1. Introduction to Mapping Sciences: Lecture #5 (Form and Structure) Form and Structure Describing primary and secondary spatial elements Explanation of spatial order/organization Relationships

2. Introduction to Mapping Sciences: Lecture #5 (Form and Structure) Form and Structure Edge Shape Orientation Composition Arrangement Connectivity Trends & Cycles Hierarchy/Order

3. Introduction to Mapping Sciences: Lecture #5 (Form and Structure) Edge Boundary Distinction between two features Change in identity

4. Introduction to Mapping Sciences: Lecture #5 (Form and Structure) Shape The geometric form of a feature Empirical shape vs. Standard shape

5. Introduction to Mapping Sciences: Lecture #5 (Form and Structure) Shape Compactness Comparison of Area to Perimeter Shape Index SI = 2(A/2.82(P) Circle = 1

6. Introduction to Mapping Sciences: Lecture #5 (Form and Structure) Shape Distortion Function of Projection and coordinate system Example is Mercator

7. Introduction to Mapping Sciences: Lecture #5 (Form and Structure) 3-D Shape Profiles Profiles are used to take cross-sections of three dimensions. They are particularly effective to represent terrain

8. Introduction to Mapping Sciences: Lecture #5 (Form and Structure) Orientation Direction

9. Introduction to Mapping Sciences: Lecture #5 (Form and Structure) Composition Homogeneity The consistent dispersion of a single feature. Uniformity can occur in size, shape, orientation, dispersion, connectivity etc. Diversity (heterogeneity) A mixture of features (e.g. biodiveristy). Can apply to housing, agriculture forests etc. Community Diversity with a strong component among the assemblage of features. Ecologist often talk about "plant communities" and urban planners about"sense of community".

10. Introduction to Mapping Sciences: Lecture #5 (Form and Structure) Arrangement Dispersion Spacing

11. Introduction to Mapping Sciences: Lecture #5 (Form and Structure) Terminology ClusteredScatteredRandom

12. Introduction to Mapping Sciences: Lecture #5 (Form and Structure) Measures of Central Tendency Mean Center Weighted Mean Center Median Center

13. Introduction to Mapping Sciences: Lecture #5 (Form and Structure) Mean Center Similar to arithmetic mean, only with two coordinates

14. Introduction to Mapping Sciences: Lecture #5 (Form and Structure) Weighted Mean Center Uses weights to ‘shift’ mean center

15. Introduction to Mapping Sciences: Lecture #5 (Form and Structure) Example

16. Introduction to Mapping Sciences: Lecture #5 (Form and Structure) Density Based Measures Quadrat Analysis Density Estimation

17. Introduction to Mapping Sciences: Lecture #5 (Form and Structure) Overview of Quadrat Analysis Overlay empty grid on distribution of points Count frequency of points within each grid cell Calculate the mean and variance of frequencies within grid cells Calculate the variance to mean ratio to determine amount of clustering Test for statistical significance Variance/mean ratio values significantly greater than 1 suggest a clustered pattern

18. Introduction to Mapping Sciences: Lecture #5 (Form and Structure) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 5 7 2 3 5 4 3 4 6 8 6 6 4 3 3 5 3 0 0 4 2 3 2 1 Empty GridMap of Incident Locations + = Image of Incident Frequencies Quadrat Summary

19. Introduction to Mapping Sciences: Lecture #5 (Form and Structure) Density Density estimation measures densities in a grid based on a distribution of points and point values. A simple density estimation method is to place a grid on a point distribution, tabulate points that fall within each cell, sum the point values, and estimate the cell's density by dividing the total point value by the cell size. A circle, rectangle, wedge, or ring based at the center of a cell may replace the cell in the calculation.

20. Introduction to Mapping Sciences: Lecture #5 (Form and Structure) Visual Kernel Estimation

21. Introduction to Mapping Sciences: Lecture #5 (Form and Structure) Kernel Estimation

22. Introduction to Mapping Sciences: Lecture #5 (Form and Structure) Kernel Estimation

23. Introduction to Mapping Sciences: Lecture #5 (Form and Structure) Distance Based Measures Euclidean Distance Nearest Neighbor Distance (Clark and Evans, 1954)

24. Introduction to Mapping Sciences: Lecture #5 (Form and Structure) Nearest Neighbor Index Expected Nearest Neighbor Distance If the actual points are randomly distributed, D A should be close to D E, thus NNI is close to unity. However, if the points are clustered, D A would be close to zero, and so is NNI. The more scattered the points are distributed, the larger the distance between points and NNI reaches its maximum at 2.1491. A: area where points distribute n: number of points Nearest Neighbor Index

25. Introduction to Mapping Sciences: Lecture #5 (Form and Structure) Connectivity Linkages ‘Distances’

26. Introduction to Mapping Sciences: Lecture #5 (Form and Structure) Connectivity A/3(n-2)

27. Introduction to Mapping Sciences: Lecture #5 (Form and Structure) Connectivity A/n(n-1)/2

28. Introduction to Mapping Sciences: Lecture #5 (Form and Structure) Connectivity A/n(n-1)

29. Introduction to Mapping Sciences: Lecture #5 (Form and Structure) Connectivity A B C D E

30. Introduction to Mapping Sciences: Lecture #5 (Form and Structure) Connectivity via Matrices ABCDEABCDE A B C D E 0100101001 1010110101 0101001010 0010100101 1101011010

31. Introduction to Mapping Sciences: Lecture #5 (Form and Structure) Trends and Cycles Trend is the tendency of a feature to increase or decrease. Some trends are physically observable (landforms, people density on subway) others need to be experienced (temperature gradient up a mountain). Some of the more simpler trends can be characterized with the terms constant, convex, concave to describe ground surface profiles and dome, plunging ridge, or saddle to describe terrain. Cyclical phenomena have a repetitive character and can be described mathematically for two and three dimensional features.

32. Introduction to Mapping Sciences: Lecture #5 (Form and Structure) Hierarchy and Order Hierarchies are usually created as way of showing the importance of different components of a system. For instance stream segments which have no tributaries are said to be first order streams. Second order have 1 tributary etc.