Spatial tolerances applied to data

1. Spatial tolerances applied to data Line weeding Dangle truncation Node matching Fuzzy tolerance

2. Simple polygon • single unit of space bounded by three (or more) lines and containing no holes • this is essentially the same definition as the cell • boundary can be irregular or regular (e.g. a square can be a polygon)

3. Complex polygon and regions • a complex polygon is a simple polygon with one (or more holes) • can be called an area • a region is composed of two or more non-connecting simple polygons (often a scale issue) • Note - in GeoMedia this is called discontinuous geometries • examples • hole = Farmer Browns field with a pond in the center • region/discontinuous geometry = the state of Hawaii, USA • note that region usually has a different definition

4. Concept of contiguity and scale • example - boundaries that include water Congressional district 1 2 3 4 5 6 What is the “entity” ? The state of Hawaii? the islands of the state of Hawaii? Is the “water” part of the congressional district?

5. Contiguity has effect on how spatial data is stored • if unit is Hawaii • store all geometries as a single entity that is discontinuous • if unit is “islands of Hawaii” • store as multiple records • example of problem : how do you calculate the area of Hawaii

6. Basic statistical unit • the smallest unit for which attribute data of a given kind are collected • the basic statistical unit may be a simple/complex polygon or it may be a region • examples - the Census block and the soils mapping unit 1 Ab 2 3 Vn Vn Two “BSUs” Ab Three “BSUs”

7. The relationship between basic attribute unit and basic map unit • attributes may be recorded for the what are simple polygons or may be regions • if there are regions then there can lead to complexity in analyses • each polygon (simple or complex) may be unique • multiple polygons refer to a single row in the table

8. 1 Ab 2 3 Vn Vn Ab One to one & one to many Block population Avg. income 1 12,345 $4,500 2 4,234 $10,345 3 18,900 $24,560 Soil map permeability pH unit Ab 3.6 6.7 Vn 4.8 7.2

9. There is not always a one to one relationships between topology and BSUs

10. Property of containment • inclusion of one spatial entity within another • points may be within areas • and possibly within lines depending on definition • lines may be within areas • and possibly within (or coincident with) lines • areas may be within areas • containment can be ordered • completely (proper subset) • USA - states - counties • partially • USA - states - Census MSA (may overlap multiple counties)

11. Determining the structure of containment may be messy • many phenomena have overlapping boundaries store shopping boundaries Store 1 Store 2 Store 3 Are there three entities or seven are there three rows in the attribute table or seven?

12. As multiple units are combined • largest common spatial unit resulting from the overlap • smallest units (cells) used to create the largest common unit • spatial primitives used to make up the smallest units (vertices, lines) • spatial unit for which data is recorded

13. Spatial ordering

14. Enclosures versus holes

15. Spatial data modeling w/out explicit topology

16. Explicit topology encoding

17. Connectivity and contiguity

18. Polygon encoding

19. Topological encoding for linear entities