ArcGIS 3-D Analyst

Triangulated Irregular Network (TIN)

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

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

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

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

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.

TIN for Waller Creek

TIN with Surface Features Classroom UT Football Stadium Waller Creek

A Portion of the TIN

Input Data for this Portion Mass Points Soft Breaklines Hard Breaklines

TIN Vertices and Triangles

TIN Surface Model Waller Creek Street and Bridge

3-D Scene

3-D Scene with Buildings

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

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

Interpoloation using Kriging Kriging weights

SemiVariagram h = separation distance between i an j

Fecal Coliform Levels in Galveston Bay

Normal Q-Q plot

2D Trend Analysis

Defining the Semivariogram

Cross Validation

Predicted Fecal Coliform Concentration

Average in each Bay