{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T16:22:15Z","timestamp":1780590135565,"version":"3.54.1"},"reference-count":61,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2022,8,29]],"date-time":"2022-08-29T00:00:00Z","timestamp":1661731200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJGI"],"abstract":"<jats:p>In this paper, we take the position that cities gain to be represented as three-dimensional spaces populated by scores of micro-scale-built spaces (buildings, rooms, passageways, squares, etc.). Effective algorithms that evaluate place-based accessibility in built structures while considering the indoor spaces\u2019 complexity at a fine granularity are essential for indoor\u2013outdoor seamless urban planning, navigation, way findings, and supporting emergencies. We present a comprehensive set of spatial modeling options and visualizations of indoor accessibility for an entire built structure based on various notions of travel impedance. Notably, we consider the metric length of the paths and their cognitive complexities due to topologic, syntactic, or integrated intricacy within our approaches. Our work presents a comprehensive selection of indoor accessibility analysis with a detailed implemental discussion that can be applied as a solid foundation for smart city applications or seamless urban research and planning. The analysis and visualization techniques presented in this paper can be easily applied to analyze and visualize built interior geographic spaces to study accessibility differentials in cities with vast vertical expansion aimed at achieving (or at avoiding) specific accessibility outcomes.<\/jats:p>","DOI":"10.3390\/ijgi11090467","type":"journal-article","created":{"date-parts":[[2022,8,29]],"date-time":"2022-08-29T21:01:31Z","timestamp":1661806891000},"page":"467","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Metric, Topological, and Syntactic Accessibility in Three-Dimensional Urban Networked Spaces: Modeling Options and Visualization"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3135-8916","authenticated-orcid":false,"given":"Thi Hong Diep","family":"Dao","sequence":"first","affiliation":[{"name":"Department of Geography and Environmental Studies, University of Colorado-Colorado Springs, Colorado Springs, CO 80920, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6651-8123","authenticated-orcid":false,"given":"Jean-Claude","family":"Thill","sequence":"additional","affiliation":[{"name":"Department of Geography and Earth Sciences and School of Data Science, University of North Carolina at Charlotte, Charlotte, NC 28223, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"601","DOI":"10.1177\/0309132514554323","article-title":"Vertical urbanisms: Opening up geographies of the three-dimensional city","volume":"39","author":"Harris","year":"2015","journal-title":"Prog. Hum. Geogr."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"815","DOI":"10.1177\/0309132519863486","article-title":"The volumetric city","volume":"44","author":"McNeill","year":"2020","journal-title":"Prog. Hum. Geogr."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1175","DOI":"10.1068\/a291175","article-title":"Measuring Accessibility: An Exploration of Issues and Alternatives","volume":"29","author":"Handy","year":"1997","journal-title":"Environ. Plan. A Econ. Space"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Cascetta, E. (2009). Transportation Systems Analysis: Models and Applications, Springer. [2nd ed.].","DOI":"10.1007\/978-0-387-75857-2"},{"key":"ref_5","unstructured":"Madden, M. (2009). Transportation Applications of Geographic Information Systems. Manual of Geographic Information Systems, ASPRS."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/j.jtrangeo.2012.03.016","article-title":"Measuring accessibility: Positive and normative implementations of various accessibility indicators","volume":"25","author":"Scott","year":"2012","journal-title":"J. Transp. Geogr."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"241","DOI":"10.2148\/benv.44.2.241","article-title":"Rotational locomotion in large-scale environments: A survey and implications for evidence-based design practice","volume":"44","author":"Kondyli","year":"2018","journal-title":"Built Environ."},{"key":"ref_8","unstructured":"Coutrot, A., Manley, E., Yesiltepe, D., Dalton, R.C., Wiener, J.M., H\u00f6lscher, C., Hornberger, M., and Spiers, H.J. (2020). Cities have a negative impact on navigation ability: Evidence from 38 countries. bioRxiv, 1\u201313."