Tables tables are rows (across) and columns (down) common format in spreadsheets multiple tables linked together create a relational database entity equals one row attribute equals one column

Conceptual structure of table one row characterizes a place one column provides a distribution of attribute two or more rows provide a comparative characterization of places two or more columns provide a correlation between attributes

Storage of spatial attributes this area creates complexity logical idea is to store one set of x and y (maybe z) coordinates per row place, x coordinate, y coordinate, (z), attribute 1 of place, attribute 2 of place works fine when places are points what to do when there are multiple vertices (lines, polygons) will discuss in detail later

Maps maps are an intermediate model between the data of “reality” and its use previously –real world > survey/measurement > map –add GIS get real world > survey/measurement > map > digitizing/scanning (encoding into computer) > analysis/manipulation > map

Geomatics today –real world > survey/measurement (GPS) = encoding > analysis/manipulation reportsmaps displays ???

Map limitations constraints of 2 dimensions variability shown via color/symbology “well known” idea reformulation of way humans think?

Maps and time critical issue how to deal with data that changes most critical (particularly) to social scientists is time modifiable area unit voting districts, counties, census units

Types of change in boundaries Proper division “improper” division (more common)

How do you compare results 1900 census to 1990 voting patterns between years etc. typically convert to standardized area measure –pop density (republicans per square mile)

Key different forms to store data in a database extensional –words, descriptors, stock prices each day, population, x and y coordinates intensional –small amount of data and rules formula fitted to stock fluctuations or population x and y of center and radius of circle

Conversions intensional to extensional –convert circle to multi-sided polygon extensional to intensional –fit a formula to a set of data points

Geometries Descriptive (“traditional” mapping) –measurement of properties of objects in space –enables true lengths, angles, lines of intersection to be determined by graphical and algebraic means Topological –relationships of components of form (i.e. mode of arrangement) Computational –concepts, principles and tools used in numeric (in contrast to algebraic) practice of geometry

Coordinate referencing essential to geometry Cartesian –x and y (sometimes z) and attribute {x,y,z,a} polar –range, bearing (sometimes azimuth) and attribute {r,b,az,a} All imply a POB (point of beginning)

Discrete entity referencing narrative bounds meets meets and bounds addresses “blocks of earth space” - city limits, county European national grid (Cartesian) P ublic Land Survey System PLSS –township/range/section

Global referencing latitude and longitude Z value implied by earth spheroid conversion of global to map via projection

Distance measurement Euclidean Manhattan network ground spherical map projection

Line simplification/generalization idea is to allow reasonable representation with fewer data elements stored maintain main elements of shape maintain topological relationship –e.g. house on “right” side of street is still on “right” side after generalization

Methods of line generalization splines proximity (min distance) angle (min angle of change) perpendicular distance need threshold value