Spatial Databases:Digital Terrain Model

Spring, 2015

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 largerthan 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

p2p1

p4

p5

l1

l3

l2l4

p3

l7

l8

l12

l9

l11

l10

l5

l6

A1

A2

A3

A4

A5A6

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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

I1I2

I3

I4

Contour line # Polygon # height

I1 PG4 150

I2 PG3 200

I3 PG8 250

I4 PG9 300

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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 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

156

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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)

(x2,y2,z2)(x3,y3,z3)

p

Find height by triangular interpolation

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Triangular Interpolation by TIN

Nodes are measured points

(x1,y1,z1)

(x2,y2,z2)(x3,y3,z3)

Normal vector of the plane

c

b

a

nn

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

p(x, y, z)

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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

T# Nodes Adjacent Triangles

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

①

④

⑦

⑤

⑧

ⓩ

⑩

⑨

③

⑥

A

B

F

C

D

G

H

E

J

I

Triangle Table

N# x y z

1 10 10 10

2 20 25 15

. . .

Node Table

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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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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 them But not the full information

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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

Structural Sections : Ridges, Valleys and BoundariesStructural Polygon : bounded by structural sections

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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

A

F E

D

C

B

A C D E F B

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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