Computing the Fewest-turn Map Directions based on the Connectivity of Natural Roads

In this paper, we introduced a novel approach to computing the fewest-turn map directions or routes based on the concept of natural roads. Natural roads are joined road segments that perceptually constitute good continuity. This approach relies on the connectivity of natural roads rather than that of road segments for computing routes or map directions. Because of this, the derived routes posses the fewest turns. However, what we intend to achieve are the routes that not only possess the fewest turns, but are also as short as possible. This kind of map direction is more effective and favorable by people, because they bear less cognitive burden. Furthermore, the computation of the routes is more efficient, since it is based on the graph encoding the connectivity of roads, which is significantly smaller than the graph of road segments. We made experiments applied to eight urban street networks from North America and Europe in order to illustrate the above stated advantages. The experimental results indicate that the fewest-turn routes posses fewer turns and shorter distances than the simplest paths and the routes provided by Google Maps. For example, the fewest-turn-and-shortest routes are on average 15% shorter than the routes suggested by Google Maps, while the number of turns is just half as much. This approach is a key technology behind FromToMap.org - a web mapping service using openstreetmap data.Comment: 12 pages, 5 figures, and 4 tables, language editing, some significant revisions, missing references adde

Defining and Generating Axial Lines from Street Center Lines for better Understanding of Urban Morphologies

Axial lines are defined as the longest visibility lines for representing individual linear spaces in urban environments. The least number of axial lines that cover the free space of an urban environment or the space between buildings constitute what is often called an axial map. This is a fundamental tool in space syntax, a theory developed by Bill Hillier and his colleagues for characterizing the underlying urban morphologies. For a long time, generating axial lines with help of some graphic software has been a tedious manual process that is criticized for being time consuming, subjective, or even arbitrary. In this paper, we redefine axial lines as the least number of individual straight line segments mutually intersected along natural streets that are generated from street center lines using the Gestalt principle of good continuity. Based on this new definition, we develop an automatic solution to generating the newly defined axial lines from street center lines. We apply this solution to six typical street networks (three from North America and three from Europe), and generate a new set of axial lines for analyzing the urban morphologies. Through a comparison study between the new axial lines and the conventional or old axial lines, and between the new axial lines and natural streets, we demonstrate with empirical evidence that the newly defined axial lines are a better alternative in capturing the underlying urban structure. Keywords: Space syntax, street networks, topological analysis, traffic, head/tail division ruleComment: 10 pages, 7 figures, and 2 tables, one figure added + minor revisio

The implications of the “palimpsest” of the grids of the main city of Piraeus on creation, transmission and application of cognitive knowledge

This research aims to investigate the local rules and constraints which govern the individual behaviours of the pedestrians of Piraeus, Port of Athens, Greece, by examining the relationship between the spatial syntax of mental representations and the spatial syntax of the environment. The overlaid urban grids of the main city create a “palimpsest” on which the mental spatial models of the users are constructed. Invoking three different criteria, three experiments were conducted in the city’s key-locations – Peraiki Coast, Mikrolimano and Sotiros Dios St. The first criterion concerned people’s access to spatial information (target locations that are out of sight vs. locations with visual access). The second and the third criterion concerned the types of the reference systems; egocentric vs. allocentric and global vs. local scale respectively. The configurational, geographical and topological characteristics of the peninsula provide rather an ambiguous sense of the ease or difficulty of the cognitive understanding of the site. Using syntactical tools of space syntax methodology (axial maps, visibility graphs, isovists) and descriptive statistics (mean averages, deviation averages, z-test, central limit theorem test) in the experiments, the close relation between the concepts of intelligibility, spatial configurations and visuospatial representations is demonstrated. The information provided to the pedestrians has an impact on their wayfinding and navigation processes. It is concluded that the cognitive knowledge of the pedestrians of Piraeus (etymological "the place over the passage") is created, transmitted and applied by the geometrical forms of the city, the morphology of the local visual field – which involves issues of configuration and scale of a space layout – and by topological relations. The most ancient grid although it contains the elements that have shaped the city’s contemporary urban space, are not easily recognisable by “strangers”, but they are mostly found in “inhabitants’” internal representations. On the contrary, the elements from the modern times are more frequently cited and they appear to dominate the cognitive model of all users

On the right track : comfort and confusion in indoor environments

Indoor navigation systems are not well adapted to the needs of their users. The route planning algorithms implemented in these systems are usually limited to shortest path calculations or derivatives, minimalizing Euclidian distance. Guiding people along routes that adhere better to their cognitive processes could ease wayfinding in indoor environments. This paper examines comfort and confusion perception during wayfinding by applying a mixed-method approach. The aforementioned method combined an exploratory focus group and a video-based online survey. From the discussions in the focus group, it could be concluded that indoor wayfinding must be considered at different levels: the local level and the global level. In the online survey, the focus was limited to the local level, i.e., local environmental characteristics. In this online study, the comfort and confusion ratings of multiple indoor navigation situations were analyzed. In general, the results indicate that open spaces and stairs need to be taken into account in the development of a more cognitively-sounding route planning algorithm. Implementing the results in a route planning algorithm could be a valuable improvement of indoor navigation support

