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Chapter 7 Force-Directed Layout with Mental Kent Academic Repository Full text document (pdf) Citation for published version Chivers, Daniel (2014) Improving Automated Layout Techniques for the Production of Schematic Diagrams. Doctor of Philosophy (PhD) thesis, University of Kent,. DOI Link to record in KAR https://kar.kent.ac.uk/50750/ Document Version UNSPECIFIED Copyright & reuse Content in the Kent Academic Repository is made available for research purposes. Unless otherwise stated all content is protected by copyright and in the absence of an open licence (eg Creative Commons), permissions for further reuse of content should be sought from the publisher, author or other copyright holder. Versions of research The version in the Kent Academic Repository may differ from the final published version. Users are advised to check http://kar.kent.ac.uk for the status of the paper. Users should always cite the published version of record. Enquiries For any further enquiries regarding the licence status of this document, please contact: [email protected] If you believe this document infringes copyright then please contact the KAR admin team with the take-down information provided at http://kar.kent.ac.uk/contact.html IMPROVING AUTOMATED LAYOUT TECHNIQUES FOR THE PRODUCTION OF SCHEMATIC DIAGRAMS A THESIS SUBMITTED TO THE UNIVERSITY OF KENT IN THE SUBJECT OF COMPUTER SCIENCE FOR THE DEGREE OF DOCTOR OF PHILOSOPHY. By Daniel Chivers November 2014 Abstract This thesis explores techniques for the automated production of schematic dia- grams, in particular those in the style of metro maps. Metro map style schemat- ics are used across the world, typically to depict public transport networks, and therefore benefit from an innate level of user familiarity not found with most other data visualisation styles. Currently, this style of schematic is used infre- quently due to the difficulties involved with creating an effective layout – there are no software tools to aid with the positioning of nodes and other features, resulting in schematics being produced by hand at great expense of time and effort. Automated schematic layout has been an active area of research for the past decade, and part of our work extends upon an effective current technique – multi-criteria hill climbing. We have implemented additional layout criteria and clustering techniques, as well as performance optimisations to improve the final results. Additionally, we ran a series of layouts whilst varying algorithm parameters in an attempt to identify patterns specific to map characteristics. This layout algorithm has been implemented into a custom-written piece of software running on the Android operating system. The software is targeted at tablet devices, using their touch-sensitive screens with a gesture recognition system to allow users to construct complex schematics using sequences of sim- ple gestures. Following on from this, we present our work on a modified force-directed layout method capable of producing fast, high-quality, angular schematic lay- outs. Our method produces superior results to the previous octilinear force- directed layout method, and is capable of producing results comparable to many of the much slower current approaches. Using our force-directed layout method ii we then implemented a novel mental map preservation technique which aims to preserve node proximity relations during optimisation; we believe this ap- proach provides a number of benefits over the the more common method of preserving absolute node positions. Finally, we performed a user study on our method to test the effect of varying levels of mental map preservation on dia- gram comprehension. iii Acknowledgements My main thanks go to my supervisor, Dr. Peter Rodgers, for his time over the duration of my Ph.D and whose advice, guidance and support have taught me invaluable research, presentation and writing skills; without which I would not have been able to complete this thesis. I would also like to express my appreciation to my parents for their unwa- vering support and encouragement throughout my time in higher education; and to my brother Stefan, whose inspiration and guidance when I was younger helped change my perspective on education and spark a passion for knowledge. It was from following in his footsteps that I discovered the field of computer sci- ence which has lead me to where I am today. To my close friend Kristy, for her resolute belief in my abilities – far exceed- ing my own, and who encouraged me to undertake a Ph.D in the first place; and to Dr. Mole, who went though the whole process simultaneously – thanks :) I would also like to extend my gratitude to Max Roberts, Martin Nollenburg,¨ Helen Purchase, and everyone else who expressed particular interest in my work and provided valuable advice and feedback on various aspects. Finally, I would like to thank all members of the computing department, in particular my colleagues in SW104 “The Zoo”, for providing an enjoyable and rewarding working environment during my time at the University of Kent. iv Contents Abstract ii Acknowledgements iv Contents v List of Tables x List of Figures xii 1 Introduction 1 1.1 Motivation . 