{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:19:10Z","timestamp":1760235550678,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2021,8,28]],"date-time":"2021-08-28T00:00:00Z","timestamp":1630108800000},"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>Urbanization is leading us to a more chaotic state where healthy living becomes a prime concern. The high-rise buildings influence the urban setting with a high shadow rate on surroundings that can have no positive impact on the general neighborhood. Nevertheless, shadows are the main factor of defeatist virtual settings, they are expensive to render in real-time. This paper investigates how the amount of sunlight varies by season and how seasons can indicate the time of year to understand how shadows vary in length at different times of the day and how they change over the seasons. We propose a novel efficient (fast and scalable) algorithm to calculate a 2.5D cast-shadow map from a given LiDAR-derived Digital Surface Model (DSM). We present a proof-of-concept demonstration to examine the technical practicability of the introduced algorithm. Tensor-based techniques such as singular value decomposition, tensor unfolding are examined and deployed to represent the multidimensional data. The proposed method exploits horizon mapping ideas and extends the method to a modern graphics algorithm (Bresenham\u2019s line drawing algorithm) to account for the DSM\u2019s underlying surface geometry. A proof-of-concept is developed utilizing Python\u2019s TensorFlow library, exploring data flow graphs and the tensor data structure. The heavy computer graphics algorithm used in this paper is parallelized using PySpark. Results explicate significant enhancements in overall performance while preserving accuracy at negligible variations.<\/jats:p>","DOI":"10.3390\/ijgi10090583","type":"journal-article","created":{"date-parts":[[2021,8,29]],"date-time":"2021-08-29T21:45:16Z","timestamp":1630273516000},"page":"583","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["An Efficient 2.5D Shadow Detection Algorithm for Urban Planning and Design Using a Tensor Based Approach"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2439-7546","authenticated-orcid":false,"given":"Sukriti","family":"Bhattacharya","sequence":"first","affiliation":[{"name":"Department for IT for Innovative Services, Luxembourg Institute of Science and Technology (LIST), L-4362 Esch-sur-Alzette, Luxembourg"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5349-3126","authenticated-orcid":false,"given":"Christian","family":"Braun","sequence":"additional","affiliation":[{"name":"Department for Environmental Research and Innovation, Luxembourg Institute of Science and Technology (LIST), L-4362 Esch-sur-Alzette, Luxembourg"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0059-6134","authenticated-orcid":false,"given":"Ulrich","family":"Leopold","sequence":"additional","affiliation":[{"name":"Department for Environmental Research and Innovation, Luxembourg Institute of Science and Technology (LIST), L-4362 Esch-sur-Alzette, Luxembourg"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2842","DOI":"10.3390\/ijgi4042842","article-title":"Applications of 3D City Models: State of the Art Review","volume":"4","author":"Biljecki","year":"2015","journal-title":"ISPRS Int. J. Geo-Inf."},{"key":"ref_2","first-page":"332","article-title":"Solar energy potential on roofs and facades in an urban landscape","volume":"97","author":"Redweik","year":"2013","journal-title":"Renew. Energy"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1016\/j.renene.2009.07.017","article-title":"Impact of street design on urban microclimate for semi arid climate (Constantine)","volume":"35","author":"Bourbia","year":"2010","journal-title":"Renew. Energy"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1007\/BF01905562","article-title":"Horizon mapping: Shadows for bump-mapped surfaces","volume":"4","author":"Max","year":"1988","journal-title":"Vis. Comput."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Blinn, J.F. (1978, January 23\u201325). Simulation of Wrinkled Surfaces. Proceedings of the 5th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH \u201978, Atlanta, GA, USA.","DOI":"10.1145\/800248.507101"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Cook, R.L. (1984, January 23\u201327). Shade Trees. Proceedings of the 11th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH \u201984, Minneapolis, MN, USA.","DOI":"10.1145\/800031.808602"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Williams, L. (1978, January 23\u201325). Casting Curved Shadows on Curved Surfaces. Proceedings of the 5th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH \u201978, Atlanta, GA, USA.","DOI":"10.1145\/800248.807402"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Reeves, W.T., Salesin, D.H., and Cook, R.L. (1987, January 27\u201331). Rendering Antialiased Shadows with Depth Maps. Proceedings of the 14th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH \u201987, Anaheim, CA, USA.","DOI":"10.1145\/37401.37435"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Crow, F.C. (1977, January 20\u201322). Shadow Algorithms for Computer Graphics. Proceedings of the 4th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH \u201977, San Jose, CA, USA.","DOI":"10.1145\/563858.563901"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Becker, B.G., and Max, N.L. (1993, January 2\u20136). Smooth Transitions Between Bump Rendering Algorithms. Proceedings of the 20th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH \u201993, Anaheim, CA, USA.","DOI":"10.1145\/166117.166141"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Wang, L., Wang, X., Tong, X., Lin, S., Hu, S., Guo, B., Shum, H.Y., Shum, H.Y., and Shum, H.Y. (2003). View-Dependent Displacement Mapping, ACM. ACM SIGGRAPH 2003 Papers.","DOI":"10.1145\/1201775.882272"},{"key":"ref_12","unstructured":"Onoue, K., Max, N., and Nishita, T. (2004, January 18\u201320). Real-Time Rendering of Bumpmap Shadows Taking Account of Surface Curvature. Proceedings of the 2004 International Conference on Cyberworlds, Tokyo, Japan."