Modeling Processes

The Real World Universe

The SPRING model is not limited to a particular Geoprocessing application area but it is capable to incorporate several different applications such as Environmental studies, Agricultural, Geology and Networks.

The following table presents a mapping as a function of the data types of all Geoprocessing application areas.

Typical Geoprocessing Applications
Applications Typical scales Data types Graphical Representations Operations
Forest 1:10.000 a 1:500.000 Rural cadastral Raster, vector Image Classif., spatial verification
Agriculture 1:25.000 a 1:250.000 Thematic data, remote sensing, DTM Raster,vector, grids, TIN Spatial Analysis, declivity
Geology 1:100.000 a 1:2,500,000 DTM, thematic data,images Raster, grids Transf. IHS, 3D visualization
Network 1:1.000 a 1:10.000 Linear networks (topology) vector Spatial verification, dedicated calculus
Urban Studies 1:1.000 a 1:25.000 Networks, urban cadastral vector Spatial verification

See also:

How to create a Project
How to create an IL
How to define a conceptual scheme in the SPRING

Overview of Modeling Process



The Conceptual Universe

In Geoprocessing, the geographical space is modeled following two complementary views: the field and object models (Worboys, 1995). The field model sees the geographical space as a continuous surface, over which varies the observed phenomena, following different distributions. For example, a vegetation map describes a distribution associating each point in the map to an specific type of vegetation cover, meanwhile a geochemical map associates to each point the contents of a mineral.

The object model represents a geographical space as a distinct and identifiable entity collection. For example, the spatial cadastral of land in a town identify each part of land as an individual data with its own attributes, distinguishing it from others. In the same way it is possible to think as geo-objects: the rivers in a hydrographical region or the airports in a state.

Geoprocessing applications deal with these two data types:

  • Fields: continuous spatial variations (approximations and discrete); they are used for spatial distributed quantities, such as, soil types, topography and minerals tenor. In practice they correspond to thematic data, images, and numerical models of the terrain.
  • Geographical objects (or objects): they are individualized and have an identification with real world elements, such as lots in a cadastral maps, and poles in an electrical network. These objects have non spatial attributes and they can be associated with more than one graphical representation. The location means to be exact and the object is distinguishable from its neighborhood.

A fundamental aspect for the distinction between fields and objects is the question related to their identity. There are thousands of areas in Brazil that can be classified as “Dusky-Red Latosol”, but there is only one “Rio de Janeiro Botanical Garden”.

A field existence is only materialized when its geographical spatial representation is defined. The geographical region defining a “Dusky-Red Latosol” area in São José dos Campos is not an individual entity. What is identifiable, in this case, is the “Paraíba Valley soil map”.

The objects has an independent existence from its map representation; in a Geoprocessing system, the objects are usually created from their own attributes and after it they can be located in the space. For example, it is possible to talk about objects such as “São José dos Campos schools”, and, specifically the “Mater Dei School”.


Conceptual Universe Classes

Initially it is important to establish the geometrical base where the model classes are defined. Starting from a continuous region on the earth surface it is possible to define the concept called geographical region (or geographical grid).

“We define a geographical region R as a general surface belonging to a geographical space, which can be represented as a plane or as a grid, depending on the appropriate cartographical projection.”

The geographical region R is used for geometrical support for geographical locations, because all geographical locations will be represented by a unique point from R. The usage of a discrete set of points facilitates a formal definition of the geographical data class and its associated operations. The geographical region definition proposed does not constrain the geometrical representation choices (vector or raster) associated to the geographical objects.

The model basic classes, defined bellow, are:


See also:
Conceptual Universe Summary

Overview of Modeling Process

Representation Universe

While discussing the representation universe, it will be pointed out what are the used structures to build up a Geoprocessing system.

The basic concept is GEOMETRICAL REPRESENTATION. A representation defines a geometrical description in an information layer, which can be specialized in one of the following:

  • raster representation: includes several ways to store geographical data in a matrix.
  • vector representation: includes different topologies for vector storage.

