In r-gris/torpor: Lazy Topology

knitr::opts_chunk$set(echo = TRUE)

My reading of 6.1.11.1 within the simple features standard http://www.opengeospatial.org/standards/sfa says that a polygon ring can intersect with itself at a point, so long as no neighbouring vertices to the point are also intersected. I.e. it's a single-vertex "touch", not a shared-edge touch.

But, it seems a single ring in the boundary cannot touch itself, but a boundary composed of multiple rings can touch another ring, but only at a point. I think the standard is a little ambiguous here, the PostGIS documentation and a blog post below confirm the behaviour of GEOS validity tests.

The standard shows examples to illustrate. The PostGIS documentation shows similar illustrations, but has one not illustrated in the standard.

The PostGIS documentation http://postgis.net/docs/using_postgis_dbmanagement.html, with example (i) within 4.3.5 is equivalent to this:

p <- rbind(
  c(0, 0), 
  c(0, 4), 
  c(4, 4), 
  c(4, 0), 
  c(0, 0), 
  c(2, 1), 
  c(1, 2), 
  c(0, 0)
)
library(sf)
pp <- st_polygon(list(p))
plot(pp)
st_is_valid(pp)

This page says that the triangle should be an interior ring, with one intersection point on the outer ring.

https://3d.bk.tudelft.nl/hledoux/blog/your-polygons-the-same/

the triangle should be represented as an interior boundary touching the exterior boundary

Rebuild pp to be with an interior ring.

idx <- list(c(1, 2, 3, 4, 5), 
            c(5, 6, 7, 5))

p2 <- st_polygon(lapply(idx, function(a) p[a, ]))

 plot(p2)  
 st_is_valid(p2)

Can we fix the first attempt?

(pfix <- st_union(sfdct::ct_triangulate(pp)))

plot(pfix, col = "grey")

st_is_valid(pfix)

Can we use this?

library(rworldxtra)
data(countriesHigh)
sf_ch <- st_as_sf(countriesHigh)
ok <- st_is_valid(sf_ch)
rebuild_ch <- sf_ch
if (any(!ok)) {
 ## sf has no triangular mesh, so explode into 
 ## a GEOMETRYCOLLECTION of triangle POLYGONs
 tri_ch <- sfdct::ct_triangulate(sf_ch[which(!ok), ])
 mp_ch <- st_union(tri_ch)

 ## and then union those into MULTIPOLYGONs again

 rebuild_ch[!ok, ] <- mp_ch
}
st_is_valid(rebuild_ch)