},{"key":"ref_13","unstructured":"Appel, A. (30\u20132, January 30). Some Techniques for Shading Machine Renderings of Solids. Proceedings of the Spring Joint Computer Conference, AFIPS \u201968 (Spring), Atlantic City, NJ, USA."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1080\/136588197242266","article-title":"Modelling Topographic Variation in Solar Radiation in a GIS Environment","volume":"11","author":"Kumar","year":"1997","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1068\/b2665","article-title":"Raster analysis of urban form","volume":"31","author":"Ratti","year":"2004","journal-title":"Environ. Plan. B Plan. Des."},{"key":"ref_16","unstructured":"Hofierka, J., Suri, M., and \u0160\u00fari, M. (2002, January 11\u201313). The solar radiation model for Open source GIS: Implementation and applications. Proceedings of the Open Source GIS\u2014GRASS Users Conference, Trento, Italy."},{"key":"ref_17","unstructured":"GRASS Development Team (2017). Geographic Resources Analysis Support System (GRASS GIS) Software, Version 7.2, Open Source Geospatial Foundation."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1016\/j.envsoft.2017.09.020","article-title":"Urban Multi-scale Environmental Predictor (UMEP): An integrated tool for city-based climate services","volume":"99","author":"Lindberg","year":"2018","journal-title":"Environ. Model. Softw."},{"key":"ref_19","unstructured":"QGIS Development Team (2019). QGIS Geographic Information System, Open Source Geospatial Foundation."},{"key":"ref_20","unstructured":"Corripio, J.G. (2014). Insol: Solar Radiation, The R Foundation for Statistical Computing. R Package Version 1.1.1."},{"key":"ref_21","unstructured":"Dorman, M. (2018). Shadow: Geometric Shadow Calculations, The R Foundation for Statistical Computing. R Package Version 0.5.0."},{"key":"ref_22","unstructured":"Fu, P., and Rich, P. (1999, January 26\u201330). Design and implementation of the Solar Analyst: An ArcView extension for modeling solar radiation at landscape scales. Proceedings of the 19th Annual ESRI User Conference, San Diego, CA, USA."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Bhattacharya, S., Braun, C., and Leopold, U. (2019, January 3\u20135). A Novel 2.5D Shadow Calculation Algorithm for Urban Environment. Proceedings of the 5th International Conference on Geographical Information Systems Theory, Applications and Management, GISTAM 2019, Heraklion, Crete, Greece.","DOI":"10.5220\/0007748602740281"},{"key":"ref_24","unstructured":"MacEachren, A.M. (2004). How Maps Work\u2014Representation, Visualization, and Design, Guilford Press."},{"key":"ref_25","unstructured":"Gr\u00f6ger, G., Kolbe, T.H., Nagel, C., and H\u00e4fele, K.H. (2012). OGC City Geography Markup Language (CityGML) Encoding Standard, 2.0.0 ed., Open Geospatial Consortium."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"280","DOI":"10.1109\/TETC.2014.2330516","article-title":"A Tensor-Based Approach for Big Data Representation and Dimensionality Reduction","volume":"2","author":"Kuang","year":"2014","journal-title":"IEEE Trans. Emerg. Top. Comput."},{"key":"ref_27","unstructured":"Abadi, M., Agarwal, A., Barham, P., Brevdo, E., Chen, Z., Citro, C., Corrado, G.S., Davis, A., Dean, J., and Devin, M. (2020, June 01). TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems. Available online: tensorflow.org."},{"key":"ref_28","unstructured":"Nandi, A. (2015). Spark for Python Developers, Packt Publishing."},{"key":"ref_29","unstructured":"Zaharia, M., Chowdhury, M., Franklin, M.J., Shenker, S., and Stoica, I. (2010, January 22). Spark: Cluster Computing with Working Sets. Proceedings of the 2nd USENIX Conference on Hot Topics in Cloud Computing, HotCloud\u201910, Boston, MA, USA."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1147\/sj.41.0025","article-title":"Algorithm for Computer Control of a Digital Plotter","volume":"4","author":"Bresenham","year":"1965","journal-title":"IBM Syst. J."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"3","DOI":"10.5194\/isprs-archives-XLII-4-W14-3-2019","article-title":"A Tensor Based Framework for Large Scale Spatio-Temporal Raster Data Processing","volume":"XLII-4\/W14","author":"Bhattacharya","year":"2019","journal-title":"ISPRS-Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Lirkov, I., Margenov, S., and Wa\u015bniewski, J. (2012). Implementation of Two Different Shadow Models into EULAG Model: Madrid Case Study. Large-Scale Scientific Computing, Springer.","DOI":"10.1007\/978-3-642-29843-1"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1016\/j.scs.2010.08.006","article-title":"Impacts of urbanization on urban structures and energy demand: What can we learn for urban energy planning and urbanization management?","volume":"1","author":"Madlener","year":"2011","journal-title":"Sustain. Cities Soc."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"801","DOI":"10.1068\/b38055","article-title":"Solar Zoning and Energy in Detached Dwellings","volume":"40","author":"Niemasz","year":"2013","journal-title":"Environ. Plan. B Plan. Des."},{"key":"ref_35","unstructured":"Bellman, R. (1957). Dynamic Programming, Princeton University Press. 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