1. Drainage Paths derived from TIN-based Digital Elevation Models Graduate student: Henrique Rennó de Azeredo Freitas Advisors: Sergio Rosim João Ricardo de Freitas Oliveira Corina da Costa Freitas National Institute for Space Research Image Processing Division São José dos Campos - Brazil 2013 INPE - Graduate Program in Applied Computing

2. Drainage Paths derived from TIN-based Digital Elevation Models Summary Introduction Related Work and Motivation Digital Elevation Models Triangulated Irregular Network (TIN) Delaunay and Constrained Delaunay Triangulation Flat Areas Drainage Paths Results Conclusions and Future Work References

3. Introduction Terrain modeling and analysis raise challenges in several areas Many important and useful results are applied in Hydrology Techniques may change improving quality of results and time efficiency Drainage Paths derived from TIN-based Digital Elevation Models

4. Related Work and Motivation Some techniques developed to calculate drainage paths from TINs: Plane gradient of triangles gives flow direction (Jones et al., 1990) Different conditions between TIN facets (Silfer et al., 1987) Trickle path traces sequence of edges and vertices from terrain features (Tsirogiannis, 2011) Geographic Information Systems (GIS) usually offer hydrology-specific functionalities Most Hydrology applications in GIS are limited to regular grids (raster) terrain models as they are much common and simple structures Drainage Paths derived from TIN-based Digital Elevation Models

5. Digital Elevation Models Digital Elevation Models are representations of terrain surfaces Drainage patterns from DEMs are very important in Hydrology Some DEM representations include: Regular Grids Triangulated Irregular Networks (TIN) Contour Lines Regular GridContour LinesTIN Drainage Paths derived from TIN-based Digital Elevation Models

6. Triangulated Irregular Networks TINs are calculated from surface-specific points with (x, y, z) coordinates They are good approximations representing main features of the terrain Delaunay Triangulation is commonly used (de Berg et al., 2008) TIN and Contour Lines Drainage Paths derived from TIN-based Digital Elevation Models

7. Delaunay Triangulation Circumcircle criteria maximizes minimum angle, avoiding skinny triangles Incremental algorithm defines a hierarchy tree structure for storage of triangles and its time complexity is O(n log n) Points are inserted one at a time locally modifying the triangulation Future C++ implementation with the Terralib library (Câmara et al., 2000) Delaunay CriteriaIncremental algorithm tree structure Drainage Paths derived from TIN-based Digital Elevation Models

8. Constrained Delaunay Triangulation Edges of the original Delaunay Triangulation could intersect contour lines segments resulting in wrong terrain features Contour lines segments are considered as restriction lines defining a Constrained Delaunay Triangulation Intersections are removed by edge rotations Triangulations before and after removing intersections Drainage Paths derived from TIN-based Digital Elevation Models

9. Flat Areas Triangles containing all vertices with same elevation values It is not possible to determine flow directions, creating discontinuities Solution: new critical points are inserted into the triangulation with interpolated elevation values Critical points are located on 2 types of edges Flat triangles and critical edges Drainage Paths derived from TIN-based Digital Elevation Models

10. Flat Areas Paths of flat triangles define the critical points to be linearly interpolated Elevations of neighboring contour lines help indicate upward/downward interpolation Branches found are also processed using previously interpolated values Paths for interpolation of critical points Drainage Paths derived from TIN-based Digital Elevation Models

11. Drainage Paths Each triangle defines a plane surface through its 3 vertices Drainage paths are calculated from a starting point in a triangle following the path of steepest descent given by the gradient of each plane Plane equation coefficients and plane gradientPaths of steepest descent in a TIN Drainage Paths derived from TIN-based Digital Elevation Models

12. Drainage Paths Gradient vectors indicate how flow continues from a vertex or another point on the edge Flow can continue either through an adjacent triangle or along an edge Gradient vectors define drainage paths Drainage Paths derived from TIN-based Digital Elevation Models

13. Drainage Paths In this work, drainage paths are calculated starting at each triangle centroid as they approximately represent their elevations Every starting point elevation is considered as a priority value and starting points are arranged from highest to lowest elevations Drainage paths being traced are connected to paths already defined All drainage paths form a graph structure where every intersection defines a graph node and gradient vectors segments are its edges connecting the nodes Drainage Paths derived from TIN-based Digital Elevation Models

