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+%D \module
+%D [ file=mp-tool.mp,
+%D version=1998.02.15,
+%D title=\CONTEXT\ \METAPOST\ graphics,
+%D subtitle=auxiliary macros,
+%D author=Hans Hagen,
+%D date=\currentdate,
+%D copyright={PRAGMA / Hans Hagen \& Ton Otten}]
+%C
+%C This module is part of the \CONTEXT\ macro||package and is
+%C therefore copyrighted by \PRAGMA. See mreadme.pdf for
+%C details.
+
+% a cleanup is needed, like using image and alike
+% use a few more "newinternal"'s
+
+%D This module is rather preliminary and subjected to
+%D changes.
+
+if known context_tool : endinput ; fi ;
+
+boolean context_tool ; context_tool := true ;
+
+%D We always want \EPS\ conforming output, so we say:
+
+prologues := 2 ; % 1 = troff, 2 = tex
+warningcheck := 0 ;
+
+%D Namespace handling:
+
+% let exclamationmark = ! ;
+% let questionmark = ? ;
+%
+% def unprotect =
+% let ! = relax ;
+% let ? = relax ;
+% enddef ;
+%
+% def protect =
+% let ! = exclamationmark ;
+% let ? = questionmark ;
+% enddef ;
+%
+% unprotect ;
+%
+% mp!some!module = 10 ; show mp!some!module ; show somemodule ;
+%
+% protect ;
+
+%D A semicolor to be used in specials: ? ? ?
+
+string semicolor ; semicolor := char 59 ;
+
+%D By including this module, \METAPOST\ automatically writes a
+%D high resolution boundingbox to the \POSTSCRIPT\ file. This
+%D hack is due to John Hobby himself.
+
+% When somehow the first one gets no HiRes, then make sure
+% that the format matches the mem sizes in the config file.
+
+% eerste " " er uit
+
+string space ; space = char 32 ;
+
+vardef ddecimal primary p =
+ decimal xpart p & " " & decimal ypart p
+enddef ;
+
+extra_endfig := extra_endfig
+ & "special "
+ & "("
+ & ditto
+ & "%%HiResBoundingBox: "
+ & ditto
+ & "&ddecimal llcorner currentpicture"
+ & "&space"
+ & "&ddecimal urcorner currentpicture"
+ & ");";
+
+%D Also handy (when we flush colors):
+
+vardef dddecimal primary c =
+ decimal redpart c & " " & decimal greenpart c & " " & decimal bluepart c
+enddef ;
+
+%D We have standardized data file names:
+
+if not known _data_prefix_ :
+
+ string _data_prefix_ ; _data_prefix_ = "mpd-" ;
+ string _data_suffix_ ; _data_suffix_ = ".tmp" ;
+
+fi ;
+
+def data_file =
+ _data_prefix_ & decimal charcode & _data_suffix_
+enddef ;
+
+%D Because \METAPOST\ has a hard coded limit of 4~datafiles,
+%D we need some trickery when we have multiple files.
+
+if unknown collapse_data :
+ boolean collapse_data ; collapse_data := false ;
+fi ;
+
+boolean savingdata ; savingdata := false ;
+
+def savedata expr txt =
+ if collapse_data :
+ write if savingdata : txt else :
+ "\MPdata{" & decimal charcode & "}{" & txt & "}"
+ fi
+ & "%" to jobname & _data_suffix_ ;
+ else :
+ write txt to data_file ;
+ fi ;
+enddef ;
+
+def startsavingdata =
+ savingdata := true ;
+ if collapse_data :
+ write
+ "\MPdata{" & decimal charcode & "}{%"
+ to
+ jobname & _data_suffix_ ;
+ fi ;
+enddef ;
+
+def stopsavingdata =
+ savingdata := false ;
+ if collapse_data :
+ write "}%" to jobname & _data_suffix_ ;
+ fi ;
+enddef ;
+
+%D Instead of a keystroke eating save and allocation
+%D sequence, you can use the \citeer {new} alternatives to
+%D save and allocate in one command.
+
+def newcolor text v = forsuffixes i=v : save i ; color i ; endfor ; enddef ;
+def newnumeric text v = forsuffixes i=v : save i ; numeric i ; endfor ; enddef ;
+def newboolean text v = forsuffixes i=v : save i ; boolean i ; endfor ; enddef ;
+def newtransform text v = forsuffixes i=v : save i ; transform i ; endfor ; enddef ;
+def newpath text v = forsuffixes i=v : save i ; path i ; endfor ; enddef ;
+def newpicture text v = forsuffixes i=v : save i ; picture i ; endfor ; enddef ;
+def newstring text v = forsuffixes i=v : save i ; string i ; endfor ; enddef ;
+
+%D Sometimes we don't want parts of the graphics add to the
+%D bounding box. One way of doing this is to save the bounding
+%D box, draw the graphics that may not count, and restore the
+%D bounding box.
