Use sf::st_intersects for interiors of polygons, not boundary?

Question

I need to run an error-check in R on polygons imported from shape files via sf::st_read. Polygons that share some boundary points are fine, but I need to throw an error if there are polygons that share interior points.

st_intersects tells me that polygons with common boundary points do intersect but I need to know only whether interiors intersect. Is there a fast, simple way to do this?

A simple example: Why would the following polygons' interiors overlap?

A1 <- st_polygon(list(rbind( 
   c(-9724223, 4954258), 
   c(-9724234, 4954063), 
   c(-9724202, 4954049), 
   c(-9724186, 4954169), 
   c(-9724211, 4954252), 
   c(-9724223, 4954258)))) 
tmp <- st_polygon(list(rbind( 
   c(-9724224, 4954255), 
   c(-9724268, 4954013), 
   c(-9724146, 4954008), 
   c(-9724148, 4954135), 
   c(-9724208, 4954257), 
   c(-9724224, 4954255)))) 

A2 <- st_difference(tmp, A1) 
st_intersects(A2, A1) 
st_overlaps(A2, A1) 
st_relate(A2, A1) 

Answer 1

Are you looking for something like st_relate which implements the DE9-IM relation scheme?

https://en.wikipedia.org/wiki/DE-9IM

This tells you how the exterior, boundary, and interior of two features relate to each other. For example two polygons that only touch at a point have no interior-interior relation (which is coded as F) and a point dimension boundary-boundary relation (coded as 0 for 0-dimension, ie a point).

Two polygons that share a side but don't overlap will have a boundary-boundary relation of 1 (a one-dimensional line) and an interior-interior relation of F. If the interior-interior relation of two polygons is 2 then they have a 2-dimensional area of overlap.

By careful consideration of the DE9IM matrix it is usually possible to test if two objects relate in any way you are interested in, and this can be tested in the pattern parameter to st_relate.