Operations With Vector Data I

HES 505 Fall 2024: Session 10

Carolyn Koehn

Announcements

Due this week: assignment revision 1

Objectives

By the end of today, you should be able to:

  • Recognize the unary, binary, and n-ary transformers

  • Articulate common uses for unary and binary transformers

  • Use unary transformations to fix invalid geometries

  • Implement common binary transformers to align and combine data

Revisiting predicates and measures

  • Predicates: evaluate a logical statement asserting that a property is TRUE

  • Measures: return a numeric value with units based on the units of the CRS

  • Unary, binary, and n-ary distinguish how many geometries each function accepts and returns

Transformations

  • Transformations: create new geometries based on input geometries

Unary Transformations

transformer returns a geometry …
centroid of type POINT with the geometry’s centroid
buffer that is larger (or smaller) than the input geometry, depending on the buffer size
jitter that was moved in space a certain amount, using a bivariate uniform distribution
wrap_dateline cut into pieces that do no longer cover the dateline
boundary with the boundary of the input geometry
convex_hull that forms the convex hull of the input geometry
line_merge after merging connecting LINESTRING elements of a MULTILINESTRING into longer LINESTRINGs.
make_valid that is valid
node with added nodes to linear geometries at intersections without a node; only works on individual linear geometries
point_on_surface with an arbitrary point on a surface
polygonize of type polygon, created from lines that form a closed ring

Common Unary Transformations

Fixing geometries

  • When all(st_is_valid(your.shapefile)) returns FALSE
  • st_make_valid has two methods:
    • original converts rings into noded lines and extracts polygons
    • structured makes rings valid first then merges/subtracts from existing polgyons
    • Verify that the output is what you expect!!
```{r}
x = st_sfc(st_polygon(list(rbind(c(0,0),c(0.5,0),c(0.5,0.5),c(0.5,0),c(1,0),c(1,1),c(0,1),c(0,0)))))
st_is_valid(x)
```
[1] FALSE

Fixing geometries with st_make_valid

```{r}
y <- x %>% st_make_valid()
st_is_valid(y)
```
[1] TRUE

Fixing Geometries with st_buffer

  • st_buffer enforces valid geometries as an output

  • Setting a 0 distance buffer leaves most geometries unchanged

  • Not all transformations do this

```{r}
z <- x %>% st_buffer(., dist=0)

st_is_valid(z)
```
[1] TRUE

Changing CRS with st_transform

  • You’ve already been using this!!

  • Does not guarantee valid geometries (use check = TRUE if you want this)

  • We’ll try to keep things from getting too complicated

Converting areas to points with st_centroid or st_point_on_surface

  • For “sampling” other datasets

  • To simplify distance calculations

  • To construct networks

id.counties <- tigris::counties(state = "ID", progress_bar=FALSE)
id.centroid <- st_centroid(id.counties)
id.pointonsurf <- st_point_on_surface(id.counties)

Creating “sampling areas”

  • Uncertainty in your point locations

  • Incorporate a fixed range around each point

  • Combine multiple points into a single polygon

hospitals.id <- landmarks.id.csv %>% 
  st_as_sf(., coords = c("longitude", "lattitude")) %>% 
  filter(., MTFCC == "K1231")
st_crs(hospitals.id) <- 4326

Creating sampling areas

hospital.buf <- hospitals.id %>%
  st_buffer(., dist=10000)

hospital.mcp <- hospitals.id %>% 
  st_convex_hull(.)

Other Unary Transformations

transformer returns a geometry …
segmentize a (linear) geometry with nodes at a given density or minimal distance
simplify simplified by removing vertices/nodes (lines or polygons)
split that has been split with a splitting linestring
transform transformed or convert to a new coordinate reference system
triangulate with Delauney triangulated polygon(s)
voronoi with the Voronoi tessellation of an input geometry
zm with removed or added Z and/or M coordinates
collection_extract with subgeometries from a GEOMETRYCOLLECTION of a particular type
cast that is converted to another type
+ that is shifted over a given vector
* that is multiplied by a scalar or matrix

Binary Transformers

Binary Transformers

function returns infix operator
intersection the overlapping geometries for pair of geometries &
union the combination of the geometries; removes internal boundaries and duplicate points, nodes or line pieces |
difference the geometries of the first after removing the overlap with the second geometry /
sym_difference the combinations of the geometries after removing where they intersect; the negation (opposite) of intersection %/%
crop crop an sf object to a specific rectangle

Binary Transformers

Common Uses of Binary Transformers

  • Relating partially overlapping datasets to each other

  • Reducing the extent of vector objects

N-ary Transformers

  • Similar to Binary (except st_crop)

  • union can be applied to a set of geometries to return its geometrical union

  • intersection and difference take a single argument, but operate (sequentially) on all pairs, triples, quadruples, etc.

Practice

Centroids and Distances

The function system.time tells you how long a function takes to run:

system.time(id.counties <- tigris::counties(state = "ID", progress_bar=FALSE))
   user  system elapsed 
   0.84    0.49    1.33

Find the counties that are the furthest distance from each other in Idaho using the polygons, centroids, and point on surface objects we created earlier. Which distance calculation is the fastest?

(You may want to refer to our session 7 example code.)

Intersections and Buffers

tigris::primary_secondary_roads() retrieves shapefiles for major roads in each state of the US.

  1. Plot just Ada county and the major roads within.

  2. Map the portion of major roads that are within 50 km (as the crow flies) of the center of Ada county. (Remember to check the units of your CRS.)

  3. Challenge: Include county borders in your plot for part 2.