1. ArcGIS 3-D Analyst

2. Triangulated Irregular Network (TIN)

3. A Mesh of Triangles Triangle is the only polygon that is always
planar in 3-D
Points
Lines
Surfaces

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

5. Delauney Triangulation
Maximize the minimum interior angle of triangles
No point lies within the circumcircle of a triangle
Yes No

6. Circumcircle of Triangle
Draw the perpendicular bisectors of each edge of the triangle
Circumcircle is centered on their intersection point
Radial lines from center have equal length

7. Inputs for Creating a TIN
Mass Points
Soft Breaklines
Hard Breaklines
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.

8. TIN for Waller Creek

9. TIN with Surface Features
Classroom
UT Football
Stadium
Waller Creek

10. A Portion of the TIN

11. Input Data for this Portion
Mass Points
Soft Breaklines
Hard Breaklines

12. TIN Vertices and Triangles

13. TIN Surface Model
Waller
Creek
Street and
Bridge

14. 3-D Scene

15. 3-D Scene with Buildings

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

17. Interpolation using Rasters
Interpolation in Spatial Analyst
Inverse distance weighting
Spline
Kriging
Interpolation in Geostatistical Analyst

18. Interpoloation using Kriging
Kriging weights

19. SemiVariagram
h = separation distance
between i an j

20. Fecal Coliform Levels in Galveston Bay

21. Normal Q-Q plot

22. 2D Trend Analysis

23. Defining the Semivariogram

24. Cross Validation

25. Predicted Fecal Coliform Concentration

26. Average in each Bay