INPE - Graduate Program in
Applied Computing
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
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
Drainage Paths derived from TIN-based
Digital Elevation Models
Introduction
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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
Related Work and Motivation
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Some techniques developed to calculate drainage paths from TINs:
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Plane gradient of triangles gives flow direction (Jones et al., 1990)
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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
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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
Digital Elevation Models
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Digital Elevation Models are representations of terrain surfaces
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Drainage patterns from DEMs are very important in Hydrology
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Some DEM representations include:
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Regular Grids
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Triangulated Irregular Networks (TIN)
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Contour Lines
Regular Grid
TIN
Contour Lines
Drainage Paths derived from TIN-based
Digital Elevation Models
Triangulated Irregular Networks
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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
Delaunay Triangulation
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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
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Future C++ implementation with the Terralib library (Câmara et al., 2000)
Delaunay Criteria
Incremental algorithm tree structure
Drainage Paths derived from TIN-based
Digital Elevation Models
Constrained Delaunay Triangulation
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Edges of the original Delaunay Triangulation could intersect contour lines
segments resulting in wrong terrain features
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Contour lines segments are considered as restriction lines defining a
Constrained Delaunay Triangulation
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Intersections are removed by edge rotations
Triangulations before and after removing intersections
Drainage Paths derived from TIN-based
Digital Elevation Models
Flat Areas
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Triangles containing all vertices with same elevation values
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It is not possible to determine flow directions, creating discontinuities
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Solution: new critical points are inserted into the triangulation with
interpolated elevation values
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Critical points are located on 2 types of edges
Flat triangles and critical edges
Drainage Paths derived from TIN-based
Digital Elevation Models
Flat Areas
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Paths of flat triangles define the critical points to be linearly interpolated
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Elevations of neighboring contour lines help indicate upward/downward
interpolation
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Branches found are also processed using previously interpolated values
Paths for interpolation of critical points
Drainage Paths derived from TIN-based
Digital Elevation Models
Drainage Paths
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Each triangle defines a plane surface through its 3 vertices
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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 gradient
Paths of steepest descent in a TIN
Drainage Paths derived from TIN-based
Digital Elevation Models
Drainage Paths
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Gradient vectors indicate how flow continues from a vertex or another
point on the edge
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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
Drainage Paths
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In this work, drainage paths are calculated starting at each triangle
centroid as they approximately represent their elevations
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Every starting point elevation is considered as a priority value and
starting points are arranged from highest to lowest elevations
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Drainage paths being traced are connected to paths already defined
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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
Drainage Paths
Nodes and edges of drainage paths graph
Drainage Paths derived from TIN-based
Digital Elevation Models
Results
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Results were obtained by processing contour lines and elevation points
of São José dos Campos - SP
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Input data from a database named “Cidade Viva” made publicly available
since 2003 by the Geoprocessing Service of the Urban Planning
Department
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Approximately 200000 points with xy resolution of nearly 20 m and
elevation differences between contour lines of 5 m
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The database contains a drainage network that is considered as a
reference drainage
Drainage Paths derived from TIN-based
Digital Elevation Models
Results
Drainage network from the “Cidade Viva” database
over a RapidEye image
Drainage Paths derived from TIN-based
Digital Elevation Models
Results
Drainage paths converge to the reference drainage network
Drainage Paths derived from TIN-based
Digital Elevation Models
Results
Drainage paths over a TIN
Drainage Paths derived from TIN-based
Digital Elevation Models
Results
Drainage networks
Drainage Paths derived from TIN-based
Digital Elevation Models
Results
Drainage networks: reference drainage (left) and tin-based drainage (right)
Drainage Paths derived from TIN-based
Digital Elevation Models
Results
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Drainage paths converge to the reference drainage network thus forming
drainage patterns very close to the real hydrologic processes governed
by the terrain surface
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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)
50000
148857
306106
1.95
100000
265069
537305
3.33
150000
396658
799328
4.92
200000
512437
1033109
6.26
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
Conclusions
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Triangulated irregular terrain models are structures that can efficiently
represent terrain surfaces
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Drainage paths defined by plane gradients are good approximations to
drainage patterns of real-world hydrologic processes
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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
Future Work
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Pit removal in order to avoid flow discontinuities
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Definitions of procedures for delineating watershed from the upstream
nodes of the drainage network
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Proposal of a method for comparison of drainage networks obtained from
regular grids and TINs
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Detailed analysis and further optimizations in the algorithms to improve
computational times
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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
References
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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
References
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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
Thank you very much!