GIS AND SCHEMATIC MAPS: A NEW SYMBIOTIC RELATIONSHIP

Daniel Elroi
City of Los Angeles
Planning Department
200 N. Spring St., 561K
Los Angeles, CA 90012

ABSTRACT

The creation of schematic maps for networks such as subway trains and electrical distribution systems is a laborious manual task. Topology, which is inherent in vector GIS database structures, makes it possible to automate the process of schematization. This potential can add new dimensions to a neglected cartographic product-type. More significantly, it can provide GIS users with a simplified visual display of complex networks, without loss of feature attribute integrity or the ability to perform geographic analysis. More efficient graphic interpretation and interaction in GIS applications where interactive use is of prime importance are suggested. The paper describes schematic maps and their advantages, then explains how they are produced. Options for the automation of these procedures are summarized. The option of using a GIS is expanded upon, and a prototype schematization package built around ARC/INFO as a student research project is delineated. Examples of possible applications of schematization in GIS are discussed, concentrating on public and commercial transportation networks and on driver support systems. Finally, applications developers are challenged to pursue this new symbiotic relationship further.

INTRODUCTION

Schematic maps are a cartographic genre which receives little attention in traditional mapping, and even less attention in GIS. This paper stems from a research project carried out at UCLA, in which the possible unidirectional benefit of GIS to the production of schematic maps was explored. In the process it became apparent that the relationship is reciprocal, and therefore significant to the study of GIS in addition to that of cartography. These maps extract and display the basic functional essence of networks by abstracting network reality into a cartographic caricature, and can therefore improve user interaction in GIS network applications.

This paper describes the design and advantages of schematic maps. It lists the steps needed to create such maps in the traditional fashion, and suggests ways to automate these steps. Following a delineation of one such automation technique, the paper concludes with a variety of applications that schematic maps can have in GIS.

A DESCRIPTION OF SCHEMATIC MAPS

Schematic maps are linear abstractions of functional networks. A functional network can be broadly described as a set of interlinked paths in geographical space through which tangible objects can flow. Roads, railways, shipping lanes and footpaths are functional networks. In schematic map design most areal features are eliminated, and scale and linear details are sacrificed in order to clarify the operational relationships in the represented networks. In subway maps--the most common application of schematic maps--only line and point features are usually to be found. Stations are represented by points and all the possible ways of making connections between stations are represented by lines. The general relative spatial positioning of the stations is shown, but most other features are omitted.

Figure 1. The River Thames is the only non-network feature on this London subway map

Topology is defined as "...the properties of geometric forms that remain invariant under certain transformations, as bending, stretching, etc…." (Random House College Dictionary, 1980). Schematic maps are graphic representations of this property, which is the very essence of networks. Since topology is an internal property these maps are fairly useless as means for interaction with networks from external perspectives (e.g. in helping to locate a subway station within a street network, using a subway map). But they are excellent in assisting the grasping of, and navigation through networks. This is particularly true where the users have little control over their passage through the networks between nodes, such as in a subway or airline network (Waldorf 1979). For all the sinuations that trains or airplanes might make between destinations, the only relevant data for users, once the network has been entered, are the general directions to be taken (e.g. the northbound train) and the proper points of transfer (e.g. switch to Delta Airlines in St. Louis). In that sense schematic maps closely mimic the way we store information about our physical environment, as cognitive maps (Waldorf 1979). These mental maps go through many processes before they are called upon to direct us through our daily interaction with our surroundings: perception, filtration, interpretation, rationalization and recollection. Accurate geographical locations become summarized as sets of references: "Building A is about west (or left) of Building B, and quite a bit north (or up above) Building C, but is best reached from Building C because the path is better lit at night." Schematic maps are analogous to these instructions (Mac Eachren 1987).

Figure 2. Verbal directions are interpreted and stored as mental maps. The transformation to a schematic map is simple

Similar logic would infer that schematic maps can be easily translated in our minds back from graphic representations to verbal instructions: "Drive northwards of Town X as far as Town A, then switch to the route that goes eastwards towards Town R, past three towns, until you reach Town F."

Figure 3. Schematic maps can be easily transferred to mental image maps and back to verbal instructions

In summary, it can be said that schematic maps show the topology of networks in simplified form. They allow users of such networks to quickly discern the relationships between nodes and their connecting arcs, and to translate that data into sequential instructions. The networks most amenable to such treatment are those where users have very few options to exercise between nodes, but where relatively large numbers of options are offered at those nodal points (intersections). This short description of schematic maps should help to explain their suitability and prevalent use for transportation networks, notably of subways, main line railways and buses, as well as of some road networks.

