Spatial Data Operations
HES 505 Fall 2025: Session 10
Matt Williamson
Goals for Today
Describe the Modifiable Areal Unit Problem (MAUP).
Link the inferential problems of the ecological fallacy to the statistical problems of the MAUP.
Modify the geometries of spatial objects to explore the MAUP.
Problems of Inference
Atomic Fallacy
Ecological Fallacy
Problems of Analysis
MAUP and the Ecological Fallacy
Modifiable Areal Unit Problem (MAUP)
Statistical relations depend on boundaries
(One) Indicator of the ecological fallacy
MAUP and the Ecological Fallacy
Modifying Spatial Objects
Changing geometries with sf
Revisiting predicates and measures
Predicates: evaluate a logical statement asserting that a property is
TRUEMeasures: 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 |
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)unioncan be applied to a set of geometries to return its geometrical unionintersectionanddifferencetake a single argument, but operate (sequentially) on all pairs, triples, quadruples, etc.
Changing geometries with terra
Changing pixel size with
aggregateanddisagg(leaves CRS unchanged)Dramatic changes and more sophisticated downsampling with
resample