{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T20:39:33Z","timestamp":1775594373226,"version":"3.50.1"},"reference-count":41,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2021,6,20]],"date-time":"2021-06-20T00:00:00Z","timestamp":1624147200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["41871293 and 41371365"],"award-info":[{"award-number":["41871293 and 41371365"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJGI"],"abstract":"<jats:p>Simplification of 3D building models is an important way to improve rendering efficiency. When existing algorithms are directly applied to simplify multi-component models, generally composed of independent components with strong topological dependence, each component is simplified independently. The consequent destruction of topological dependence can cause unreasonable separation of components and even result in inconsistent conclusions of spatial analysis among different levels of details (LODs). To solve these problems, a novel simplification method, which considers the topological dependence among components as constraints, is proposed. The vertices of building models are divided into boundary vertices, hole vertices, and other ordinary vertices. For the boundary vertex, the angle between the edge and component (E\u2013C angle), denoting the degree of component separation, is introduced to derive an error metric to limit the collapse of the edge located at adjacent areas of neighboring components. An improvement to the quadratic error metric (QEM) algorithm was developed for the hole vertex to address the unexpected error caused by the QEM\u2019s defect. A series of experiments confirmed that the proposed method could effectively maintain the overall appearance features of building models. Compared with the traditional method, the consistency of visibility analysis among different LODs is much better.<\/jats:p>","DOI":"10.3390\/ijgi10060422","type":"journal-article","created":{"date-parts":[[2021,6,20]],"date-time":"2021-06-20T22:00:02Z","timestamp":1624226402000},"page":"422","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["A Topology-Preserving Simplification Method for 3D Building Models"],"prefix":"10.3390","volume":"10","author":[{"given":"Biao","family":"Wang","sequence":"first","affiliation":[{"name":"Jiangsu Provincial Key Laboratory of Geographic Information Science and Technology, Key Laboratory for Land Satellite Remote Sensing Applications of Ministry of Natural Resources, School of Geography and Ocean Science, Nanjing University, Nanjing 210023, China"}]},{"given":"Guoping","family":"Wu","sequence":"additional","affiliation":[{"name":"Jiangsu Provincial Key Laboratory of Geographic Information Science and Technology, Key Laboratory for Land Satellite Remote Sensing Applications of Ministry of Natural Resources, School of Geography and Ocean Science, Nanjing University, Nanjing 210023, China"}]},{"given":"Qiang","family":"Zhao","sequence":"additional","affiliation":[{"name":"Jiangsu Provincial Key Laboratory of Geographic Information Science and Technology, Key Laboratory for Land Satellite Remote Sensing Applications of Ministry of Natural Resources, School of Geography and Ocean Science, Nanjing University, Nanjing 210023, China"}]},{"given":"Yaozhu","family":"Li","sequence":"additional","affiliation":[{"name":"Jiangsu Provincial Key Laboratory of Geographic Information Science and Technology, Key Laboratory for Land Satellite Remote Sensing Applications of Ministry of Natural Resources, School of Geography and Ocean Science, Nanjing University, Nanjing 210023, China"}]},{"given":"Yiyuan","family":"Gao","sequence":"additional","affiliation":[{"name":"Jiangsu Provincial Key Laboratory of Geographic Information Science and Technology, Key Laboratory for Land Satellite Remote Sensing Applications of Ministry of Natural Resources, School of Geography and Ocean Science, Nanjing University, Nanjing 210023, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8536-8645","authenticated-orcid":false,"given":"Jiangfeng","family":"She","sequence":"additional","affiliation":[{"name":"Jiangsu Provincial Key Laboratory of Geographic Information Science and Technology, Key Laboratory for Land Satellite Remote Sensing Applications of Ministry of Natural Resources, School of Geography and Ocean Science, Nanjing University, Nanjing 210023, China"},{"name":"Jiangsu Center for Collaborative Innovation in Novel Software Technology and Industrialization, Nanjing University, Nanjing 210023, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Xie, J., and Feng, C.-C. (2016). An Integrated Simplification Approach for 3D Buildings with Sloped and Flat Roofs. ISPRS Int. J. Geo-Inf., 5.","DOI":"10.3390\/ijgi5080128"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1145\/360349.360354","article-title":"Hierarchical geometric models for visible surface algorithms","volume":"19","author":"Clark","year":"1976","journal-title":"Commun. ACM"},{"key":"ref_3","unstructured":"Gr\u00f6ger, G., Kolbe, T.H., Nagel, C., and H\u00e4fele, K.-H. (2012). OGC city geography markup language (CityGML) encoding standard. Open Geospat. Consort."