On 9/22/2018 3:41 PM, Alan Braslau wrote:
On Sat, 22 Sep 2018 13:45:17 +0200
Hans Hagen <j.ha...@xs4all.nl> wrote:
On 9/22/2018 12:08 PM, Floris van Manen wrote:
It does not seem to work for all character combinations.
e.g. B&T works, C&T works, C&M works, but N&T does not work.
not N&M
Why would that be?
Thanks
.Floris
On 22 Sep 2018, at 11:27, Hans Hagen <j.ha...@xs4all.nl
<mailto:j.ha...@xs4all.nl>> wrote:
On 9/22/2018 10:35 AM, Henri Menke wrote:
Dear list,
Challanged by a very old TeX.SX question
https://tex.stackexchange.com/questions/180510
I wanted to calculate all the intersection points between two
characters. Therefore I ripped off the \showshape macro to load the
outlines from the font and convert them to MetaPost paths. Then I try
to find all intersections by cutting the path.
It somewhat works but for some reason, in the MWE below two intersection
points are missing. I also have the feeling that my implementation is
extremely inefficient. I would very much appreciate some hints by the
MetaPost experts!
Cheers, Henri
---
\startluacode
-- That's a simple reimplemetation of the showshape macro
function outlinepaths(character)
local fontid = font.current()
local shapedata = fonts.hashes.shapes[fontid] -- by index
local chardata = fonts.hashes.characters[fontid] -- by unicode
local shapeglyphs = shapedata.glyphs or { }
character = utf.byte(character)
local c = chardata[character]
if c then
if not c.index then
return {}
end
local glyph = shapeglyphs[c.index]
if glyph and (glyph.segments or glyph.sequence) then
local units = shapedata.units or 1000
local factor = 100/units
local paths = fonts.metapost.paths(glyph,factor)
return paths
end
end
end
\stopluacode
\def\mpdefineoutlines#1#2{\ctxlua{
local char = "\luaescapestring{#1}"
local outlines = outlinepaths("#2")
local len = \letterhash outlines
tex.print("path " .. char .. "[];")
tex.print(char .. "n := " .. len .. ";")
for i, path in ipairs(outlines) do
tex.print(char .. "[" .. i .. "] := " .. path .. ";")
end
}}
\starttext
\startMPpage
pair shift; shift := (1cm,-1cm);
numeric angle; angle := 5;
\mpdefineoutlines{B}{B}
\mpdefineoutlines{T}{T}
nofill B2;
nofill B3;
eofill B1 withcolor .5[blue,white];
fill T1 shifted (shift) rotated (angle) withcolor .5[red,white];
path r;
numeric n; n := 0;
for i = 1 upto Bn:
for j = 1 upto Tn:
r := B[i];
forever:
pair q;
r := r cutbefore (T[j] shifted (shift) rotated (angle));
exitif length cuttings = 0;
r := subpath(epsilon, length r) of r;
q = point 0 of r;
n := n + 1;
dotlabel.urt(textext("\tfx" & decimal n), q);
endfor;
endfor ;
endfor ;
\stopMPpage
\stoptext
You migh find more when you go top double mode .. anyway, these
intersection calculations are not that accurate so you normally need
to apply some overkill.
- a bit cleaned up outlinepath function
- use document namespace
- add helper for defineoutline
- do 4 runs over the shapes (probably too many now)
- more neutral fill code
It makes a nice example for the metafun (although then I'd do it
slightly different). We need some rounding becaus eotherwise you get
similar points (you can add a message(q) someplace).
