Geometry Data Operations and Troubleshooting

HES 505 Fall 2025: Session 11

Matt Williamson

The Vector Data Model

  • Coordinates define the Vertices (i.e., discrete x-y locations) that comprise the geometry

  • The organization of those vertices define the shape of the vector

  • General types: points, lines, polygons

Representing vector data in R

From Lovelace et al.
  • sf hierarchy reflects increasing complexity of geometry
    • st_point, st_linestring, st_polygon for single features
    • st_multi* for multiple features of the same type
    • st_geometrycollection for multiple feature types
    • st_as_sfc creates the geometry list column for many sf operations

Revisiting Simple Features

  • The sf package relies on a simple feature data model to represent geometries
    • hierarchical
    • standardized methods
    • complementary binary and human-readable encoding
type description
POINT single point geometry
MULTIPOINT set of points
LINESTRING single linestring (two or more points connected by straight lines)
MULTILINESTRING set of linestrings
POLYGON exterior ring with zero or more inner rings, denoting holes
MULTIPOLYGON set of polygons
GEOMETRYCOLLECTION set of the geometries above

Standaridized Methods

We can categorize sf operations based on what they return and/or how many geometries they accept as input.

  • Output Categories

    • 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

    • Transformations: create new geometries based on input geometries.

  • Input Geometries

    • Unary: operate on a single geometry at a time (meaning that if you have a MULTI* object the function works on each geometry individually)
    • Binary: operate on pairs of geometries
    • n-ary: operate on sets of geometries

Common Problems with Vector Data

  • Vectors and scale

  • Slivers and overlaps

  • Undershoots and overshoots

  • Self-intersections and rings

Topology Errors - Saylor Acad.

We’ll use st_is_valid() (a predicate) to check this, but fixing can be tricky

Fixing Problematic Topology

  • st_make_valid() (a transformer) for simple cases

  • st_buffer (also a transformer) with dist=0

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
```{r}
library(sf)
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

Revisiting the Raster Data Model

  • Vector data describe the “exact” locations of features on a landscape (including a Cartesian landscape)

  • Raster data represent spatially continuous phenomena (NA is possible)

  • Depict the alignment of data on a regular lattice (often a square)

    • Operations mimic those for matrix objects in R

  • Geometry is implicit; the spatial extent and number of rows and columns define the cell size

Rasters with terra

  • syntax is different for terra compared to sf

  • Representation in Environment is also different

  • Can break pipes, Be Explicit

Rasters by Construction

Rasters by Construction

mtx <- matrix(1:16, nrow=4)
mtx
     [,1] [,2] [,3] [,4]
[1,]    1    5    9   13
[2,]    2    6   10   14
[3,]    3    7   11   15
[4,]    4    8   12   16
rstr <- terra::rast(mtx)
rstr
class       : SpatRaster 
size        : 4, 4, 1  (nrow, ncol, nlyr)
resolution  : 1, 1  (x, y)
extent      : 0, 4, 0, 4  (xmin, xmax, ymin, ymax)
coord. ref. :  
source(s)   : memory
name        : lyr.1 
min value   :     1 
max value   :    16

Note: you must have raster or terra loaded for plot() to work on Rast* objects; otherwise you get Error in as.double(y) : cannot coerce type 'S4' to vector of type 'double'

Rasters by Construction: Origin

  • Origin defines the location of the intersection of the x and y axes
r <- rast(xmin=-4, xmax = 9.5, ncols=10)
r[] <- runif(ncell(r))
origin(r)
[1] 0.05 0.00
r2 <- r
origin(r2) <- c(2,2)

Rasters by Construction: Resolution

  • Geometry is implicit; the spatial extent and number of rows and columns define the cell size
  • Resolution (res) defines the length and width of an individual pixel
r <- rast(xmin=-4, xmax = 9.5, 
          ncols=10)
res(r)
[1] 1.35 1.00
r2 <- rast(xmin=-4, xmax = 5, 
           ncols=10)
res(r2)
[1] 0.9 1.0
r <- rast(xmin=-4, xmax = 9.5, 
          res=c(0.5,0.5))
ncol(r)
[1] 27
r2 <- rast(xmin=-4, xmax = 9.5, 
           res=c(5,5))
ncol(r2)
[1] 3

Predicates and measures in terra

Extending predicates

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

  • terra does not follow the same hierarchy as sf so a little trickier

Unary predicates in terra

  • Can tell us qualities of a raster dataset

  • Many similar operations for SpatVector class (note use of .)

predicate asks…
is.lonlat Does the object have a longitude/latitude CRS?
inMemory is the object stored in memory?
is.factor Are there categorical layers?
hasValues Do the cells have values?

Unary predicates in terra

  • global: tests if the raster covers all longitudes (from -180 to 180 degrees) such that the extreme columns are in fact adjacent
r <- rast()
is.lonlat(r)
[1] TRUE
is.lonlat(r, global=TRUE)
[1] TRUE
  • perhaps: If TRUE and the crs is unknown, the method returns TRUE if the coordinates are plausible for longitude/latitude
crs(r) <- ""
is.lonlat(r)
[1] NA
is.lonlat(r, perhaps=TRUE, warn=FALSE)
[1] TRUE
crs(r) <- "+proj=lcc +lat_1=48 +lat_2=33 +lon_0=-100 +ellps=WGS84"
is.lonlat(r)
[1] FALSE

Binary predicates in terra

  • Take exactly 2 inputs, return 1 matrix of cell locs where value is TRUE

  • adjacent: identifies cells adajcent to a set of raster cells

Unary measures in terra

  • Slightly more flexible than sf

  • One result for each layer in a stack

measure returns
cellSize area of individual cells
expanse summed area of all cells
values returns all cell values
ncol number of columns
nrow number of rows
ncell number of cells
res resolution
ext minimum and maximum of x and y coords
origin the orgin of a SpatRaster
crs the coordinate reference system
cats categories of a categorical raster

Binary measures in terra

  • Returns a matrix or SpatRaster describing the measure
measure returns
distance shortest distance to non-NA or vector object
gridDistance shortest distance through adjacent grid cells
costDistance Shortest distance considering cell-varying friction
direction azimuth to cells that are not NA