+%D
+%D \starttypen
+%D push_boundingbox currentpicture;
+%D pop_boundingbox currentpicture;
+%D \stoptypen
+%D
+%D The bounding box can be called with:
+%D
+%D \starttypen
+%D boundingbox currentpicture
+%D inner_boundingbox currentpicture
+%D outer_boundingbox currentpicture
+%D \stoptypen
+%D
+%D Especially the latter one can be of use when we include
+%D the graphic in a document that is clipped to the bounding
+%D box. In such occasions one can use:
+%D
+%D \starttypen
+%D set_outer_boundingbox currentpicture;
+%D \stoptypen
+%D
+%D Its counterpart is:
+%D
+%D \starttypen
+%D set_inner_boundingbox p
+%D \stoptypen
+
+path pushed_boundingbox;
+
+def push_boundingbox text p =
+ pushed_boundingbox := boundingbox p;
+enddef;
+
+def pop_boundingbox text p =
+ setbounds p to pushed_boundingbox;
+enddef;
+
+vardef boundingbox primary p =
+ if (path p) or (picture p) :
+ llcorner p -- lrcorner p -- urcorner p -- ulcorner p
+ else :
+ origin
+ fi -- cycle
+enddef;
+
+vardef inner_boundingbox primary p =
+ top rt llcorner p --
+ top lft lrcorner p --
+ bot lft urcorner p --
+ bot rt ulcorner p -- cycle
+enddef;
+
+vardef outer_boundingbox primary p =
+ bot lft llcorner p --
+ bot rt lrcorner p --
+ top rt urcorner p --
+ top lft ulcorner p -- cycle
+enddef;
+
+def innerboundingbox = inner_boundingbox enddef ;
+def outerboundingbox = outer_boundingbox enddef ;
+
+vardef set_inner_boundingbox text q =
+ setbounds q to inner_boundingbox q;
+enddef;
+
+vardef set_outer_boundingbox text q =
+ setbounds q to outer_boundingbox q;
+enddef;
+
+%D Some missing functions can be implemented rather
+%D straightforward:
+
+numeric Pi ; Pi := 3.1415926 ;
+
+vardef sqr primary x = (x*x) enddef ;
+vardef log primary x = (if x=0: 0 else: mlog(x)/mlog(10) fi) enddef ;
+vardef ln primary x = (if x=0: 0 else: mlog(x)/256 fi) enddef ;
+vardef exp primary x = ((mexp 256)**x) enddef ;
+vardef inv primary x = (if x=0: 0 else: x**-1 fi) enddef ;
+
+vardef pow (expr x,p) = (x**p) enddef ;
+
+vardef asin primary x = (x+(x**3)/6+3(x**5)/40) enddef ;
+vardef acos primary x = (asin(-x)) enddef ;
+vardef atan primary x = (x-(x**3)/3+(x**5)/5-(x**7)/7) enddef ;
+vardef tand primary x = (sind(x)/cosd(x)) enddef ;
+
+%D Here are Taco Hoekwater's alternatives (but
+%D vardef'd and primaried).
+
+pi := 3.1415926 ; radian := 180/pi ; % 2pi*radian = 360 ;
+
+vardef tand primary x = (sind(x)/cosd(x)) enddef ;
+vardef cotd primary x = (cosd(x)/sind(x)) enddef ;
+
+vardef sin primary x = (sind(x*radian)) enddef ;
+vardef cos primary x = (cosd(x*radian)) enddef ;
+vardef tan primary x = (sin(x)/cos(x)) enddef ;
+vardef cot primary x = (cos(x)/sin(x)) enddef ;
+
+vardef asin primary x = angle((1+-+x,x)) enddef ;
+vardef acos primary x = angle((x,1+-+x)) enddef ;
+
+vardef invsin primary x = ((asin(x))/radian) enddef ;
+vardef invcos primary x = ((acos(x))/radian) enddef ;
+
+vardef acosh primary x = ln(x+(x+-+1)) enddef ;
+vardef asinh primary x = ln(x+(x++1)) enddef ;
+
+vardef sinh primary x = save xx ; xx = exp xx ; (xx-1/xx)/2 enddef ;
+vardef cosh primary x = save xx ; xx = exp xx ; (xx+1/xx)/2 enddef ;
+
+%D We provide two macros for drawing stripes across a shape.
+%D The first method (with the n suffix) uses another method,
+%D slower in calculation, but more efficient when drawn. The
+%D first macro divides the sides into n equal parts. The
+%D first argument specifies the way the lines are drawn, while
+%D the second argument identifier the way the shape is to be
+%D drawn.
+%D
+%D \starttypen
+%D stripe_path_n
+%D (dashed evenly withcolor blue)
+%D (filldraw)
+%D fullcircle xscaled 100 yscaled 40 shifted (50,50) withpen pencircle scaled 4;
+%D \stoptypen
+%D
+%D The a (or angle) alternative supports arbitrary angles and
+%D is therefore more versatile.
+%D
+%D \starttypen
+%D stripe_path_a
+%D (withpen pencircle scaled 2 withcolor red)
+%D (draw)
+%D fullcircle xscaled 100 yscaled 40 withcolor blue;
+%D \stoptypen
+%D
+%D The first alternative obeys:
+
+stripe_n := 10;
+stripe_slot := 3;
+
+%D When no pen dimensions are passed, the slot determines
+%D the spacing.
