# Geometric binary predicates on pairs of simple feature geometry sets

Source:`R/geom-predicates.R`

`geos_binary_pred.Rd`

Geometric binary predicates on pairs of simple feature geometry sets

## Usage

```
st_intersects(x, y, sparse = TRUE, ...)
st_disjoint(x, y = x, sparse = TRUE, prepared = TRUE)
st_touches(x, y, sparse = TRUE, prepared = TRUE, ...)
st_crosses(x, y, sparse = TRUE, prepared = TRUE, ...)
st_within(x, y, sparse = TRUE, prepared = TRUE, ...)
st_contains(x, y, sparse = TRUE, prepared = TRUE, ..., model = "open")
st_contains_properly(x, y, sparse = TRUE, prepared = TRUE, ...)
st_overlaps(x, y, sparse = TRUE, prepared = TRUE, ...)
st_equals(
x,
y,
sparse = TRUE,
prepared = FALSE,
...,
retain_unique = FALSE,
remove_self = FALSE
)
st_covers(x, y, sparse = TRUE, prepared = TRUE, ..., model = "closed")
st_covered_by(x, y = x, sparse = TRUE, prepared = TRUE, ..., model = "closed")
st_equals_exact(x, y, par, sparse = TRUE, prepared = FALSE, ...)
st_is_within_distance(x, y = x, dist, sparse = TRUE, ...)
```

## Arguments

- x
object of class

`sf`

,`sfc`

or`sfg`

- y
object of class

`sf`

,`sfc`

or`sfg`

; if missing,`x`

is used- sparse
logical; should a sparse index list be returned (

`TRUE`

) or a dense logical matrix? See below.- ...
Arguments passed on to

`s2::s2_options`

`snap`

Use

`s2_snap_identity()`

,`s2_snap_distance()`

,`s2_snap_level()`

, or`s2_snap_precision()`

to specify how or if coordinate rounding should occur.`snap_radius`

As opposed to the snap function, which specifies the maximum distance a vertex should move, the snap radius (in radians) sets the minimum distance between vertices of the output that don't cause vertices to move more than the distance specified by the snap function. This can be used to simplify the result of a boolean operation. Use -1 to specify that any minimum distance is acceptable.

`duplicate_edges`

Use

`TRUE`

to keep duplicate edges (e.g., duplicate points).`edge_type`

One of 'directed' (default) or 'undirected'.

`validate`

Use

`TRUE`

to validate the result from the builder.`polyline_type`

One of 'path' (default) or 'walk'. If 'walk', polylines that backtrack are preserved.

`polyline_sibling_pairs`

One of 'discard' (default) or 'keep'.

`simplify_edge_chains`

Use

`TRUE`

to remove vertices that are within`snap_radius`

of the original vertex.`split_crossing_edges`

Use

`TRUE`

to split crossing polyline edges when creating geometries.`idempotent`

Use

`FALSE`

to apply snap even if snapping is not necessary to satisfy vertex constraints.`dimensions`

A combination of 'point', 'polyline', and/or 'polygon' that can used to constrain the output of

`s2_rebuild()`

or a boolean operation.

- prepared
logical; prepare geometry for

`x`

, before looping over`y`

? See Details.- model
character; polygon/polyline model; one of "open", "semi-open" or "closed"; see Details.

- retain_unique
logical; if

`TRUE`

(and`y`

is missing) return only indexes of points larger than the current index; this can be used to select unique geometries, see examples. This argument can be used for all geometry predicates; see also distinct.sf to find records where geometries AND attributes are distinct.- remove_self
logical; if

`TRUE`

(and`y`

is missing) return only indexes of geometries different from the current index; this can be used to omit self-intersections; see examples. This argument can be used for all geometry predicates- par
numeric; parameter used for "equals_exact" (margin);

- dist
distance threshold; geometry indexes with distances smaller or equal to this value are returned; numeric value or units value having distance units.

## Value

If `sparse=FALSE`

, `st_predicate`

(with `predicate`

e.g. "intersects") returns a dense logical matrix with element `i,j`

`TRUE`

when `predicate(x[i], y[j])`

(e.g., when geometry of feature i and j intersect); if `sparse=TRUE`

, an object of class `sgbp`

with a sparse list representation of the same matrix, with list element `i`

an integer vector with all indices j for which `predicate(x[i],y[j])`

is `TRUE`

(and hence a zero-length integer vector if none of them is `TRUE`

). From the dense matrix, one can find out if one or more elements intersect by `apply(mat, 1, any)`

, and from the sparse list by `lengths(lst) > 0`

, see examples below.