\startluacode
function document.outlinepaths(character)
local chardata = fonts.hashes.characters[true] -- by unicode
local shapedata = fonts.hashes.shapes[true] -- by index
local c = chardata[character]
if c and c.index and shapedata then
local shapeglyphs = shapedata.glyphs or { }
local glyph = shapeglyphs[c.index]
if glyph and (glyph.segments or glyph.sequence) then
local units = shapedata.units or 1000
local factor = 100/units
return fonts.metapost.paths(glyph,factor)
end
end
return { }
end
function document.defineoutline(char,target)
local outlines = document.outlinepaths(char)
local nofpaths = #outlines
context("path %s[] ;",target)
context("numeric %sn ; %sn := %s ;",target,target,nofpaths)
for i=1,nofpaths do
context("%s[%i] := %s ; ",target,i,outlines[i])
end
end
\stopluacode
\def\mpdefineoutlines#1#2{\ctxlua{document.defineoutline(\number`#1,"#2")}}
\starttext
\startMPpage
pair shift ; shift := (1cm,-1cm);
numeric angle ; angle := 5;
\mpdefineoutlines{B}{B}
\mpdefineoutlines{T}{T}
for i=1 upto Bn - 1 : nofill B[i] ; endfor ;
eofill B[Bn] withcolor .5[blue,white] ;
for i=1 upto Tn :
T[i] := T[i] shifted shift rotated angle ;
endfor ;
for i=1 upto Tn - 1 : nofill T[i] ; endfor ;
eofill T[Tn] withcolor .5[red,white] ;
pair found[] ;
boolean isnew ;
numeric n ; n := 0 ;
pair rq ;
def GoForIt(expr how) =
path r ;
for i = 1 upto Bn :
for j = 1 upto Tn :
r := B[i] ;
forever:
pair q ;
if how = 1 :
r := r cutbefore T[j] ;
elseif how = 2 :
r := r cutbefore reverse T[j] ;
elseif how = 3 :
r := reverse r cutbefore T[j] ;
else :
r := reverse r cutbefore reverse T[j] ;
fi ;
exitif length cuttings = 0 ;
r := subpath(epsilon, length r) of r ;
q = point 0 of r ;
isnew := true ;
rq := round(q);
for f=1 upto n :
if found[f] = rq :
isnew := false ;
exitif true ;
fi ;
endfor ;
if isnew :
n := n + 1 ;
drawdot q withpen pencircle scaled 4 ;
draw textext("\strut\ttbf " & decimal n) ysized 3
shifted q withcolor white ;
found[n] := rq ;
fi ;
endfor;
endfor ;
endfor ;
enddef ;
for i=1 upto 4 : GoForIt(i) ; endfor ;
\stopMPpage
\stoptext
Ok, a different approach then (probably still not all points as we need
to loop over segments but better) .. no more time now.
It also shows that we don't need lua/tex juggling as we already can have
the paths in mp. (For sure now someone can complain that this is not
well documented.)
\starttext
\startMPdefinitions
% will be added to metafun:
def filloutlinetext(expr o) =
draw image (
save n, m ; numeric n, m ; n := m := 0 ;
for i within o :
n := n + 1 ;
endfor ;
for i within o :
m := m + 1 ;
if n = m :
eofill
else :
nofill
fi pathpart i ;
endfor ;
)
enddef ;
def drawoutlinetext(expr o) =
draw image (
% nicer for properties
for i within o :
draw pathpart i ;
endfor ;
)
enddef ;
def outlinetexttopath(text o, p, n) =
scantokens("numeric " & str n & ";") ;
scantokens("path " & str p & "[];") ;
n := 0 ;
for i within o : p[incr(n)] := pathpart i ; endfor ;
enddef ;
\stopMPdefinitions
\startMPdefinitions
% outlinetexttopath(Bo)(B)(Bn) ;
%
% Bn := listsize(T)
def showoverlapinoutlines(expr first, second) =
path p_i, p_j, s_i, s_j ;
numeric n_i, n_j, index ;
pair found ;
index := 0 ;
for i within first :
for j within second :
p_i := pathpart i ; n_i := length(p_i) ;
p_j := pathpart j ; n_j := length(p_j) ;
for ii = 0 upto n_i - 1 :
