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-- | |
-- viznodelist.lua | |
-- speedata publisher | |
-- | |
-- Written 2010-2020 by Patrick Gundlach. | |
-- This file is released in the spirit of the well known MIT license | |
-- (see https://opensource.org/licenses/MIT for more information) | |
-- | |
-- visualizes nodelists using graphviz | |
-- usage example: | |
-- \setbox0\hbox{\vbox{\hbox{abc}}\vbox{x}} | |
-- \directlua{ | |
-- require("viznodelist") | |
-- viznodelist.nodelist_visualize(0,"mybox.gv") | |
-- } | |
-- | |
-- \bye | |
-- and then open "mybox.gv" with graphviz | |
-- | |
-- nodelist_visualize takes three arguments: | |
-- 1: the number of the box or the box itself (when called from Lua) | |
-- 2: the filename of the dot-file to create | |
-- 3: the options table (optional). Known keywords: | |
-- - showdisc = <boolean> (defaults to false) | |
-- | |
-- | |
-- Newest file is at https://gist.github.com/pgundlach/556247 | |
local io,string,table = io,string,table | |
local assert,tostring,type = assert,tostring,type | |
local tex,texio,node,unicode,font,status=tex,texio,node,unicode,font,status | |
local pairs = pairs | |
local print = print | |
module(...) | |
local factor = 2^16 | |
-- tostring(a_node) looks like "<node nil < 172 > nil : hlist 2>", so we can | |
-- grab the number in the middle (172 here) as a unique id. So the node | |
-- is named "node172" | |
local function get_nodename(n) | |
return "\"n" .. string.gsub(tostring(n), "^<node%s+%S+%s+<%s+(%d+).*","%1") .. "\"" | |
end | |
local function link_to( n,nodename,label ) | |
if n then | |
local t = node.type(n.id) | |
local nodename_n = get_nodename(n) | |
if t=="temp" or t=="nested_list" then return end | |
local ret | |
if label=="prev" then | |
-- ignore nodes where node.prev.next does not exist. | |
-- TODO: this should be more clever: ignore prev pointers of the first nodes in a list. | |
if not n.next then return end | |
ret = string.format("%s:%s:w -> %s:title\n",nodename,label,get_nodename(n)) | |
elseif label=="head" then | |
ret = string.format("%s:%s -> %s:title\n",nodename,label,get_nodename(n)) | |
else | |
ret = string.format("%s:%s -> %s:title\n",nodename,label,get_nodename(n)) | |
end | |
return ret | |
end | |
end | |
local function get_subtype( n ) | |
typ = node.type(n.id) | |
local subtypes = { | |
hlist = { | |
[0] = "unknown origin", | |
"created by linebreaking", | |
"explicit box command", | |
"parindent", | |
"alignment column or row", | |
"alignment cell", | |
}, | |
glyph = { | |
[0] = "character", | |
"glyph", | |
"ligature", | |
}, | |
disc = { | |
[0] = "\\discretionary", | |
"\\-", | |
"- (auto)", | |
"h&j (simple)", | |
"h&j (hard, first item)", | |
"h&j (hard, second item)", | |
}, | |
glue = { | |
[0] = "skip", | |
[1] = "lineskip", | |
[2] = "baselineskip", | |
[3] = "parskip", | |
[4] = "abovedisplayskip", | |
[5] = "belowdisplayskip", | |
[6] = "abovedisplayshortskip", | |
[7] = "belowdisplayshortskip", | |
[8] = "leftskip", | |
[9] = "rightskip", | |
[10] = "topskip", | |
[11] = "splittopskip", | |
[12] = "tabskip", | |
[13] = "spaceskip", | |
[14] = "xspaceskip", | |
[15] = "parfillskip", | |
[16] = "thinmuskip", | |
[17] = "medmuskip", | |
[18] = "thickmuskip", | |
[100] = "leaders", | |
[101] = "cleaders", | |
[102] = "xleaders", | |
[103] = "gleaders" | |
}, | |
rule = { | |
[2] = "image" | |
} | |
} | |
subtypes.whatsit = node.whatsits() | |
if subtypes[typ] then | |
return subtypes[typ][n.subtype] or tostring(n.subtype) | |
else | |
return tostring(n.subtype) | |
end | |
assert(false) | |
end | |
local function label(n,tab ) | |
local typ = node.type(n.id) | |
local nodename = get_nodename(n) | |
