between the traditional version of raster data models and their object-oriented version are less prominent than those for vector data models. Objectoriented implementation of the raster data model not only keeps the same spatial partition as in the traditional one, but also maintains the basic form of array of cells. The cells may be aggregated into different levels of blocks according to the needed generality. Each block can be treated as a software object. Note that it is the entire array of cells or a block of cells, rather than an individual cell, which is implemented as a software object. Occasionally, individual researchers may treat cells as objects in their own in-house object-oriented GIS applications. While technically feasible, the conceptual advantage of this practice (individual cell objects) is, however, subject to debate. Both vector and raster data models can support the representation of the five types of spatial objects, spatial regions, and fields, though to various degrees. The appropriate choice of spatial data models depends on the compatibility between a data model and the conceptual model of phenomena, that is, spatial objects, regions, and fields. Spatial Data Models for Spatial Objects Spatial objects include the category of individuals discussed earlier. The vector representation for spatial objects is rather straightforward. The discrete form and the use of spatial features (points, lines, polygons, or their derivatives) as the basic unit (as opposed to grid cells in rater data models) make vector data models inherently compatible with spatial objects. This allows vector data models to readily support the representation of scale, boundary, attributes, processes, and mobility of spatial objects. Attributes of spatial objects can be internal (geometric, socioeconomic, etc.), background environment, and spatiotemporal. Vector data models can readily support them. The representation of the scale and boundary of spatial objects can be accommodated by internal attributes, such as shape. The mobility of an object can be supported by updating the spatial and temporal attributes, as discussed earlier. The processes of spatial objects may include the actions of individuals, the
interactions between them, and their interactions with the background environment. Because spatial databases mostly support spatially oriented processes, additional tools may be required to support the representation of some of the other spatial and nonspatial processes. For raster data models, a single cell or an assemblage of connected cells may be used to represent a spatial object, depending on its scale and geometry. Because the basic unit of raster data models is a cell, not a spatial feature, the representation of boundary is implicit. For attributes and processes, their representation is, in general, straightforward. Because a raster database does not have the built-in ability to identify a spatial object, for processes that require spatial objects as the basis, additional programming tools are normally needed. It is seldom a challenge for raster data models to support these tools. The mobility of spatial objects, one of the typical processes, can be represented as a sequential change of attribute for a cell or an assemblage of cells along the path of movement. Raster data models are the simplest way to partition a continuous and complex space into a finite number of discrete pieces. Strictly speaking, raster data models are not entirely compatible with spatial objects conceptually, and a square cell does not resemble most spatial features. It is the simple form and regular arrangement of cells that provide raster data models with the flexibility to support the representation of spatial objects. Spatial Data Models for Spatial Regions Spatial regions include two categories, the regions of individuals and regions in mass, as discussed earlier. Spatial regions are most likely to be represented as lines or polygons in vector data models. Because a spatial region can be perceived as a spatial object, as opposed to a field, the vector data models are conceptually compatible with its representation. The vector representation can support the scale, boundary, attributes, and processes associated with spatial regions, as would they for spatial objects. Unlike spatial objects that are independent of their background environment, spatial regions are bound to the field from which they are extracted. To represent their mobility, it is necessary not only to update the location of a mobile region, but also the rest of field needs to be updated in order to fill the ‘hole’ left by the region. Raster representation of spatial regions is similar to that for spatial objects. An assemblage of cells, rather than a single cell, is most likely to be used to spatially approximate a region. Because of the inherent advantages in representing heterogeneous and dynamic phenomena, it is easier for raster data models to represent the mobility of both spatial objects and regions than vector models.
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Because of the dual quality of spatial regions, that is, they are perceived as discrete spatial objects, but are always parts of a continuous field, a number of representation strategies have been proposed to accommodate this dual quality. These strategies use the raster data model for the internal variation of a region, and integrate a vector data model to support the identity of the region. Spatial Data Models for Fields Fields include the categories of masses of individuals and continuous masses. Both vector and raster data models can be conceptually compatible with a field and, thus, able to support the representation of their characteristics. These characteristics include the spatial continuity, the spatial variation of attributes and processes, and the dynamics of these attributes and process. Six data models have been discussed specifically for the representation of fields. These are polygons, triangulated irregular networks (TINs), contours, cell grids, point grids, and irregular points. Of these, polygons, TINs, contours, and irregular points are vector data models, while cell grids and point grids are raster models. Of the four vector models, the polygon and TIN models partition space into contiguous regions with explicit boundaries. They support the representation of those fields that consist of discrete spatial regions. Each individual polygon may be perceived as a spatial object, but collectively, they are parts of a continuous field. The polygon model can readily support the representation of the spatial continuity of a field, and the spatial variation of attributes, processes, and their dynamics, as it would for spatial regions. For fields with a linear form, such as networks consisting of discrete linear spatial regions, the same principles apply. The TIN model can be considered a special kind of polygon model. The delineation of triangles in a TIN is based on the locations of prominent attribute values, such as value peaks, ridges, passes, and valleys. The resultant triangles contain homogeneous values in slope and aspect and linearly varying values in elevation. TINs, however, are not used frequently in human geography. Contours and irregular points, though in a vector form, are intended to represent a continuously varying space, rather than points, linear-shaped spatial objects, and regions. Strictly speaking, the contour lines and irregular points do not partition the space. They present attribute values of a field at sampled locations, either along the contour lines or at certain point locations. If needed, attribute values for the rest of the field may be estimated based on those at the sampled locations. These two models can support the representation of spatial continuity, spatial variation of attributes and processes, and their dynamics through a sampled form.
