# 1 Intro

## Exercise 1.1.

List five differences between raster and vector data.

- raster data have values for pixels, vector data for points, lines of polygons
- spatial locations of raster pixels are constrained to a grid, vector data coordinates can have arbitrary locations (only limited by floating point representation of coordinates)
- raster data lend themselves well to represent spatially continuously observed variables (such as imagery) or spatially continuously varying variables (such as elevation or temperature); vector data lend themselves well to represent spatially discrete features such as houses and roads, or administrative regions.
- raster data cover their spatial extent completely: every point is part of a single pixel; vector data may contain holes, or have intersecting geometries where points belong to multiple polygons.
- the operations on raster data are often simple mathematical (raster algebra) operations that include spatial operations; such simple operations are usually not available for vector data.
- raster data has trivial topology: it is clear which 4 or 8 pixels are the neighbours of every pixel; for vector data spatial there are more types of relationships, and these relationships are more complicated to detect.

The answer “Raster data is continuous data while vector data is discrete data.” is not complete: a raster of land use type represens a discrete (type) variable, a polygon map with population density represents a continuous variable. The difference lies in *spatially* continuous variables like elevation or temperature which are more easily represented by raster data, and *spatially* discrete features, such as houses and roads, which are easier represented by vector data.

## Exercise 1.2.

In addition to those listed below figure 1.1, list five further graphical components that are often found on a map.

- scale bar
- data source
- well defined title, subtitle
- orientation indicator, north arrow
- further reference elements: seas, land mass, rivers

## Exercise 1.3.

Why the numeric information shown in figure 1.4 misleading (or meaningless):

The values shown in figure 1.4 are population *total* associated with their respective counties. Without the county boundaries the meaning disappears: raster pixels do not contain population totals per pixel, population totals over larger regions or populations densities can no longer be derived based on this raster map alone.

## Exercise 1.4.

Under which conditions would you expect strong differences when doing geometrical operations on \(S^2\), compared to doing them on \(R^2\)

- when computing distances between two points at large distance from each other
- when determining what the shortest line is between two points, in particular near to the poles, or when the antimeridian crosses this line