{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T00:10:20Z","timestamp":1773101420140,"version":"3.50.1"},"reference-count":27,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2019,10,22]],"date-time":"2019-10-22T00:00:00Z","timestamp":1571702400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004295","name":"Shandong University of Science and Technology","doi-asserted-by":"publisher","award":["No. 2019TDJH103"],"award-info":[{"award-number":["No. 2019TDJH103"]}],"id":[{"id":"10.13039\/501100004295","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"The National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["No: 41930535"],"award-info":[{"award-number":["No: 41930535"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJGI"],"abstract":"<jats:p>Triangulated irregular networks (TINs) are widely used in terrain visualization due to their accuracy and efficiency. However, the conventional algorithm for multi-scale terrain rendering, based on TIN, has many problems, such as data redundancy and discontinuities in scale transition. To solve these issues, a method based on a detail-increment model for the construction of a continuous-scale hierarchical terrain model is proposed. First, using the algorithm of edge collapse, based on a quadric error metric (QEM), a complex terrain base model is processed to a most simplified model version. Edge collapse records at different scales are stored as compressed incremental information in order to make the rendering as simple as possible. Then, the detail-increment hierarchical terrain model is built using the incremental information and the most simplified model version. Finally, the square root of the mean minimum quadric error (MMQE), calculated by the points at each scale, is considered the smallest visible object (SVO) threshold that allows for the scale transition with the required scale or the visual range. A point cloud from Yanzhi island is converted into a hierarchical TIN model to verify the effectiveness of the proposed method. The results show that the method has low data redundancy, and no error existed in the topology. It can therefore meet the basic requirements of hierarchical visualization.<\/jats:p>","DOI":"10.3390\/ijgi8100465","type":"journal-article","created":{"date-parts":[[2019,10,23]],"date-time":"2019-10-23T11:46:59Z","timestamp":1571831219000},"page":"465","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Continuous-Scale 3D Terrain Visualization Based on a Detail-Increment Model"],"prefix":"10.3390","volume":"8","author":[{"given":"Bo","family":"Ai","sequence":"first","affiliation":[{"name":"College of Geomatics, Shandong University of Science and Technology, Qingdao 266590, China"},{"name":"Qingdao Yuehai Information Service Co, Ltd., Qingdao 266590, China"}]},{"given":"Linyun","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Geomatics, Shandong University of Science and Technology, Qingdao 266590, China"}]},{"given":"Fanlin","family":"Yang","sequence":"additional","affiliation":[{"name":"College of Geomatics, Shandong University of Science and Technology, Qingdao 266590, China"}]},{"given":"Xianhai","family":"Bu","sequence":"additional","affiliation":[{"name":"College of Geomatics, Shandong University of Science and Technology, Qingdao 266590, China"}]},{"given":"Yaoyao","family":"Lin","sequence":"additional","affiliation":[{"name":"College of Geomatics, Shandong University of Science and Technology, Qingdao 266590, China"}]},{"given":"Guannan","family":"Lv","sequence":"additional","affiliation":[{"name":"Qingdao Yuehai Information Service Co, Ltd., Qingdao 266590, China"}]}],"member":"1968","published-online":{"date-parts":[[2019,10,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1016\/0010-4485(87)90066-2","article-title":"Terrain modelling in surveying and civil engineering","volume":"19","author":"Petrie","year":"1987","journal-title":"Comput. Aided Des."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1111\/1467-9671.00062","article-title":"Multiscale terrain and topographic modelling with the implicit TIN","volume":"4","author":"Kidner","year":"2000","journal-title":"Trans. GIS"},{"key":"ref_3","first-page":"65","article-title":"Decimation of triangle meshes","volume":"92","author":"Schroeder","year":"1992","journal-title":"Siggraph"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1016\/j.cageo.2011.09.013","article-title":"LiDAR data reduction using vertex decimation and processing with GPGPU and multicore CPU technology","volume":"43","author":"Oryspayev","year":"2012","journal-title":"Comput. Geosci."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Li, W., Chen, Y., Wang, Z., Zhao, W., and Chen, L. (2014, January 24\u201326). An improved decimation of triangle meshes based on curvature. Proceedings of the International Conference on Rough Sets and Knowledge Technology, Shanghai, China.","DOI":"10.1007\/978-3-319-11740-9_25"},{"key":"ref_6","unstructured":"Li, N., Gao, P.D., Lu, Y.Q., Li, A., and Yu, W.H. (2008, January 20\u201322). A New Adaptive Mesh Simplification Method Using Vertex Clustering with Topology-and-Detail Preserving. Proceedings of the International Symposium on Information Science & Engineering, Shanghai, China."