+%D
+%D The angle alternative is influenced by:
+
+stripe_gap := 5;
+stripe_angle := 45;
+
+def stripe_path_n (text s_spec) (text s_draw) expr s_path =
+ do_stripe_path_n (s_spec) (s_draw) (s_path)
+enddef;
+
+def do_stripe_path_n (text s_spec) (text s_draw) (expr s_path) text s_text =
+ begingroup
+ save curpic, newpic, bb, pp, ww;
+ picture curpic, newpic;
+ path bb, pp;
+ pp := s_path;
+ curpic := currentpicture;
+ currentpicture := nullpicture;
+ s_draw pp s_text;
+ bb := boundingbox currentpicture;
+ newpic := currentpicture;
+ currentpicture := nullpicture;
+ ww := min(ypart urcorner newpic - ypart llcorner newpic,
+ xpart urcorner newpic - xpart llcorner newpic);
+ ww := ww/(stripe_slot*stripe_n);
+ for i=1/stripe_n step 1/stripe_n until 1:
+ draw point (1+i) of bb -- point (3-i) of bb
+ withpen pencircle scaled ww s_spec ;
+ endfor;
+ for i=0 step 1/stripe_n until 1:
+ draw point (3+i) of bb -- point (1-i) of bb
+ withpen pencircle scaled ww s_spec;
+ endfor;
+ clip currentpicture to pp;
+ addto newpic also currentpicture;
+ currentpicture := curpic;
+ addto currentpicture also newpic;
+ endgroup
+enddef;
+
+def stripe_path_a (text s_spec) (text s_draw) expr s_path =
+ do_stripe_path_a (s_spec) (s_draw) (s_path)
+enddef;
+
+def do_stripe_path_a (text s_spec) (text s_draw) (expr s_path) text s_text =
+ begingroup
+ save curpic, newpic, pp; picture curpic, newpic; path pp ;
+ pp := s_path ;
+ curpic := currentpicture;
+ currentpicture := nullpicture;
+ s_draw pp s_text ;
+ def do_stripe_rotation (expr p) =
+ (currentpicture rotatedaround(center p,stripe_angle))
+ enddef ;
+ s_max := max
+ (xpart llcorner do_stripe_rotation(currentpicture),
+ xpart urcorner do_stripe_rotation(currentpicture),
+ ypart llcorner do_stripe_rotation(currentpicture),
+ ypart urcorner do_stripe_rotation(currentpicture));
+ newpic := currentpicture;
+ currentpicture := nullpicture;
+ for i=-s_max-.5stripe_gap step stripe_gap until s_max:
+ draw (-s_max,i)--(s_max,i) s_spec;
+ endfor;
+ currentpicture := do_stripe_rotation(newpic);
+ clip currentpicture to pp ;
+ addto newpic also currentpicture;
+ currentpicture := curpic;
+ addto currentpicture also newpic;
+ endgroup
+enddef;
+
+%D A few normalizing macros:
+%D
+%D \starttypen
+%D xscale_currentpicture ( width )
+%D yscale_currentpicture ( height )
+%D xyscale_currentpicture ( width, height )
+%D scale_currentpicture ( width, height )
+%D \stoptypen
+
+% def xscale_currentpicture(expr the_width) =
+% natural_width := xpart urcorner currentpicture - xpart llcorner currentpicture;
+% currentpicture := currentpicture scaled (the_width/natural_width) ;
+% enddef;
+%
+% def yscale_currentpicture(expr the_height ) =
+% natural_height := ypart urcorner currentpicture - ypart llcorner currentpicture;
+% currentpicture := currentpicture scaled (the_height/natural_height) ;
+% enddef;
+%
+% def xyscale_currentpicture(expr the_width, the_height) =
+% natural_width := xpart urcorner currentpicture - xpart llcorner currentpicture;
+% natural_height := ypart urcorner currentpicture - ypart llcorner currentpicture;
+% currentpicture := currentpicture
+% xscaled (the_width/natural_width)
+% yscaled (the_height/natural_height) ;
+% enddef;
+%
+% def scale_currentpicture(expr the_width, the_height) =
+% xscale_currentpicture(the_width) ;
+% yscale_currentpicture(the_height) ;
+% enddef;
+
+% nog eens uitbreiden zodat path en pic worden afgehandeld.
+
+% natural_width := xpart urcorner currentpicture - xpart llcorner currentpicture;
+% currentpicture := currentpicture scaled (the_width/natural_width) ;
+
+% TODO TODO TODO TODO, not yet ok
+
+primarydef p xsized w =
+ (p if (bbwidth (p)>0) and (w>0) : scaled (w/bbwidth (p)) fi)
+enddef ;
+
+primarydef p ysized h =
+ (p if (bbheight(p)>0) and (h>0) : scaled (h/bbheight(p)) fi)
+enddef ;
+
+primarydef p xysized s =
+ begingroup ;
+ save wh, w, h ; pair wh ; numeric w, h ;
+ wh := paired (s) ; w := bbwidth(p) ; h := bbheight(p) ;
+ (p if (w>0) and (h>0) :
+ if xpart wh > 0 : xscaled (xpart wh/w) fi
+ if ypart wh > 0 : yscaled (ypart wh/h) fi
+ fi)
+ endgroup
+enddef ;
+
+primarydef p sized wh =
+ (p xysized wh)
+enddef ;
+
+def xscale_currentpicture(expr w) =
+ currentpicture := currentpicture xsized w ;
+enddef;
+
+def yscale_currentpicture(expr h) =
+ currentpicture := currentpicture ysized h ;
+enddef;
+
+def xyscale_currentpicture(expr w, h) =
+ currentpicture := currentpicture xysized (w,h) ;
+enddef;
+
+def scale_currentpicture(expr w, h) =
+ currentpicture := currentpicture xsized w ;
+ currentpicture := currentpicture ysized h ;
+enddef;
+
+%D A full circle is centered at the origin, while a unitsquare
+%D is located in the first quadrant. Now guess what kind of
+%D path fullsquare and unitcircle do return.
