1. Modeling Surfaces Using Triangulated Irregular Network Raster Interpolation From Points
The C.W. Post College of Long Island University, ArcGIS 3-D Analyst,
( 307-acre campus located 25 miles east of Manhattan , Brookville, New York)

2. Surface terrain model for city of Austin, TX ArcGIS 3-D Analyst
Shoal creek
Waller creek

3. Triangulated Irregular Network (TIN) Algorithm for interpolating irregularly-spaced data to represent terrain heights for terrain modeling
UT Campus

4. TIN Digital representation of the terrain
Preserves details of a shape on the terrain, more accurate representation of urban area
Break lines represent significant terrain features like a lake or cliff that cause a change in slope
Relatively few points are required to represent large, flat, or smoothly continuous areas
Requires a much smaller number of points than a gridded DTM (The digital terrain model) in order to represent the surface terrain with equal accuracy

5. Steps to Form a Surface From TIN
A triangular mesh is drawn on the control and determined data points
A perimeter around the data points is established.
The points are connected in a manner that smallest triangle formed from any three points is constructed (convex hull)
To connect the interior points, Delaunay triangulation is used (lines from one triangle do not cross lines of another)
A surface is created by integrating all of the triangles over the domain
Additional elevation data such as spot elevations at summits and depressions and break lines are also collected for the TIN model

6. A Mesh of Triangles in 2-D
Points
Face
Edge
Triangle is the only
polygon that is always
planar in 3-D
Points
Lines
Surfaces
Each triangle defines a terrain surface, or facet assumed to be of
uniform slope and aspect over the triangle

7. TIN Triangles in 3-D (x3, y3, z3) (x1, y1, z1) (x2, y2, z2) z y
Projection in (x,y) plane x

8. Delauney Triangulation
Developed around 1930 to design the triangles efficiently
Geometrically related to theissen tesselations
Maximize the minimum interior angle of triangles that can be formed
No point lies within the circumcircle of a triangle that is contained in mesh
Yes
More uniform representation of terrain No

9. Inputs for Creating a TIN
Mass Points
Soft Breaklines
Hard Breaklines
Mass Points define points anywhere on landscape
Hard breaklines define locations of abrupt surface change (e.g. streams, ridges, road kerbs, building footprints, dams)
Soft breaklines are used to ensure that known z values along a linear feature are maintained in the tin.

10. TIN with Linear Surface Features
Classroom
UT Football
Stadium
Waller Creek
City of Austin digitized all the buildings to get emergency vehicles quickly

11. A Portion of the TIN in Large View

12. Input data for this portion
Mass Points
not inside building
Soft Breaklines
along the hills
Hard Breaklines
along the roads

13. TIN Vertices and Triangles

14. ESRI TIN Engine Integrated Terrain Model, ARCGIS 9.2
Creates varying levels of conditions and points to produce pyramid style TINs on the fly
Provides an efficient methodology for working with mass data
Results in a single dataset that can rapidly deploy and visualize TIN based surfaces at multiple scale
Courtesy,

15. TIN Surface Model
Waller
Creek
Street and
Bridge

16. Data Sources to Develop TINs
LIDAR (Light Detection and Ranging; or Laser Imaging Detection and Ranging)
Aerial photogrammetry

17. LIDAR An optical remote sensing technology
Masures properties of scattered light to find range and/or other information of a distant target
LIDAR sensor was mounted on-board
During the flight, the LIDAR sensor pulses a narrow, high frequency laser pulse toward the earth through a port opening in the bottom of the aircraft's fuselage
The LIDAR sensor records the time difference between the emission of the laser beam and the return of the reflected laser signal to the aircraft
Range to an object is determined by measuring the time delay between transmission of a pulse and detection of the reflected signal to the aircraft
Points are distributed across the space, push-broom sensor
Amazing degrees of details. Resolution is 1/9 arc second
1 arc second DEM = 30 m
1/3 arc second DEM = 10 m

18. LIDAR Terrain Surface for Powder River, Wyoming
Source: Roberto Gutierrez, UT Bureau of Economic Geology

19. NCALM National Center for Airborne Laser Mapping
Sponsored by the National Science Foundation (NSF) (
Operated jointly by the Department of Civil and Coastal Engineering, College of Engineering, University of Florida (UF) and the Department of Earth and Planetary Science, University of California- Berkeley (UCB)
Invites proposals from graduate students seeking airborne laser swath mapping (ALSM) observations covering limited areas (generally no more than 40 square kilometers) for use in research to earn an M.S. or PhD degree.
Proposals must be submitted on-line by November 30, 2006