## Details

If `prepared`

is `TRUE`

, and `x`

contains POINT geometries and `y`

contains polygons, then the polygon geometries are prepared, rather than the points.

For most predicates, a spatial index is built on argument `x`

; see https://r-spatial.org/r/2017/06/22/spatial-index.html.
Specifically, `st_intersects`

, `st_disjoint`

, `st_touches`

`st_crosses`

, `st_within`

, `st_contains`

, `st_contains_properly`

, `st_overlaps`

, `st_equals`

, `st_covers`

and `st_covered_by`

all build spatial indexes for more efficient geometry calculations. `st_relate`

, `st_equals_exact`

, and do not; `st_is_within_distance`

uses a spatial index for geographic coordinates when `sf_use_s2()`

is true.

If `y`

is missing, `st_predicate(x, x)`

is effectively called, and a square matrix is returned with diagonal elements `st_predicate(x[i], x[i])`

.

Sparse geometry binary predicate (`sgbp`

) lists have the following attributes: `region.id`

with the `row.names`

of `x`

(if any, else `1:n`

), `ncol`

with the number of features in `y`

, and `predicate`

with the name of the predicate used.

for `model`

, see https://github.com/r-spatial/s2/issues/32

`st_contains_properly(A,B)`

is true if A intersects B's interior, but not its edges or exterior; A contains A, but A does not properly contain A.

See also st_relate and https://en.wikipedia.org/wiki/DE-9IM for a more detailed description of the underlying algorithms.

`st_equals_exact`

returns true for two geometries of the same type and their vertices corresponding by index are equal up to a specified tolerance.

## Note

For intersection on pairs of simple feature geometries, use
the function `st_intersection`

instead of `st_intersects`

.

## Examples

```
pts = st_sfc(st_point(c(.5,.5)), st_point(c(1.5, 1.5)), st_point(c(2.5, 2.5)))
pol = st_polygon(list(rbind(c(0,0), c(2,0), c(2,2), c(0,2), c(0,0))))
(lst = st_intersects(pts, pol))
#> Sparse geometry binary predicate list of length 3, where the predicate
#> was `intersects'
#> 1: 1
#> 2: 1
#> 3: (empty)
(mat = st_intersects(pts, pol, sparse = FALSE))
#> [,1]
#> [1,] TRUE
#> [2,] TRUE
#> [3,] FALSE
# which points fall inside a polygon?
apply(mat, 1, any)
#> [1] TRUE TRUE FALSE
lengths(lst) > 0
#> [1] TRUE TRUE FALSE
# which points fall inside the first polygon?
st_intersects(pol, pts)[[1]]
#> [1] 1 2
# remove duplicate geometries:
p1 = st_point(0:1)
p2 = st_point(2:1)
p = st_sf(a = letters[1:8], geom = st_sfc(p1, p1, p2, p1, p1, p2, p2, p1))
st_equals(p)
#> Sparse geometry binary predicate list of length 8, where the predicate
#> was `equals'
#> 1: 1, 2, 4, 5, 8
#> 2: 1, 2, 4, 5, 8
#> 3: 3, 6, 7
#> 4: 1, 2, 4, 5, 8
#> 5: 1, 2, 4, 5, 8
#> 6: 3, 6, 7
#> 7: 3, 6, 7
#> 8: 1, 2, 4, 5, 8
st_equals(p, remove_self = TRUE)
#> Sparse geometry binary predicate list of length 8, where the predicate
#> was `equals', with remove_self = TRUE
#> 1: 2, 4, 5, 8
#> 2: 1, 4, 5, 8
#> 3: 6, 7
#> 4: 1, 2, 5, 8
#> 5: 1, 2, 4, 8
#> 6: 3, 7
#> 7: 3, 6
#> 8: 1, 2, 4, 5
(u = st_equals(p, retain_unique = TRUE))
#> Sparse geometry binary predicate list of length 8, where the predicate
#> was `equals', with retain_unique = TRUE
#> 1: 2, 4, 5, 8
#> 2: 4, 5, 8
#> 3: 6, 7
#> 4: 5, 8
#> 5: 8
#> 6: 7
#> 7: (empty)
#> 8: (empty)
# retain the records with unique geometries:
p[-unlist(u),]
#> Simple feature collection with 2 features and 1 field
#> Geometry type: POINT
#> Dimension: XY
#> Bounding box: xmin: 0 ymin: 1 xmax: 2 ymax: 1
#> CRS: NA
#> a geom
#> 1 a POINT (0 1)
#> 3 c POINT (2 1)
```