+
+path fullsquare, unitcircle ;
+
+fullsquare := unitsquare shifted - center unitsquare ;
+unitcircle := fullcircle shifted urcorner fullcircle ;
+
+%D Some more paths:
+
+path urcircle, ulcircle, llcircle, lrcircle ;
+
+urcircle := origin--(+.5,0)&(+.5,0){up} ..(0,+.5)&(0,+.5)--cycle ;
+ulcircle := origin--(0,+.5)&(0,+.5){left} ..(-.5,0)&(-.5,0)--cycle ;
+llcircle := origin--(-.5,0)&(-.5,0){down} ..(0,-.5)&(0,-.5)--cycle ;
+lrcircle := origin--(0,-.5)&(0,-.5){right}..(+.5,0)&(+.5,0)--cycle ;
+
+path tcircle, bcircle, lcircle, rcircle ;
+
+tcircle = origin--(+.5,0)&(+.5,0){up} ..(0,+.5)..{down} (-.5,0)--cycle ;
+bcircle = origin--(-.5,0)&(-.5,0){down} ..(0,-.5)..{up} (+.5,0)--cycle ;
+lcircle = origin--(0,+.5)&(0,+.5){left} ..(-.5,0)..{right}(0,-.5)--cycle ;
+rcircle = origin--(0,-.5)&(0,-.5){right}..(+.5,0)..{left} (0,+.5)--cycle ;
+
+path urtriangle, ultriangle, lltriangle, lrtriangle ;
+
+urtriangle := origin--(+.5,0)--(0,+.5)--cycle ;
+ultriangle := origin--(0,+.5)--(-.5,0)--cycle ;
+lltriangle := origin--(-.5,0)--(0,-.5)--cycle ;
+lrtriangle := origin--(0,-.5)--(+.5,0)--cycle ;
+
+path unitdiamond, fulldiamond ;
+
+unitdiamond := (.5,0)--(1,.5)--(.5,1)--(0,.5)--cycle ;
+fulldiamond := unitdiamond shifted - center unitdiamond ;
+
+%D More robust:
+
+% let normalscaled = scaled ;
+% let normalxscaled = xscaled ;
+% let normalyscaled = yscaled ;
+%
+% def scaled expr s = normalscaled (s) enddef ;
+% def xscaled expr s = normalxscaled (s) enddef ;
+% def yscaled expr s = normalyscaled (s) enddef ;
+
+%D Shorter
+
+primarydef p xyscaled q =
+ begingroup ; save qq ; pair qq ; qq = paired(q) ;
+ ( p
+ if xpart qq<>0 : xscaled (xpart qq) fi
+ if ypart qq<>0 : yscaled (ypart qq) fi )
+ endgroup
+enddef ;
+
+%D Experimenteel, zie folder-3.tex.
+
+def set_grid(expr w, h, nx, ny) =
+ boolean grid[][] ; boolean grid_full ;
+ grid_w := w ;
+ grid_h := h ;
+ grid_nx := nx ;
+ grid_ny := ny ;
+ grid_x := round(w/grid_nx) ; % +.5) ;
+ grid_y := round(h/grid_ny) ; % +.5) ;
+ grid_left := (1+grid_x)*(1+grid_y) ;
+ grid_full := false ;
+ for i=0 upto grid_x:
+ for j=0 upto grid_y:
+ grid[i][j] := false ;
+ endfor ;
+ endfor ;
+enddef ;
+
+vardef new_on_grid(expr _dx_, _dy_) =
+ dx := _dx_ ;
+ dy := _dy_ ;
+ ddx := min(round(dx/grid_nx),grid_x) ; % +.5),grid_x) ;
+ ddy := min(round(dy/grid_ny),grid_y) ; % +.5),grid_y) ;
+ if not grid_full and not grid[ddx][ddy]:
+ grid[ddx][ddy] := true ;
+ grid_left := grid_left-1 ;
+ grid_full := (grid_left=0) ;
+ true
+ else:
+ false
+ fi
+enddef ;
+
+%D usage: \type{innerpath peepholed outerpath}.
+%D
+%D beginfig(1);
+%D def fullsquare = (unitsquare shifted -center unitsquare) enddef ;
+%D fill (fullsquare scaled 200) withcolor red ;
+%D path p ; p := (fullcircle scaled 100) ; bboxmargin := 0 ;
+%D fill p peepholed bbox p ;
+%D endfig;
+
+secondarydef p peepholed q =
+ begingroup ;
+ save start ; pair start ; start := point 0 of p ;
+ if xpart start >= xpart center p :
+ if ypart start >= ypart center p :
+ urcorner q -- ulcorner q -- llcorner q -- lrcorner q --
+ reverse p -- lrcorner q -- cycle
+ else :
+ lrcorner q -- urcorner q -- ulcorner q -- llcorner q --
+ reverse p -- llcorner q -- cycle
+ fi
+ else :
+ if ypart start > ypart center p :
+ ulcorner q -- llcorner q -- lrcorner q -- urcorner q --
+ reverse p -- urcorner q -- cycle
+ else :
+ llcorner q -- lrcorner q -- urcorner q -- ulcorner q --
+ reverse p -- ulcorner q -- cycle
+ fi
+ fi
+ endgroup
+enddef ;
+
+boolean intersection_found ;
+
+secondarydef p intersection_point q =
+ begingroup
+ save x_, y_ ;
+ (x_,y_) = p intersectiontimes q ;
+ if x_<0 :
+ intersection_found := false ;
+ center p % origin
+ else :
+ intersection_found := true ;
+ .5[point x_ of p, point y_ of q]
+ fi
+ endgroup
+enddef ;
+
+%D New, undocumented, experimental:
+
+vardef tensecircle (expr width, height, offset) =
+ ((-width/2,-height/2) ... (0,-height/2-offset) ...
+ (+width/2,-height/2) ... (+width/2+offset,0) ...
+ (+width/2,+height/2) ... (0,+height/2+offset) ...
+ (-width/2,+height/2) ... (-width/2-offset,0) ... cycle)
+enddef ;
+
+%vardef tensecircle (expr width, height, offset) =
+% ((-width/2,-height/2)..(0,-height/2-offset)..(+width/2,-height/2) &
+% (+width/2,-height/2)..(+width/2+offset,0)..(+width/2,+height/2) &
+% (+width/2,+height/2)..(0,+height/2+offset)..(-width/2,+height/2) &
+% (-width/2,+height/2)..(-width/2-offset,0)..(-width/2,-height/2)..cycle)
+%enddef ;
+
+vardef roundedsquare (expr width, height, offset) =
+ ((offset,0)--(width-offset,0){right} ..
+ (width,offset)--(width,height-offset){up} ..
+ (width-offset,height)--(offset,height){left} ..
+ (0,height-offset)--(0,offset){down} .. cycle)
+enddef ;
+
+%D Some colors.