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1023\/B:GEIN.0000017746.44824.70","article-title":"A Structural Approach to the Model Generalization of an Urban Street Network","volume":"8","author":"Jiang","year":"2004","journal-title":"GeoInformatica"},{"key":"ref_10","first-page":"475","article-title":"Network and psychological effects in urban movement","volume":"Volume 3693","author":"Cohn","year":"2005","journal-title":"COSIT 2005: Spatial Information Theory"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"102319","DOI":"10.1016\/j.trd.2020.102319","article-title":"Is accessibility an idea whose time has finally come?","volume":"83","author":"Handy","year":"2020","journal-title":"Transp. Res. Part D Transp. Environ."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"103086","DOI":"10.1016\/j.jtrangeo.2021.103086","article-title":"What are we missing when we measure accessibility? Comparing calculated and self-reported accounts among older people","volume":"93","author":"Jean","year":"2021","journal-title":"J. Transp. Geogr."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1857","DOI":"10.1177\/23998083211070567","article-title":"Walking in the cities without ground, how 3d complex network volumetrics improve analysis","volume":"49","author":"Zhang","year":"2022","journal-title":"Environ. Plan. B Urban Anal. City Sci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1016\/j.jtrangeo.2010.11.007","article-title":"Traveling in the three-dimensional city: Implementation issues and applications in route planning, accessibility, and location analyses","volume":"19","author":"Thill","year":"2011","journal-title":"J. Transp. Geogr."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1080\/13658816.2011.597753","article-title":"Spatio-temporal location modeling in a 3D indoor environment: The case of AEDs as emergency medical devices","volume":"26","author":"Dao","year":"2011","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_16","first-page":"288","article-title":"Indoor three-dimensional accessibility auditing for computer-aided architectural design","volume":"22","author":"Dao","year":"2018","journal-title":"Trans. Geogr. Inf. Sci."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1016\/j.compenvurbsys.2010.09.001","article-title":"Editorial\u2014GeoVisualization and the Digital City","volume":"34","author":"Dykes","year":"2010","journal-title":"Comput. Environ. Urban Syst."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/j.proeng.2017.02.357","article-title":"The Smart City Concept in the 21st Century","volume":"181","author":"Eremia","year":"2017","journal-title":"Procedia Eng."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"106804","DOI":"10.1016\/j.buildenv.2020.106804","article-title":"Review of multi-domain approaches to indoor environmental perception and behaviour","volume":"176","author":"Schweiker","year":"2020","journal-title":"Build. Environ."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"284","DOI":"10.1177\/0963721410383243","article-title":"Getting lost in buildings","volume":"19","author":"Carlson","year":"2010","journal-title":"Curr. Dir. Psychol. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"117","DOI":"10.3130\/jaabe.17.117","article-title":"Quantifying the Visual Experience of Three-dimensional Built Environments","volume":"17","author":"Chang","year":"2018","journal-title":"J. Asian Arch. Build. Eng."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"582","DOI":"10.1177\/0013916502034005002","article-title":"Spatial Choice and Preference in Multilevel Movement Networks","volume":"34","author":"Chang","year":"2002","journal-title":"Environ. Behav."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Hillier, B., and Hanson, J. (1984). The Social Logic of Space, Cambridge University Press.","DOI":"10.1017\/CBO9780511597237"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Van Nes, A., and Yamu, C. (2021). Introduction to Space Syntax in Urban Studies, Springer Nature.","DOI":"10.1007\/978-3-030-59140-3"},{"key":"ref_25","unstructured":"Turner, A. (2000). Angular Analysis: A Method for the Quantification of Space, Centre for Advanced Spatial Analysis, UCL. Working Paper 23."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"539","DOI":"10.1068\/b32067","article-title":"From Axial to Road-Centre Lines: A New Representation for Space Syntax and a New Model of Route Choice for Transport Network Analysis","volume":"34","author":"Turner","year":"2007","journal-title":"Environ. Plan. B Plan. Des."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Turner, A. (2009). The Role of Angularity in Route Choice: An Analysis of Motorcycle Courier GPS Traces. COSIT 2009: Spatial Information Theory, Springer. Lecture Notes in Computer Science.","DOI":"10.1007\/978-3-642-03832-7_30"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/S0198-9715(99)00017-4","article-title":"Geometric accessibility and geographic information: Extending desktop GIS to space syntax","volume":"23","author":"Jiang","year":"1999","journal-title":"Comput. Environ. Urban Syst."