Representation Universe


See also:
Differences between vector representation and scanning !
How to convert from vector to scanning ?
How to convert from scanning to vector ?

Raster Representation Hierarchy

THE RASTER GEOMETRICAL REPRESENTATION can be specialized in classes as presented in the figure bellow.


RASTER REPRESENTATION class hierarchy.

The derived classes in the RASTER REPRESENTATION are:
  1. REGULAR GRID: a regular grid is just a matrix composed by real numbers .
  2. GREY LEVEL IMAGE: an image represented by a matrix composed by numbers, where each value corresponds to a gray level for a pixel in the image.
  3. THEMATIC IMAGE: a matrix representation for a THEMATIC geo-field, for example, in a thematic image an element in a matrix with value 2 can be associated to the theme “Araucária Forest”.
  4. SYNTHETIC IMAGE (or ENCODED): this is the representation of a color image used to show images as colored compositions in graphical layers false-color.

Vector Representations Hierarchy

In order to define this hierarchy we need first to define better what is understood by geometrical primitives: 2D coordinates, 3D coordinates, 2D node, network node, arcs, oriented arcs, contour lines and polygons.

Given a geographical region R, it is possible to define:

  1. 2D COORDINATE: A 2D coordinate is a composed object with a singular location (xi, yj) E R.
  2. 3D COORDINATE: A 3D coordinate is a composed object with a singular location (xi, yj, z), where (xi, yj) E R.
  3. 2D POINT: A 2D point is an object that has its descriptive attributes and a 2D coordinate.
  4. 2D LINE: A 2D line has attributes including a set of 2D coordinates.
  5. ISOLINE: An contour line has a 2D line, associated to a real value (height).
  6. ORIENTED arc: an oriented arc has a 2D line, associated to an oriented path.
  7. 2D NODE: a 2D node includes a 2D coordinate (xi, yi) E R and a list L of 2D lines. A 2D node represents a connection among two or more lines used to keep the structure topology;
  8. NETWORK NODE: a network node has a 2D node and an oriented arc list, where to each instance it is associated an impedance and a cost;
  9. 3D NODE: an instance of this class has a 3D coordinate (xi, yi, z) and a list L of 2D lines. This is a connection among three or more lines in a triangular grid;
  10. POLYGON: A polygon has a list of 2D lines and a list of 2D nodes, describing the polygon external area coordinates and internal area coordinates.

Once the vector geometrical primitives are defined it is possible to establish the vector geometrical representation hierarchy, as shown in the figure bellow.


VECTOR REPRESENTATION - Hierarchy classes.

The figure above shows the distinctions in the specialization relationships (“is-a”), an instance inclusion, (“part-of”), the inclusion of a set of instances (“set-of”) the inclusion of an instance identifiers list (“list-of”). This last relationship will be used to keep the 2D topology. Consider here the following vector REPRESENTATION specializations:
  1. SET OF 2D POINTS: this class instance is a set of 2D points, used to keep isolated locations in space (e.g. oil pumps in an area).
  2. SET OF CONTOUR LINES: this class instance is a set of lines, where each line has a height, and there is no intersection among lines.
  3. PLANAR SUBDIVISION : given a geographical region R, this class instance has a set of polygons Pg, 2D lines L, and 2D nodes N.
  4. ORIENTED GRAPH: this class instance is a representation composed by a set of network nodes and a set of 2D oriented arcs.
  5. TRIANGULAR GRID: this class instance has a set of 3D nodes and a set L of 2D lines such that there is an intersection among all lines, but only at their starting or ending points.
  6. 3D POINTS MAP: this class instance is a set of 3D coordinates. It is a set of 3D samples.

Overview of Modeling Process



Implementation Universe

While discussing the implementation universe it will be pointed out what data structures can be used to build up a Geoprocessing system. In this universe concrete programming decisions are treated with a large number of variations. These decisions can take into account the current application, the available algorithms to handle the geographical data and the hardware performance. For a deeper discussion about geographical operators implementation problems see Gutting et al. (1995).

