Spatial Databases: Digital Terrain Model

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Spatial DatabasesDigital Terrain Model

• Spring, 2007
• Ki-Joune Li

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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

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Representation of 2.5-D data

• Well-Known Methods
• Contour Lines
• DEM (Digital Elevation Model)
• TIN (Triangulated Irregular Network)

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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
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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

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DEM (Digital Elevation Model)

• Grid division and one height data to each grid
• 2-D array of height data

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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

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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)
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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
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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

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Data Structure for TIN
?

• Two tables

?
?
D
A
?
E
C
B
?
?
J
?
H
F
I
G
?
?
?
Triangle Table
Node Table
T Nodes Nodes Nodes Adjacent Triangles Adjacent Triangles Adjacent Triangles
T N1 N2 N3 T1 T2 T3
A 1 2 4 B EX EX
B 2 4 5 F C A
. . . . . . . . . . . . . . . . . . . . .
J 6 9 10 EX E I
N x y z
1 10 10 10
2 20 25 15
. . . . . . . . . . . .
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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

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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
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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

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Example of SPIN
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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

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Example of SPIN
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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

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Adjacency of Polygons

• Polygonal Irregular Network
• Adjacency Graph
• Improve Search Performance

F
E
A
B
D
C
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Basic Algorithms with SPIN

• Estimation of Height

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SPIN Plane Region
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SPIN Mountain Region
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Comparison