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"647","DOI":"10.1016\/j.physa.2007.05.064","article-title":"A topological pattern of urban street networks: Universality and peculiarity","volume":"384","author":"Jiang","year":"2007","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"P07008","DOI":"10.1088\/1742-5468\/2008\/07\/P07008","article-title":"Self-organized natural roads for predicting traffic flow: A sensitivity study","volume":"2008","author":"Jiang","year":"2008","journal-title":"J. Stat. Mech. Theory Exp."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1119","DOI":"10.1080\/13658810701690448","article-title":"Street-based topological representations and analyses for predicting traffic flow in GIS","volume":"23","author":"Jiang","year":"2009","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_32","first-page":"63","article-title":"Challenges in multilevel wayfinding: A case study with the space syntax technique","volume":"39","author":"Vrachliotis","year":"2010","journal-title":"Environ. Plan. B Plan. Des."},{"key":"ref_33","first-page":"510","article-title":"Using Space Syntax and Information Visualization for Spatial Behavior Analysis and Simulation","volume":"10","author":"Wang","year":"2019","journal-title":"Int. J. Adv. Comput. Sci. Appl."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1016\/j.compenvurbsys.2018.11.009","article-title":"A new 3D space syntax metric based on 3D isovist capture in urban space using remote sensing technology","volume":"74","author":"Kim","year":"2019","journal-title":"Comput. Environ. Urban Syst."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"643","DOI":"10.1007\/s11116-019-10072-0","article-title":"Using multiple hybrid spatial design network analysis to predict longitudinal effect of a major city centre redevelopment on pedestrian flows","volume":"48","author":"Cooper","year":"2019","journal-title":"Transportation"},{"key":"ref_36","unstructured":"Jiang, B., and Yao, X. (2010). Object-oriented data model of an indoor\/outdoor urban transportation network and route planning analysis. Geospatial Analysis and Modeling of Urban Structure and Dynamics, Springer."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1023\/A:1014276309416","article-title":"3D urban models: Recent developments in the digital modelling of urban environments in three-dimensions","volume":"52","author":"Shiode","year":"2001","journal-title":"GeoJournal"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"512","DOI":"10.1111\/j.1467-8306.2007.00561.x","article-title":"A Three-Dimensional Navigable Data Model to Support Emergency Response in Microspatial Built-Environments","volume":"97","author":"Lee","year":"2007","journal-title":"Ann. Assoc. Am. Geogr."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/j.jtrangeo.2018.11.005","article-title":"Shortest path distance vs. least directional change: Empirical testing of space syntax and geographic theories concerning pedestrian route choice behaviour","volume":"74","author":"Shatu","year":"2018","journal-title":"J. Transp. Geogr."},{"key":"ref_40","unstructured":"ESRI (2022, July 30). ArcGIS Indoors: Turn Your CAD and BIM Data into a Workplace Map. Available online: https:\/\/mediaspace.esri.com\/media\/t\/1_r1tznq5f."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1080\/17489725.2014.975289","article-title":"Comparing indoor and outdoor network models for automatically calculating turns","volume":"8","author":"Vanclooster","year":"2014","journal-title":"J. Locat. Based Serv."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"678","DOI":"10.1038\/s43588-021-00130-y","article-title":"Vector-based pedestrian navigation in cities","volume":"1","author":"Bongiorno","year":"2021","journal-title":"Nat. Comput. Sci."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1506304","DOI":"10.1080\/23311916.2018.1506304","article-title":"Emergency evacuation of people with disabilities: A survey of drills, simulations, and accessibility","volume":"5","author":"Hashemi","year":"2018","journal-title":"Cogent Eng."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"7459","DOI":"10.1109\/TII.2020.2974252","article-title":"Accurate and Efficient Indoor Pathfinding Based on Building Infor-mation Modeling Data","volume":"16","author":"Zhou","year":"2020","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1111\/j.1538-4632.2003.tb01102.x","article-title":"Measuring Accessibility for People with a Disability","volume":"35","author":"Church","year":"2003","journal-title":"Geogr. Anal."