2022 / Day 24: Fantasy
When preparing the 2022 / day 21: Kontur World Population map and arriving at grouped-at-equator idea it looked like a ring of fire, and the train of thought through my head was:
- this looks like a ring of fire
- heh, Johnny Cash
- I wonder if Joaquin Phoenix sang himself in the movie?
- Really liked Don’t worry, he won’t get very far on foot
- that Dan Brown-based movie a couple of nights ago I saw… meeeh.
- what was it called? There was reference to Dante and the Boticelli Inferno painting.
- yeah, Inferno could be it. But a ring of fire? I could do a map on that.
- wait didn’t Galileo participate in arguments establishing the location and size of the Inferno?
- [checks interwebs]
- bingo! the Florentin Museo Galilei gives some basic estimates that Antonio Manetti was using in his calculations.
So if the Earth has a circumference of 20400 miles - and that’s most probably in the olden units, which could be
1 miglio = 2833+1⁄3 braccii = 1653.67 m
as “Italian units of measurement#Florence” @ Wikipedia
suggests. But it really doesnt’t matter in this case because we’ll be doing this
completely unitless (srid = 0) with the structure taken from
and some starter numbers:
- circumference of the Earth is
20400which means the radius is3245.45 - every ring seems to be
405.0+(15.0/22.0)width (cumulative sum) - the cuppola is 60° along the meridian line. Since the Earth is a sphere
that means that the cuppola is an arc with a length of
20400 / (360/60) = 3400.
In the end all the numbers don’t add up correctly for me, but the output looks similarish. So will have to do at the moment.
This query is really a mess and needs to be looked at some later point of time. But the general idea is to construct the vertical bisection (enlarged 60° cone) separately from the rest of the rings.
So we construct the cone_shapes that we’ll use afterwards as the 100-unit marker
lines aswell.
Generate a series of buffers in rings. Build the vertical bisection parts
in section_a as areas cut at the correct angles with cone_shapes. Dump the
points, and dump the segments, and snap points on all lines. Calculate
shared paths to see which rings need to be collapsed to straight lines.
Create the extra line for the river Acheronte. And then union it all
together trying to classify (using a single query and a single layer in QGIS
again) and label things.
Oh. And I hate labelling! With a passion.
/* Hells depth re: Antonio Manetti is 3245 miles, cone
vertex angle 60deg along meridian */
with
/* the 60 degree cone lines used to divide up
the buffers*/
cone_shapes as (
select
s,
st_reverse(
st_makeline(
array[
st_startpoint(geom),
st_point(0,0,0),
st_endpoint(geom)
]
)
) as geom
from (
select
s,
st_linesubstring(
b.geom,
0 + (s::numeric*200.0)/st_length(b.geom),
2.0*(3400.0)/st_length(geom) -
(s::numeric*200.0)/st_length(b.geom)
) as geom
from (
select
st_rotate(
st_boundary(
st_buffer(
st_point(0,0,0),
2.0*3245.45,
'quad_segs=64'
)
),
radians(120)
) as geom
) b,
generate_series(0, 10, 1) s
) d
),
rings as (
select
/* geom - the outer ring
p_geom - the inner ring
v_geom - the vertical cone geom*/
ring_no,
coalesce(
st_difference(
geom, lead(geom) over (order by ring_no)
),
geom
) as geom,
coalesce(
st_difference(
geom,
p_geom
),
geom
) as p_geom,
coalesce(
st_difference(
v_geom,
lead(v_geom) over (order by ring_no)
),
v_geom
) as v_geom
from (
select
abs(s-8) as ring_no,
s * (405.0+(15.0/22.0)) as f,
/* separate rings for outer rings*/
st_rotate(st_setsrid(
st_buffer(
st_point(0,0,0),
s * (405.0+(15.0/22.0)),
'quad_segs=64'
),0
), radians(90)) as geom,
/* separate rings for inner*/
st_rotate(st_setsrid(
st_buffer(
st_point(0,0,0),
s * (405.0+(15.0/22.0)) - p.w ,
'quad_segs=64'
),0
), radians(90)) as p_geom,
/* separate rings for the vertical section. easier this way*/
st_setsrid(
st_buffer(
st_point(0,0,0),
sum(v.height) over (order by v.i rows unbounded preceding),
'quad_segs=64'
),0
) as v_geom
from
generate_series(1,8,1) s
join lateral unnest(
array[
(730.0 +(5/22)),
(405.0 + (15.0/22.0)),
(405.0 + (15.0/22.0)),
(405.0 + (15.0/22.0)),
(405.0 + (15.0/22.0)),
(405.0 + (15.0/22.0)),
(405.0 + (15.0/22.0)),
(405.0 + (15.0/22.0))
]
) with ordinality v(height, i) on true
left join lateral unnest(
array[
/* off Manettis drawing. adds the last 87.5,0
to work. something is rotten here*/
75.0, 112.5, 50, 62.5, 75, 87.5, 87.5, 0
]
) with ordinality p(w, i) on true
where
s = v.i and s=p.i
order by s desc
) r
),
section_a as (
select
ring_no,
geom as geom
from (
select
r.ring_no, c.s,
(st_dump(st_split(r.v_geom, c.geom))).*,
o.elem, o.i
from
rings r,
cone_shapes c,
/* which cone line we'll use
to split the vertical rings*/
unnest(
array[0,0,1,2,3,4,7,10]
) with ordinality o(elem, i)
where
o.i-1 = r.ring_no and
c.s = o.elem
) f
where
path[1] = 2
),
pts as (
/* vertical cut levels need snapping to work*/
select
ring_no, pts.path[1] as point_ord,
pts.geom as geom
from section_a
join lateral
st_dumppoints(
st_removepoint(
st_boundary(section_a.geom),
0
)
) pts on true
),
segs as (
select
ring_no, seg.path[1] as p, seg.geom
from section_a
join lateral
st_dumpsegments(
st_boundary(section_a.geom)
) seg on true
),
snapped as (
select
ring_no,
st_makeline(
array_agg(geom order by ring_no, p)
) as geom
from (
select
segs.ring_no,
segs.p,
case
when pts.geom is not null then
st_addpoint(segs.geom, pts.geom, 1)
else
segs.geom
end as geom
from
segs
left join pts on
pts.ring_no = segs.ring_no + 1 and
st_dwithin(pts.geom, segs.geom, 1) and
st_linelocatepoint(segs.geom, pts.geom) > 0 and
st_linelocatepoint(segs.geom, pts.geom) < 1
) f
group by
ring_no
),
section_a_floors as (
/* create vertical rings floors*/
select
path,
case
when
/* the cuppola remains an arc*/
left_ring_no is null and
right_ring_no = 0 then
st_removepoint(
st_removepoint(geom,st_numpoints(geom)-1),
0
)
when
/* make floors straight*/
coalesce(left_ring_no, 0) > 0 and
coalesce(right_ring_no, 0) > 0 then
st_makeline(
st_startpoint(geom),
st_endpoint(geom)
)
else
geom
end as geom,
left_ring_no, right_ring_no
from (
/* calculate left and right for vertical ring bisects*/
select
path[1], geom, lpt, rpt,
l.ring_no as left_ring_no, r.ring_no as right_ring_no
from (
select
(st_dump(st_linemerge(st_union(geom)))).*
from (
select
st_node(st_collect(geom)) as geom
from
snapped
) sec
) a
join lateral
st_lineinterpolatepoint(
st_offsetcurve(a.geom, 0.1),
0.5
) lpt on true
join lateral
st_lineinterpolatepoint(
st_offsetcurve(a.geom, -0.1),
0.5
) rpt on true
left join lateral (
select
section_a.ring_no
from
section_a
where
st_within(lpt, section_a.geom)
) l on true
left join lateral (
select
section_a.ring_no
from
section_a
where
st_within(rpt, section_a.geom)
) r on true
) d
),
acheronte as (
