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

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On 22 Sep 2018, at 11:27, Hans Hagen mailto:j.hagen@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 ----------------------------------------------------------------- Hans Hagen | PRAGMA ADE Ridderstraat 27 | 8061 GH Hasselt | The Netherlands tel: 038 477 53 69 | www.pragma-ade.nl | www.pragma-pod.nl -----------------------------------------------------------------

On 9/22/2018 3:41 PM, Alan Braslau wrote:

On Sat, 22 Sep 2018 13:45:17 +0200 Hans Hagen 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 mailto:j.hagen@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 -----------------------------------------------------------------