THE PRODUCTION OF SCHEMATIC MAPS

The use of schematic maps can be traced back to Roman times. Most of the earlier maps were of the strip map subclass which depicted routes in linear form. The Peutinger Table is believed to be an eleventh or twelfth century copy of the earliest known strip map, dating back to third century Rome (Mac Eachren 1987). However, though schematic maps have persisted since then, only a negligible amount of work has been written about them, and the process by which they are produced has never been codified. According to Petchenik (1974) "... style emerges when many examples have some recognizable and widely accepted visual similarity." Waldorf (1979), in an excellent and solitary study of schematic maps, identified four steps necessary to duplicate this style:

1. Eliminate all features that are not functionally relevant
2. Eliminate any networks (or portions of networks) not functionally relevant to the single system chosen for mapping
3. All geometric invariants of the network's structure are relaxed except topological accuracy
4. Symbolize routes and junctures abstractly

This author has expanded on the graphic manipulations that need to be performed (Elroi 1988):

1. Simplify lines to their most elementary shapes
2. Re-orient lines to conform to a regular grid, such that they all run horizontally, vertically or at a forty-five degree diagonal
3. Expand scale in congested areas at the expense of scale in areas of lesser node density

Figure 4. Simplification of lines

Figure 5. Conformity to a regular grid

Figure 6. Differential scale adjustment

Each step is optional but builds on the one previous to it. Inasmuch as schematic maps caricaturize reality, the cartographer may take great liberties with manipulating the image in order to achieve graphic clarity. The correct topology of the network, however, must be preserved at all times, for without it the entire principle of these maps is lost. It is for these reasons that the manual manufacture of schematic maps from originally planimetrically-correct network maps is very time consuming. For example, in the 1970s an amateur cartographer, Bob Hickman, experimentally re-drew the Paris subway map, which is traditionally only nominally schematicized. The new map, which in resembling the London subway map was superior in clarity and cartographic quality, took over 300 hours to accomplish (Observer circa 1978). A more recent map, Rand McNally's Southern California Freeways map, although previously compiled and simplified, nevertheless took over 75 hours to nominally schematicize (Purvis 1988). It is the lack of documentation and standardization in this subject, as well as the amount of effort that it demands, which has made this cartographic product scarce at any given time.

AUTOMATION OF THE SCHEMATIZATION PROCESS

Much graphic and cartographic work has been computerized in the past two decades, and it is now possible to apply this knowledge to the schematization process. Four actual schematization routes can be proposed: manual graphic, mechanical, interactive using CAD, and batched using GIS. The first is an iterative method, whereby the cartographer searches for the most pleasing solution graphically, adjusting and readjusting the network until it has reached a satisfactory state without loss of topology. This is the accepted method, and is quite simply too labor-intensive. Next is an untested mechanical method whereby the planimetrically-correct network is duplicated with colored elastic strings over a matrix pegboard. Pegs are then inserted into each resultant polygon and shifted around for the best result. This device may be difficult to implement but it does provide a regular matrix background as well as the ability to eliminate line details easily, and helps to assure that topology is maintained. The third method is the interactive use of a CAD system. The raw network can be easily digitized and then schematicized. Whereas this is still an iterative procedure of trial and error attempts , results can be obtained quickly, previous attempts stored, and output to paper can be easily arranged. This method, however, cannot provide a means for checking that topology remains intact. It would therefore require just as much visual scrutiny and iteration as the manual method, and would not be amenable to batch automation.

The fourth method involves the use of a GIS system. Vector structures in GIS inherently contain the means for recording topology. Therefore, GIS provides the most important tool for creating schematic maps, which as stated previously, are in themselves graphic representations of topology. A typical arc file in GIS would list the to- and from-node numbers, and the right- and left-polygon numbers. Another way in which topology is recorded is as the sequence in which arcs describe polygons. Therefore, if during an attempt at schematization a loss of topology is detected, the attempt can be aborted and another one initiated. It is this ability to check topological integrity during schematization which permits the iterative process to be performed in batch mode and therefore be automated.

