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-- diagmiddle.lua: words for drawing arrows between the sides of rectangles.
-- This file:
-- http://angg.twu.net/dednat6/dednat6/diagmiddle.lua.html
-- http://angg.twu.net/dednat6/dednat6/diagmiddle.lua
-- (find-angg "dednat6/dednat6/diagmiddle.lua")
-- Author: Eduardo Ochs <[email protected]>
-- Version: 2019dec08
-- License: GPL3
--
--
-- This is a hack! I wrote this to draw the middle arrows in
-- adjunctions, and then adapted it to draw arrows in the middle of
-- slanted rectangles, like in this diagram:
-- http://angg.twu.net/dednat6.html#a-big-example
--
-- It worked well enough for me, so I've kept it... the algorithm that
-- the "splitdist*" functions use to calculate the phantom nodes is a
-- bit hard to explain, and I would love to 1) write better docs for
-- it, 2) implement variants of it that people would find clearer. If
-- you want me to work on (1) on (2) please do get in touch, and I'll
-- stop postponing this!
--
-- A link to a very old implementation of this:
-- (find-dn4 "experimental.lua" "splitdist")
-- «.midpoint» (to "midpoint")
-- «.midpoint-tests» (to "midpoint-tests")
-- «.splitdist» (to "splitdist")
-- «.splitdist-tests» (to "splitdist-tests")
-- «.splitdists» (to "splitdists")
-- «.splitdists-tests» (to "splitdists-tests")
-- «.harrownodes» (to "harrownodes")
-- «.varrownodes» (to "varrownodes")
-- «.dharrownodes» (to "dharrownodes")
-- «.dvarrownodes» (to "dvarrownodes")
require "diagforth" -- (find-dn6 "diagforth.lua")
phantomnode = "\\phantom{O}"
-- «midpoint» (to ".midpoint")
forths["midpoint"] = function ()
-- local node1, node2 = ds[2], ds[1]
local node1, node2 = ds:pick(1), ds:pick(0)
local midx, midy = (node1.x + node2.x)/2, (node1.y + node2.y)/2
ds:pock(1, storenode{x=midx, y=midy, TeX=phantomnode})
ds:pop()
end
-- «midpoint-tests» (to ".midpoint-tests")
-- (find-dn6 "diagforth.lua" "high-level-tests")
--[==[
• (eepitch-lua51)
• (eepitch-kill)
• (eepitch-lua51)
dofile "diagmiddle.lua"
na = function (nodeid)
local n = nodes[tonumber(nodeid) or nodeid]
return "("..n.x..","..n.y.."):"..(n.tag or "")
end
nas = function (str) return (str:gsub("%S+", na)) end
run = dxyrun
run [[ 2Dx 100 +20 ]]
run [[ 2D 100 a,b <=== a ]]
run [[ 2D - - ]]
run [[ 2D | <-> | ]]
run [[ 2D v v ]]
run [[ 2D +20 c ==> b|->c ]]
= nas "1 2 3 4"
= nas "a c"
PP(xs)
PP(lasty) --> 120
PP(nodes)
PPV(nodes)
PP(nodes["a"])
PP(nodes["a,b"])
--]==]
-- Words for drawing arrows in the middle of rectangles (in adjunctions).
-- Actually these words build the vertex nodes for those arrows.
-- "harrownodes" is for horizontal arrows,
-- "varrownodes" is for vertical arrows,
-- "dharrownodes" and
-- "dvarrownodes" are for diagonal arrows.
-- They all expect two nodes on the stack, "node1" and "node2", and
-- they read three parameters with getwordasluaexpr(): "dx0", "dx1",
-- and "dx2" (or "dy0", "dy1" and "dy2").
-- "dx0" controls how far from "node1" the arrow starts,
-- "dx1" controls the length of the arrow,
-- "dx2" controls how far from "node2" the arrow starts.
-- Some of dx0, dx1, and dx2 can be nil; see "splitdist" below.
-- "harrownodes" uses y = (node1.y+node2.y)/2.
-- "varrownodes" uses x = (node1.x+nodex.y)/2.
-- This needs more documentation. Sorry.
-- Also, the "\phantom{O}" shouldn't be hardcoded.
-- «splitdist» (to ".splitdist")
splitdist = function (x1, x2, dx0, dx1, dx2)
local dx = x2-x1
local rest = dx-(dx0 or 0)-(dx1 or 0)-(dx2 or 0)
local type = (dx0 and "n" or "_")..(dx1 and "n" or "_")..