local subtype = get_subtype(n) | |
local ret = string.format("%s [ label = \"<title> name: %s (id %s) | <sub> type: %s | { <prev> prev |<next> next }",nodename or "??",typ or "??",string.gsub(nodename,"\"","") or "??",subtype or "?") | |
if tab then | |
for i=1,#tab do | |
if tab[i][1] then | |
ret = ret .. string.format("|<%s> %s",tab[i][1],tab[i][2]) | |
end | |
end | |
end | |
return ret .. "\"]\n" | |
end | |
local function draw_node( n,tab ) | |
local ret = {} | |
if not tab then | |
tab = {} | |
end | |
local nodename = get_nodename(n) | |
local attlist = n.attr | |
if attlist then | |
attlist = attlist.next | |
while attlist do | |
tab[#tab + 1] = { "", string.format("attr%d=%d",attlist.number, attlist.value) } | |
attlist = attlist.next | |
end | |
end | |
local properties = node.getproperty(n) | |
if properties then | |
for k,v in pairs(properties) do | |
tab[#tab + 1] = { "", string.format("%s=%s\\l",k, v) } | |
end | |
end | |
ret[#ret + 1] = label(n,tab) | |
ret[#ret + 1] = link_to(n.next,nodename,"next") | |
ret[#ret + 1] = link_to(n.prev,nodename,"prev") | |
return table.concat(ret) | |
end | |
local function sanitize(num) | |
if num > 0x110000 then num = 65533 end | |
local c = unicode.utf8.char(num) | |
local ret = c:gsub("\"","\\\"") | |
return ret | |
end | |
local function draw_action( n ) | |
local nodename = get_nodename(n) | |
local ret = string.format("%s [ label = \"<title> name: %s ", nodename, "action") | |
local tab = { | |
{"action_type", string.format("action_type: %s", tostring(n.action_type))}, | |
{"action_id" , string.format("action_id: %s",tostring(n.action_id))}, | |
{"named_id", string.format("named_id: %s",tostring(n.named_id))}, | |
{"file", string.format("file: %s",tostring(n.file))}, | |
{"new_window" , string.format("new_window: %s",tostring(n.new_window))}, | |
{"data", string.format("data: %s",tostring(n.data):gsub(">","\\>"):gsub("<","\\<"))}, | |
{"refcount" , string.format("ref_count: %s",tostring(n.ref_count))}, | |
} | |
for i=1,#tab do | |
if tab[i][1] then | |
ret = ret .. string.format("|<%s> %s",tab[i][1],tab[i][2]) | |
end | |
end | |
return ret .. "\"]\n" | |
end | |
local function dot_analyze_nodelist( head, options ) | |
local ret = {} | |
local typ,nodename | |
while head do | |
typ = node.type(head.id) | |
nodename = get_nodename(head) | |
if typ == "hlist" then | |
local tmp = {} | |
if head.width ~= 0 then | |
local width = string.format("width %gpt",head.width / factor) | |
tmp[#tmp + 1] = {"width",width} | |
end | |
if head.height ~= 0 then | |
local height= string.format("height %gpt",head.height / factor) | |
tmp[#tmp + 1] = {"height",height} | |
end | |
if head.depth ~= 0 then | |
local depth = string.format("depth %gpt",head.depth / factor) | |
tmp[#tmp + 1] = {"depth",depth} | |
end | |
if head.glue_set ~= 0 then | |
local glue_set = string.format("glue_set %g",head.glue_set) | |
tmp[#tmp + 1] = {"glue_set",glue_set} | |
end | |
if head.glue_sign ~= 0 then | |
local glue_sign = string.format("glue_sign %g",head.glue_sign) | |
tmp[#tmp + 1] ={"glue_sign",glue_sign} | |
end | |
if head.glue_order ~= 0 then | |
local glue_order = string.format("glue_order %d",head.glue_order) | |
tmp[#tmp + 1] = {"glue_order",glue_order} | |
end | |
if head.shift ~= 0 then | |
local shift = string.format("shift %gpt",head.shift / factor) | |
tmp[#tmp + 1] = {"shift",shift } | |
end | |
tmp[#tmp + 1] = {"head", "head"} | |
ret[#ret + 1] = draw_node(head, tmp) | |
if head.head then | |
ret[#ret + 1] = link_to(head.head,nodename,"head") | |
ret[#ret + 1] = dot_analyze_nodelist(head.head,options) | |
end | |
elseif typ == "vlist" then | |
local tmp = {} | |