/* extra line for the river*/
select
0 as path,
st_intersection(
l,
st_buildarea(
st_addpoint(s.geom, st_pointn(s.geom, 1))
)
) as geom,
a.left_ring_no, a.right_ring_no
from
section_a_floors a,
cone_shapes s
join lateral
st_offsetcurve(a.geom, -75) g on true
join lateral
st_makeline(
st_point(st_xmin(s.geom), st_ymin(g)),
st_point(st_xmax(s.geom), st_ymin(g))
) l on true
where
a.left_ring_no = 2 and
a.right_ring_no = 1 and
s.s = 0
)
/* and pull it all together*/
select
row_number() over()::int as oid,
case
when
cl in (
'section_floor', 'acheronte', 'iso'
) then
st_scale(geom, 1.8, 2.1)
else
geom
end as geom, cl, lbl,
left_ring_no, right_ring_no
from (
/* vertical ring bisect lines*/
select
path,
geom as geom, cl, lbl,
left_ring_no, right_ring_no
from (
select
*, 'section_floor' as cl,
case
when
left_ring_no = 7 and right_ring_no = 6 then
'7.cerchio Violenti'
when
left_ring_no = 6 and right_ring_no = 5 then
'5. e 6.cer. Iracodi & Heretici'
when
left_ring_no = 5 and right_ring_no = 4 then
'4.cerchio Prodighi et Avari'
when
left_ring_no = 4 and right_ring_no = 3 then
'3.cerchio Golosi'
when
left_ring_no = 3 and right_ring_no = 2 then
'2.cerchio Lussur'
when
left_ring_no = 2 and right_ring_no = 1 then
'Primo cerchio Limbo'
when
left_ring_no = 1 and right_ring_no = 0 then
'Volta della Terra che cuopre il Voto dell''Inferno.'
else
null
end as lbl
from
section_a_floors
union all
/* extra river line for the vertical bisect*/
select
*, 'acheronte' as cl, 'Acheronte.' as lbl
from
acheronte
) fl
union all
/* degree-isolines to display on top of vertical bisection*/
select
-1, st_linesubstring(cs.geom, fr.val[1], fr.val[2]) as geom,
'iso' as cl, l.l[cs.s+1] as lbl,
null, null
from
cone_shapes cs, (
select
array[
'C','CC','CCC','CCCC','D',
'DC', 'DCC', 'DCCC','DCCCC', 'M'] as l
) l
join lateral (
select
st_intersection(cs.geom, f.geom) as geom
from section_a_floors f
where
f.right_ring_no = 0 and
f.left_ring_no is null
) fl on true
join lateral (
select
array_agg(f order by f) as val
from (
select
st_linelocatepoint(cs.geom, p.geom) as f
from (
select (st_dump(fl.geom)).geom
) p
) d
) fr on true
union all
/* central iso-degree line for the vertical bisection*/
select
-1, st_reverse(st_makeline(st_point(0,0), st_point(0, y.max))) as geom,
'iso' as cl, '730 5/22 Burrato' as lbl,
null, null
from (
select
max(st_ymax(geom))
from
section_a_floors
) y
union all
/* rings, both inner and outer*/
select
-2 as path,
st_boundary(geom) as geom, cl as cl, lbl as lbl,
null as left_ring_no, ring_no as right_ring_no
from (
select
r.ring_no, lbl, cl, (st_dump(st_split(r.geom, c.geom))).*
from
cone_shapes c, (
select
ring_no, geom as geom, 'outer_section' as cl ,
case
when ring_no =0 then ''
when ring_no =1 then 'Limbo'
when ring_no =2 then 'Carnali'
when ring_no =3 then 'Golosi'
when ring_no =4 then 'Prodighi et Avari'
when ring_no =5 then 'Iracondi'
when ring_no =6 then 'Violenti'
when ring_no =7 then ''
else null
end as lbl
from rings
union all
select
ring_no, p_geom as geom,'inner_section' as cl ,
case
when ring_no =1 then 'Pianta dell'''
when ring_no =2 then 'Primo chercio'
when ring_no =3 then '2.cerchio'
when ring_no =4 then '3.cerchio'
when ring_no =5 then '4.cerchio'
when ring_no =6 then '5.e6.c'
when ring_no =7 then '7.c'
else null
end as lbl
from rings
) r
where
c.s = 0 and
r.ring_no > 0
) r
where
path[1] = 1
) g
;