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

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 p8 p7 p6 p2 p1 p4 p5 l1 l3 l2 l4 p3 l7 l8
l12 l9
l11
l10 l5 l6 A1 A2 A3 A4 A5 A6

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
Contour line #
Polygon #
height I1
PG4
150 I2
PG3
200 I3
PG8
250 I4
PG9
300 I2 I1 I4 I3

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

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. Triangular Interpolation by TIN
Nodes are measured points
Normal vector of the plane n
p(x, y, z)
(x1,y1,z1)
(x2,y2,z2)
(x3,y3,z3)
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 Triangle Table Node Table ⓩ ③ ① D A⑩ B C ⑥ ④ ⑤ J H F I G ⑨ ⑦ ⑧
Triangle Table
Node Table T#
Nodes
Adjacent Triangles N1 N2 N3 T1 T2 T3 A 1 2 4 B EX 5 F C
. . . J 6 9 10 E I N# x y z 1 10 2 20 25 15
. . .

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. Geo-morphological Properties vs. Height
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 them
But not the full information
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

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

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

20. Basic Algorithms with SPIN
Estimation of Height

21. SPIN : Plane Region

22. SPIN : Mountain Region

23. Comparison