® Sponsored by Navigation in Urban Areas 98th OGC Technical Committee Washington, DC USA John R. Herring 8 March 2016 Copyright © 2016 Open Geospatial Consortium

OGC ® Seven Bridges of Königsberg 1736: St. Petersburg, Leonard Euler presented a negative solution to walking the seven bridges each only once – inventing graph theory and topology. 1893: Poincare, in algebraic topology proofs, describes dual graphs. 1959: Dijkstra’s published a shortest path algorithm for graphs. Copyright © 2016 Open Geospatial Consortium : Hart, Nilsson & Raphael heuristics to improve Dijkstra’s algorithm performance; A* (A star) 2005: “ISO — Tracking and navigation” describes multimodal networks using transfer nodes (nodes in multiple transport networks) 2014: IndoorGML use dual graphs to create Indoor Navigation graphs 2014: i-locate.eu (G. Conti, Trilogis) puts it all together in a system design for seamless indoor- outdoor navigation (among other issues).i-locate.eu 2

OGC ® Directed, Weighted Graphs Nodes Points where edges meet. Directed Edges Paths between from one node to another Each edge has two, but if the edge is “one-way”, only the navigable one is in the graph Copyright © 2016 Open Geospatial Consortium Weights Numeric weight: the “cost” of traversing a directed edge Weights are not always equal for different directions. Common units are time, distance or cost/money 3

OGC ® Example table for previous graph EdgeStartEndW e1n1n e1n2n1100. e2n2n e2n3n275. e3n4n1180. e4n5n2200. e5n3n650. e6n4n e6n5n475. Copyright © 2016 Open Geospatial Consortium EdgeStartEndW e7n5n650. -e7n6n565. e8n4n7123. e9n8n5180. e10n9n6150. e11n7n8100. e12n8n e12n9n850. 4

OGC ® Dijkstra's algorithm Finds shortest paths (weights) from one node to another. –The base algorithm is exhaustive. “A*” variant uses a lower bound distance function between nodes such that d(n1,n2) ≤ path-length(n1,n2). –Most distancenavigation algorithm use A* with “d” geodesic distance Dijkstra's algorithm is well and often documented –Wikipedia article on it is accurate. The best-practice navigation optimization is the use of Dijkstra or A* with variations on “distance”, “time” or “cost”. –e.g. Google Maps on transit routes takes “transfer time” into account for metro routes (as least suggested by “backward engineering”) Copyright © 2016 Open Geospatial Consortium 5

OGC ® Multi-Modal = Linked Graphs Multimodal navigation essentially uses “co- located” “transfer nodes” on both modal networks. In cases where multiple “transfer” are possible, the metrics need to be on a common basis. Copyright © 2016 Open Geospatial Consortium 6

OGC ® Poincaré duality (1893) dual graphs The Poincaré dual of a “face-edge-node” graph –face to node –node to face, –boundary edges to adjacency linkages Area-boundary-area navigation becomes node-edge-node navigation Adjacency graph becomes connectivity graph by keeping only “accessible” link (with doors) Thiessen polygons ↔ TIN Copyright © 2016 Open Geospatial Consortium 7

OGC ® Polygon skeleton (1877, 1995,…) Indoor GML 2014 Rooms: –centers, points of interest; doors; entry and thresholds; –connectors: elevators, stairs Transfer Node: –entry or network threshold; should link to “address” Copyright © 2016 Open Geospatial Consortium ⇉ 8

OGC ® Multi-Modal Networks (2005) Combine network by use of common transfer nodes. Building ↔ Walkways ↔ Roads ↔ Railroads Bus/train/metro stations /stops and Building entrances act as Transfer nodes in a multimodal systems Location by GPS or WiFi. Copyright © 2016 Open Geospatial Consortium 9

OGC ® Proof of concepts & System Design: Indoor/outdoor location and asset management through open geodata; (2014-present) –i-locate: –Designs, Open source implementations, Pilots –Blog from OGC: OGC members involved: –Giuseppe Conti, Trilogis (Project Coordinator) –Prof. Ki-Joune Li, Pusan National University (IndoorGML) Copyright © 2016 Open Geospatial Consortium 10

OGC ® Question s? Copyright © 2016 Open Geospatial Consortium 11

OGC ® Copyright © 2016 Open Geospatial Consortium Extra Slides from I-locate

OGC ® Objective: to create a «virtual hub» for indoor/outdoor mapping 13

OGC ® Provision of interoperable indoor/outdoor LBS Web- and mobile-based visualization and management of open indoor GI Crowdsourcing-oriented provision of open GI regarding indoor/outdoor spaces Open communication interfaces (open standards) Scalability Objective: development of open source i-locate toolkit 14

OGC ® Delivery of the toolkit 15

OGC ® Delivery of the “virtual hub” 16

OGC ® Screenshots of i-locate mobile client 17

OGC ® Interconnecting indoor – outdoor: the concept Entrance of the building is a special node – anchor point where outdoor and indoor networks are connected 18

OGC ® i-locate indoor/outdoor routing 19 Based on the OpenTripPlanner (OTP) open-source platform for multimodal routing It supports multiple indoorGML graphs and outdoor OpenStreetMap data Deployed at: Routing service Routing algorithm Navigation graph Indoor Graphs Outdoor Graphs indoorGML OpenStreetMap Multimodal routing Avoidance setting Etc. Start/end locations (latitude/longitude/level) Travel plan (with turn-by-turn navigation information)

OGC ® Handling of IndoorGML 20 Allows: Arbitrary file upload by portal users File download by other toolkit components – useful for indoor maps and metadata IndoorGML download by routing component User provided files I-Locate Portal Upload / Download component Routing subsystem Client Application Maps, metadata Navigation Graph (IndoorGML) Route