Basic Concepts of GIS January 29, 2013

What is GIS? “A powerful set of tools for collecting, storing, retrieving, transforming and displaying spatial data”

A Geographic Information System requires: (1) Data containing locational information (2) An ability to store or readily compute the spatial interrelations that describe how the data are connected (also known as topology) Having information about how the data was collected, its precision and accuracy (metadata) is preferable, but not essential.

Computational geometry – branch of mathematics that deals with the spatial relationships between and among objects All features/objects are one of the following types: 0 dimensions - point (node) 1 dimension - line (arc, link) 2 dimensions - area (polygon) 3 dimensions - volume Topology

Spatial relations example

Examples of Spatial/Topological Relations: Belongs (New Castle, Kent and Sussex belong to Delaware) Comprises (Delaware comprises New Castle, Kent and Sussex) Located in (The city of Wilmington is located in New Castle) Borders on (New Castle borders on Kent but not Sussex) Is a certain distance from (Wilmington is 47 miles from Dover) Is within a certain distance of (Dover is within 60 miles of every point in the state of Delaware)

Until about 1995, a GIS stored topological information explicitly: Node topology - a listing of nodes and the links that meet at each node Link topology - a listing of links and the nodes that bound them, as well as the polygons to the left and right of each link Polygon topology - a listing of polygons and the links that define them Since that time, topological information is not stored, but calculated on the fly using various algorithms (more on this later!)

The shape file has long been the standard file type for GIS information Consists of a minimum of three parts: -.shp – the feature geometry itself -.shx – shape index format; a positional index to allow seeking forwards and backwards quickly -.dbf – the data attributes A shape file contains a collection of points, lines, or polygons – never a mixture!

Find the distance from Albany to Buffalo: GIS program, or Google Earth: Simple calculation executable through a drop-down menu Non-GIS: Obtain the coordinates for Albany and Buffalo. Type in the Pythagorean distance formula. If your coordinates are in latitude and longitude, add cosine terms to account for the curvature of the earth. Add additional trigonometric terms to account for the non- spherical nature of the earth. GIS vs. non-GIS

Find the counties that border Albany County: GIS program: Simple calculation executable through a drop- down menu Regular database (brute force approach): Create a table of all coordinate points defining the borders of every county in New York. Match Albany county coordinates against all county coordinates. (An exact match is not good enough if coverage is not clean – or if the Hudson River is stored as a separate object – you would then need to write code to find points that are within some small distance of one another.) Google Earth: No obvious solution

2 Broad Models of Reality: 1. Space is occupied by entities: real-world phenomena that are not divisible into phenomena of the same kind. Examples: County Building Disease case 2. Space is occupied by continuously varying attributes. Examples: Air pollution Temperature Elevation Vector vs. raster

2 Broad Models of Reality: 1. Space is occupied by entities: real-world phenomena that are not divisible into phenomena of the same kind. Examples: County Building Disease case 2. Space is occupied by continuously varying attributes. Examples: Air pollution Temperature Elevation Vector model Raster model

Vector and raster representations of a river:

Distance Perimeter Area Centroid Some basic GIS functions:

Centroid

Distanc e

Area and Perimeter

Centroid

Intersect Buffer Polygon Overlay Combine/Split Objects Some more basic GIS functions:

Select all from SchoolDist, ZIP where SchoolDist.obj intersects ZIP.obj Intersect

Buffer

Buffer +Intersect

Polygon Overlay

Combine/split objects

Advanced Spatial Analysis Functions in GIS: Shortest Path Routing Location-Allocation Nearest Neighbor Spatial autocorrelation Spatial interpolation Advanced functions

Shortest path

Routing

Location-Allocation

Nearest neighbor

HighNone Spatial autocorrelation

Spatial interpolation

Now to look at some algorithms… Point in polygon: Ray-tracing and the even-odd rule

Many points in many polygons: The grid-based method

Polygon intersection: The bounding-box rectangle method

Shortest path: Dykstra’s algorithm