if head.width ~= 0 then | |
local width = string.format("width %gpt",head.width / factor) | |
tmp[#tmp + 1] = {"width",width} | |
end | |
if head.height ~= 0 then | |
local height= string.format("height %gpt",head.height / factor) | |
tmp[#tmp + 1] = {"height",height} | |
end | |
if head.depth ~= 0 then | |
local depth = string.format("depth %gpt",head.depth / factor) | |
tmp[#tmp + 1] = {"depth",depth} | |
end | |
if head.glue_set ~= 0 then | |
local glue_set = string.format("glue_set %g",head.glue_set) | |
tmp[#tmp + 1] = {"glue_set",glue_set} | |
end | |
if head.glue_sign ~= 0 then | |
local glue_sign = string.format("glue_sign %g",head.glue_sign) | |
tmp[#tmp + 1] ={"glue_sign",glue_sign} | |
end | |
if head.glue_order ~= 0 then | |
local glue_order = string.format("glue_order %d",head.glue_order) | |
tmp[#tmp + 1] = {"glue_order",glue_order} | |
end | |
if head.shift ~= 0 then | |
local shift = string.format("shift %gpt",head.shift / factor) | |
tmp[#tmp + 1] = {"shift",shift } | |
end | |
tmp[#tmp + 1] = {"head", "head"} | |
ret[#ret + 1] = draw_node(head, tmp) | |
if head.head then | |
ret[#ret + 1] = link_to(head.head,nodename,"head") | |
ret[#ret + 1] = dot_analyze_nodelist(head.head,options) | |
end | |
elseif typ == "glue" then | |
local subtype = get_subtype(head) | |
local spec | |
if node.has_field(head,"spec") then | |
spec = head.spec | |
else | |
spec = head | |
end | |
local spec_string = string.format("%gpt", spec.width / factor) | |
if spec.stretch ~= 0 then | |
local stretch_order, shrink_order | |
if spec.stretch_order == 0 then | |
stretch_order = string.format(" + %gpt",spec.stretch / factor) | |
else | |
stretch_order = string.format(" + %g fi%s", spec.stretch / factor, string.rep("l",spec.stretch_order - 1)) | |
end | |
spec_string = spec_string .. stretch_order | |
end | |
if spec.shrink ~= 0 then | |
if spec.shrink_order == 0 then | |
shrink_order = string.format(" - %gpt",spec.shrink / factor) | |
else | |
shrink_order = string.format(" - %g fi%s", spec.shrink / factor, string.rep("l",spec.shrink_order - 1)) | |
end | |
spec_string = spec_string .. shrink_order | |
end | |
if head.leader then | |
ret[#ret + 1] = draw_node(head,{ {"subtype", subtype},{"spec",spec_string},{"leaders","leaders"} }) | |
ret[#ret + 1] = dot_analyze_nodelist(head.leader,options) | |
ret[#ret + 1] = link_to(head.leader,nodename,"leaders") | |
else | |
ret[#ret + 1] = draw_node(head,{ {"subtype", subtype},{"spec",spec_string} }) | |
end | |
elseif typ == "kern" then | |
ret[#ret + 1] = draw_node(head,{ {"kern", string.format("kern: %gpt",head.kern / factor) } }) | |
elseif typ == "rule" then | |
local wd,ht,dp | |
if head.width == -1073741824 then wd = "width: flexible" else wd = string.format("width: %gpt", head.width / factor) end | |
if head.height == -1073741824 then ht = "height: flexible" else ht = string.format("height: %gpt", head.height / factor) end | |
if head.depth == -1073741824 then dp = "depth: flexible" else dp = string.format("depth: %gpt", head.depth / factor) end | |
local subtype | |
ret[#ret + 1] = draw_node(head,{ {"wd", wd },{"ht", ht },{"dp", dp } }) | |
elseif typ == "penalty" then | |
ret[#ret + 1] = draw_node(head,{ {"penalty", string.format("%d",head.penalty) } }) | |
elseif typ == "disc" then | |
if options.showdisc then | |
ret[#ret + 1] = draw_node(head, { {"pre","pre"},{"post","post"},{"replace","replace"} }) | |
if head.pre then | |
ret[#ret + 1] = dot_analyze_nodelist(head.pre,options) | |
ret[#ret + 1] = link_to(head.pre,nodename,"pre") | |
end | |
if head.post then | |
ret[#ret + 1] = dot_analyze_nodelist(head.post,options) | |
ret[#ret + 1] = link_to(head.post,nodename,"post") | |
end | |
