## geometric measures

##### FC-18 - Adjacency and connectivity • List different ways connectivity can be determined in a raster and in a polygon dataset
• Explain the nine-intersection model for spatial relationships
• Demonstrate how adjacency and connectivity can be recorded in matrices
• Calculate various measures of adjacency in a polygon dataset
• Create a matrix describing the pattern of adjacency in a set of planar enforced polygons
• Describe real world applications where adjacency and connectivity are a critical component of analysis
##### FC-17 - Proximity and distance decay • Describe real world applications where distance decay is an appropriate representation of the strength of spatial relationships (e.g., shopping behavior, property values)
• Explain the rationale for using different forms of distance decay functions
• Explain how a semi-variogram describes the distance decay in dependence between data values
• Outline the geometry implicit in classical “gravity” models of distance decay
• Plot typical forms for distance decay functions
• Write typical forms for distance decay functions
• Write a program to create a matrix of pair-wise distances among a set of points
• Describe real world applications where distance decay would not be an appropriate representation of the strength of spatial relationships (e.g., distance education, commuting, telecommunications)
##### FC-16 - Area and Region • List reasons why the area of a polygon calculated in a GIS might not be the same as the real world object it describes
• Demonstrate how the area of a region calculated from a raster data set will vary by resolution and orientation
• Outline an algorithm to find the area of a polygon using the coordinates of its vertices
• Explain how variations in the calculation of area may have real world implications, such as calculating density
• Delineate regions using properties, spatial relationships, and geospatial technologies
• Exemplify regions found at different scales
• Explain the relationship between regions and categories
• Identify the kinds of phenomena commonly found at the boundaries of regions
• Explain why general-purpose regions rarely exist
• Differentiate among different types of regions, including functional, cultural, physical, administrative, and others
• Compare and contrast the opportunities and pitfalls of using regions to aggregate geographic information (e.g., census data)
• Use established analysis methods that are based on the concept of region (e.g., landscape ecology)
• Explain the nature of the Modifiable Areal Unit Problem (MAUP)
##### FC-14 - Distance, Length, and Direction • Describe several different measures of distance between two points (e.g., Euclidean, Manhattan, network distance, spherical)
• Explain how different measures of distance can be used to calculate the spatial weights matrix
• Explain why estimating the fractal dimension of a sinuous line has important implications for the measurement of its length
• Explain how fractal dimension can be used in practical applications of GIS
• Explain the differences in the calculated distance between the same two places when data used are in different projections
• Outline the implications of differences in distance calculations on real world applications of GIS, such as routing and determining boundary lengths and service areas
• Estimate the fractal dimension of a sinuous line
• Describe operations that can be performed on qualitative representations of direction
• Explain any differences in the measured direction between two places when the data are presented in a GIS in different projections
• Compute the mean of directional data
• Compare and contrast how direction is determined and stated in raster and vector data
• Define “direction” and its measurement in different angular measures
##### FC-18 - Adjacency and connectivity • List different ways connectivity can be determined in a raster and in a polygon dataset
• Explain the nine-intersection model for spatial relationships
• Demonstrate how adjacency and connectivity can be recorded in matrices
• Calculate various measures of adjacency in a polygon dataset
• Create a matrix describing the pattern of adjacency in a set of planar enforced polygons
• Describe real world applications where adjacency and connectivity are a critical component of analysis
##### FC-17 - Proximity and distance decay • Describe real world applications where distance decay is an appropriate representation of the strength of spatial relationships (e.g., shopping behavior, property values)
• Explain the rationale for using different forms of distance decay functions
• Explain how a semi-variogram describes the distance decay in dependence between data values
• Outline the geometry implicit in classical “gravity” models of distance decay
• Plot typical forms for distance decay functions
• Write typical forms for distance decay functions
• Write a program to create a matrix of pair-wise distances among a set of points
• Describe real world applications where distance decay would not be an appropriate representation of the strength of spatial relationships (e.g., distance education, commuting, telecommunications)
##### FC-16 - Area and Region • List reasons why the area of a polygon calculated in a GIS might not be the same as the real world object it describes
• Demonstrate how the area of a region calculated from a raster data set will vary by resolution and orientation
• Outline an algorithm to find the area of a polygon using the coordinates of its vertices
• Explain how variations in the calculation of area may have real world implications, such as calculating density
• Delineate regions using properties, spatial relationships, and geospatial technologies
• Exemplify regions found at different scales
• Explain the relationship between regions and categories
• Identify the kinds of phenomena commonly found at the boundaries of regions
• Explain why general-purpose regions rarely exist
• Differentiate among different types of regions, including functional, cultural, physical, administrative, and others
• Compare and contrast the opportunities and pitfalls of using regions to aggregate geographic information (e.g., census data)
• Use established analysis methods that are based on the concept of region (e.g., landscape ecology)
• Explain the nature of the Modifiable Areal Unit Problem (MAUP)
##### FC-14 - Distance, Length, and Direction • Describe several different measures of distance between two points (e.g., Euclidean, Manhattan, network distance, spherical)
• Explain how different measures of distance can be used to calculate the spatial weights matrix
• Explain why estimating the fractal dimension of a sinuous line has important implications for the measurement of its length
• Explain how fractal dimension can be used in practical applications of GIS
• Explain the differences in the calculated distance between the same two places when data used are in different projections
• Outline the implications of differences in distance calculations on real world applications of GIS, such as routing and determining boundary lengths and service areas
• Estimate the fractal dimension of a sinuous line
• Describe operations that can be performed on qualitative representations of direction
• Explain any differences in the measured direction between two places when the data are presented in a GIS in different projections
• Compute the mean of directional data
• Compare and contrast how direction is determined and stated in raster and vector data
• Define “direction” and its measurement in different angular measures
##### FC-16 - Area and Region • List reasons why the area of a polygon calculated in a GIS might not be the same as the real world object it describes
• Demonstrate how the area of a region calculated from a raster data set will vary by resolution and orientation
• Outline an algorithm to find the area of a polygon using the coordinates of its vertices
• Explain how variations in the calculation of area may have real world implications, such as calculating density
• Delineate regions using properties, spatial relationships, and geospatial technologies
• Exemplify regions found at different scales
• Explain the relationship between regions and categories
• Identify the kinds of phenomena commonly found at the boundaries of regions
• Explain why general-purpose regions rarely exist
• Differentiate among different types of regions, including functional, cultural, physical, administrative, and others
• Compare and contrast the opportunities and pitfalls of using regions to aggregate geographic information (e.g., census data)
• Use established analysis methods that are based on the concept of region (e.g., landscape ecology)
• Explain the nature of the Modifiable Areal Unit Problem (MAUP)
##### FC-18 - Adjacency and connectivity • List different ways connectivity can be determined in a raster and in a polygon dataset
• Explain the nine-intersection model for spatial relationships
• Demonstrate how adjacency and connectivity can be recorded in matrices
• Calculate various measures of adjacency in a polygon dataset
• Create a matrix describing the pattern of adjacency in a set of planar enforced polygons
• Describe real world applications where adjacency and connectivity are a critical component of analysis