14. Drainage Paths Nodes and edges of drainage paths graph Drainage Paths derived from TIN-based Digital Elevation Models

15. Results Results were obtained by processing contour lines and elevation points of São José dos Campos - SP Input data from a database named “Cidade Viva” made publicly available since 2003 by the Geoprocessing Service of the Urban Planning Department Approximately 200000 points with xy resolution of nearly 20 m and elevation differences between contour lines of 5 m The database contains a drainage network that is considered as a reference drainage Drainage Paths derived from TIN-based Digital Elevation Models

16. Results Drainage network from the “Cidade Viva” database over a RapidEye image Drainage Paths derived from TIN-based Digital Elevation Models

17. Results Drainage paths converge to the reference drainage network Drainage Paths derived from TIN-based Digital Elevation Models

18. Results Drainage paths over a TIN Drainage Paths derived from TIN-based Digital Elevation Models

19. Results Drainage networks Drainage Paths derived from TIN-based Digital Elevation Models

20. Results Drainage networks: reference drainage (left) and tin-based drainage (right) Drainage Paths derived from TIN-based Digital Elevation Models

21. Results Drainage paths converge to the reference drainage network thus forming drainage patterns very close to the real hydrologic processes governed by the terrain surface The primary and most significant concern to be considered is the quality of the results altough computational times are also important Number of points Number of triangles Number of graph nodes Total execution time (s) 500001488573061061.95 1000002650695373053.33 1500003966587993284.92 20000051243710331096.26 Executed on a PC with Intel Core i7 2.93 GHz CPU and 8 GB of RAM memory Drainage Paths derived from TIN-based Digital Elevation Models

22. Conclusions Triangulated irregular terrain models are structures that can efficiently represent terrain surfaces Drainage paths defined by plane gradients are good approximations to drainage patterns of real-world hydrologic processes Procedures and algorithms developed for processing TINs have low computational time complexities The methods proposed in this work for removing flat areas, interpolating critical points elevations and delineating drainage paths are efficient and consistent with real-world water flow distribution Drainage Paths derived from TIN-based Digital Elevation Models

23. Future Work Pit removal in order to avoid flow discontinuities Definitions of procedures for delineating watershed from the upstream nodes of the drainage network Proposal of a method for comparison of drainage networks obtained from regular grids and TINs Detailed analysis and further optimizations in the algorithms to improve computational times Integration of the triangulation structure and the proposed methods into the TerraHidro platform with the Terralib library Drainage Paths derived from TIN-based Digital Elevation Models

24. References Barbalić, D., Omerbegović, V. (1999). “Correction of horizontal areas in TIN terrain modeling–algorithm”, http://proceedings.esri.com/library/userconf/proc99/proceed/papers/pap924/ p924.htm Câmara, G., Souza, R. C. M., Pedrosa, B. M., Vinhas, L., Monteiro, A. M. V., Paiva, J. A., Carvalho, M. T., Gattass, M. (2000). TerraLib: technology in support of GIS innovation. In II Brazilian Symposium on Geoinformatics, GeoInfo2000, pages 1–8. De Berg, M., Cheong, O., Van Kreveld, M. and Overmars, M. (2008). Computational Geometry – Algorithms and Applications, Springer, 3rd edition. Drainage Paths derived from TIN-based Digital Elevation Models

25. References Jones, N. L., Wright, S. G., Maidment, D. R. (1990). Watershed delineation with triangle-based terrain models. In Journal of Hydraulic Engineering, pages 1232–1251. Prefeitura Municipal de São José dos Campos. (2003). Base de Dados “Cidade Viva”. Departamento de Planejamento Urbano, Serviço de Geoprocessamento (in Portuguese). Tsirogiannis, C. P. (2011). Analysis of flow and visibility on triangulated terrains. PhD Thesis. Eindhoven University of Technology. Zhu, Y. and Yan, L. (2010). An improved algorithm of constrained Delaunay triangulation based on the diagonal exchange. In 2nd International Conference on Future Computer and Communication, pages 827–830. Drainage Paths derived from TIN-based Digital Elevation Models

26. Thank you very much! Drainage Paths derived from TIN-based Digital Elevation Models