Ever and always relationships

eContains({geometry,tquadbin},{geometry,tquadbin}) → boolean
aContains({geometry,tquadbin},{geometry,tquadbin}) → boolean
eCovers({geometry,tquadbin},{geometry,tquadbin}) → boolean
aCovers({geometry,tquadbin},{geometry,tquadbin}) → boolean
eTouches({geometry,tquadbin},{geometry,tquadbin}) → boolean
aTouches({geometry,tquadbin},{geometry,tquadbin}) → boolean
eDisjoint({geometry,tquadbin},{geometry,tquadbin}) → boolean
eDisjoint({geography,th3index},{geography,th3index}) → boolean
eDisjoint({geography,ts2cell},{geography,ts2cell}) → boolean
aDisjoint({geometry,tquadbin},{geometry,tquadbin}) → boolean
aDisjoint({geography,th3index},{geography,th3index}) → boolean
aDisjoint({geography,ts2cell},{geography,ts2cell}) → boolean
eIntersects({geometry,tquadbin},{geometry,tquadbin}) → boolean
eIntersects({geography,th3index},{geography,th3index}) → boolean
eIntersects({geography,ts2cell},{geography,ts2cell}) → boolean
aIntersects({geometry,tquadbin},{geometry,tquadbin}) → boolean
aIntersects({geography,th3index},{geography,th3index}) → boolean
aIntersects({geography,ts2cell},{geography,ts2cell}) → boolean
eDwithin({geometry,tquadbin},{geometry,tquadbin},float) → boolean
eDwithin({geography,th3index},{geography,th3index},float) → boolean
eDwithin({geography,ts2cell},{geography,ts2cell},float) → boolean
aDwithin({geometry,tquadbin},{geometry,tquadbin},float) → boolean
aDwithin(th3index,th3index,float) → boolean
aDwithin(ts2cell,ts2cell,float) → boolean

A relationship of a cell is the one of its boundary, as cellToBoundary returns it, and each grid is related in the one reading that states its cells exactly. A QUADBIN tile is bounded by meridians and parallels, which are straight lines in longitude and latitude, so a tquadbin is related through the temporal geometry of its boundary, to a geometry or another tquadbin, with the full set of relationships of the temporal geometry types. An H3 or S2 cell is bounded by great-circle arcs, so a th3index or ts2cell is related through the temporal geography of its boundary, to a geography or another cell of its grid, answered on the sphere and with a distance in metres; it has the relationships a temporal geography has, which state no containment and no touching. A geometry passed to an H3 or S2 relationship is read as the geography PostGIS converts it to. Each relationship has three quantified forms: the e-prefixed ever form returns true when the relationship holds at some instant, the a-prefixed always form when it holds at every instant, and the t-prefixed temporal form of the next section returns a tbool of the instant-by-instant result. eContains states whether one boundary contains the other, interiors only, and eCovers the same with the boundary included; eIntersects whether the boundaries share at least one point, eDisjoint whether they share none, eTouches whether they share a boundary point but no interior point, and eDwithin whether they lie within the distance passed as the third argument. The last example is a point H3 assigns to the resolution-0 cell and that lies 91 km outside the polygon joining the cell's vertices with straight lines in longitude and latitude.

SELECT eIntersects(geography 'Polygon((4.2 50.7,4.5 50.7,4.5 50.9,
  4.2 50.9,4.2 50.7))', th3index '871fa4418ffffff@2001-01-01');
-- t
SELECT eIntersects(geometry 'SRID=4326;Polygon((4.2 50.7,4.5 50.7,4.5 50.9,
  4.2 50.9,4.2 50.7))', tquadbin '48a6227affffffff@2001-01-01');
-- t
SELECT eIntersects(geography 'Polygon((4.2 50.7,4.5 50.7,4.5 50.9,
  4.2 50.9,4.2 50.7))', ts2cell '47c3c@2001-01-01');
-- t
SELECT eIntersects(th3index '8009fffffffffff@2001-01-01',
  geography 'Point(16.6328 71.9281)');
-- t