##### 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-42 - Distance Operations

Distance is a central concept in geography, and consequently, there are various types of operations that leverage the concept of distance. This short article introduces common distance measures, the purpose of distance operations, different types of operations and considerations, as well as sample applications in the physical and social domains. Distance operations can be performed on both vector or raster data, but the operations and results may differ. While performing distance operations, it is important to remember how distance is conceptualized while performing the operation.