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A topological enabled three-dimensional model based on constructive solid geometry and boundary representation


Ordinary triangular mesh model can be constructed from discrete point cloud. However, this kind of model contains large amount of data. It is not only difficult to split, but also lacks topological relation information. We proposed a CSG–BRep (Constructive Solid Geometry—Boundary Representation) topological model to overcome these problems. CSG–BRep model can record topological relationship of 3D model in great detail. We first introduced aspects of the topological model: location, orientation and sub-shape. Then we proposed two algorithms to access topological structure. We also proposed algorithms for performing Boolean operation on CSG–BRep models. Finally, we demonstrated CSG–BRep construction using LIDAR point cloud as a data source. We would show that, compared to ordinary triangular mesh model, CSG–BRep model is composable and can effectively reduce data volume. In addition, CSG–BRep model has detailed topological relation information, allowing further querying and analysis of 3D spatial topological information.

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  1. Chen, J., Zhao, R.L.: Spatial relationsin GIS: a survey on its key issues and research progress. Acta Geodaetica Cartogr. Sin. 28(2), 95–102 (1999)

    Google Scholar 

  2. Choudhary, A., Kandemir, M., No, J., et al.: Data management for large—scale scientific computations in high performance distributed systems. Cluster Comput. 3(1), 45–60 (2000)

    Article  Google Scholar 

  3. Wang, Y., Liu, Z., Liao, H., et al.: Improving the performance of GIS polygon overlay computation with MapReduce for spatial big data processin. Cluster Comput. 18(2), 1–10 (2015)

    Article  MathSciNet  Google Scholar 

  4. Lin, L.I., Zhigang, Z.H.A.O., Renzhong, G.U.O., Biao, H.E.: Research on 3D topology construction of space objects. Geomat. Inf. Sci. Wuhan Univ. 37(06), 719–723 (2012)

    Google Scholar 

  5. Zhenfeng, S.H.A.O., Deren, L.I., Qimin, C.: 3D topological reconstruction of complicated buildings based on stereo image pair. Editor. Board Geomat. Inf. Sci. Wuhan Univ. 29(11), 999–1003 (2004)

    Google Scholar 

  6. Changbin, W.U., Guonian, L.V.: Research on several problems of spatial topological relations. J. Geo Inf. Sci. 12(4), 524–531 (2010)

    Google Scholar 

  7. Zhao, L., Chen, L., Ranjan, R., et al.: Geographical information system parallelization for spatial big data processing: a review. Cluster Comput. 1–14 (2015)

  8. Zhanlong, C.H.E.N., Qiqi, F.E.N.G., Xincai, W.U.: Representation model of topological relations between complex planar objects. Acta Geod. Cartogr. Sin. 44(4), 438–444 (2015)

    Google Scholar 

  9. Li, S.J.: A complete classification of topological relations using the 9-intersection method. Int. J. Geogr. Inf. Sci. 20(6), 589–610 (2006)

    Article  Google Scholar 

  10. Du, S.H., Guo, L., Wang, Q., Qin, Q.M.: Efficiently computing and deriving topological relation matrices between complex regions with broad boundaries. ISPRS J. Photogramm. Remote Sens. 63(6), 593–609 (2008)

    Article  Google Scholar 

  11. Bradley, P.E., Paul, N.: Comparing G-maps with other topological data structures. Springer J. GeoInformatica 18(3), 595–620 (2014)

    Article  Google Scholar 

  12. , James, F.D.: Constructive Solid Geometry, Computer Graphics: Principles and Practice, pp. 557–558. Addison-Wesley (1996)

  13. Kim, B.C., Mun, D.: Feature-based simplification of boundary representation models using sequential iterative volume decomposition. Elsevier J. Comput. Graph. 38(38), 97–107 (2014)

    Article  Google Scholar 

  14. Levine, J.A., Jadhav, S., Bhatia, H., Pascucci, V., Bremer, P.T.: A quantized boundary representation of 2D flows. Wiley J. Comput. Graph. Forum 31(3pt1), 945–954 (2012)

    Article  Google Scholar 

  15. Daum, S., Borrmann, A.: Processing of topological BIM queries using boundary representation based methods. Elsevier J. Adv. Eng. Inf. 28(4), 272–286 (2014)