+
+color cyan ; cyan = (0,1,1) ;
+color magenta ; magenta = (1,0,1) ;
+color yellow ; yellow = (1,1,0) ;
+
+%D Well, this is the dangerous and naive version:
+
+def drawfill text t =
+ fill t ;
+ draw t ;
+enddef;
+
+%D This two step approach saves the path first, since it can
+%D be a function. Attributes must not be randomized.
+
+def drawfill expr c =
+ path _c_ ; _c_ := c ;
+ do_drawfill
+enddef ;
+
+def do_drawfill text t =
+ draw _c_ t ;
+ fill _c_ t ;
+enddef;
+
+def undrawfill expr c =
+ drawfill c withcolor background
+enddef ;
+
+%D Moved from mp-char.mp
+
+vardef paired (expr d) =
+ if pair d : d else : (d,d) fi
+enddef ;
+
+vardef tripled (expr d) =
+ if color d : d else : (d,d,d) fi
+enddef ;
+
+primarydef p enlarged d =
+ (p llmoved d -- p lrmoved d -- p urmoved d -- p ulmoved d -- cycle)
+enddef;
+
+primarydef p llenlarged d =
+ (p llmoved d -- lrcorner p -- urcorner p -- ulcorner p -- cycle)
+enddef ;
+
+primarydef p lrenlarged d =
+ (llcorner p -- p lrmoved d -- urcorner p -- ulcorner p -- cycle)
+enddef ;
+
+primarydef p urenlarged d =
+ (llcorner p -- lrcorner p -- p urmoved d -- ulcorner p -- cycle)
+enddef ;
+
+primarydef p ulenlarged d =
+ (llcorner p -- lrcorner p -- urcorner p -- p ulmoved d -- cycle)
+enddef ;
+
+primarydef p llmoved d =
+ ((llcorner p) shifted (-xpart paired(d),-ypart paired(d)))
+enddef ;
+
+primarydef p lrmoved d =
+ ((lrcorner p) shifted (+xpart paired(d),-ypart paired(d)))
+enddef ;
+
+primarydef p urmoved d =
+ ((urcorner p) shifted (+xpart paired(d),+ypart paired(d)))
+enddef ;
+
+primarydef p ulmoved d =
+ ((ulcorner p) shifted (-xpart paired(d),+ypart paired(d)))
+enddef ;
+
+primarydef p leftenlarged d =
+ ((llcorner p) shifted (-d,0) -- lrcorner p --
+ urcorner p -- (ulcorner p) shifted (-d,0) -- cycle)
+enddef ;
+
+primarydef p rightenlarged d =
+ (llcorner p -- (lrcorner p) shifted (d,0) --
+ (urcorner p) shifted (d,0) -- ulcorner p -- cycle)
+enddef ;
+
+primarydef p topenlarged d =
+ (llcorner p -- lrcorner p --
+ (urcorner p) shifted (0,d) -- (ulcorner p) shifted (0,d) -- cycle)
+enddef ;
+
+primarydef p bottomenlarged d =
+ (llcorner p shifted (0,-d) -- lrcorner p shifted (0,-d) --
+ urcorner p -- ulcorner p -- cycle)
+enddef ;
+
+%D Saves typing:
+
+% vardef bottomboundary primary p = (llcorner p -- lrcorner p) enddef ;
+% vardef rightboundary primary p = (lrcorner p -- urcorner p) enddef ;
+% vardef topboundary primary p = (urcorner p -- ulcorner p) enddef ;
+% vardef leftboundary primary p = (ulcorner p -- llcorner p) enddef ;
+
+vardef bottomboundary primary p =
+ if pair p : p else : (llcorner p -- lrcorner p) fi
+enddef ;
+
+vardef rightboundary primary p =
+ if pair p : p else : (lrcorner p -- urcorner p) fi
+enddef ;
+
+vardef topboundary primary p =
+ if pair p : p else : (urcorner p -- ulcorner p) fi
+enddef ;
+
+vardef leftboundary primary p =
+ if pair p : p else : (ulcorner p -- llcorner p) fi
+enddef ;
+
+%D Nice too:
+
+primarydef p superellipsed s =
+ superellipse
+ (.5[lrcorner p,urcorner p],
+ .5[urcorner p,ulcorner p],
+ .5[ulcorner p,llcorner p],
+ .5[llcorner p,lrcorner p],
+ s)
+enddef ;
+
+primarydef p squeezed s =
+ ((llcorner p .. .5[llcorner p,lrcorner p] shifted ( 0, ypart paired(s)) .. lrcorner p) &
+ (lrcorner p .. .5[lrcorner p,urcorner p] shifted (-xpart paired(s), 0) .. urcorner p) &
+ (urcorner p .. .5[urcorner p,ulcorner p] shifted ( 0,-ypart paired(s)) .. ulcorner p) &
+ (ulcorner p .. .5[ulcorner p,llcorner p] shifted ( xpart paired(s), 0) .. llcorner p) & cycle)
+enddef ;
+
+primarydef p randomshifted s =
+ begingroup ; save ss ; pair ss ; ss := paired(s) ;
+ p shifted (-.5xpart ss + uniformdeviate xpart ss,
+ -.5ypart ss + uniformdeviate ypart ss)
+ endgroup
+enddef ;
+
+%primarydef p randomized s =
+% for i=0 upto length(p)-1 :
+% ((point i of p) randomshifted s) .. controls
+% ((postcontrol i of p) randomshifted s) and
+% ((precontrol (i+1) of p) randomshifted s) ..
+% endfor cycle
+%enddef ;
+
+primarydef p randomized s =
+ (if path p :
+ for i=0 upto length(p)-1 :
+ ((point i of p) randomshifted s) .. controls
+ ((postcontrol i of p) randomshifted s) and
+ ((precontrol (i+1) of p) randomshifted s) ..
