Digital Terrain Models by M. Varshosaz 1 DTM by M. Varshosaz.
Digital Terrain Model (DTM). Idea of DTM Aim: height interpolation at any point based on...
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![Page 1: Digital Terrain Model (DTM). Idea of DTM Aim: height interpolation at any point based on measured/known points Interpolation method Continuous interpolation.](https://reader036.fdocuments.net/reader036/viewer/2022062308/56649d095503460f949db057/html5/thumbnails/1.jpg)
Digital Terrain Model (DTM)
![Page 2: Digital Terrain Model (DTM). Idea of DTM Aim: height interpolation at any point based on measured/known points Interpolation method Continuous interpolation.](https://reader036.fdocuments.net/reader036/viewer/2022062308/56649d095503460f949db057/html5/thumbnails/2.jpg)
Idea of DTM
Aim: height interpolation at any point based on measured/known points
Interpolation method
•Continuous interpolation preferred (0 order, 1st order, 2nd order continuity)
•Good approximation of the surface of the earth
Digital Elevation Modeling Journal
A digital terrain model (DTM) is a topographic model of the bare earth that can be manipulated by computer program (Wikipedia)
![Page 3: Digital Terrain Model (DTM). Idea of DTM Aim: height interpolation at any point based on measured/known points Interpolation method Continuous interpolation.](https://reader036.fdocuments.net/reader036/viewer/2022062308/56649d095503460f949db057/html5/thumbnails/3.jpg)
Layout of base points
Regular layout base points (tesselation/GRID)
Irregular base points
+
Break linesextremal points
+
Boundary restrictions(e.g. lakes)
![Page 4: Digital Terrain Model (DTM). Idea of DTM Aim: height interpolation at any point based on measured/known points Interpolation method Continuous interpolation.](https://reader036.fdocuments.net/reader036/viewer/2022062308/56649d095503460f949db057/html5/thumbnails/4.jpg)
Collection of elevation dataTopographic survey (irregular points and breaklines)
Photogrammetry (grid, contours)
Contour line digitizing (contours + extremal points + breaklines)
Radar measurements (SRTM Shuttle Radar Topography Mission)1” resolution (30 m) US only3” resolution (100 m)
Leveling of grid points
GTOPO30 30” resolution
Sample data
![Page 5: Digital Terrain Model (DTM). Idea of DTM Aim: height interpolation at any point based on measured/known points Interpolation method Continuous interpolation.](https://reader036.fdocuments.net/reader036/viewer/2022062308/56649d095503460f949db057/html5/thumbnails/5.jpg)
Creation of a DTM
Regular layout (Rectangular Grid, DEM)
•Inverse Distance Weight (IDW)
•Kriging
Triangulated Irregular Network (TIN)
•Optimal, non overlapping triangle network, minimal sum of perimeters
•Delaunay triangulation
•Interpolated points from irregular base points
•Original base points are used
•Surface interpolation (trends)
![Page 6: Digital Terrain Model (DTM). Idea of DTM Aim: height interpolation at any point based on measured/known points Interpolation method Continuous interpolation.](https://reader036.fdocuments.net/reader036/viewer/2022062308/56649d095503460f949db057/html5/thumbnails/6.jpg)
IDW (Shepard 1968)
n
iii fwyxF
1
),(w – weightf – function value at the base point
n
j
pj
pi
i
t
tw
1
t – distance between base point and interpolated point
p – usual value is 2
Distance limit
Direction restriction (quarters)
![Page 7: Digital Terrain Model (DTM). Idea of DTM Aim: height interpolation at any point based on measured/known points Interpolation method Continuous interpolation.](https://reader036.fdocuments.net/reader036/viewer/2022062308/56649d095503460f949db057/html5/thumbnails/7.jpg)
Kriging (Krige 1951)
n
ii
n
iii wvwv
11
1ˆ Linear combination the elevation ofbase points
Conditions for the weight used:
Unbiased estimationEstimate minimal standard deviation
Variograms (geostatistics)
)(
1
2
)(21
)(hn
iPP hiiZZ
hnh
h – distance from base point
Effective distance, (h) doesn’t change as h increased
Least squares method
![Page 8: Digital Terrain Model (DTM). Idea of DTM Aim: height interpolation at any point based on measured/known points Interpolation method Continuous interpolation.](https://reader036.fdocuments.net/reader036/viewer/2022062308/56649d095503460f949db057/html5/thumbnails/8.jpg)
Surface interpolation
Polynom interpolation
One continuous surface (global solution)
Dynamic surfaces (local, patchwork)
Spline interpolation
...),( 243210 xaxyayaxaayxf
2nd order continuity between cubic polynoms
Sample
33
2210 xaxaxaay
Sample 2
![Page 9: Digital Terrain Model (DTM). Idea of DTM Aim: height interpolation at any point based on measured/known points Interpolation method Continuous interpolation.](https://reader036.fdocuments.net/reader036/viewer/2022062308/56649d095503460f949db057/html5/thumbnails/9.jpg)
Delaunay triangulation (1934)
Minimize the sum of the perimeter of the non overlapping triangles
Algorithm (incremental):
Start from an optimal triangle contains all the base pointsthen add a new point and divide the triangle
Condition: no points in the inscribedcircle of the triangle
Sample
![Page 10: Digital Terrain Model (DTM). Idea of DTM Aim: height interpolation at any point based on measured/known points Interpolation method Continuous interpolation.](https://reader036.fdocuments.net/reader036/viewer/2022062308/56649d095503460f949db057/html5/thumbnails/10.jpg)
Voronoi cells
DTM manipulation:
•Add point
•Add breakline
•Add triangle or polygon
•Erase part
Dual problem of DelaunayTriangulation. Areas nearest to the base points.
![Page 11: Digital Terrain Model (DTM). Idea of DTM Aim: height interpolation at any point based on measured/known points Interpolation method Continuous interpolation.](https://reader036.fdocuments.net/reader036/viewer/2022062308/56649d095503460f949db057/html5/thumbnails/11.jpg)
Areas of DTM applications
Contour line interpolation
Cross sections
Viewshed analysis
Slope category map
Aspect (slope direction)
Watershed analysis
Flow directions
Modeling (e.g. erosion)
Planning of roads, railways, pipelines
Visualization of the terrainVolume calculation
Reduction (terrain correction) of gravity measurements
Rectification of airbone or satellite photos
Hydrology example
3D view of DTM