1. GIS - - the best way to create ugly maps FAST

2. More bad maps…

3. Representing and Transforming Graphic symbols size, symbology, value, saturation, shape, arrangement, texture, focus Classification procedures are used to ease user interpretation Natural, quantile, equal interval, s.d. Cartogram transformations distort area or distance for some specific reason More examples: US Transportation Survey

5. Components of Geographic Information Geographic Information Theme Time Space Nominal Ordinal Interval Ratio Points Lines Areas Volumes

6. (A Start at) a Typology of Thematic Maps fixedcontrolled measured geologicaltimethemelocation map census datatimelocationtheme weatherlocationtimetheme report tide tablethemelocationtime flood hydro.locationtimetheme grid cell datatimelocation theme

7. n Vector and Raster - two main families n Representation of geographic information: –Raster: location controlled, attribute measured < values are stored in ordered array, so that position in the array defines geographic location –Vector: attribute controlled, location measured < geographic coordinates are stored separately from attributes, connected with Identifiers Geographic Data Models V (v1,v2) 34312345 154021524 21351064

8. Rasters How to represent phenomena conceived as fields or discrete objects? Raster Divide the world into square cells Register the corners to the Earth Represent discrete objects as collections of one or more cells Represent fields by assigning attribute values to cells More commonly used to represent fields than discrete objects Characteristics: Pixel size The size of the cell or picture element, defining the level of spatial detail All variation within pixels is lost Assignment scheme The value of a cell may be an average over the cell, or a total within the cell, or max, or min, or the commonest value in the cell, or presence/absence, or… It may also be the value found at the cell’s central point, or systematic analigned

9. Legend Mixed conifer Douglas fir Oak savannah Grassland Raster representation. Each color represents a different value of a nominal- scale field denoting land cover class.

10. The mixed pixel problem

11. RASTERS… Each cell can be owned by only one feature. Rasters are easy to understand, easy to read and write, and easy to draw on the screen. A grid or raster maps directly onto an array. Grids are poor at representing points, lines and areas, but good at surfaces. Grids are a natural representation for scanned or remotely sensed data. Grids suffer from the mixed pixel problem. Grid compression techniques used in GIS are run- length encoding and quad trees.

12. Rasters and vectors can be flat files … if they are simple Vector-based line Raster-based line 4753456 623412 4753436 623424 4753462 623478 4753432 623482 4753405 623429 4753401 623508 4753462 623555 4753398 623634 0000000000000000 0001100000100000 1010100001010000 1100100001010000 0000100010001000 0000100010000100 0001000100000010 0010000100000001 0111001000000001 0000111000000000 0000000000000000 Flat File

13. Compacting Raster n from simple matrix to......run-length encoding...row differences encoding, TIFF...Quadtrees, Morton numbers 10 3 203 1 21

14. Vector - Land Records GIS Survey 9 / / // / / 30.5’26.23’ 20.37’26.23’ 45.81’ 35.44’ R 10’ 12 13 Survey point Computation Link Surveyed feature

15. Vector Data Structure Alternatives 1 n Development trends: –increasing complexity, refining logic –making geographic relationships EXPLICIT n Spaghetti files (1974...) –the original CIA format –lines and points which the reader must organize n Polygon loops (location lists): –polygons stored as objects, polygon shading is easy, IF CORRECT! –problems: common line defined twice; slivers between adjacent polygons because boundaries not necessarily the same (x 1,y 1 ) (x 2,y 2 ) (x 3,y 3 ) (x 4,y 4 ) (x 5,y 5 ) (x 6,y 6 )

16. n Point dictionary –polygon descriptions refer to lists of fixed points with coordinates (point dictionaries) –similar to polygon loops, but instead of coordinates of vertices in polygon descriptions - IDs of vertices n Topological data structure –Organizes Points, Lines, and Areas as Nodes, Chains, and Polygons –The model: nodes bound chains, chains co-bound polygons; chains co-bound nodes, polygons co-bound chains... –the structure stores topological relationships between nodes, chains, and polygons; these relationships are used in defining chains through nodes, polygons through chains, etc. –Provides for contiguity, better quality control... Vector Data Structure Alternatives 2 1 2 3 4 5

17. Topology n TOPOLOGY: study of basic spatial relationships based on intuitive notions of space (those not requiring numerical measurements); fundamental level of mathematics of space; n Topology IS NOT topography –TOPOGRAPHY: measurement/representation of earth elevation and related features (a form of general/ reference map) n Why topology in cartography/GIS –lines are coded once - avoids redundancy –data quality issue: [topo]-logical consistency

18. Basic arc topology n1 n2 1 2 3 A B ArcFromToPLPRn1xn1yn2xn2y 1n1n2ABxyxy Topological Arcs File

19. Arc/node map data structure with files 1 1,2,3,4,5,6,7 Arcs File POLYGON “A” A : 1,2, Area, Attributes File of Arcs by Polygon 1 2 3 4 5 6 7 8 9 10 11 12 13 1 x y 2 x y 3 x y 4 x y 5 x y 6 x y 7 x y 8 x y 9 x y 10 x y 11 x y 12 x y 13 x y P o i n t s F i l e 1 2 2 1,8,9,10,11,12,13,7

20. Tracking Topological Relationships n Connectivity –nodes bound chains –chains bound polygons in turn, –chains are bounded by nodes –polygons are bounded by chains ABC 1 2 3 4 I II III IV U V VI IDVerticesFromToLeftRight I 14AU II 12UB III 13BA IV 32BC V 43AC VI 24UC ID Chains 1 2 3 4 ID Chains A B C U Chain table Node table Polygon table ID Coord a b c d … Point table

21. Typical Digitizing Situations this is ideal, but... overshoot, and what to do with it undershoot, and what to do

22. Interrelationships between semantic and spatial structures Each string is marked with left and right labels Trying to assemble polygons from these strings: there may be more than one label “to the left” of all strings forming a closed polygon… a standard topological error... However, these labels may be in container relationship in a domain map Planar Enforcement Is Not Enough

23. Automatic labeling results… 1 2 3 4

24. Special Cases: 1 B: basal nucleus of Meynert (C0004788) B: basal nucleus of Meynert (C0004788) LGP: lateral globus pallidus, C0262267 LGP: lateral globus pallidus, C0262267 Basal nucleus cells (B) are within LGP, but their precise locations not known  polygon is coded LGP, B is a secondary descriptor Basal nucleus cells (B) are within LGP, but their precise locations not known  polygon is coded LGP, B is a secondary descriptor

25. Special Cases: 3 DG: dentate gyrus, C0152314 DG: dentate gyrus, C0152314 PoDG: polymorph layer of the dentate gyrus PoDG: polymorph layer of the dentate gyrus CA1: field CA1 of hippocampus (C0019564) CA1: field CA1 of hippocampus (C0019564) All of them have a common parent: hippocampus  a common parent is used to label polygon; polylines are labeled separately All of them have a common parent: hippocampus  a common parent is used to label polygon; polylines are labeled separately