This theory was put to the test as a student project which was performed by this author at UCLA in 1987 (Elroi 1988). A prototype software enhancement package--SCHEMATIC--for the ARC/INFO GIS product was designed with the intention of examining the possibility of automating the schematization process. Structurally, the package consists of an interactive portion and a batched portion. The former is divided into a standard ARC/INFO digitizing and graphic editing section, and into a short session allowing the user to specify the range of schematization parameters he or she wishes the program to attempt in the batched portion. The iterative schematization process itself which attempts to obtain the optimum amount of schematization is highly CPU intensive, and is therefore carried out in batched mode. It is controlled by a set of topology checking algorithms which were written specifically for this project, but which in the long run may prove useful in other GIS database quality control procedures. The schematization procedure consists of a line simplification algorithm, as well as an ARC/INFO command which moves nodes to the location of the nearest nodes on a background control grid, if such nodes occur within a specified search distance. This distance, as well as the parameter for the simplification algorithm, are given a range and an increment by the user, and the program progresses through each increment, until one of the topology checks fails. The final product is then manipulated further in an interactive editing session, to assure conformity to a horizontal-vertical-diagonal grid format, and to add stations and annotation.

The most relevant result yielded by SCHEMATIC is that it is possible to automate the schematization process and to reduce the amount of human effort involved by between seventy and ninety percent. It yet remains to be determined which is the best method for schematization and the appropriate range of parameters to be used in the process. But the assumption that vector-based GIS is well suited for this task was proven correct.

THE BENEFITS OF SCHEMATIC MAPS FOR GIS

The obvious and immediate benefit of the ability to automate the schematization process is that more members of this cartographic genre might now be produced. Therefore it is possible that more schematic maps will be used in transportation systems, site location guides, and so forth. Realistically speaking, however, such a supposition may be a mere intellectual exercise, due to the cost of developing this software ability up to a commercial standard, if the only benefit was the publication of a few more printed maps. Where the true benefit can be realized is in the incorporation of the schematization process to the proliferating numbers of GIS network applications.

Currently there is much interest and research being directed at networks, outside of GIS. Software is being written to assist in transportation network planning, scheduling, dispatching, case and load tracking, resource allocation, and emergency preparedness, to name the major fields. Geographical data for these networks is today, for the most part, obtained from CAD-produced maps. These are unidirectional relationships, where the map is used to provide data such as the shortest distance between points to the analytical portion of the software, which then absorbs this information and proceeds independently of the geo-database. As more people realize the potential of GIS for continuous interaction between the user, the graphic environment, the database and the algorithms, it is predicted that more network applications will utilize GIS rather than CAD systems. As a result, users will execute more sessions involving interaction with the graphic display in order to reach decisions. Where the mapped networks are of a complex and congested nature, it is suggested here that schematic displays will be able to greatly assist in such interactions. Six possible applications are discussed below.

Many network software functions deal only with inter-nodal relationships and interactions, i.e. linkages. As mentioned earlier in the paper, it is often only relevant that package X will be transferred from City A to City B, where Agent C will hand carry it to City D. The nature of the route is immaterial once the package is on its way. Of greater importance is the ability to pick out the route between A and B clearly on a map, where these might be two cities in the dense East Coast Megalopolis, or two towns in the sparse High Plains. Schematic maps can simplify this task by providing an alternative display, in place of the map originally digitized into the database. GIS allows for this option by enabling arc attributes on the original map to be attached to those on the display map, so that the user can reference database attributes through the simplified display. Schematic distortion is by this method transparent to the analytical tools of the GIS, which will continue to use the original attributes. Easier comprehension and faster response time are facilitated by providing only the barest details necessary for comprehension and only those elements that explain the functional topology of the network, and by expanding the scale in congested areas at the expense of scale in sparse areas.

Figure 7. The user bypasses the graphic database but has
full access to the attribute database

A 1984 issue of The Logistics and Transportation Review listed at least eight microcomputer based dispatching and route planning software packages for the trucking industry (Anderson 1984). Numerous trucking and railway companies are now adopting such computerized dispatching and load tracking systems. Just as subway systems are characterized by dense concentrations of lines and stations in downtown areas, so do trucking routes converge on major cities. As a result lines which represent these routes tend to coalesce when the whole network is displayed at one scale and on one map. An acceptable solution would be to provide inset maps for these areas, but this would clutter the map when a large number of insets is included. Dr. A. J. Horowitz of the University of Wisconsin has developed a transportation network design software, the General Network Editor (Horowitz 1987). According to Horowitz "it is only important that the visual representation be sufficiently heterogeneous so that the user can readily identify what each graphical element in the network is supposed to be." Therefore, by expanding the scale in those areas, and by straightening all lines and aligning them with a grid, the schematic map solution simplifies differentiation between route options and destination locations.