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"123","DOI":"10.5194\/isprsannals-II-5-123-2014","article-title":"Establishing an appropriate level of detail (LoD) for a building information model (BIM)-West Block, Parliament Hill, Ottawa, Canada","volume":"2","author":"Fai","year":"2014","journal-title":"ISPRS Ann. Photogramm. Remote Sens. Spat. Inf. Sci."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Uusitalo, P., Sepp\u00e4nen, O., Lappalainen, E., Peltokorpi, A., and Olivieri, H. (2019). Applying level of detail in a BIM-based project: An overall process for lean design management. Buildings, 9.","DOI":"10.3390\/buildings9050109"},{"key":"ref_6","unstructured":"Besuievsky, G., Barroso, S., Beckers, B., and Patow, G. (2014). A Configurable LoD for Procedural Urban Models intended for Daylight Simulation. Proceedings of UDMV, Eurographics Association."},{"key":"ref_7","first-page":"4","article-title":"54 Surface Simplification and 3d Geome-Try Compression","volume":"2","author":"Rossignac","year":"2004","journal-title":"Triangle"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Wang, Y., Zheng, J., and Wang, H. (2019). Fast mesh simplification method for three-dimensional geometric models with feature-preserving efficiency. Sci. Program.","DOI":"10.1155\/2019\/4926190"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Ribelles, J., Heckbert, P.S., Garland, M., Stahovich, T., and Srivastava, V. (2001). Finding and removing features from polyhedra. Proceedings of DETC, American Society Of Mechanical Engineers.","DOI":"10.1115\/DETC2001\/DAC-21068"},{"key":"ref_10","unstructured":"Kada, M. (2007, January 19\u201323). Scale-dependent simplification of 3D building models based on cell decomposition and primitive instancing. Proceedings of the International Conference on Spatial Information Theory, Melbourne, Australia."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/j.isprsjprs.2012.01.002","article-title":"Mathematical morphology-based generalization of complex 3D building models incorporating semantic relationships","volume":"68","author":"Zhao","year":"2012","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1111\/tgis.12518","article-title":"An appearance-preserving simplification method for complex 3D building models","volume":"23","author":"She","year":"2019","journal-title":"Trans. GIS"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1016\/j.isprsjprs.2013.07.006","article-title":"Geometric structure simplification of 3D building models","volume":"84","author":"Li","year":"2013","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Rossignac, J., and Borrel, P. (1993). Multi-resolution 3D approximations for rendering complex scenes. Modeling in Computer Graphics, Springer.","DOI":"10.1007\/978-3-642-78114-8_29"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Schroeder, W.J., Zarge, J.A., and Lorensen, W.E. (1992, January 26\u201331). Decimation of triangle meshes. Proceedings of the 19th Annual Conference on Computer Graphics and Interactive Techniques, Chicago, IL, USA.","DOI":"10.1145\/133994.134010"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Hoppe, H., DeRose, T., Duchamp, T., McDonald, J., and Stuetzle, W. (1993, January 2\u20136). Mesh optimization. Proceedings of the 20th Annual Conference on Computer Graphics and Interactive Techniques, Anaheim, CA, USA.","DOI":"10.1145\/166117.166119"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Hinker, P., and Hansen, C. (1993). Geometric optimization. Proceedings Visualization\u201993, IEEE.","DOI":"10.1109\/VISUAL.1993.398868"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Garland, M., and Heckbert, P.S. (1997, January 3\u20138). Surface simplification using quadric error metrics. Proceedings of the 24th Annual Conference on Computer Graphics and Interactive Techniques, Los Angeles, CA, USA.","DOI":"10.1145\/258734.258849"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"204","DOI":"10.1145\/353981.353995","article-title":"Image-driven simplification","volume":"19","author":"Lindstrom","year":"2000","journal-title":"ACM Trans. Graph. (ToG)"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Luebke, D., and Hallen, B. (2001). Perceptually driven simplification for interactive rendering. Eurographics Workshop on Rendering Techniques, Springer.","DOI":"10.1007\/978-3-7091-6242-2_21"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Cohen-Steiner, D., Alliez, P., and Desbrun, M. (2004). Variational shape approximation. ACM SIGGRAPH 2004 Papers, Association for Computing Machinery.","DOI":"10.1145\/1186562.1015817"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1016\/j.cag.2008.05.005","article-title":"driven simplification using mutual information","volume":"32","author":"Sbert","year":"2008","journal-title":"Comput. Graph."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1007\/s11760-013-0450-5","article-title":"Simplification method for textured polygonal meshes based on structural appearance","volume":"7","author":"Chover","year":"2013","journal-title":"Signal Image Video Process."},{"key":"ref_24","unstructured":"Thiemann, F., and Sester, M. (2004, January 20\u201321). Segmentation of buildings for 3D-generalisation. Proceedings of the ICA Workshop on Generalisation and Multiple Representation, Leicester, UK."