Post on 21-Dec-2015
Introduction to Mapping Sciences: Lecture #5 (Form and Structure)
Form and Structure
Describing primary and secondary spatial elements
Explanation of spatial order/organization
Relationships
Introduction to Mapping Sciences: Lecture #5 (Form and Structure)
Form and Structure
Edge
Shape
Orientation
Composition
Arrangement
Connectivity
Trends & Cycles
Hierarchy/Order
Introduction to Mapping Sciences: Lecture #5 (Form and Structure)
Edge
Boundary
Distinction between two features
Change in identity
Introduction to Mapping Sciences: Lecture #5 (Form and Structure)
Shape
The geometric form of a feature
Empirical shape vs. Standard shape
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
Introduction to Mapping Sciences: Lecture #5 (Form and Structure)
Shape Distortion
Function of Projection and coordinate system
Example is Mercator
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
Introduction to Mapping Sciences: Lecture #5 (Form and Structure)
Orientation
Direction
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".
Introduction to Mapping Sciences: Lecture #5 (Form and Structure)
Arrangement
Dispersion
Spacing
Introduction to Mapping Sciences: Lecture #5 (Form and Structure)
Terminology
Clustered Scattered Random
Introduction to Mapping Sciences: Lecture #5 (Form and Structure)
Measures of Central Tendency
Mean Center
Weighted Mean Center
Median Center
Introduction to Mapping Sciences: Lecture #5 (Form and Structure)
Mean Center
Similar to arithmetic mean, only with two coordinates
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Introduction to Mapping Sciences: Lecture #5 (Form and Structure)
Weighted Mean Center
Uses weights to ‘shift’ mean center
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Introduction to Mapping Sciences: Lecture #5 (Form and Structure)
Example
Introduction to Mapping Sciences: Lecture #5 (Form and Structure)
Density Based Measures
Quadrat Analysis
Density Estimation
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
Introduction to Mapping Sciences: Lecture #5 (Form and Structure)
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Empty Grid Map of Incident Locations
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Quadrat Summary
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.
Introduction to Mapping Sciences: Lecture #5 (Form and Structure)
Visual Kernel Estimation
Introduction to Mapping Sciences: Lecture #5 (Form and Structure)
Kernel Estimation
Introduction to Mapping Sciences: Lecture #5 (Form and Structure)
Kernel Estimation
Introduction to Mapping Sciences: Lecture #5 (Form and Structure)
Distance Based Measures
Euclidean Distance
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Nearest Neighbor Distance (Clark and Evans, 1954)
Introduction to Mapping Sciences: Lecture #5 (Form and Structure)
Nearest Neighbor Index
Expected Nearest Neighbor Distance
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If the actual points are randomly distributed, DA should be close to DE, thus NNI is close to unity. However, if the points are clustered, DA 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 distributen: number of points
Nearest Neighbor Index
Introduction to Mapping Sciences: Lecture #5 (Form and Structure)
Connectivity
Linkages
‘Distances’
Introduction to Mapping Sciences: Lecture #5 (Form and Structure)
Connectivity
A/3(n-2)
Introduction to Mapping Sciences: Lecture #5 (Form and Structure)
Connectivity
A/n(n-1)/2
Introduction to Mapping Sciences: Lecture #5 (Form and Structure)
Connectivity
A/n(n-1)
Introduction to Mapping Sciences: Lecture #5 (Form and Structure)
Connectivity
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Introduction to Mapping Sciences: Lecture #5 (Form and Structure)
Connectivity via Matrices
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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.
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.