Form and Structure

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

Form and Structure

Describing primary and secondary spatial elements

Explanation of spatial order/organization

Relationships


Form and Structure

Edge

Shape

Orientation

Composition

Arrangement

Connectivity

Trends & Cycles

Hierarchy/Order


Edge

Boundary

Distinction between two features

Change in identity


Shape

The geometric form of a feature

Empirical shape vs. Standard shape


Shape Compactness

Comparison of Area to Perimeter

Shape Index

SI = 2(A/2.82(P)

Circle = 1


Shape Distortion

Function of Projection and coordinate system

Example is Mercator


3-D Shape

Profiles

Profiles are used to take cross-sections of three dimensions.

They are particularly effective to represent terrain


Orientation

Direction


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".


Arrangement

Dispersion

Spacing


Terminology

Clustered Scattered Random


Measures of Central Tendency

Mean Center

Weighted Mean Center

Median Center


Mean Center

Similar to arithmetic mean, only with two coordinates

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Weighted Mean Center

Uses weights to ‘shift’ mean center

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Example


Density Based Measures

Quadrat Analysis

Density Estimation


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


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Quadrat Summary


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.


Visual Kernel Estimation


Kernel Estimation


Distance Based Measures

Euclidean Distance

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Nearest Neighbor Distance (Clark and Evans, 1954)


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


Connectivity

Linkages

‘Distances’


Connectivity

A/3(n-2)


Connectivity

A/n(n-1)/2


Connectivity

A/n(n-1)


Connectivity

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Connectivity via Matrices

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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.


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.

Form and Structure

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