In Canada and Britain computer systems are being experimented with, which produce individualized road and transportation network maps (Magnenat-Thalmann 1982, Robb 1987). Since they are designed to assist the user in travelling only to specific destinations, it is possible that these maps would be more easily used by travelers if they were schematicized. Of course, the less homogeneous the networks and the more route selection choices that are available, as in the case of a drive through the British countryside, the less effective such simplified maps would be. Expressway or freeway travelers, on the other hand, would find such maps useful, since not unlike travel in a train, route selections are few, and errors can be rectified in a straightforward way.

Both the British system referred to above, known as CARTRIPS, and a non-cartographic system operated by the Automobile Association of Great Britain provide computerized sets of directions for reaching user-selected destinations. The recommended routes are based on drivers' choices of the fastest, shortest, or most scenic routes (Robbins 1986). Both provide road numbers and travel distance on each road, and in the case of the non-cartographic system, also furnish signpost information and other landmarks. Instructions such as "turn left at the second light," "bear right," or "go south ten miles," which these systems provide can be easily translated into the type of linear features used in schematic maps (see Figure 2). Therefore, any further developments of direction-giving software might include a schematic output option as well.

Another possible application relates to a standard planning tool. This is the semi-cartographic representation of traffic volumes using lines of varying thicknesses to represent major arteries. It should not require much elaboration to explain how a schematic display may improve the clarity and speed with which such diagrams can be produced, while the analytical powers of the GIS can automatically calculate and allocate the line thicknesses. Successful attempts have already been made to automate this procedure, but they lack the simplified display technique described here.

It can be suggested that even users who are very familiar with a certain network may yet benefit from the schematic option. During a flood, for example, when major road closures are relayed to an emergency preparedness center, ambulance drivers can be given quickly-produced schematic printouts of the best available routes. Since the drivers are already well familiar with the road network, a simplified map will be sufficient to provide the vital information needed. Unlike the hapless British motorist mentioned above, extensive side street detail need not be provided since these drivers do not need much assistance in the unlikely event that they get lost.

With all the possible applications suggested above, it can be argued that such systems would be easier to implement in the typical American city which is nearly schematic by design, than in the more tangled European cities. Whereas it is true that the latter may pose a greater technical challenge for schematization, it can be countered that the more complex a network, the more it calls out for simplification. This is one of many arguments which will have to be postponed until these applications are experimented with, an eventuality that hopefully will occur as a result of this paper.

CONCLUSIONS

Schematic maps, resembling flow charts in computer programs and in organizational management, help people navigate through complex but homogeneous networks. Whether of roads, railways or air routes, these maps abstract linear features until they bespeak only of their function, not their location. The tedious and unpopular manual method of schematization, although not previously codified, can be broken into a set of tasks. And as with most manual tasks that can be described in such a way, schematization too can be computerized and thus be made more easily available. This is most effectively achieved with the graphic and analytic capabilities of a vector-based Geographic Information System in which topology--the inviolate component of networks--is inherent and easily addressed. This has been demonstrated by the SCHEMATIC enhancement package for ARC/INFO.

Schematic maps can prove to be important for user interface in interactive GIS applications, as well as for an array of cartographic GIS products. The vast amount of data that can be associated with networks in GIS is invaluable for analysis and interpretation, but is not necessarily beneficial to the presentation of the results of these analyses or of the networks themselves. Schematic maps can, in many instances, provide the solution that has until now gone largely untried. Movements through complex systems can be easily traced, connections quickly compared, and destinations located with this method of display. The technique can only he applied in certain circumstances, but for those cases it is worth weighing the possibilities.

Probably no memorable mentions will be made of those who decide to pursue this research further, but it is important for this author to share his opinions with like-minded individuals in the field. If an interest can be inspired in one who has the facilities to carry these thoughts further, then this paper has served its purpose. And if all it can do is expose a few more people to an aspect of cartography which has rarely been written about, then too has it been worth the effort.

REFERENCES