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Earth Science Informatics

, Volume 12, Issue 4, pp 581–597 | Cite as

Improving and evaluating boundary algebra filling for identifying polygon intersections

  • Chen ZhouEmail author
  • Manchun Li
Research Article
  • 52 Downloads

Abstract

Polygon intersection is important for data processing in geographic information systems. For large datasets, spatial indexing methods such as R-tree allow the identification of polygon intersections, but often retrieve inaccurate results. An improved boundary algebra filling (iBAF) method was preliminarily proposed as an alternative to R-tree. However, its applicability, performance, and accuracy require optimization, and its application conditions remain to be unveiled. This study develops version iBAF 2.0 for a more efficient identification and evaluates performance for different computational intensities and applications. Both intersecting polygons and raster zones within intersections can be rapidly grouped in the rasterized cells of input polygons. The resulting polygons can then be generated by configuring the polygon groups or converting the zones into vectors. We use complexity ratio CR, which is defined as the sum of the number of polygons in each actually intersecting group divided by the total number of polygons, to represent the computational intensity. Two land-use datasets containing 4295 and 741,562 polygons are considered, and we establish test cases containing the same polygons with varying CR. Experimental results show that iBAF 2.0 outperforms R-tree when applied to topology verification; however, its performance is conditional for polygon overlay and area calculation between two layers. Specifically, iBAF 2.0 exhibits higher-efficiency grouping of polygons and raster zones when CR exceeds specific thresholds. In addition, better scalability is achieved compared to R-tree when polygons with complex shapes and additional layers are considered.

Keywords

Geographic information systems Polygon intersection Polygon rasterization Boundary algebra filling R-tree 

Notes

Funding information

This work was supported by the National Key R&D Program of China (Grant number 2017YFB0504205).

Compliance with ethical standards

Conflict of interest

No potential conflict of interest was reported by the authors.

