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Spatial Databases: Digital Terrain Model

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F:(x,y) h : one height value at each point. Efficient to represent ... Ridges, Valley and Transfluent. Most Frequently Used Geomorphological Information ... – PowerPoint PPT presentation

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Title: Spatial Databases: Digital Terrain Model


1
Spatial DatabasesDigital Terrain Model
  • Spring, 2007
  • 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

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
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
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 (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

?
?
D
A
?
E
C
B
?
?
J
?
H
F
I
G
?
?
?
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
Geomorphological 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
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
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
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