},{"key":"ref_46","unstructured":"Kim, H., Jun, C., Cho, Y., and Kim, G. (2008, January 3\u201311). Indoor spatial analysis using space syntax. Proceedings of the International Archives of the Photogrammetry, Remote Sensing and Spatial Information Science, Beijing, China. Part B2."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"1039","DOI":"10.1016\/j.aej.2019.09.007","article-title":"Assessment of elementary school buildings in Erbil city using space syntax analysis and school teachers\u2032 feedback","volume":"58","author":"Mustafa","year":"2019","journal-title":"Alex. Eng. J."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"100525","DOI":"10.1016\/j.softx.2020.100525","article-title":"sDNA: 3d Spatial Network Analysis for GIS, CAD, Command Line and Python","volume":"12","author":"Cooper","year":"2020","journal-title":"SoftwareX"},{"key":"ref_49","unstructured":"Thomson, R.C. (2003, January 17\u201319). Bending the axial line: Smoothly continuous road centre-line segments as a basis for road network analysis. Proceedings of the 4th International Space Syntax Symposium, London, UK."},{"key":"ref_50","unstructured":"Dalton, N.S., Peponis, J., and Dalton, R. (2003, January 17\u201319). To tame a TIGER one has to know its nature-extending weighted angular integration analysis to the description of GIS road centerline data for large scale urban analysis. Proceedings of the 4th International Space Syntax Symposium, London, UK."},{"key":"ref_51","unstructured":"van Nes, A. (2005, January 13\u201317). Continuity lines in the axial system. Proceedings of the 5th International Symposium on Space Syntax, Delft, The Netherlands."},{"key":"ref_52","unstructured":"Jiang, B., and Liu, X. (2009, January 16\u201318). AxialGen_a research prototype for automatically generating the axial map. Proceedings of the CUPUM 2009b, Hong Kong, China."},{"key":"ref_53","unstructured":"U.S. Department of Justice (2022, August 24). ADA Requirements: Wheelchairs, Mobility Aids, and Other Power-Driven Mobility Devices. Civil Rights Division Disability Rights Section, Available online: https:\/\/www.ada.gov\/opdmd.htm#:~:text=Under%20the%20new%20rules%2C%20covered,facility%20where%20members%20of%20the."},{"key":"ref_54","unstructured":"ADA National Network (2022, August 11). Opening Doors to Everyone. Available online: https:\/\/adata.org\/factsheet\/opening-doors-everyone."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1007\/BF01386390","article-title":"A note on two problems in connexion with graphs","volume":"1","author":"Dijkstra","year":"1959","journal-title":"Numer. Math."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/j.sbspro.2013.10.598","article-title":"A New Measure of Accessibility based on Perceived Opportunities","volume":"87","author":"Cascetta","year":"2013","journal-title":"Procedia Soc. Behav. Sci."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1080\/01944365908978307","article-title":"How accessibility shapes land use","volume":"25","author":"Hansen","year":"1959","journal-title":"J. Am. Inst. Plan."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1016\/j.chaos.2015.05.022","article-title":"The distance-decay function of geographical gravity model: Power law or exponential law?","volume":"77","author":"Chen","year":"2015","journal-title":"Chaos Solitons Fractals"},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"1273","DOI":"10.1111\/tgis.12574","article-title":"A generic space definition framework to support seamless indoor\/outdoor navigation systems","volume":"23","author":"Yan","year":"2019","journal-title":"Trans. GIS"},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"985","DOI":"10.1080\/17538947.2021.1913522","article-title":"A unified 3D space-based navigation model for seamless navigation in indoor and outdoor","volume":"14","author":"Yan","year":"2021","journal-title":"Int. J. Digit. Earth"},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1146\/annurev.clinpsy.3.022806.091415","article-title":"Ecological momentary assessment","volume":"4","author":"Shiffman","year":"2008","journal-title":"Annu. Rev. Clin. Psychol."}],"container-title":["ISPRS International Journal of Geo-Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2220-9964\/11\/9\/467\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:19:43Z","timestamp":1760141983000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2220-9964\/11\/9\/467"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,29]]},"references-count":61,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2022,9]]}},"alternative-id":["ijgi11090467"],"URL":"https:\/\/doi.org\/10.3390\/ijgi11090467","relation":{},"ISSN":["2220-9964"],"issn-type":[{"value":"2220-9964","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,8,29]]}}}