Automatic generation of puzzle tile maps for spatial-temporal data visualization

Highlights

• Puzzle tile map is a static 2D representation for visualizing spatial-temporal data.

• The mapping method of tiles considers not only geographic positions but also orientation of districts.

• Puzzle connection points can represent not only the order of time-series data but also the change between the quantities of two adjacent pieces.

• Generating tile maps is designed for non-contiguous geographical data specifically.

Abstract

Tile maps are a visualization tool to display geographic data without the accurate representation of geographic boundaries. Each region in a tile map is represented as a tile of identical shape and size. The tiles are fit in a regular grid at positions that approximate their geographic positions such that large regions do not dominate the map visualization, and information in small regions can be enhanced. In this study, the automatic generation of a tile map composed of puzzle tiles is proposed for spatial-temporal data visualization. A puzzle tile is an extension of a standard square tile. A sequence of connected and directional pieces in a puzzle tile is used to represent time-varying quantities in a geographic region. To generate a puzzle tile map, the proposed method includes algorithms for optimizing district-to-tile mapping according to not only geographic positions but also region orientations and for placing puzzle pieces in a tile. The proposed puzzle tile map can serve as a choropleth map in which the ordered pieces in a tile are shaded in proportion to the measurements of a statistical time variable, such as a time sequence of fertility rates, air pollution (PM2.5), or transfer of residential property, being displayed on a 2D map. Experimental demonstrations of various cases show that the proposed methods for district-to-tile mapping optimization and puzzle generation are feasible for automatic puzzle tile map generation. User studies show the capabilities of the puzzle tile map in terms of usability, readability, and comparability of spatial-temporal data visualization.

Introduction

Maps can be classified into two categories, namely, topographic maps and thematic maps. Topographic maps accurately display the location of an object in a space, and thematic maps focus on combining specific themes with maps [1]. With the development of information visualization techniques, thematic maps have elicited increasing attention in visualization and computer graphics. Tile maps are important tools in thematic cartography, and their characteristics are distinct from those of well-known tools, such as choropleths, cartograms, and symbol maps [2]. The tiles in a tile map are placed in a grid at positions that approximate their geographic positions so that each tile has an identical shape and size. Tile maps provide an easy means to visualize the level of variability within a region and how a measurement varies across a geographic area. Furthermore, complex data can be shown on tiles in a consistent format that allows users to intuitively and easily compare data among tiles, as shown in Fig. 1. Compared with choropleths, cartograms, and symbol maps, tile maps have the clear and simple appearances.

Large amounts of time-series data exist in our daily life, and these data are generally visualized by diagrams, such as line charts and heat maps [3]. Most of these time-series data contain geographic information, which is referred to as spatial-temporal data. Spatial-temporal data cannot be exposed by diagrams. Geographic information plays an important role in this type of data. Thus, how to intuitively and clearly display spatial-temporal data is a challenge that requires urgent attention. 2D choropleths with time sliders [4] and 3D choropleths [5], [6] are common means to visualize spatial-temporal data with the aid of a geographical map. Time-series data are displayed in a geographical map with the aid of time sliders to manually display time-varying quantities or 3D graphical widgets and to represent the profiles of time-varying quantities in 3D space. In their study on information availability in 2D and 3D displays [7], Smallman et al. concluded that the readability of 2D displays generally outperforms that of 3D displays because of the simplicity of 2D displays and the occlusion problem in 3D displays. Therefore, in this study, 2D graphical widgets, that is, 2D puzzle pieces, are used in tile maps instead of time sliders or 3D widgets in a geographic map. A tile with puzzle pieces in a map is called a puzzle tile map, which can show spatial-temporal data in a single and static 2D diagram.

The proposed method for generating a puzzle tile map includes algorithms to optimize district-to-tile mapping according to geographic positions and orientations and to place puzzle pieces in a tile for time-series data visualization. The resulting puzzle tiles can display spatial-temporal data in a 2D map, reveal time-varying quantities in a sequence of puzzle pieces, and facilitate comparisons of time-varying quantities among puzzle tiles. Compared with related tile map generation study [2], [8], [9], this study proposes the use of puzzle pieces to display time-series data of a region and establishes an algorithm to optimize district-to-tile mapping. The remainder of this paper is organized as follows. Section 2 reviews related work. Section 3 introduces the overview of puzzle tile map. Section 4 describes the tile map generation. Section 5 demonstrates the puzzle representation. Section 6 discusses the experimental results and user studies. Section 7 presents the conclusions and future work.