Computer-aided design of bus route maps

The bus route map is a diagram that aims to convey necessary information for map readers to find an appropriate way of moving from an origin to a destination. Design of bus route map is a complicated and time-consuming task that requires careful consideration of readability and aesthetics. This paper proposes a new computational method for designing bus route maps. The method helps us to reduce six types of undesirable elements in bus route maps, i.e., gap, shift, crossing, overlap, misalignment, and acute bend. The method consists of two phases: line layout phase determines the relative order of bus routes on each road segment and map layout phase calculates the actual position of bus routes drawn on a map. This paper applies the method to the design of bus route maps of Chiba City, Japan. The result supports the effectiveness of the method as well as reveals open topics for future research.     

Accuracy of areal interpolation: A comparison of alternative methods

This paper discusses the accuracy of spatial data estimated by areal interpolation, a process of transferring data from one zonal system to another. A stochastic model is proposed which represents areal interpolations in diverse geographic situations. The model is used to examine the relationship between estimation accuracy and the spatial distribution of estimation error from a theoretical viewpoint. The analysis shows that the uniformity in error distribution improves the accuracy of areal interpolation. Four areal interpolation methods are then assessed through numerical examinations. From this it is found that the accuracy of simple interpolation methods heavily depends on the appropriateness of their hypothetical distributions, whereas the accuracy of intelligent methods depends on the fitness of the range of supplementary data for that of true distribution. Received: 19 February 1999/Accepted 17 September 1999     

A computational procedure for joining separate map sheets

Map sheets have been often used as a basic spatial unit for managing spatial data produced from paper maps. This often results in incompatibility between adjacent map sheets, because spatial objects do not cross the boundaries smoothly and even the boundaries themselves do not match their neighbors exactly. To solve the problem this paper proposes a computational procedure for joining separate map sheets to obtain seamless spatial data. Line objects digitized separately in different map sheets are considered, which are frequently used to represent road networks, gas pipelines, and boundaries of polygon objects. The procedure consists of three steps: (1) extraction of end nodes, (2) detection of matching nodes, and (3) transformation of the map sheet. Each step goes interactively so that unexpected errors can be avoided by human observation. To test the validity of the procedure, map sheets are combined containing the road network data of Tokyo 23-ku area, Japan. This revised version was published online in July 2006 with corrections to the Cover Date.     

A PDF-based analysis of the spatial structure of retailing

The present paper proposes a new method for analyzing the spatial structure of retailing, using microscale locational data of individual retail stores. The method is based on the probability density function (PDF) of stores estimated from their locational data, and consequently it is applicable to both micro- and macro-scale retail analyses. The PDF approach provides a set of quantitative methods that permit us (1) to measure the degree of agglomeration, (2) to classify spatial patterns of store location, (3) to analyze the relationship between the size and function of retail agglomerations, and (4) to analyze the spatial structure of retail agglomeration. An empirical study is performed to test the validity of the method, and some empirical findings are shown. This revised version was published online in July 2006 with corrections to the Cover Date.     

A method for analyzing the expansion and shrinkage of point pattern

This article proposes a new method for analyzing the spatial expansion and shrinkage of point patterns. Spatial expansions of epidemic diseases and market areas are represented as the expansions of point patterns when disease cases and store customers are represented as points. The spatial expansion and shrinkage have been studied in many scientific fields. Existing analytical methods, however, are not sufficient for treating complicated spatiotemporal patterns. To answer this demand, this article develops a new method for analyzing the expansion and shrinkage of points. Three vector measures evaluate the degree and direction of expansion and shrinkage as functions of location and time. They are visualized as vector maps, which are valid for capturing the global spatiotemporal pattern as well as for discussing the local variation. Summary measures of these vectors allow us to grasp the overall spatiotemporal pattern efficiently. To test the validity of the proposed method, this article applies it to the analysis of visitors to Shinjuku and Ginza in Tokyo. The proposed measures permitted us to evaluate the spatiotemporal pattern of the visitors in detail and to consider its underlying structure from various perspectives, which indicated the soundness of the technique.     

Trajectories of Moving Objects on a Network: Detection of Similarities,Visualization of Relations,and Classification of Trajectories

Development in techniques of spatial data acquisition enables us to easily record the trajectories of moving objects. Movement of human beings, animals, and birds can be captured by GPS loggers. The obtained data are analyzed by visualization, clustering, and classification to detect patterns frequently or rarely found in trajectories. To extract a wider variety of patterns in analysis, this article proposes a new method for analyzing trajectories on a network space. The method first extracts primary routes as subparts of trajectories. The topological relations among primary routes and trajectories are visualized as both a map and a graph‐based diagram. They permit us to understand the spatial and topological relations among the primary routes and trajectories at both global and local scales. The graph‐based diagram also permits us to classify trajectories. The representativeness of primary routes is evaluated by two numerical measures. The method is applied to the analysis of daily travel behavior of one of the authors. Technical soundness of the method is discussed as well as empirical findings.     

A method for evaluating the degree of spatial and temporal avoidance in spatial point patterns

Journal of Geographical Systems - This paper develops a new method for evaluating the degree of spatial and temporal avoidance in spatial point patterns. We consider point patterns that change over...     

Analysis of the relations among spatial tessellations

A spatial tessellation is a set of regions that are collectively exhaustive and mutually exclusive except for the boundaries. In geographical analysis, it may represent such administrative units as census tracts, postal zones, and electoral or school districts. Spatial tessellations of a certain area are often closely related to each other. Areas of local communities are related to school districts, market areas of retail stores, and administrative units. Postal zones and census tracts are determined by collecting or dividing administrative units. Analysis of such relations among tessellations often reveals their underlying spatial phenomena. To this end, this paper proposes a new exploratory method for analyzing the relations among spatial tessellations. It aims to detect spatial patterns, especially those with a hierarchical structure, and to provide a tessellation classification scheme. Topological relations and similarity measures are introduced to evaluate the relations between tessellation pair. For more tessellations, tree representations are proposed. These not only visualize relations, but also provide a means of classifying tessellations. The method is applied to the analysis of two sets of spatial tessellations: one with five hypothetical tessellations, and another with 34 candidate plans for the new Doshusei administrative system in Japan. The application reveals the properties of the method and quantitative measures used in analysis.     

Accuracy of quantized Voronoi diagrams

Quantization of spatial objects, which usually means vector‐to‐raster conversion in GIS and remote sensing, is a basic operation used for handling spatial data from data creation to visualization. Since quantization is an approximation of spatial objects, it inevitably yields errors in measuring their properties such as area, perimeter, diameter, and so forth. This paper discusses the accuracy of a quantized Voronoi diagram, a spatial tessellation generated from a set of points. A measure is proposed to evaluate the accuracy of the area of Voronoi regions calculated after quantization. In one‐dimensional space the measure is expressed as an explicit function of the expected number of generators in a cell. In two‐dimensional space, on the other hand, the measure is defined by an implicit function, whose approximation is derived in an explicit form. These functions permit us to evaluate the accuracy of quantization in relation to the size of lattice cells and the density of Voronoi generators. This leads to an appropriate choice of a lattice to keep the quality of a quantized Voronoi diagram at a desirable level.