+ endfor
+ if cycle p :
+ cycle
+ else :
+ ((point length(p) of p) randomshifted s)
+ fi
+ elseif pair p :
+ p randomshifted s
+ elseif color p :
+ if color s :
+ (uniformdeviate redpart s * redpart p,
+ uniformdeviate greenpart s * greenpart p,
+ uniformdeviate bluepart s * bluepart p)
+ elseif pair s :
+ ((xpart s + uniformdeviate (ypart s - xpart s)) * p)
+ else :
+ (uniformdeviate s * p)
+ fi
+ else :
+ p + uniformdeviate s
+ fi)
+enddef ;
+
+%D Not perfect (alternative for interpath)
+
+vardef interpolated(expr s, p, q) =
+ save m ; m := max(length(p),length(q)) ;
+ (if path p :
+ for i=0 upto m-1 :
+ s[point (i /m) along p,
+ point (i /m) along q] .. controls
+ s[postcontrol (i /m) along p,
+ postcontrol (i /m) along q] and
+ s[precontrol ((i+1)/m) along p,
+ precontrol ((i+1)/m) along q] ..
+ endfor
+ if cycle p :
+ cycle
+ else :
+ s[point infinity of p,
+ point infinity of q]
+ fi
+ else :
+ a[p,q]
+ fi)
+enddef ;
+
+%D Interesting too:
+
+% primarydef p parallel s =
+% begingroup ; save q, b ; path q ; numeric b ;
+% b := xpart (lrcorner p - llcorner p) ;
+% q := p if b>0 : scaled ((b+2s)/b) fi ;
+% (q shifted (center p-center q))
+% endgroup
+% enddef ;
+
+%primarydef p parallel s =
+% begingroup ; save q, w,h ; path q ; numeric w, h ;
+% w := bbwidth(p) ; h := bbheight(p) ;
+% q := p if (w>0) and (h>0) :
+% xyscaled ((w+2*xpart paired(s))/w,(h+2*ypart paired(s))/h) fi ;
+% (q shifted (center p-center q))
+% endgroup
+%enddef ;
+
+vardef punked primary p =
+ (point 0 of p for i=1 upto length(p)-1 : -- point i of p endfor
+ if cycle p : -- cycle else : -- point length(p) of p fi)
+enddef ;
+
+vardef curved primary p =
+ (point 0 of p for i=1 upto length(p)-1 : .. point i of p endfor
+ if cycle p : .. cycle else : .. point length(p) of p fi)
+enddef ;
+
+primarydef p blownup s =
+ begingroup
+ save _p_ ; path _p_ ; _p_ := p xysized
+ (bbwidth (p)+2(xpart paired(s)),
+ bbheight(p)+2(ypart paired(s))) ;
+ (_p_ shifted (center p - center _p_))
+ endgroup
+enddef ;
+
+%D Rather fundamental.
+
+% vardef rightpath expr p =
+% save q, t, b ; path q ; pair t, b ;
+% t := (ulcorner p -- urcorner p) intersection_point p ;
+% b := (llcorner p -- lrcorner p) intersection_point p ;
+% if xpart directionpoint t of p < 0 : p := reverse p ; fi ;
+% q := p cutbefore b ;
+% q := q if xpart point 0 of p > 0 : & p fi cutafter t ;
+% q
+% enddef ;
+%
+% vardef leftpath expr p =
+% save q, t, b ; path q ; pair t, b ;
+% t := (ulcorner p -- urcorner p) intersection_point p ;
+% b := (llcorner p -- lrcorner p) intersection_point p ;
+% if xpart directionpoint t of p < 0 : p := reverse p ; fi ;
+% q := p cutbefore t ;
+% q := q if xpart point 0 of p > 0 : & p fi cutafter b ;
+% q
+% enddef ;
+
+def leftrightpath(expr p, l) =
+ save q, t, b ; path q ; pair t, b ;
+ t := (ulcorner p -- urcorner p) intersection_point p ;
+ b := (llcorner p -- lrcorner p) intersection_point p ;
+ if xpart directionpoint t of p < 0 : p := reverse p ; fi ;
+ q := p cutbefore if l: t else: b fi ;
+ q := q if xpart point 0 of p > 0 : &
+ p fi cutafter if l: b else: t fi ;
+ q
+enddef ;
+
+vardef leftpath expr p = leftrightpath(p,true ) enddef ;
+vardef rightpath expr p = leftrightpath(p,false) enddef ;
+
+%D Drawoptions
+
+def saveoptions =
+ save _op_ ; def _op_ = enddef ;
+enddef ;
+
+%D Tracing.
+
+let normaldraw = draw ;
+let normalfill = fill ;
+
+def drawlineoptions (text t) = def _lin_opt_ = t enddef ; enddef ;
+def drawpointoptions (text t) = def _pnt_opt_ = t enddef ; enddef ;
+def drawcontroloptions(text t) = def _ctr_opt_ = t enddef ; enddef ;
+def drawlabeloptions (text t) = def _lab_opt_ = t enddef ; enddef ;
+def draworiginoptions (text t) = def _ori_opt_ = t enddef ; enddef ;
+def drawboundoptions (text t) = def _bnd_opt_ = t enddef ; enddef ;
+def drawpathoptions (text t) = def _pth_opt_ = t enddef ; enddef ;
+
+def resetdrawoptions =
+ drawlineoptions (withpen pencircle scaled 1pt withcolor .5white) ;
+ drawpointoptions (withpen pencircle scaled 4pt withcolor black) ;
+ drawcontroloptions(withpen pencircle scaled 2.5pt withcolor black) ;
+ drawlabeloptions () ;
+ draworiginoptions (withpen pencircle scaled 1pt withcolor .5white) ;
+ drawboundoptions (dashed evenly _ori_opt_) ;
+ drawpathoptions (withpen pencircle scaled 5pt withcolor .8white) ;
+enddef ;
+
+resetdrawoptions ;
+
+%D Path.