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The dynamics can be supported by updating the attributes of the contours and points. The representation of field can take full advantage of raster data models, including cell grids and point grids. Their simple form, the explicit representation of attributes, the easy representation of spatial variation, and the support for spatial operations allow the grid models to effectively represent the spatial continuity, spatial variation of attributes and processes, and their dynamics. Due to their inability to identify discrete spatial objects and regions, grid models are most appropriate for continuous fields lacking explicit regions. In these fields, individual grid cells are the result of a simple form of spatial partition. Each cell is a part of a continuous field, not any meaningful spatial object or region.
Composite Structures Both raster and vector data models have been implemented in a layered structure. Raster data models are inherently constrained to a single layer. For vector data models, an individual layer is determined by both theme (e.g., land ownership, delivery areas, or electoral districts) and geometry (e.g., points, lines, or polygons). For example, an urban landscape may consist of residential, commercial, industrial areas (polygons), streets (lines), and individual humans (points). In many GIS software packages, this landscape must be prepared in three layers, a polygon, a line, and a point layer, respectively, although all belong to a single theme. It is theoretically and technically feasible to develop a ‘composite’ structure to support the representation of different geometries or themes in a single layer. For the example above, all three types of geometric features can be presented in a single layer to support modeling and analysis. Computing methods, such as object-oriented and component-based modeling, can support the implementation of the composite structure. The theoretical design of such composite structure, on the other hand, has been discussed in the literature only recently. A multigeometry and multitheme ‘object fields’ has been developed for environmental management recently. Vector data of various geometries and themes are integrated with a continuous raster field of a different theme for comprehensive modeling. Furthermore, the nineintersection system is a notable theoretical development to support the complex topology between points, lines, and polygons. The implementation of a composite structure requires sophisticated vector databases. Continued theoretical development in the research community and the technical development from the GIS software industry are critical for advancing this composite structure or any other more advanced spatial data models.
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See also: First Law of Geography.
Further Reading Bian, L. (2007). Object-oriented representation of environmental phenomena – is everything best represented as an object? Annals of the Association of American Geographers 97, 266--280. Burrough, P. A. and Frank, A. U. (eds.) (1996). Geographic Objects with Indeterminate Boundaries. London: Taylor & Francis. Couclelis, H. (1992). People manipulate objects (but cultivate fields): Beyond the raster-vector debate in GIS. In Frank, A. U., Campari, I. & Formentini, U. (eds.) Theories and Methods of Spatio-Temporal Reasoning in Geographic Space, pp 65--77. Berlin: Springer-Verlag. Cova, T. J. and Goodchild, M. F. (2002). Extending geographical representation to include fields of spatial objects. International Journal of Geographical Information Science 16, 509--532. Egenhofer, M. J. and Franzosa, R. (1991). Point-set topological spatial relation. International Journal of Geographical Information Systems 5, 161--174. Goodchild, M. F. (1992). Geographical data modeling. Computers and Geosciences 18, 401--408. Kemp, K. K. (1997). Fields as a framework for integrating GIS and environmental process models. Part 1: Representing spatial continuity. Transactions in GIS 1, 219--234. Martin, D. J. (1999). Spatial representation: The social scientist’s perspective. In Longley, P. A., Goodchild, M. F., Maguire, D. J. & Rhind, D. W. (eds.) Geographical Information Systems, pp 71--80. New York: Wiley.
Mcintosh, J. and Yuan, M. (2005). A framework to enhance semantic flexibility for analysis of distributed phenomena. International Journal of Geographical Information Science 19, 999--1018. Montello, D. R. (2003). Regions in geography: Process and content. In Duckham, M., Goodchild, M. F. & Worboys, M. F. (eds.) Foundations of Geographic Information Science, pp 173--189. London: Taylor & Francis. Peuquet, D. J. (1994). It’s about time: A conceptual framework for the representation of temporal dynamics in geographic information systems. Annals of the Association of American Geographers 84, 441--461. Peuquet, D. J., Smith, B. and Brogaad, B. (1999). The Ontology of Fields, Report of Specialist Meeting Held under the Auspices of the Varenius Project. Santa Barbara, CA: National Center for Geographic Information and Analysis. Smith, B. and Mark, D. M. (1998). Ontology and geographic kinds. In Poiker, T. K. & Chrisman, N. (eds.) Proceedings of International Symposium on Spatial Data Handling (SDH’98), pp 308--320. Vancouver, BC: International Geographical Union. Worboys, M. F. (1994). Object-oriented approaches to geo-referenced information. International Journal of Geographical Information Systems 8, 385--399. Zubin, D. (1989). Untitled. In Mark, D. M., Frank, A. U., Egenhofer, M. J., Freundschuh, S., McGranaghan, M. & White, R. M. (eds.) Languages of Spatial Relations: Report on the Specialist Meeting for NCGIA Research Initiative 2, Technical Report 89–2, pp 13--17. Santa Barbara, CA: National Center for Geographic Information and Analysis.