if head.replace then | |
ret[#ret + 1] = dot_analyze_nodelist(head.replace,options) | |
ret[#ret + 1] = link_to(head.replace,nodename,"replace") | |
end | |
else | |
ret[#ret + 1] = draw_node(head, { } ) | |
end | |
elseif typ == "glyph" then | |
local ch = string.format("char: '%s'",sanitize(head.char)) | |
local lng = string.format("lang: %d",head.lang) | |
local fnt = string.format("font: %d",head.font) | |
local wd = string.format("width: %gpt", head.width / factor) | |
local ht = string.format("height: %gpt", head.height / factor) | |
local dp = string.format("depth: %gpt", head.depth / factor) | |
local comp | |
if options.showdisc then | |
comp = {"comp","components"} | |
else | |
comp = {} | |
end | |
ret[#ret + 1] = draw_node(head,{ {"char", ch} ,{"lang",lng },{"font",fnt},{"width", wd},{"height", ht},{"depth", dp}, comp }) | |
if head.components and options.showdisc then | |
ret[#ret + 1] = dot_analyze_nodelist(head.components,options) | |
ret[#ret + 1] = link_to(head.components,nodename,"comp") | |
end | |
elseif typ == "math" then | |
ret[#ret + 1] = draw_node(head, { "math", head.subtype == 0 and "on" or "off" }) | |
elseif typ == "whatsit" then | |
local st = get_subtype(head) | |
if st == "dir" then | |
ret[#ret + 1] = draw_node(head, { { "dir", head.dir } }) | |
elseif st == "pdf_start_link" then | |
local wd = string.format("width (pt): %gpt", head.width / factor) | |
local ht = string.format("height: %gpt", head.height / factor) | |
local dp = string.format("depth %gpt", head.depth / factor) | |
local objnum = string.format("objnum %d",head.objnum) | |
ret[#ret + 1] = draw_action(head.action) | |
ret[#ret + 1] = link_to(head.action,nodename,"action") | |
ret[#ret + 1] = draw_node(head, {{ "subtype", "pdf_start_link"}, {"width", wd},{"widthraw",head.width}, {"height" , ht}, {"depth",dp}, {"objnum", objnum}, {"action", "action"}}) | |
elseif st == "pdf_end_link" then | |
ret[#ret + 1] = draw_node(head, {{ "subtype", "pdf_end_link"}}) | |
elseif st == "pdf_literal" then | |
ret[#ret + 1] = draw_node(head,{ {"subtype", "literal"},{"data",data} }) | |
elseif st == "pdf_refximage" then | |
local wd = string.format("width (pt): %gpt", head.width / factor) | |
local ht = string.format("height: %gpt", head.height / factor) | |
local dp = string.format("depth %gpt", head.depth / factor) | |
local objnum = string.format("objnum %d",head.objnum or 0) | |
ret[#ret + 1] = draw_node(head,{ {"subtype", "image"},{"width", wd}, {"height" , ht}, {"depth",dp}, {"objnum", objnum} }) | |
elseif st == "pdf_colorstack" then | |
local stack,cmd,data | |
stack = string.format("stack: %d",head.stack) | |
if status.luatex_version < 79 then | |
cmd = string.format("cmd: %d", head.cmd) | |
else | |
cmd = string.format("cmd: %d", head.command) | |
end | |
data = string.format("data: %s", head.data) | |
ret[#ret + 1] = draw_node(head,{ {"subtype", "colorstack"},{"stack",stack},{"cmd",cmd},{"data",data} }) | |
elseif st == "user_defined" then | |
local uid,t, val | |
uid = string.format("user_id= %s",tostring(head.user_id)) | |
t = string.format("type = %s",tostring(head.type)) | |
val = string.format("value = %s", tostring(head.value)) | |
ret[#ret + 1] = draw_node(head,{ {"subtype", "user_defined"},{"userid",uid},{"type",t},{"value",val} }) | |
elseif st == "local_par" then | |
ret[#ret + 1] = draw_node(head, {{ "subtype","local_par"}}) | |
elseif st == "pdf_dest" then | |
local namedid = string.format("named_id=%s",tostring(head.named_id)) | |
local destid = string.format("dest_id=%s",tostring(head.dest_id)) | |
ret[#ret + 1] = draw_node(head, { {"named_id",namedid},{"dest_id",destid} }) | |
elseif st == "pdf_annot" then | |
