1. Spatial Databases: Digital Terrain Model Spring, 2015 Ki-Joune Li

2. STEMPNU 2 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 p8p8 p7p7 p6p6 p2p2 p1p1 p4p4 p5p5 l1l1 l3l3 l2l2 l4l4 p3p3 l7l7 l8l8 l 12 l9l9 l 11 l 10 l5l5 l6l6 A1A1 A2A2 A3A3 A4A4 A5A5 A6A6

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

4. STEMPNU 4 Contour Lines (Contour Lines, Iso-lines) Most popular method for paper maps  Set of pairs (polygon, h)  Nested polylines I1I1 I2I2 I3I3 I4I4 Contour line #Polygon #height I1I1 PG 4 150 I2I2 PG 3 200 I3I3 PG 8 250 I4I4 PG 9 300

5. STEMPNU 5 Contour Lines (Contour Lines, Iso-lines) Not good for digital maps due to  Size of data  Difficulty to process and extract useful information  Low accuracy due to multiple approximations to compute contour lines from measured points

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

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

9. STEMPNU 9 Triangular Interpolation by TIN Nodes are measured points (x1,y1,z1)(x1,y1,z1) (x2,y2,z2)(x2,y2,z2) (x3,y3,z3)(x3,y3,z3) Normal vector of the plane n For a given point p(x, y) the height z is computed by the equation a (x- x 1 ) + b (y- y 1 ) + c (z- z 1 ) = 0 p(x, y, z)

10. STEMPNU 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. STEMPNU 11 Data Structure for TIN Two tables T#NodesAdjacent Triangles N1N2N3T1T2T3 A124BEX B245FCA... J6910EXEI ① ④ ⑦ ⑤ ⑧ ⓩ ⑩ ⑨ ③ ⑥ A B F C D G H E J I Triangle Table N#xyz 110 2202515... Node Table

12. STEMPNU 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. STEMPNU 13 Geo-morphological Properties vs. Height TIN Height of this point ? 745.6 m What is the optimal path from p to q ? p q 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 We should derive themBut not the full information

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

16. STEMPNU 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. STEMPNU 17 Example of SPIN

18. STEMPNU 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. STEMPNU 19 Adjacency of Polygons Polygonal Irregular Network  Adjacency Graph  Improve Search Performance A F E D C B ACDEFB

20. STEMPNU 20 Basic Algorithms with SPIN Estimation of Height

21. STEMPNU 21 SPIN : Plane Region

22. STEMPNU 22 SPIN : Mountain Region

23. STEMPNU 23 Comparison