+
+def drawpath expr p =
+ normaldraw p _pth_opt_
+enddef ;
+
+%D Arrow.
+
+vardef drawarrowpath expr p =
+ save autoarrows ; boolean autoarrows ; autoarrows := true ;
+ drawarrow p _pth_opt_
+enddef ;
+
+%def drawarrowpath expr p =
+% begingroup ;
+% save autoarrows ; boolean autoarrows ; autoarrows := true ;
+% save arrowpath ; path arrowpath ; arrowpath := p ;
+% _drawarrowpath_
+%enddef ;
+%
+%def _drawarrowpath_ text t =
+% drawarrow arrowpath _pth_opt_ t ;
+% endgroup ;
+%enddef ;
+
+def midarrowhead expr p =
+ arrowhead p cutafter
+ (point length(p cutafter point .5 along p)+ahlength on p)
+enddef ;
+
+vardef arrowheadonpath (expr p, s) =
+ save autoarrows ; boolean autoarrows ; autoarrows := true ;
+ arrowhead p if s<1 : cutafter (point (s*arclength(p)+.5ahlength) on p) fi
+enddef ;
+
+%D Points.
+
+def drawpoint expr c =
+ if string c :
+ string _c_ ; _c_ := "(" & c & ")" ;
+ dotlabel.urt(_c_, scantokens _c_) ;
+ drawdot scantokens _c_
+ else :
+ dotlabel.urt("(" & decimal xpart c & "," & decimal ypart c & ")", c) ;
+ drawdot c
+ fi _pnt_opt_
+enddef ;
+
+%D PathPoints.
+
+def drawpoints expr c = path _c_ ; _c_ := c ; do_drawpoints enddef ;
+def drawcontrolpoints expr c = path _c_ ; _c_ := c ; do_drawcontrolpoints enddef ;
+def drawcontrollines expr c = path _c_ ; _c_ := c ; do_drawcontrollines enddef ;
+def drawpointlabels expr c = path _c_ ; _c_ := c ; do_drawpointlabels enddef ;
+
+def do_drawpoints text t =
+ for _i_=0 upto length(_c_) :
+ normaldraw point _i_ of _c_ _pnt_opt_ t ;
+ endfor ;
+enddef;
+
+def do_drawcontrolpoints text t =
+ for _i_=0 upto length(_c_) :
+ normaldraw precontrol _i_ of _c_ _ctr_opt_ t ;
+ normaldraw postcontrol _i_ of _c_ _ctr_opt_ t ;
+ endfor ;
+enddef;
+
+def do_drawcontrollines text t =
+ for _i_=0 upto length(_c_) :
+ normaldraw point _i_ of _c_ -- precontrol _i_ of _c_ _lin_opt_ t ;
+ normaldraw point _i_ of _c_ -- postcontrol _i_ of _c_ _lin_opt_ t ;
+ endfor ;
+enddef;
+
+boolean swappointlabels ; swappointlabels := false ;
+
+def do_drawpointlabels text t =
+ for _i_=0 upto length(_c_) :
+ pair _u_ ; _u_ := unitvector(direction _i_ of _c_)
+ rotated if swappointlabels : - fi 90 ;
+ pair _p_ ; _p_ := (point _i_ of _c_) ;
+ _u_ := 12 * defaultscale * _u_ ;
+ normaldraw thelabel ( decimal _i_,
+ _p_ shifted if cycle _c_ and (_i_=0) : - fi _u_ ) _lab_opt_ t ;
+ endfor ;
+enddef;
+
+%D Bounding box.
+
+def drawboundingbox expr p =
+ normaldraw boundingbox p _bnd_opt_
+enddef ;
+
+%D Origin.
+
+numeric originlength ; originlength := .5cm ;
+
+def draworigin text t =
+ normaldraw (origin shifted (0, originlength) --
+ origin shifted (0,-originlength)) _ori_opt_ t ;
+ normaldraw (origin shifted ( originlength,0) --
+ origin shifted (-originlength,0)) _ori_opt_ t ;
+enddef;
+
+%D Axis.
+
+numeric tickstep ; tickstep := 5mm ;
+numeric ticklength ; ticklength := 2mm ;
+
+def drawxticks expr c = path _c_ ; _c_ := c ; do_drawxticks enddef ;
+def drawyticks expr c = path _c_ ; _c_ := c ; do_drawyticks enddef ;
+def drawticks expr c = path _c_ ; _c_ := c ; do_drawticks enddef ;
+
+% Adding eps prevents disappearance due to rounding errors.
+
+def do_drawxticks text t =
+ for i=0 step -tickstep until xpart llcorner _c_ - eps :
+ if (i<=xpart lrcorner _c_) :
+ normaldraw (i,-ticklength)--(i,ticklength) _ori_opt_ t ;
+ fi ;
+ endfor ;
+ for i=0 step tickstep until xpart lrcorner _c_ + eps :
+ if (i>=xpart llcorner _c_) :
+ normaldraw (i,-ticklength)--(i,ticklength) _ori_opt_ t ;
+ fi ;
+ endfor ;
+ normaldraw (llcorner _c_ -- ulcorner _c_)
+ shifted (-xpart llcorner _c_,0) _ori_opt_ t ;
+enddef ;
+
+def do_drawyticks text t =
+ for i=0 step -tickstep until ypart llcorner _c_ - eps :
+ if (i<=ypart ulcorner _c_) :
+ normaldraw (-ticklength,i)--(ticklength,i) _ori_opt_ t ;
+ fi ;
+ endfor ;
+ for i=0 step tickstep until ypart ulcorner _c_ + eps :
+ if (i>=ypart llcorner _c_) :
+ normaldraw (-ticklength,i)--(ticklength,i) _ori_opt_ t ;
+ fi ;
+ endfor ;
+ normaldraw (llcorner _c_ -- lrcorner _c_)
+ shifted (0,-ypart llcorner _c_) _ori_opt_ t ;
+enddef ;
+
+def do_drawticks text t =
+ drawxticks _c_ t ;
+ drawyticks _c_ t ;
+enddef ;
+
+%D All of it except axis.