local wd = string.format("width (pt): %gpt", head.width / factor) | |
local ht = string.format("height: %gpt", head.height / factor) | |
local dp = string.format("depth %gpt", head.depth / factor) | |
local objnum = string.format("objnum %d",head.objnum) | |
local data = string.format("data: %s", string.gsub(head.data,"<","\\<" ):gsub(">","\\>" )) | |
ret[#ret + 1] = draw_node(head, {{ "subtype","pdf_annot"},{"width", wd}, {"height" , ht}, {"depth",dp}, {"objnum",objnum},{"data",data}}) | |
elseif st == "pdf_save" then | |
ret[#ret + 1] = draw_node(head, {{ "subtype","pdf_save" }}) | |
elseif st == "pdf_restore" then | |
ret[#ret + 1] = draw_node(head, {{ "subtype","pdf_restore" }}) | |
else | |
ret[#ret + 1] = draw_node(head, {{ "subtype",st }}) | |
texio.write_nl(string.format("whatsit type %s not handled",st)) | |
end | |
else | |
-- texio.write_nl(string.format("not handled id %d",head.id)) | |
ret[#ret + 1] = draw_node(head, { }) | |
end | |
head = head.next | |
end | |
return table.concat(ret) | |
end | |
function nodelist_visualize( box,filename,options ) | |
assert(box,"No box given") | |
assert(filename,"No filename given") | |
local box_to_analyze | |
if type(box)=="number" then | |
box_to_analyze = tex.box[box] | |
else | |
box_to_analyze = box | |
end | |
local gv = dot_analyze_nodelist(box_to_analyze,options or {}) | |
local outfile = io.open(filename,"wb") | |
outfile:write([[ | |
digraph g { | |
graph [ | |
rankdir = "LR" | |
]; | |
node [ shape = "record"] | |
]]) | |
outfile:write(gv) | |
outfile:write("}\n") | |
outfile:close() | |
end | |
An issue with hlist and vlist nodes. Field list
should be renamed to head
. To quote from the LuaTeX manual:
Note: the new field name head
was introduced in 0.65 to replace the old name list
. Use of the name list
is now deprecated, but it will stay available until at least version 0.80.
I missed your comment, sorry. I will rename head/list and have a look at the edges departing from list/head field. Thank you very much for your comment!
An RFE this time: In user-defined whatsit nodes, would it be possible to show fields user_id
, type
and value
?
Thanks @hennigs, I've finally implemented your suggestions.
To limit output for quickly checking a node's neighbours max_prev
, max_next
and max_head
options would be useful, i.e. called on node n
with max_head=1
would draw n
and n.head
but not n.head.head
, but instead a dangling arrow.
I have also witten a package which visualizes the node lists. My package nodetree tries to solve the challenge to visualize the node structure in a different approach. https://www.ctan.org/pkg/nodetree
I tried the code on the AtBeginShipoutBox with luatex 1.07 from texlive 2018 pretest:
\documentclass{article}
\usepackage{atbegshi,lipsum}
\AtBeginShipout {%
\directlua{require("viznodelist")
viznodelist.nodelist_visualize(tex.box["AtBeginShipoutBox"],"mybox.gv")}}
\pagestyle{empty}
\begin{document}
abc
\end{document}
When I try to convert this to a pdf with dot.exe I get a warning
Warning: node n80, port title unrecognized
Warning: node n80, port title unrecognized
and there is a mysterious n80
node in the middle:
I can confirm this (Linux, TeXLive 2017, luatex 1.0.4). I get
Warning: node n78, port title unrecognized
...Rolf
Another issue with current TeXLive (2018, luatex 1.09.0). If I compile ulrikes (u-fischer) example above I see the following error:
./viznodelist.lua:124: attempt to index a nil value (field 'spe
c')
stack traceback:
./viznodelist.lua:124: in upvalue 'dot_analyze_nodelist'
./viznodelist.lua:120: in upvalue 'dot_analyze_nodelist'
./viznodelist.lua:152: in function 'viznodelist.nodelist_visualize'
[\directlua]:1: in main chunk.
<argument> ...list_visualize("AtBeginShipoutBox","mybox.gv")}
l.10 \end{document}
It would be nice to see a graphic of the ShipoutBox. Thanks in advance.
@u-fischer I cannot reproduce this problem with my installation of tl2018.
@rolfn I don't have LuaTeX 1.09 at the moment (& I don't know how to upgrade)
Both: sorry for the late reply, I somehow don't get a notice when there are new comments here.
@pgundlach: I still get the node message:
\dot.exe -Tpdf mybox.gv -o dot.pdf
Warning: node n80, port title unrecognized
Warning: node n80, port title unrecognized
Regarding the luatex1.09 error: As it uses lua5.3 you should probably replace glue_set %d
by glue_set %.0f
(twice).
@pgundlach: Fails with a lua error when HarfBuzz renderer is used instead of Node renderer for the following short test-case (Noto Sans Devanagari is available from google fonts GitHub here, though I guess any Devanagari font should do). I encountered this same error in my code while playing with char fields in glyph nodes, someone posted a solution (which I don't really understand) on stack exchange. Please have a look: HarfBuzz UTF-8 issue as it causes visnodelist.lua
to produce error. Btw, thanks for the script, graphical visualization helps debug otherwise inhumane tex debug experience. @Josef-Friedrich I filed a bug on your package nodetree
too, it seems we all are affected by the same issue :)
\documentclass{article}
\usepackage[lmargin=0.5in,tmargin=0.5in,rmargin=0.5in,bmargin=0.5in]{geometry}
\usepackage{fontspec}
%\newfontscript{Devanagari}{deva,dev2}
\newfontfamily{\devanagarifam}{Noto Sans Devanagari}[Script=Devanagari, Scale=1, Renderer=HarfBuzz]
\begin{document}
\setbox0=\hbox{Hey \devanagarifam एक गांव -- में मोहन} % The error happens on compound glyph: 'में'. As a slightly longer test case, replace contents of box 0 with: Příliš žluťoučký \textit{kůň} úpěl \hbox{ďábelské} ódy difference diffierence. \devanagarifam एक गांव -- में मोहन नाम का लड़का रहता था। उसके पिताजी एक मामूली मजदूर थे।
\directlua{
require("viznodelist")
viznodelist.nodelist_visualize(0,"mybox.gv")
}
\box0
\end{document}
Error:
./viznodelist.lua:332: bad argument #1 to 'char' (invalid value)
stack traceback:
[C]: in field 'char'
./viznodelist.lua:332: in upvalue 'dot_analyze_nodelist'
./viznodelist.lua:226: in upvalue 'dot_analyze_nodelist'
./viznodelist.lua:421: in function 'viznodelist.nodelist_visualize'
[\directlua]:1: in main chunk.
l.16 }
I have also witten a package which visualizes the node lists. My package nodetree tries to solve the challenge to visualize the node structure in a different approach. https://www.ctan.org/pkg/nodetree
@Josef-Friedrich I really like and use nodetree a lot! Thank you for sharing this (I know this is an old message)
@reportaman Thank you for the bug report. I now present everything I can't display as U+FFFD REPLACEMENT CHARACTER (�). Not sure if this is the best way to do, but better than an error.
@pgundlach: Its not the best way to do it as the characters used in the test case do actually have unicode code-points. They could be hidden in the way LuaHBTeX uses 'char' field of glyph nodes. I think they are using it as a 'string' now? I have dissected the problem further in my comment on same bug filed on package nodetree here. Please review, and let us know what you think.
@reportaman I'll have a look if I can use get_glyph_info. Since viznodelist is used outside LaTeX/Luaotfload, I am not sure if I implement this.
@pgundlach: Thanks! You might also be interested in this question posted on TeX.SE, given you have a tool (Speedata publisher) with LuaTeX backbone: LuaTeX glyph reordering issue.
An issue with hlist and vlist nodes. Edges departing from the field labelled list always head south, while in most cases they should head east, like, e.g., the edges departing from next fields do.