drainage paths derived from tin-based digital elevation models graduate student: henrique rennó de...

Drainage Paths derived from TIN-based Digital Elevation Models

Graduate student:Henrique Rennó de Azeredo Freitas

Advisors:Sergio Rosim

João Ricardo de Freitas OliveiraCorina da Costa Freitas

National Institute for Space ResearchImage Processing Division

São José dos Campos - Brazil2013

INPE - Graduate Program in Applied Computing


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

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


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


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 Grid Contour LinesTIN


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


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 Criteria Incremental algorithm tree structure


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


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


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

• 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 gradient Paths of steepest descent in a TIN


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

• 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

Nodes and edges of drainage paths graph


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


Results

Drainage network from the “Cidade Viva” databaseover a RapidEye image


Results

Drainage paths converge to the reference drainage network


Results

Drainage paths over a TIN


Results

Drainage networks


Results

Drainage networks: reference drainage (left) and tin-based drainage (right)


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)

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


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


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


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.


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.


Thank you very much!


drainage paths derived from tin-based digital elevation models graduate student: henrique rennó de...

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