Operations With Vector Data I

HES 505 Fall 2023: Session 11

Matt Williamson

Today’s Plan

Image Source: USGS

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 a (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 (chapter @ref(cs))
triangulate with Delauney triangulated polygon(s) (figure @ref(fig:vor))
voronoi with the Voronoi tessellation of an input geometry (figure @ref(fig:vor))
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.