    Article  Google Scholar 

  16. Bao, Z., Grabowski, H.: Converting boundary representations to exact bintrees. Elsevier J. Comput. Ind. 37(1), 55–66 (1998)

    Article  Google Scholar 

  17. An, N., et al.: Storing spatial data on a network of workstations. Cluster Computing. 2(4), 259–270 (1999)

    Article  Google Scholar 

  18. Liu, K., Shi, W.: Extended model of topological relations between spatial objects in geographic information systems. Int. J. Appl. Earth Obs. Geoinf., 9(3):264–275 (2007)

  19. Nonaka, H., Ohsawa, Y.: A method of caching topology on implicit topology model. J-STAGE J. Theory Appl. GIS 11(1):9–17 (2003)

  20. Nian, R., He, B., Lendasse, A.: 3D object recognition based on a geometrical topology model and extreme learning machine. Springer J. Neural Comput. Appl. 22(3), 427–433 (2013)

    Article  Google Scholar 

  21. He, B., Li, L., Guo, R., Shi, Y.: 3D topological reconstruction of heterogeneous buildings considering exterior topology. Geomat. Inf. Sci. Wuhan Univ. 26(5), 579–583 (2011)

  22. Zhang, H., Yu, J., Liu, Y., Du, P.: Establishment of 3D topology for laneway based on spatial reasoning. Geogr. Geo-Inf. Sci. 25(4), 53–55 (2009)

  23. Boess, V., Ammermann, C., Niederwestberg, D., Denkena, B.: Contact zone analysis based on multidexel workpiece model and detailed tool geometry representation. Elsevier J. Procedia CIRP 4, 41–45 (2012)

  24. Lauren, L., Beghini, A.P., Rodrigo E., Menezes, I.F.M., Celes, W., Paulino, G.H.: An object-oriented framework for finite element analysis based on a compact topological data structure. Elsevier J. Adv. Eng. Softw. 68, 40–48 (2014)

  25. van Oosterom, P.: Variable-scale topological data structures suitable for progressive data transfer: the GAP-face tree and GAP-edge forest. J. Cartogr. Geogr. Inf. Sci. 32(4), 331–346 (2005)

    Article  Google Scholar 

  26. Dung, L.-R., Huang, C.-M., Yin-Yi, W.: Implementation of RANSAC algorithm for feature-based image registration. J. Comput. Commun. 1(6), 46–50 (2013)

    Article  Google Scholar 

  27. Yue, Z., Christian, C., Hervé, L.: Automatic needle detection and tracking in 3D ultrasound using an ROI-based RANSAC and Kalman method. J. Ultrason. imaging 35(4), 283–306 (2013)

    Article  Google Scholar 

  28. Schnabel, R., Wahl, R., Klein, R.: Efficient RANSAC for point-cloud shape detection. Comp. Graph. Forum 26(2), 214–226 (2007)

    Article  Google Scholar 

  29. Martínez, F., Ogayar, C., Jiménez, J.R., Rueda, A.J.: A simple algorithm for Boolean operations on polygons. Elsevier J. Adv. Eng. Softw. 64, 11–19 (2013)

    Article  Google Scholar 

  30. Pereira, A.M.B., Arruda, M.C., de Miranda, A.C.O., Lira, W.W.M., Martha, L.F.: Boolean operations on multi-region solids for mesh generation. Springer J. Eng. Comput. 28(3), 225–239 (2012)

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This paper was supported by plan projects National Administration of Surveying,Mapping and Geoinformation of China (Grant No. 2013CH-15) and by the National Natural Science Foundation of China (Grant No. 41301429). Project also supported by the Special Scientific Research Fund of Surveying Public Welfare Profession of China (Grant No. 201512009), and by science and technology planning project of Beijing Municipal Education Commission (Grant No. 2016 subprojects49) and by Beijing Natural Science Foundation (No. 8142014).

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Correspondence to Huang Ming.

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Ming, H., Yanzhu, D., Jianguang, Z. et al. A topological enabled three-dimensional model based on constructive solid geometry and boundary representation. Cluster Comput 19, 2027–2037 (2016).

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  • Triangular mesh
  • CSG–BRep
  • Topological model
  • Boolean operations
  • Spatial topological query