Spatial Databases: Digital Terrain Model

1. Spatial Databases:Digital Terrain Model Spring, 2018 Ki-Joune Li

2. l1 p1 p2 l4 l2 A1 p4 p3 l5 l3 l8 A6 A5 A2 A4 l6 l7 p5 l9 p6 l12 A3 l10 p8 p7 l11 2.5-D Objects vs. 3-D Objects • Representation Methods of Terrain • 2.5-D representation • 3-D representation • 3-Dimensional Objects • More rich information • More complicated and larger than 2-D objects • 2.5- Data • F:(x,y)  h : one height value at each point • Efficient to represent surfaces or field data

3. Representation of 2.5-D data • Well-Known Methods • Contour Lines • DEM (Digital Elevation Model) • TIN (Triangulated Irregular Network)

4. Contour Lines (Contour Lines, Iso-lines) • Most popular method for paper maps • Set of pairs (polygon, h) • Nested polylines I2 I1 I4 I3

5. Contour Lines (Contour Lines, Iso-lines) • Not good for digital maps due to • Size of data • Difficulty to process andextract useful information • Low accuracy due tomultiple approximationsto compute contour linesfrom measured points

6. 156 DEM (Digital Elevation Model) • Grid division and one height data to each grid • 2-D array of height data

7. DEM (Digital Elevation Model) • Most popular method due to its simplicity • Problems • Large volume of data • Expensive computation as well as large amount data • Low accuracy due to stair-effect

8. TIN (Triangulated Irregular Network) • Set of triangulated mashes • Relatively Small Volume (x1,y1,z1) Find height by triangular interpolation p (x3,y3,z3) (x2,y2,z2)

9. (x1,y1,z1) (x3,y3,z3) (x2,y2,z2) Triangular Interpolation by TIN Nodes are measured points Normal vector of the plane n p(x, y, z) For a given point p(x, y) the height z is computed by the equation a (x- x1) + b (y- y1) + c (z- z1) = 0

10. TIN (Triangulated Irregular Network) • Triangulation • Delaunay Triangulation • Triangulation that circumcircle of a triangle is an empty circle • Duality of Voronoi diagram • Providing accurate interpolation method • Constraint Triangulation • Respect break lines: No intersection with break lines • Example: Falls

11. Data Structure for TIN ⓩ • Two tables ③ ① D A ⑩ E C B ⑥ J ⑤ ④ H F I G ⑨ ⑦ ⑧ Triangle Table Node Table

12. Weak Points of TIN • Large Volume of Data • Tradeoff Relationship between Size and Accuracy • Loss of Geo-morphological Properties • Originally designed for Height Estimation • No consideration on the representation of Geo-morphological Properties

13. Height of this point ? 745.6 m What is the optimal path from p to q ? p q We should derive them But not the full information Geo-morphological Properties vs. Height Very difficult to find it with only height data→ Need some geomorphological Information. (e.g. saddle points and ridges) By TIN, they are implicitly and partially described TIN

14. SPIN • TIN : Height Representation • With a set of triangles and • Linear interpolation • SPIN: Geo-morphological Representation • With a set of geo-morphological (or Structural) polygons • Constrained (Delaunay) Triangulation and • Linear interpolation

15. Structural Sections : Ridges, Valleys and BoundariesStructural Polygon : bounded by structural sections Example of SPIN

16. Ridge and Valley • Geomorphological Properties to be Considered by SPIN • Ridges, Valley and Transfluent • Most Frequently Used Geomorphological Information • Drainage Network, Path Analysis, etc. • Not Derivable from TIN

17. Example of SPIN

18. Observations of SPIN • Some structural sections • Dangling Sections • Constraints of Triangulation • Face of a Structural Polygon : no more plane surface • More than three vertices • But relatively Homogeneous • Number of vertices • Significantly Reduced • Improvement of Accuracy

19. A C D E F B Adjacency of Polygons • Polygonal Irregular Network • Adjacency Graph • Improve Search Performance F E A B D C

20. Basic Algorithms with SPIN • Estimation of Height

21. SPIN : Plane Region

22. SPIN : Mountain Region

23. Comparison