s_i := subpath(ii,ii+1) of p_i ;
for jj = 0 upto n_j - 1 :
s_j := subpath(jj,jj+1) of p_j ;
found := s_i intersection_point s_j ;
if intersection_found :
index := index + 1 ;
drawdot found withpen pencircle scaled 4
withtransparency (1,.5);
draw textext("\strut\ttbf " & decimal
index) ysized 3 shifted found withcolor white withtransparency (1,.5);
fi ;
endfor ;
endfor ;
endfor ;
endfor ;
enddef ;
\stopMPdefinitions
\startMPpage
picture first ; first := outlinetext.p("N") ; first := first
scaled 10 ;
picture second ; second := outlinetext.p("T") ; second := second
scaled 10 ;
second := second rotatedaround(center second, 5) shifted (1,-1) ;
filloutlinetext(first ) withcolor .5[blue,white] ;
filloutlinetext(second) withcolor .5[red,white] ;
drawoutlinetext(first ) ;
drawoutlinetext(second) ;
showoverlapinoutlines(first, second) ;
\stopMPpage
\startMPdefinitions
def showoverlap(expr f, s) =
picture first ; first := outlinetext.p(f) ; first := first
scaled 10 ;
picture second ; second := outlinetext.p(s) ; second := second
scaled 10 ;
filloutlinetext(first ) withcolor .5blue ;
drawoutlinetext(first ) ;
filloutlinetext(second) withcolor .5red ;
drawoutlinetext(second) ;
showoverlapinoutlines(first, second) ;
enddef ;
\stopMPdefinitions
\startMPpage
showoverlap("N","T") ;
\stopMPpage
\startMPpage
showoverlap("\$","Q") ;
\stopMPpage
\startMPpage
showoverlap("\tttf ABC","\tttf PQR") ;
\stopMPpage
\stoptext
Take a look, also, at the crossingunder macro in mp-tool.mpiv
something
% based on crossingunder
def showoverlapinoutlines(expr first, second) =
begingroup ;
save p, q, n, t, a, b, c, bcuttings, hold, found ;
path p, q ;
numeric n, t[], hold ;
path a, b, c, bcuttings, hold[] ;
pair found ;
c := makepath(currentpen scaled crossingscale) ;
t[0] := n := hold := 0 ;
for f within first :
for s within second :
p := pathpart f ;
q := pathpart s ;
a := p ;
for i=1 upto crossingnumbermax : % safeguard
clearxy ; z = a intersectiontimes q ;
if x < 0 :
exitif hold < 1 ;
a := hold[hold] ; hold := hold - 1 ;
clearxy ; z = a intersectiontimes q ;
fi
(t[incr n], whatever) = p intersectiontimes point x
of a ;
if x = 0 :
a := a cutbefore c shifted point x of a ;
elseif x = length a :
a := a cutafter c shifted point x of a ;
else : % before or after?
b := subpath (0,x) of a cutafter c
shifted point x of a ;
bcuttings := cuttings ;
a := subpath (x,length a) of a cutbefore c
shifted point x of a ;
clearxy ; z = a intersectiontimes q ;
if x < 0 :
a := b ;
cuttings := bcuttings ;
else :
if length bcuttings > 0 :
clearxy ; z = b intersectiontimes q ;
if x >= 0 :
hold[incr hold] := b ;
fi
fi
fi
fi
if length cuttings = 0 :
exitif hold < 1 ;
a := hold[hold] ; hold := hold - 1 ;
fi
endfor ;
endfor ;
endfor ;
t[incr n] = length p ;
for i=1 upto n :
found := point t[i] of p ;
drawdot found withpen pencircle scaled 4 withtransparency
(1,.5);
draw textext("\strut\ttbf " & decimal i) ysized 3 shifted
found withcolor white withtransparency (1,.5);
endfor ;
endgroup ;
enddef ;
-----------------------------------------------------------------
Hans Hagen | PRAGMA ADE
Ridderstraat 27 | 8061 GH Hasselt | The Netherlands
tel: 038 477 53 69 | www.pragma-ade.nl | www.pragma-pod.nl
-----------------------------------------------------------------
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