One of the main aspects to take into account in the implementation universe is the usage of spatial indexation structures. The access methods to spatial data are composed of data structures and recovery and search algorithms and they represent a determinant component in the system performance. A survey of this issues are presented at Cox Junior (1991) and Rezende (1992).

These methods work over multidimensional keys and divide themselves according to the representation of associated data: points (e.g.: K-D trees), lines and polygons (e.g.: R trees and R+) and images (e.g.: quaternal trees). These and other methods has presented large performance improves in the geographical data access (mainly for the lines and points cases).

The limiting factor for a large set of access methods studied is that they were designed to process in the main memory. In a large SGBDG it is required to access data efficiently in the secondary memory. This is true in both cases, for vector or raster data. For vector data Mediano, Casanova and Dreux (1994) presented a way to use an extension of B trees in order to show only the relevant geographical data for a certain scale, without running unnecessary procedures. This structure, called V-tree, allow to access multi resolution data and it is very convenient as support for skim methods in a large Database.

Overview of Modeling Process

Relationship among the universes in the model

The “four universes modeling” paradigm (Gomes and Velho, 1995) considers that the mapping process among universes is not reversible and it admits alternatives. Following these relations will be discussed.

From the Real World to the Conceptual Universe

The path from the real world to the conceptual universe considers some variations, as the application domain. In some cases, the mapping is direct, for instance, the satellite images and topographical or geophysical measures are naturally mapped to GEOCAMPO instances. In the city maps or political division map cases. The association with GEO-OBJECT classes and GEO-OBJECT MAPS is also direct.

The thematic data collections can be used in two different interpretations, depending on its usage: when it is related to an inventory task (such as a vegetation map in the Amazon), it should be modeled as GEOFIELD instances (or, more specifically as a THEMATIC class). In detailed studies on averages and large scales (such as an economical-ecological) where each region is characterized by specific qualifiers, it is convenient that such a data collection is associated to a GEOOBJECT instance and GEO-OBJECT MAP.

From the Conceptual Universe to its Representation

This mapping presents several nonexclusive options:

  • Instances from the data_remote_sensing class are usually stored as gray level or synthetic images;
  • A numerical geo-field can be represented either as a matrix (regular grid) or as a vector (set of contour lines, triangular grid and set of 3D points);
  • A thematic geo-field can be represented either as a topologically structured vector (planar sub-division), or as a matrix (thematic image);
  • Cadastral instances are represented as a planar sub-division instances or a set of 2D points;
  • A network is represented as an oriented graph.

The literature has enforced the idea that a general GIS has to provide all the possible representation options.

From Representation to Implementation

As it was mentioned before, the implementation universe is a concrete programming decision. Following we will present some practical issues to be considered:

  • Storing the 3D points in K-D trees (Bentley, 1975) provides a significant gain for applications such as a regular grid generation from a sparse sample set;
  • Using the quaternal trees (Samet, 1990) to store gray level images is not efficient. For the thematic map case, although it is used in at least one commercial system (SPANS), the gain is not considerable;
  • The use of R-trees (Gutman, 1984) or V-trees (Mediano et al., 1994) is only efficient when it is completed by search algorithms and procedures that use the properties of these structures.

Overview of Modeling Process

Summary

To better understand the relations among the different universes (levels) in the model, the table bellow presents several entity examples from the real world and their correspondence in the model.

Correlations among model universes
Real world universe Conceptual Universe Representation Universe Implementation Universe
Vegetation map Thematic Geo-field Thematic Image Planar Sub Division 2D Matrix 2D Lines (with R-Tree)
Altimetric map Numeric Geo-field Regular Grid, Triangular Grid, 3D Points Set, Contour lines Set 2D Matrix, 2D Lines and 3D Nodes, 3D Points (KD-tree), 2D Lines
Urban lots Geo-objects
Map of lots Cadastral Planar Sub Division 2D Lines (with R-Tree)
Electric network Network Oriented Graph 2D Lines(with R-Tree)

Overview of Modeling Process