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Rau, J.-Y., Chen, L.-C., Tsai, F., Hsiao, K.-H., and Hsu, W.-C. (2006). Lod generation for 3d polyhedral building model. Pacific-Rim Symposium on Image and Video Technology, Springer.","DOI":"10.1007\/11949534_5"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.isprsjprs.2016.04.005","article-title":"3D building reconstruction from ALS data using unambiguous decomposition into elementary structures","volume":"118","author":"Borkowski","year":"2016","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Fan, H., Meng, L., and Jahnke, M. (2009). Generalization of 3D buildings modelled by CityGML. Advances in GIScience, Springer.","DOI":"10.1007\/978-3-642-00318-9_20"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1007\/s00450-014-0283-7","article-title":"Geometry simplification according to semantic constraints","volume":"31","author":"Ladenhauf","year":"2016","journal-title":"Comput. Sci. Res. Dev."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"02001","DOI":"10.1051\/3u3d\/201202001","article-title":"Measuring the impact of 3D data geometric modeling on spatial analysis: Illustration with Skyview factor","volume":"2012","author":"Brasebin","year":"2012","journal-title":"Usage Usability Util. 3D City Models\u2013Eur. COST Action TU0801"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1179\/1752270613Y.0000000059","article-title":"Voxel based volumetric visibility analysis of urban environments","volume":"45","author":"Shashkov","year":"2013","journal-title":"Surv. Rev."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1007\/s12061-014-9122-2","article-title":"Using three-dimensional volumetric analysis in everyday urban planning processes","volume":"8","author":"Ahmed","year":"2015","journal-title":"Appl. Spat. Anal. Policy"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Gergelova, M.B., Kuzevicova, Z., Labant, S., Kuzevic, S., and Mizak, J. (2020). Roof\u2019s Potential and Suitability for PV Systems Based on LiDAR: A Case Study of Kom\u00e1rno, Slovakia. Sustainability, 12.","DOI":"10.3390\/su122310018"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1016\/j.enbuild.2014.06.043","article-title":"Building Information Modeling (BIM)-based daylighting simulation and analysis","volume":"81","author":"Kota","year":"2014","journal-title":"Energ Build."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"109953","DOI":"10.1016\/j.enbuild.2020.109953","article-title":"Parametric modeling and surface-specific sensitivity analysis of PV module layout on building skin using BIM","volume":"216","author":"Salimzadeh","year":"2020","journal-title":"Energ Build."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/j.cad.2008.11.006","article-title":"Consistency constraints and 3D building reconstruction","volume":"41","author":"Horna","year":"2009","journal-title":"Comput. Aided Des."},{"key":"ref_36","first-page":"4","article-title":"Data consistency checks for building a 3D model: A case study of Technical University, Delft Campus, The Netherlands","volume":"2010","author":"Ghawana","year":"2010","journal-title":"Geospat. World"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Alam, N., Wagner, D., Wewetzer, M., von Falkenhausen, J., Coors, V., and Pries, M. (2014). Towards automatic validation and healing of CityGML models for geometric and semantic consistency. Innovations in 3D Geo-Information Sciences, Springer.","DOI":"10.1007\/978-3-319-00515-7_5"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1016\/j.isprsjprs.2016.03.003","article-title":"The variants of an LOD of a 3D building model and their influence on spatial analyses","volume":"116","author":"Biljecki","year":"2016","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_39","unstructured":"Van Oosterom, P. (1994). Reactive Data Structures for Geographic Information Systems, Oxford University Press, Inc."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"2005","DOI":"10.1002\/nme.1620371203","article-title":"Efficient three-dimensional Delaunay triangulation with automatic point creation and imposed boundary constraints","volume":"37","author":"Weatherill","year":"1994","journal-title":"Int. J. Numer. Methods Eng."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/j.cageo.2015.07.005","article-title":"An improved texture-related vertex clustering algorithm for model simplification","volume":"83","author":"Jing","year":"2015","journal-title":"Comput. Geosci."}],"container-title":["ISPRS International Journal of Geo-Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2220-9964\/10\/6\/422\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:19:48Z","timestamp":1760163588000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2220-9964\/10\/6\/422"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,20]]},"references-count":41,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2021,6]]}},"alternative-id":["ijgi10060422"],"URL":"https:\/\/doi.org\/10.3390\/ijgi10060422","relation":{},"ISSN":["2220-9964"],"issn-type":[{"value":"2220-9964","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,6,20]]}}}