},{"key":"ref_7","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":"Chen","year":"2015","journal-title":"Comput. Geosci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/j.precisioneng.2012.08.002","article-title":"Freeform surface filtering using the lifting wavelet transform","volume":"37","author":"Jiang","year":"2013","journal-title":"Precis. Eng."},{"key":"ref_9","first-page":"15","article-title":"Lazy wavelet simplification using scale-dependent dense geometric variability descriptors","volume":"19","author":"Cioaca","year":"2017","journal-title":"J. Control Eng. Appl. Inform."},{"key":"ref_10","unstructured":"Loop, C. (1987). Smooth Subdivision Surfaces Based on Triangles. [Master\u2019s Thesis, Department of Mathematics, University of Utah]."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"500","DOI":"10.1109\/TVCG.2010.83","article-title":"Approximation of Loop subdivision surfaces for fast rendering","volume":"17","author":"Li","year":"2011","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"731","DOI":"10.1016\/j.jcp.2015.06.044","article-title":"Isogeometric analysis based on extended Loop\u2019s subdivision","volume":"299","author":"Pan","year":"2015","journal-title":"J. Comput. Phys."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"160","DOI":"10.1145\/78956.78958","article-title":"A butterfly subdivision scheme for surface interpolation with tension control","volume":"9","author":"Dyn","year":"1990","journal-title":"ACM Trans. Graph. (TOG)"},{"key":"ref_14","first-page":"622","article-title":"Iterative process to improve simple adaptive subdivision surfaces method with Butterfly scheme","volume":"55","author":"Husain","year":"2011","journal-title":"World Acad. Sci. Eng. Technol."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Vlachos, A., Peters, J., Boyd, C., and Mitchell, J.L. (2001, January 19\u201321). Curved PN triangles. Proceedings of the 2001 Symposium on Interactive 3D Graphics, Research Triangle Park, NC, USA.","DOI":"10.1145\/364338.364387"},{"key":"ref_16","unstructured":"Schwarz, M., Staginski, M., and Stamminger, M. (2006). GPU-based rendering of PN triangle meshes with adaptive tessellation. Proceedings of Vision, Modeling, and Visualization, Akademische Verlagsgesellschaft Aka GmbH."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/j.isprsjprs.2017.04.013","article-title":"A morphologically preserved multi-resolution TIN surface modeling and visualization method for virtual globes","volume":"129","author":"Zheng","year":"2017","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/j.isprsjprs.2018.03.001","article-title":"Local curvature entropy-based 3D terrain representation using a comprehensive Quadtree","volume":"139","author":"Chen","year":"2018","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Hoppe, H. (1996, January 4\u20139). Progressive Meshes. Proceedings of the 23rd Annual Conference on Computer Graphics and Interactive Techniques, New Orleans, LA, USA.","DOI":"10.1145\/237170.237216"},{"key":"ref_20","unstructured":"Shafae, M., and Pajarola, R. (2003, January 8\u201310). Dstrips: Dynamic triangle strips for real-time mesh simplification and rendering. Proceedings of the 11th Pacific Conference on Computer Graphics and Applications, Canmore, AB, Canada."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"332","DOI":"10.1016\/j.cag.2013.11.013","article-title":"Adaptive multi-chart and multiresolution mesh representation","volume":"38","author":"Maximo","year":"2014","journal-title":"Comput. Graph."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1007\/s00531-005-0491-2","article-title":"Erosional processes, topographic length-scales and geomorphic evolution in arid climatic environments: The \u2018Lluta collapse\u2019, northern Chile","volume":"94","author":"Strasser","year":"2005","journal-title":"Int. J. Earth Sci."},{"key":"ref_23","unstructured":"Schilling, A., Basanow, J., and Zipf, A. (2007, January 3\u20136). Vector based Mapping of Polygons on Irregular Terrain Meshes for Web 3D Map Services. Proceedings of the 3rd International Conference on Web Information Systems and Technologies (WEBIST), Barcelona, Spain."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Hu, Y., Zhu, J., Li, W., Zhang, Y., Zhu, Q., Qi, H., Zhang, H., Cao, Z., Yang, W., and Zhang, P. (2018). Construction and optimization of three-dimensional disaster scenes within mobile virtual reality. ISPRS Int. J. Geo-Inf., 7.","DOI":"10.3390\/ijgi7060215"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1457","DOI":"10.1130\/GES01282.1","article-title":"High-resolution 3D surface modeling of a fossil oyster reef","volume":"12","author":"Djuricic","year":"2016","journal-title":"Geosphere"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Garland, M., and Heckbert, P.S. (1997, January 3\u20138). Surface simplification using quadric error metric. Proceedings of the 24th Annual Conference on Computer Graphics and Interactive Techniques, Los Angeles, CA, USA.","DOI":"10.1145\/258734.258849"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1080\/02693799208901921","article-title":"Algorithms for automated line generalization based on a natural principle of objective generalization","volume":"6","author":"Li","year":"1992","journal-title":"Int. J. Geogr. Inf. 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