1. Geographic Information Systems
GIS Analysis and Modeling

2. 5. (6) Spatial Interpolation
Predict the unknown value at a location using the known values at surrounding area
Linear interpolation
Thiessen polygon
Inverse distance weighted
Trend surface
Fourier series
Kriging

3. 5. (6) Spatial Interpolation
Linear interpolation
Known and predicted values after interpolation
Known values

5. 5. (6) Spatial Interpolation
Thiessen polygon
- Defines area of influence around a point in a way that polygon boundaries are equidistant to neighboring points

6. Obstetrical Delivery Hospital Regions (Constructed Using Thiessen Polygons): North Carolina, 1989
                                                                                                   
This map uses Thiessen polygons to construct regions: in this case, obstetrical delivery hospital regions. This technique can be utilized with little technology, using nodal points to construct polygons and, ultimately, regions.
Source: “Using Geographic Methods to Understand Health Issues,” U.S. Department of Health and Human Services
is Spatial Interpolation?

7. 3. Interpolation – Proximal ..

8. 5. (6) Spatial Interpolation
Inverse Distance weighted
- IDW works by using a weight based on the distances from an unknown value to known values
Arthur Lambor, Cornel University
© Paul Bolstad, GIS Fundamentals

9. 5. (6) Spatial Interpolation
Trend surface
- Polynomial regression to fit a least-square surface to the input points
First-order (linear) trend surface
Second-order (quadratic) trend surface
is Spatial Interpolation?

10. Trends of one, two, and three independent variables for polynomial equations of the first, second, and third orders (after Harbaugh, 1964).

11. 5. (6) Spatial Interpolation
Fourier series
Single harmonic in X1 direction
Two harmonics in X1 direction
Single harmonic in both X1 and X2 directions
Two harmonics in both directions

12. 5. (6) Spatial Interpolation
Kriging
- It takes one step further from inverse distance weighted interpolation because it accounts for not only the distances between a location with unknown value to the locations with known values, but also distances between the location with known values
Arthur Lambor, Cornel University

13. Theissen
Arthur Lambor, Cornel University

14. Inverse Distance Weighting
Arthur Lambor, Cornel University

15. Kriging
Arthur Lambor, Cornel University

16. 5. (7) Proximity Analysis (Buffering)
The identification of a zone of interest around an entity or a set of entities

17. Buffering

18. Buffering A multi-distance buffer (each ring is 150 m)
A single distance buffer (250 m)

19. 5. (8) Network Analysis
A network is a set of interconnected lines making up a set of features through which resources can flow
The shortest path problem
The traveling salesperson problem
Location-allocation

20. The Shortest Path Problem
An evaluation of links and turns required to traverse a network between required stops
It can be the shortest, fastest, or least-costly route between any number of origins and destinations, with any number of intermediate points

21. The Shortest Path Problem
Shortest and fastest routes

22. The Shortest Path Problem
Traffic assignment

23. The Traveling Salesperson Problem
An evaluation of best sequence to visit each of a set of stops and the best route between the stops

24. Vehicle Routing/Dispatching
Pickup and delivery routing

25. Location-Allocation
A match between supply and demand involving the movement of people, goods, information, and services
Determining what areas are within 10 minutes of a fire station
Locating schools within 30 min walking distance for children

26. Location Allocation Delineate service areas

27. Location Allocation Evaluate possible facility locations

28. Trip Generation/Production
Estimate the number of trips, by purpose, that are produced or originate in each zone of a study area

29. Readings
Chapter 5,6,9,10