All Paths Lead to Rome

All roads lead to Rome is the core idea of the puzzle game Roma. It is played on an $n \times n$ grid consisting of quadratic cells. Those cells are grouped into boxes of at most four neighboring cells and are either filled, or to be filled, with arrows pointing in cardinal directions. The goal of the game is to fill the empty cells with arrows such that each box contains at most one arrow of each direction and regardless where we start, if we follow the arrows in the cells, we will always end up in the special Roma-cell. In this work, we study the computational complexity of the puzzle game Roma and show that completing a Roma board according to the rules is an \NP-complete task, counting the number of valid completions is #Ptime-complete, and determining the number of preset arrows needed to make the instance \emph{uniquely} solvable is $\Sigma_2^P$-complete. We further show that the problem of completing a given Roma instance on an $n\times n$ board cannot be solved in time $\mathcal{O}\left(2^{{o}(n)}\right)$ under ETH and give a matching dynamic programming algorithm based on the idea of Catalan structures

Graph Theory Applications in Advanced Geospatial Research

Geospatial sciences include a wide range of applications, from environmental monitoring transportation to infrastructure planning, as well as location-based analysis and services. Graph theory algorithms in mathematics have emerged as indispensable tools in these domains due to their capability to model and analyse spatial relationships efficiently. This article explores the applications of graph theory algorithms in geospatial sciences, highlighting their role in network analysis, spatial connectivity, geographic information systems, and various other spatial problem-solving scenarios like digital twin. The article provides a comprehensive idea about graph theory's key concepts and algorithms that assist the geospatial modelling processes and insights into real-world geospatial challenges and opportunities. It lists the extensive research, innovative technologies and methodologies implemented in this domain

ANALYSIS OF SPACE, COGNITION AND PEDESTRIAN MOVEMENT

Understanding the movement of people in urban areas is one of the most significant issues on spatial science with a wide range of applications in urban design, public health, public safety and intelligent transportation system. Urban planners, cognitive scientists, computer engineers, and geographers have contributed to an understanding of pedestrian movement from aspects of configurational analysis, knowledge representation, computational models, and space-time patterns respectively. However, no previous studies provide comprehensive solutions to pedestrian movement taking both space and cognition into account. Combining these disciplines allows us as researchers to not only explain correlations between spatial layouts and pedestrian flows but also understand how and why environmental perception and spatial knowledge are used by pedestrians to orient themselves and navigate through space. My research proposes a theoretical framework of space, cognition and movement to fill in interdisciplinary gaps of pedestrian movement studies. The core of this framework lies in the hypothesis that where people choose to hold activities and how people choose to get there depends on individuals’ cognitive maps of the environment. This cognitive map consists of the salient layout of spatial features as well as the prominent utilities afforded by these features. The analysis proceeds from three dimensions: (1) space syntax to characterize spatial configuration or structure, (2) space semantics to address the distribution of activities, and (3) spatial cognition to capture one’s knowledge about the space. The proposed framework was used to guide an empirical study conducted at the University of Oklahoma Norman Campus. Space was characterized by two aspects of space syntax and space semantics. For syntactical analysis, the study not only used measures of network centrality to examine network effects on pedestrian movement but also improved them by varying concepts of distance, adding distance decay effects, and weighting spatial heterogeneity of activities. Betweenness centrality calculated by the shortest length and weighted by distance decay effects resulted in the best description of observed pedestrian flows. In semantical analysis, functional centrality was described by density and diversity. Only functional density significantly contributed to modeling pedestrian flows. This study provided evidence that pedestrian movement depended on the spatio-functional interactions. The distribution of activities not only took the location advantage provided by spatial configuration but also reinforced network effects on pedestrian movement. This study not only examined aggregated patterns of pedestrian movement but also investigated individual variations in cognitive maps and wayfinding behaviors. The sketch map analysis suggested that as people became more familiar with the environment, the increase of completeness and accuracy was observed in their cognitive maps. Completeness was described by number of landmarks in sketch maps while accuracy concentrated on the relative positions between pairs of landmarks. Landmark served as the organizing concept of cognitive map. Betweenness centrality, functional density, and familiarity significantly contributed to modeling the presence of landmarks. When landmarks were used in navigation, this study developed a landmark-based pathfinding method. Landmark-based pathfinding resulted in a better description of routes selected by survey participants. In sum, individual cognitive maps, particularly the organization of landmarks, serve as the core in determining where pedestrians choose to hold activities and how to get there. Finally, the study developed the conceptual agent-based model (ABM) for pedestrian movement. The core of this ABM lies in a cognizing agent that is able to solve pathfinding tasks based on perceptual information and knowledge of cognitive map. The research outcomes not only improve the understanding of spatial and cognitive factors on pedestrian wayfinding but also contribute to several disciplines. Architects and urban planners can adopt the framework of pedestrian movement to test, assess and improve existing spatial layouts and possible design alternatives. Computer scientists and Geographic Information System developers can use the specification of cognitive map to implement landmark based navigation system. Cognitive scientists and psychologists can apply the comprehensive model of pedestrian movement in research on human wayfinding behaviors for people with different perceptual abilities