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