References

  1. Beckmann N, Kriegel HP, Schneider R, Seeger B (1990) The R*-tree: an efficient and robust access method for points and rectangles. In: Proceedings of the 1990 ACM SIGMOD International Conference on Management of Data, pp 322–331.  https://doi.org/10.1145/93597.98741
  2. Belciu AV, Olaru S (2010) Optimizing Spatial Databases. Inform Econ J 14(2):61–71Google Scholar
  3. Chang KT (2008) Introduction to geographic information systems. McGraw-Hill, New YorkGoogle Scholar
  4. De Berg M, Van Kreveld M, Overmars M, Schwarzkopf OC (2000) Computational geometry. Springer, BerlinCrossRefGoogle Scholar
  5. Dong H, Cheng ZL, Fang JY (2009) One rasterization approach algorithm for high performance map overlay. In: proceedings of 17th international conference on Geoinformatics.  https://doi.org/10.1109/GEOINFORMATICS.2009.5293561
  6. Fan JF, Kong WH, Ma T, Zhou CH, Ji M, Zhou YK (2015) RaPC: a rasterization-based polygon clipping algorithm and its error analysis. Acta Geod Carto Sinica 44(3):338–345.  https://doi.org/10.11947/j.AGCS.2015.20140017 CrossRefGoogle Scholar
  7. Fan JF, He HX, Hu TY, Li GH, Liu Q, Zhou YK (2018) Rasterization computing-based parallel vector polygon overlay analysis algorithms using OpenMP and MPI. IEEE Access 6(99):21427–21441.  https://doi.org/10.1109/ACCESS.2018.2825452 CrossRefGoogle Scholar
  8. Finkel RA, Bentley JL (1974) Quad trees a data structure for retrieval on composite keys. Acta Informatica 4(1):1–9.  https://doi.org/10.1007/bf00288933 CrossRefGoogle Scholar
  9. Gao Y, Wu B, Luo JX, Qiu HP (2017) GPU-based arbitrary polygon intersection area algorithm. In: Proceedings of 3rd international symposium on mechatronics and industrial informatics (ISMII 2017), pp 99–105.  https://doi.org/10.12783/dtetr/ismii2017/16652
  10. Gomboš IM, Žalik B (2006) Point-in-polygon tests for geometric buffers. Comput Geosci 31(10):1201–1212.  https://doi.org/10.1016/j.cageo.2005.03.009 CrossRefGoogle Scholar
  11. Greiner G, Hormann K (1998) Efficient clipping of arbitrary polygons. ACM T Graphic 17(2):71–83.  https://doi.org/10.1145/274363.274364 CrossRefGoogle Scholar
  12. Guttman A (1984) R-trees: a dynamic index structure for spatial searching. In: Proceedings of the 1984 ACM SIGMOD International Conference on Management of DataGoogle Scholar
  13. Hormann K, Agathos A (2001) The point in polygon problem for arbitrary polygons. Comput Geom 20:131–144.  https://doi.org/10.1016/S0925-7721(01)00012-8 CrossRefGoogle Scholar
  14. Kim DH, Kim MJ (2006) An extension of polygon clipping to resolve degenerate cases. Comput Aided Design Appl 3(1–4):447–456.  https://doi.org/10.1080/16864360.2006.10738483 CrossRefGoogle Scholar
  15. Liu YK, Wang XQ, Bao SZ, Gomboši M, Žalik B (2007) An algorithm for polygon clipping, and for determining polygon intersections and unions. Comput Geosci 33(5):589–598.  https://doi.org/10.1016/j.cageo.2006.08.008 CrossRefGoogle Scholar
  16. Longley PA, Goodchild MF, Maguire DJ, Rhind DW (2015) Geographic information science and systems. John Wiley & Sons, New YorkGoogle Scholar
  17. Martínez F, Rueda AJ, Feito FR (2009) A new algorithm for computing Boolean operations on polygons. Comput Geosci 35(6):1177–1185.  https://doi.org/10.1016/j.cageo.2008.08.009 CrossRefGoogle Scholar
  18. Puri S, Prasad SK (2014) Output-sensitive parallel algorithm for polygon clipping. In: Proceedings of IEEE International Conference on Parallel Processing, pp 241–250.  https://doi.org/10.1109/ICPP.2014.33
  19. Puri S, Prasad SK (2015) A parallel algorithm for clipping polygons with improved bounds and a distributed overlay processing system using MPI. In: Proceedings of IEEE/ ACM International Symposium on Cluster, Cloud and Grid Computing, pp 576–585.  https://doi.org/10.1109/CCGrid.2015.43
  20. Puri S, Agarwal D, He X, Prasad SK (2013) MapReduce algorithms for GIS polygonal overlay processing. In: Proceedings of IEEE 27th International Parallel and Distributed Processing Symposium Workshops & PhD Forum (IPDPSW), pp 1009–1016.  https://doi.org/10.1109/IPDPSW.2013.254
  21. Ren FH (1989) Theory, method and application of geographical information system. Peking University, DissertationGoogle Scholar
  22. Sellis T, Roussopoulos N, Faloutsos C (1987) The R+-tree: a dynamic index for multi-dimensional objects. In: proceedings of the 13th international conference on very large data. Bases:507–518Google Scholar
  23. Shi X (2012) System and Methods for Parallelizing Polygon Overlay Computation in Multiprocessing Environment. US 20120320087 A1Google Scholar
  24. Vatti BR (1992) A generic solution to polygon clipping. Commun ACM 35(7):56–63.  https://doi.org/10.1145/129902.129906 CrossRefGoogle Scholar
  25. Wang F (1993) A parallel intersection algorithm for vector polygon overlay. IEEE Comput Graph 13(2):74–81.  https://doi.org/10.1109/38.204970 CrossRefGoogle Scholar
  26. Wang JC, Cui C, Pu YX, Ma JS, Chen G (2010) A novel algorithm of buffer construction based on run-length encoding. Cartogr J 47(3):198–210.  https://doi.org/10.1179/000870410X12786821061413 CrossRefGoogle Scholar
  27. Wang JC, Cui C, Chen G, Pu YX, Ma JS (2012a) A new trapezoidal-mesh based data model for spatial operations. Int J Digit Earth 5(2):165–183.  https://doi.org/10.1080/17538947.2011.580860 CrossRefGoogle Scholar
  28. Wang KB, Huai Y, Lee RB, Wang FS, Zhang XD, Saltz JH (2012b) Accelerating pathology image data cross-comparison on CPU-GPU hybrid systems. PVLDB 5:1543–1554.  https://doi.org/10.14778/2350229.2350268 CrossRefGoogle Scholar
  29. Wang Y, Liu ZL, Liao HY (2015) Improving the performance of GIS polygon overlay computation with MapReduce for spatial big data processing. Cluster Comput 18(2):507–516.  https://doi.org/10.1007/s10586-015-0428-x CrossRefGoogle Scholar
  30. Weiler K, Atherton P (1977) Hidden surface removal using polygon area sorting. In: Proceedings of the 4th Annual Conference on Computer Graphics and Interactive Techniques, pp 214–222.  https://doi.org/10.1145/563858.563896
  31. Zhou XF, Abel DJ, Truffet D (1998) Data partitioning for parallel spatial join processing. GeoInformatica 2(2):175–204.  https://doi.org/10.1023/A:1009755931056 CrossRefGoogle Scholar
  32. Zhou CH, Ou Y, Yang L, Qin B (2007) An equal area conversion model for rasterization of vector polygons. Sci China Ser D 50(S1):169–175.  https://doi.org/10.1007/s11430-007-5013-6 CrossRefGoogle Scholar
  33. Zhou C, Chen ZJ, Li MC (2018) A parallel method to accelerate geospatial operations involving polygon intersections. Int J Geogr Inf Sci 32(12):2402–2426.  https://doi.org/10.1080/13658816.2018.1508689 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Geography and Ocean ScienceNanjing UniversityNanjingPeople’s Republic of China

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