20. Aerial photogrammetry (Stereo photographic coverage)
The aerial photos are taken using a stereoscopic camera
Two pictures of a particular area are simultaneously taken, but from slightly different angles, overlapping photographs
The overlapping area of the two resulting photos is called a stereo pair
Using a computer, stereoplotter, the stereo pair can be viewed as a single image with the appearance of depth or relief

21. Aerial photogrammetry (Stereo photographic coverage)
The aerial photos are taken using a stereoscopic camera
Two pictures of a particular area are simultaneously taken, but from slightly different angles, overlapping photographs
The overlapping area of the two resulting photos is called a stereo pair
Using a computer, stereoplotter, the stereo pair can be viewed as a single image with the appearance of depth or relief
Ground control points are established based on ground surveys or aerial triangulation and are viewed in the stereoplotter in conjunction with the stereo pair
The image coordinates of any (x,y,z) point in stereoscopic image pair can be determined and randomly selected and digitized

22. 3-D ArcScene, Austin, TX Aerial photogrammetry

23. 3-D Scene with Buildings

24. Some advantages of TINS
Fewer points are needed to represent the topography---less computer disk space
Points can be concentrated in important areas where the topography is variable and a low density of points can be used in areas where slopes are constant.
Points of known elevation such as surveyed benchmarks can easily be incorporated
Areas of constant elevation such as lakes can easily be incorporated
Lines of slope inflection such as ridgelines and steep canyons streams can be incorporated as breaklines in TINS to force the TIN to reflect these breaks in topography

25. Geostatistics Why interpolate?
Analogy: Spatially distributed objects are spatially correlated; things that are close together tend to have similar characteristics

26. Interpolation using Rasters
Interpolation in Spatial Analyst
Inverse distance weighting (IDW)
Spline
TOPOGRID, Topo to Raster (creation of hydrologically correct digital elevation models)
Kriging (utilize the statistical properties of the measured points & quantify the spatial autocorrelation among measured points )
Interpolation in Geostatistical Analyst

27. ArcGIS Spatial Analyst to create a surface using IDW interpolation
IDW weights
assigned arbitrarily

28. Example for a linear IDW interpolation

29. Using the ArcGIS Spatial Analyst to create a surface using IDW interpolation
Each input point has a local influence that diminishes with distance
It weights the points closer to the processing cell greater than those farther away
With a fixed radius, the radius of the circle to find input points is the same for each interpolated cell
By specifying a minimum count, within the fixed radius, at least a minimum number of input points is used in the calculation of each interpolated cell
A higher power puts more emphasis on the nearest points, creating a surface that has more detail but is less smooth
A lower power gives more influence to surrounding points that are farther away, creating a smoother surface. Search is more globally

30. Topo to Raster interpolation

31. ArcGIS Spatial Analyst to create a surface using Topo to Raster interpolation
Designed for the creation of hydrologically correct digital elevation models
Interpolates a hydrologically correct surface from point, line, and polygon
Based on the ANUDEM program developed by Michael Hutchinson (1988, 1989)
The ArcGIS 9.x implementation of TopoGrid from ArcInfo Workstation 7.x
The only ArcGIS interpolator designed to work intelligently with contour inputs
Iterative finite difference interpolation technique
It is optimized to have the computational efficiency of local interpolation methods, such as (IDW) without losing the surface continuity of global interpolation methods, such as Kriging and Spline

32. Using the ArcGIS Spatial Analyst to create a surface using Spline interpolation
Best for generating gently varying surfaces such as elevation, water table heights, or pollution concentrations
Fits a minimum-curvature surface through the input points
Fits a mathematical function to a specified number of nearest input points while passing through the sample points
The REGULARIZED option usually produces smoother surfaces than those created with the TENSION
For the REGULARIZED, higher values used for the Weight parameter produce smoother surfaces
For the TENSION, higher values for the Weight parameter result in somewhat coarser surfaces but with surfaces that closely conform to the control points
The greater the value of Number of Points, the smoother the surface of the output raster

33. Example for a 2-D Spline interpolation

34. Interpoloation using Kriging
Things that are close to one another are more alike than those farther away : spatial autocorrelation
As the locations get farther away, the measured values will have little relationship with the value of the prediction location
Kriging weights
based on semivariogram

35. SemiVariagram
Captures spatial dependence between samples by plotting semivariance against seperation distance
Sill The height that the semivariogram reaches when it levels off.
Range: The distance at which the semivariogram levels off to the sill
Nugget effect: a discontinuity at the origin (the measurement error and microscale variation )

36. SemiVariagram
h = separation distance
between i an j

37. Case study Legend White Hat Niobrara Elkhorn North Platte Loup
Missouri tributaries
Niobrara
North Platte
South Platte
Middle Platte
Republican
Little Blue
Big Blue
Nemaha
Lower Platte
White Hat
River basin boundary
State boundary
Automatic weather station
High : 5422 meters
Low : 836 meters
Legend