(dx2 and "n" or "_")
if type=="_n_" then
return x1+rest/2, x2-rest/2
elseif type=="nn_" then
return x1+dx0+rest/2, x2-rest/2
elseif type=="_nn" then
return x1+rest/2, x2-dx2-rest/2
elseif type=="n_n" then
return x1+dx0, x2-dx2
end
local p = function (n) return n or "nil" end
print("Bad splitdist pattern: "..p(dx0).." "..p(dx1).." "..p(dx2))
end
-- «splitdist-tests» (to ".splitdist-tests")
--[[
• (eepitch-lua51)
• (eepitch-kill)
• (eepitch-lua51)
dofile "diagmiddle.lua"
= splitdist(100, 200, nil, 10, nil) --> 145 155
= splitdist(100, 200, 20, 10, nil) --> 155 165
= splitdist(100, 200, nil, 10, 20) --> 135 145
= splitdist(100, 200, 20, nil, 30) --> 120 170
= splitdist(200, 100, nil, 10, nil) --> 145 155
--]]
-- «splitdists» (to ".splitdists")
-- (find-dn4file "experimental.lua" "dharrownodes = ")
proportional = function (w0, w1, w2, z0, z2)
local way = (w1 - w0)/(w2 - w0)
return z0 + (z2 - z0)*way
end
proportionals = function (w0, w1a, w1b, w2, z0, z2)
return proportional(w0, w1a, w2, z0, z2),
proportional(w0, w1b, w2, z0, z2)
end
splitdists = function (w0, w2, dw0, dw1, dw2, z0, z2)
local w1a, w1b = splitdist(w0, w2, dw0, dw1, dw2)
local z1a, z1b = proportionals(w0, w1a, w1b, w2, z0, z2)
return w1a, w1b, z1a, z1b
end
-- New, 2019oct06:
harrownodes0 = function (x0, y0, x2, y2, dx0, dx1, dx2)
local x1a, x1b = splitdist(x0, x2, dx0, dx1, dx2)
local y1 = (y0 + y2)/2
return x1a, y1, x1b, y1
end
varrownodes0 = function (x0, y0, x2, y2, dy0, dy1, dy2)
local y1a, y1b = splitdist(y0, y2, dy0, dy1, dy2)
local x1 = (x0 + x2)/2
return x1, y1a, x1, y1b
end
dharrownodes0 = function (x0, y0, x2, y2, dx0, dx1, dx2)
local x1a, x1b = splitdist(x0, x2, dx0, dx1, dx2)
local y1a, y1b = proportionals(x0, x1a, x1b, x2, y0, y2)
return x1a, y1a, x1b, y1b
end
dvarrownodes0 = function (x0, y0, x2, y2, dy0, dy1, dy2)
local y1a, y1b = splitdist(y0, y2, dy0, dy1, dy2)
local x1a, x1b = proportionals(y0, y1a, y1b, y2, x0, x2)
return x1a, y1a, x1b, y1b
end
-- «splitdists-tests» (to ".splitdists-tests")
--
--[[
• (eepitch-lua51)
• (eepitch-kill)
• (eepitch-lua51)
dofile "diagmiddle.lua"
= proportional (10, 15, 20, 100, 200) --> 150
= proportionals(10, 14, 16, 20, 100, 200) --> 140 160
= splitdist (10, 20, nil, 2, nil) --> 14 16
= splitdists (10, 20, nil, 2, nil, 100, 200) --> 14 16 140 160
= harrownodes0 (10, 100, 20, 200, nil, 2, nil) --> 14 150 16 150
= varrownodes0 (10, 100, 20, 200, nil, 20, nil) --> 15 140 15 160
= dharrownodes0 (10, 100, 20, 200, nil, 2, nil) --> 14 140 16 160
= dvarrownodes0 (10, 100, 20, 200, nil, 20, nil) --> 14 140 16 160
--]]
-- «harrownodes» (to ".harrownodes")
-- «varrownodes» (to ".varrownodes")
harrownodes = function (dx0, dx1, dx2, TeX1, TeX2)
local node0, node2 = ds:pick(1), ds:pick(0)
local x0, y0, x2, y2 = node0.x, node0.y, node2.x, node2.y
local x1a, y1a, x1b, y1b = harrownodes0(x0, y0, x2, y2, dx0, dx1, dx2)
ds:push(storenode{x=x1a, y=y1a, TeX=(TeX1 or phantomnode)})
ds:push(storenode{x=x1b, y=y1b, TeX=(TeX2 or phantomnode)})
end
varrownodes = function (dy0, dy1, dy2, TeX1, TeX2)
