The resulting nz_avheight objects have the same geometry as the aggregating object nz but with a new column representing the mean average height of points within each region of New Zealand (other summary functions such as median() and sd() can be used in place of mean()). Nz_avheight2 = nz %>% st_join ( nz_height ) %>% group_by ( Name ) %>% summarize (elevation = mean ( elevation, na.rm = TRUE ) ) The spatial join operation is done by st_join(), which adds the name_long variable to the points, resulting in random_joined which is illustrated in Figure 4.3 (bottom left - see 04-spatial-join.R).Д«efore creating the joined dataset, we use spatial subsetting to create world_random, which contains only countries that contain random points, to verify the number of country names returned in the joined dataset should be four (see the top right panel of Figure 4.3). The random_points object (top left) has no attribute data, while the world (top right) does. The scenario is illustrated in Figure 4.3. Y = runif (n = 10, min = bb_world, max = bb_world ) ) random_points = random_df %>% st_as_sf (coords = c ( 'x', 'y' ) ) %>% # set coordinates st_set_crs ( 4326 ) # set geographic CRS X = runif (n = 10, min = bb_world, max = bb_world ), Set.seed ( 2018 ) # set seed for reproducibility ( bb_world = st_bbox ( world ) ) # the world's bounds #> xmin ymin xmax ymax #> -180.0 -89.9 180.0 83.6 random_df = tibble ( This is demonstrated in the following command which returns the opposite of st_intersects(), points that do not intersect with Canterbury (see Section 4.2.2): These alternative spatial operators can be specified with the op = argument, a third argument that can be passed to the [ operator for sf objects. Intersects is the default spatial subsetting operator, a default that returns TRUE for many types of spatial relations, including touches, crosses and is within. These determine the type of spatial relationship that features in the target object must have with the subsetting object to be selected, including touches, crosses or within (see Section 4.2.2). Various topological relations can be used for spatial subsetting. Instead of y being of class logical or integer - a vector of TRUE and FALSE values or whole numbers - for spatial subsetting it is another spatial ( sf) object. Like attribute subsetting x subsets features of a target x using the contents of a source object y. The points in Canterbury were created with the [ subsetting operator (highlighted in gray, right). Map algebra is also the prerequisite for distance calculations on rasters, a technique which is covered in Section 4.3.6.ДЇIGURE 4.1: Illustration of spatial subsetting with red triangles representing 101 high points in New Zealand, clustered near the central Canterbuy region (left). Spatial subsetting of raster objects is covered in Section 4.3.1 merging several raster вЂtilesвЂ™ into a single object is covered in Section 4.3.8.ДЇor many applications, the most important spatial operation on raster objects is map algebra, as we will see in Sections 4.3.2 to 4.3.6. Spatial operations also apply to raster objects. These are covered in Section 4.2.2, on topological relations.ДЄnother unique aspect of spatial objects is distance.ДЄll spatial objects are related through space, and distance calculations can be used to explore the strength of this relationship. The type of spatial relationship between objects must be considered. When posing such questions, it becomes apparent that spatial operations differ substantially from attribute operations on data frames: Or is simply crossing or being within a certain distance sufficient?

Spatial joins can be used to find road speed limits related with administrative zones, even when no zone ID is provided.Д«ut this raises the question: should the road completely fall inside a zone for its values to be joined?

To illustrate the point, imagine you are researching road safety. Spatial operations differ from non-spatial operations in some ways, however. Spatial joining (Section 4.2.3) and aggregation (Section 4.2.5) also have non-spatial counterparts, covered in the previous chapter. This is especially true for vector operations: Section 3.2 on vector attribute manipulation provides the basis for understanding its spatial counterpart, namely spatial subsetting (covered in Section 4.2.1). The content builds on the previous chapter because many spatial operations have a non-spatial (attribute) equivalent. This chapter shows how spatial objects can be modified in a multitude of ways based on their location and shape. Spatial operations are a vital part of geocomputation.

Vector and raster separation studio 4