PostGIS: intersections of set of collinear line segments, with counts - postgresql

Question

I have a set of collinear line segments (may be mutually disjoint, contained, or overlapping).
I want to make a new set of line segments where the segments are disjoint or touching (not overlapping), and each line segment has a count of the original line segments that cover it.
For example, suppose the original set is (drawn non-collinearly for illustration):
A----------------------B
C---------------------------D
E-----F
G-------------H
I-------J
the desired new set would be:
A-------C---E-----F-----B-----------D G-------------H-------J
1 2 3 2 1 1 1
(only the point coordinates matter, the new set does not share point objects with the old set)
How can I achieve this with PostGIS?
Related question: suppose I start with a table of line segments, not all collinear, how do I write the entire query that groups the collinear segments together and then applies the solution to my first question?
Thanks for any help!

Answer 1

Setup (for later queries):
create table lines (
id serial primary key,
label text not null,
line_data geometry(linestring) not null
);
insert into lines(label, line_data)
values ('A-B', ST_MakeLine(ST_MakePoint(-3, -6), ST_MakePoint( 1, 2))),
('D-C', ST_MakeLine(ST_MakePoint( 2, 4), ST_MakePoint(-2, -4))),
('E-F', ST_MakeLine(ST_MakePoint(-1, -2), ST_MakePoint( 0, 0))),
('G-H', ST_MakeLine(ST_MakePoint( 3, 6), ST_MakePoint( 4, 8))),
('I-J', ST_MakeLine(ST_MakePoint( 4, 8), ST_MakePoint( 5, 10))),
('P-L', ST_MakeLine(ST_MakePoint( 1, 0), ST_MakePoint( 2, 2))),
('X-Y', ST_MakeLine(ST_MakePoint( 2, 2), ST_MakePoint( 0, 4)));
Notes:
I purposely switched your D and C points to demonstrate a need for vector negation
The P-L line is parallel with your example lines (but not collinear)
The X-Y line has nothing to do with the others
the solutions below obviously won't work, when you have linestrings that have more than 2 points and those are not on the same line (so when a single linestring is not straight).
The ST_Union aggregate function can split your collinear linestrings. You'll just need to calculate how many lines are containing those.
However, grouping by collinearity is not that simple. I did not find any out-of-the-box solution for this, but you can calculate it (this will not calculate counts yet):
select string_agg(label, ','), ST_AsText(ST_Multi(ST_Union(line_data)))
from lines
group by (
select case
when ST_SRID(s) <> ST_SRID(e) then row(ST_SRID(s), s, null)
when ST_X(s) = ST_X(e) then row(ST_SRID(s), ST_SetSRID(ST_MakePoint(ST_X(s), 1.0), ST_SRID(s)), null)
when ST_Y(s) = ST_Y(e) then row(ST_SRID(s), ST_SetSRID(ST_MakePoint(1.0, ST_Y(e)), ST_SRID(s)), null)
else (
select row(
ST_SRID(s),
(select case
when ST_Y(rv) < 0
then ST_SetSRID(ST_MakePoint(-ST_X(rv), -ST_Y(rv)), ST_SRID(s))
else rv
end), -- normalized vector (negated when necessary, but same for all parallel lines)
(ST_X(e) * ST_Y(s) - ST_X(s) * ST_Y(e)) / (ST_X(e) - ST_X(s)) -- solution of the linear equaltion, where x=0
)
from coalesce(1.0 / nullif(ST_Distance(s, e), 0), 0) dmi, -- distance's multiplicative inverse
ST_TransScale(e, -ST_X(s), -ST_Y(s), dmi, dmi) rv -- raw vector (translated and scaled)
)
end
from ST_StartPoint(line_data) s,
ST_EndPoint(line_data) e
)
will produce:
X-Y | MULTILINESTRING((2 2,0 4))
P-L | MULTILINESTRING((1 0,2 2))
E-F,A-B,I-J,G-H,D-C | MULTILINESTRING((-3 -6,-2 -4),(-2 -4,-1 -2),(-1 -2,0 0),(0 0,1 2),(2 4,1 2),(3 6,4 8),(4 8,5 10))
To calculate counts, JOIN your original data again, where the splitted lines are contained by (ST_Contains) your original lines:
select ST_AsText(splitted_line), count(line_data)
from (select ST_Multi(ST_Union(line_data)) ml
from lines
group by (
select case
when ST_SRID(s) <> ST_SRID(e) then row(ST_SRID(s), s, null)
when ST_X(s) = ST_X(e) then row(ST_SRID(s), ST_SetSRID(ST_MakePoint(ST_X(s), 1.0), ST_SRID(s)), null)
when ST_Y(s) = ST_Y(e) then row(ST_SRID(s), ST_SetSRID(ST_MakePoint(1.0, ST_Y(e)), ST_SRID(s)), null)
else (
select row(
ST_SRID(s),
(select case
when ST_Y(rv) < 0
then ST_SetSRID(ST_MakePoint(-ST_X(rv), -ST_Y(rv)), ST_SRID(s))
else rv
end), -- normalized vector (negated when necessary, but same for all parallel lines)
(ST_X(e) * ST_Y(s) - ST_X(s) * ST_Y(e)) / (ST_X(e) - ST_X(s)) -- solution of the linear equaltion, where x=0
)
from coalesce(1.0 / nullif(ST_Distance(s, e), 0), 0) dmi, -- distance's multiplicative inverse
ST_TransScale(e, -ST_X(s), -ST_Y(s), dmi, dmi) rv -- raw vector (translated and scaled)
)
end
from ST_StartPoint(line_data) s,
ST_EndPoint(line_data) e)) al,
generate_series(1, ST_NumGeometries(ml)) i,
ST_GeometryN(ml, i) splitted_line
left join lines on ST_Contains(line_data, splitted_line)
group by splitted_line
will return:
LINESTRING(-3 -6,-2 -4) | 1
LINESTRING(-2 -4,-1 -2) | 2
LINESTRING(-1 -2,0 0) | 3
LINESTRING(0 0,1 2) | 2
LINESTRING(2 2,0 4) | 1
LINESTRING(1 0,2 2) | 1
LINESTRING(2 4,1 2) | 1
LINESTRING(3 6,4 8) | 1
LINESTRING(4 8,5 10) | 1