local node0, node2 = ds:pick(1), ds:pick(0)
local x0, y0, x2, y2 = node0.x, node0.y, node2.x, node2.y
local x1a, y1a, x1b, y1b = varrownodes0(x0, y0, x2, y2, dy0, dy1, dy2)
ds:push(storenode{x=x1a, y=y1a, TeX=(TeX1 or phantomnode)})
ds:push(storenode{x=x1b, y=y1b, TeX=(TeX2 or phantomnode)})
end
-- «dharrownodes» (to ".dharrownodes")
-- «dvarrownodes» (to ".dvarrownodes")
dharrownodes = function (dx0, dx1, dx2, TeX1, TeX2)
local node0, node2 = ds:pick(1), ds:pick(0)
local x0, y0, x2, y2 = node0.x, node0.y, node2.x, node2.y
local x1a, y1a, x1b, y1b = dharrownodes0(x0, y0, x2, y2, dx0, dx1, dx2)
ds:push(storenode{x=x1a, y=y1a, TeX=(TeX1 or phantomnode)})
ds:push(storenode{x=x1b, y=y1b, TeX=(TeX2 or phantomnode)})
end
dvarrownodes = function (dy0, dy1, dy2, TeX1, TeX2)
local node0, node2 = ds:pick(1), ds:pick(0)
local x0, y0, x2, y2 = node0.x, node0.y, node2.x, node2.y
local x1a, y1a, x1b, y1b = dvarrownodes0(x0, y0, x2, y2, dy0, dy1, dy2)
ds:push(storenode{x=x1a, y=y1a, TeX=(TeX1 or phantomnode)})
ds:push(storenode{x=x1b, y=y1b, TeX=(TeX2 or phantomnode)})
end
forths["harrownodes"] = function ()
harrownodes(getwordasluaexpr(), getwordasluaexpr(), getwordasluaexpr())
end
forths["varrownodes"] = function ()
varrownodes(getwordasluaexpr(), getwordasluaexpr(), getwordasluaexpr())
end
forths["dharrownodes"] = function ()
dharrownodes(getwordasluaexpr(), getwordasluaexpr(), getwordasluaexpr())
end
forths["dvarrownodes"] = function ()
dvarrownodes(getwordasluaexpr(), getwordasluaexpr(), getwordasluaexpr())
end
-- Old versions (commented out in 2019oct06):
-- harrownodes = function (dx0, dx1, dx2, TeX1, TeX2)
-- local node1, node2 = ds:pick(1), ds:pick(0)
-- local midy = (node1.y + node2.y)/2
-- local x1, x2 = splitdist(node1.x, node2.x, dx0, dx1, dx2)
-- ds:push(storenode{x=x1, y=midy, TeX=(TeX1 or phantomnode)})
-- ds:push(storenode{x=x2, y=midy, TeX=(TeX2 or phantomnode)})
-- end
-- varrownodes = function (dy0, dy1, dy2, TeX1, TeX2)
-- local node1, node2 = ds:pick(1), ds:pick(0)
-- local midx = (node1.x + node2.x)/2
-- local y1, y2 = splitdist(node1.y, node2.y, dy0, dy1, dy2)
-- ds:push(storenode{x=midx, y=y1, TeX=(TeX1 or phantomnode)})
-- ds:push(storenode{x=midx, y=y2, TeX=(TeX2 or phantomnode)})
-- end
-- dharrownodes = function (dx0, dx1, dx2, TeX1a, TeX1b)
-- local node0, node2 = ds:pick(1), ds:pick(0)
-- local x0, x2, y0, y2 = node0.x, node2.x, node0.y, node2.y
-- local x1a, x1b, y1a, y1b = splitdists(x0, x2, dx0, dx1, dx2, y0, y2)
-- ds:push(storenode{x=x1a, y=y1a, TeX=(TeX1a or phantomnode)})
-- ds:push(storenode{x=x1b, y=y1b, TeX=(TeX1b or phantomnode)})
-- end
-- dvarrownodes = function (dy0, dy1, dy2, TeX1a, TeX1b)
-- local node0, node2 = ds:pick(1), ds:pick(0)
-- local x0, x2, y0, y2 = node0.x, node2.x, node0.y, node2.y
-- local y1a, y1b, x1a, x1b = splitdists(y0, y2, dy0, dy1, dy2, x0, x2)
-- ds:push(storenode{x=x1a, y=y1a, TeX=(TeX1a or phantomnode)})
-- ds:push(storenode{x=x1b, y=y1b, TeX=(TeX1b or phantomnode)})
-- end
-- Local Variables:
-- coding: utf-8-unix
-- End: