SQL 2D histogram

sqlite3 tmp.sqlite 'create table t(x integer, y integer)'
sqlite3 tmp.sqlite <<EOF
insert into t values
  (0, 0),
  (1, 1),
  (2, 2),
  (3, 3),
  (4, 4),
  (5, 5),
  (6, 6),
  (7, 7),
  (8, 8),
  (9, 9),
  (10, 10),
  (11, 11),
  (12, 12),
  (13, 13),
  (14, 14),
  (15, 15),
  (16, 16),
  (17, 17),
  (18, 18),
  (19, 19),

  (2, 18)
EOF
sqlite3 tmp.sqlite 'create index txy on t(x, y)'

sqlite3 tmp.sqlite <<EOF
select
  floor(x/5)*5 as x,
  floor(y/5)*5 as y,
  count(*) as cnt
from t
group by 1, 2
order by 1, 2
EOF

0|0|5
0|15|1
5|5|5
10|10|5
15|15|5

sqlite3 tmp.sqlite <<EOF
select x, y, sum(cnt) from (
  select
      floor(x/5)*5 as x,
      floor(y/5)*5 as y,
      count(*) as cnt
    from t
    group by 1, 2
  union
  select *, 0 as cnt from generate_series(0, 15, 5) inner join (select * from generate_series(0, 15, 5))
)
group by x, y
EOF

0|0|5
0|5|0
0|10|0
0|15|1
5|0|0
5|5|5
5|10|0
5|15|0
10|0|0
10|5|0
10|10|5
10|15|0
15|0|0
15|5|0
15|10|0
15|15|5