4 1.2 Research Goals / Contributions . 8 1.3 Statement of Publications . 9 1.4 Summary of Chapters . 11 1.5 Summary . 12 2 Background 13 2.1 Schematic Mapping . 13 2.1.1 Published Metro Maps . 14 2.1.2 The Metro Map Metaphor . 18 2.2 Graph Drawing . 21 2.2.1 Force-directed Layout . 23 2.2.2 Search-based Layout . 37 2.2.3 Additional Notes on Force-directed and Search-based Lay- out . 43 v 2.2.4 Dynamic Layout and Mental Map Preservation . 44 2.3 Automated Schematic Layout . 46 2.3.1 Topologically Correct Schematic Maps . 46 2.3.2 Octilinear Force-directed Layout . 48 2.3.3 Multi-criteria Hill Climber . 50 2.3.4 Mixed-Integer Linear Programming . 53 2.3.5 Simulated Annealing . 56 2.3.6 Path Simplification . 58 2.3.7 Focus+Context Least-Squares Conjugate Gradient . 59 2.3.8 Ant Colony System . 61 2.3.9 Curved Metro Map Layout . 63 2.4 Summary . 65 3 Improving the User Interface 67 3.1 Interface . 69 3.1.1 Draw Mode . 69 3.1.2 Move Mode . 70 3.1.3 Contextual Menu . 71 3.2 Gestures . 72 3.2.1 Minimum direct length to be classified as an edge . 73 3.2.2 Minimum straightness to be classified as an edge . 73 3.2.3 Minimum actual length to be classified as a station . 73 3.2.4 Minimum straightness to be classified as a station . 74 3.2.5 Minimum number of sharp bends to be classified as a bend point . 74 3.2.6 Minimum average radius to be classified as a junction . 74 3.3 Connections . 77 3.4 Labelling . 78 3.5 Summary . 78 4 Multi-criteria Hill Climbing Optimiser 80 4.1 Overview . 81 4.1.1 Extensions & Modifications . 81 vi 4.1.2 Definitions . 84 4.2 Pre-processing . 85 4.2.1 Swap 2-degree junctions for stations . 86 4.2.2 Add bends proportional to station counts . 87 4.2.3 Identify periphery line sections . 87 4.2.4 Align nodes to grid . 88 4.3 Main Layout Process . 89 4.3.1 Iterations and Search Distance . 90 4.3.2 Single Node Movement . 91 4.3.3 Node Clustering . 92 4.3.4 Mid-processing . 95 4.4 Layout Criteria & Objective Function . 96 4.4.1 Octilinearity . 97 4.4.2 Edge Length . 97 4.4.3 Line Straightness . 98 4.4.4 Line Straightness through Junctions (LSJ) . 98 4.4.5 Line Straightness along Peripheries (LSP) . 99 4.4.6 Angular Resolution . 100 4.4.7 Parallels . 101 4.4.8 Occlusions & Crossings . 101 4.4.9 Balance . 101 4.4.10 Topology . 103 4.4.11 Criteria Weighting . 103 4.5 Minimum Working Example . 104 4.6 Automated Label Layout . 106 4.6.1 Placement Fitness . 106 4.6.2 Label Placement . 107 4.6.3 Summary . 109 4.7 Produced Layout Example & Comparison . 111 4.8 Summary . 113 5 Exploring the Effects of Parameter Manipulation 114 5.1 Testing Procedure . 114 vii 5.2 Optimiser Performance . 117 5.3 Results – Fitness . 118 5.3.1 Grid Spacing . 124 5.4 Results – Iterations and Optimisation Time . 126 5.5 Discussion . 129 5.6 Summary . 131 6 Force-directed Octilinear Layout 133 6.1 Motivation . 133 6.2 Graphs – FDOL . 134 6.2.1 Graph Creation and Modification . 134 6.2.2 Layout . 135 6.2.3 Automated Label Placement . 138 6.3 Implementation of Octilinearity . 138 6.3.1 Grid Snapping . 138 6.3.2 Edge Rotation . 139 6.3.3 Simultaneous Force-Directed and Edge-Rotation Forces (1) 143 6.3.4 Simultaneous Force-Directed and Edge-Rotation Forces (2) 144 6.3.5 Sequential Force-Directed and Edge-Rotation Forces . 145 6.3.6 Semi-Simultaneous Force-Directed and Edge-Rotation Forces146 6.3.7 Schematic Resizing . 150 6.3.8 Auto-scaled Postponed Semi-Simultaneous Layout . 153 6.3.9 Small Edge Length Forces Using Hooke’s law . 154 6.3.10 Fine-Tuning . 156 6.3.11 Post-Processing to Further Straighten Peripheries . 156 6.3.12 Force Switchover Changes . 157 6.4 Alternate Resolution Angular Layout . 159 6.5 Results . 160 6.6 Summary . 161 7 Force-directed Layout & Mental Map Preservation 166 7.1 Delaunay Triangulation Calculation . 167 7.1.1 Circumcircle Calculation . 168 viii 7.2 Using the Triangulation as a Frame . 170 7.3 Combination with Octilinear Forces . 172 7.4 Node Oscillation in High-Strength Frames . 172 7.5 Similarity Method . 174 7.6 Frame Strength . 176.
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