+
+def drawwholepath expr p =
+ draworigin ;
+ drawpath p ;
+ drawcontrollines p ;
+ drawcontrolpoints p ;
+ drawpoints p ;
+ drawboundingbox p ;
+ drawpointlabels p ;
+enddef ;
+
+%D Tracing.
+
+def visualizeddraw expr c =
+ if picture c : normaldraw c else : path _c_ ; _c_ := c ; do_visualizeddraw fi
+enddef ;
+
+def visualizedfill expr c =
+ if picture c : normalfill c else : path _c_ ; _c_ := c ; do_visualizedfill fi
+enddef ;
+
+def do_visualizeddraw text t =
+ draworigin ;
+ drawpath _c_ t ;
+ drawcontrollines _c_ ;
+ drawcontrolpoints _c_ ;
+ drawpoints _c_ ;
+ drawboundingbox _c_ ;
+ drawpointlabels _c_ ;
+enddef ;
+
+def do_visualizedfill text t =
+ if cycle _c_ : normalfill _c_ t fi ;
+ draworigin ;
+ drawcontrollines _c_ ;
+ drawcontrolpoints _c_ ;
+ drawpoints _c_ ;
+ drawboundingbox _c_ ;
+ drawpointlabels _c_ ;
+enddef ;
+
+def visualizepaths =
+ let fill = visualizedfill ;
+ let draw = visualizeddraw ;
+enddef ;
+
+def naturalizepaths =
+ let fill = normalfill ;
+ let draw = normaldraw ;
+enddef ;
+
+extra_endfig := extra_endfig & " naturalizepaths ; " ;
+
+%D Normally, arrowheads don't scale well. So we provide a
+%D hack.
+
+boolean autoarrows ; autoarrows := false ;
+numeric ahfactor ; ahfactor := 2.5 ;
+
+def set_ahlength (text t) =
+ ahlength := (ahfactor*pen_size(_op_ t)) ; % _op_ added
+enddef ;
+
+vardef pen_size (text t) =
+ save p ; picture p ; p := nullpicture ;
+ addto p doublepath (top origin -- bot origin) t ;
+ (ypart urcorner p - ypart lrcorner p)
+enddef ;
+
+%D The next two macros are adapted versions of plain
+%D \METAPOST\ definitions.
+
+def _finarr text t =
+ if autoarrows : set_ahlength (t) fi ;
+ draw _apth t ;
+ filldraw arrowhead _apth t ;
+enddef;
+
+def _findarr text t =
+ if autoarrows : set_ahlength (t) fi ;
+ draw _apth t ;
+ fill arrowhead _apth withpen currentpen t ;
+ fill arrowhead reverse _apth withpen currentpen t ;
+enddef ;
+
+%D Handy too ......
+
+vardef pointarrow (expr pat, loc, len, off) =
+ save l, r, s, t ; path l, r ; numeric s ; pair t ;
+ t := if pair loc : loc else : point loc along pat fi ;
+% draw t withpen pencircle scaled 10 withcolor .5white ;
+ s := len/2 - off ; if s<=0 : s := 0 elseif s>len : s := len fi ;
+ r := pat cutbefore t ;
+ r := (r cutafter point (arctime s of r) of r) ;
+ s := len/2 + off ; if s<=0 : s := 0 elseif s>len : s := len fi ;
+ l := reverse (pat cutafter t) ;
+ l := (reverse (l cutafter point (arctime s of l) of l)) ;
+ (l..r)
+enddef ;
+
+def rightarrow (expr pat,tim,len) = pointarrow(pat,tim,len,-len) enddef ;
+def leftarrow (expr pat,tim,len) = pointarrow(pat,tim,len,+len) enddef ;
+def centerarrow (expr pat,tim,len) = pointarrow(pat,tim,len, 0) enddef ;
+
+%D The \type {along} and \type {on} operators can be used
+%D as follows:
+%D
+%D \starttypen
+%D drawdot point .5 along somepath ;
+%D drawdot point 3cm on somepath ;
+%D \stoptypen
+%D
+%D The number denotes a percentage (fraction).
+
+primarydef pct along pat = % also negative
+ (arctime (pct * (arclength pat)) of pat) of pat
+enddef ;
+
+% primarydef len on pat =
+% (arctime len of pat) of pat
+% enddef ;
+
+primarydef len on pat =
+ (arctime if len>0 : len else : (arclength(pat)+len) fi of pat) of pat
+enddef ;
+
+% this cuts of a piece from both ends
+
+% tertiarydef pat cutends len =
+% begingroup ; save tap ; path tap ;
+% tap := pat cutbefore (point len on pat) ;
+% (tap cutafter (point -len on tap))
+% endgroup
+% enddef ;
+
+tertiarydef pat cutends len =
+ begingroup ; save tap ; path tap ;
+ tap := pat cutbefore (point (xpart paired(len)) on pat) ;
+ (tap cutafter (point -(ypart paired(len)) on tap))
+ endgroup
+enddef ;
+
+%D To be documented.
+
+path freesquare ;
+
+freesquare := ((-1,0)--(-1,-1)--(0,-1)--(+1,-1)--
+ (+1,0)--(+1,+1)--(0,+1)--(-1,+1)--cycle) scaled .5 ;
+
+numeric freelabeloffset ; freelabeloffset := 3pt ;
+numeric freedotlabelsize ; freedotlabelsize := 3pt ;
+
+vardef thefreelabel (expr str, loc, ori) =
+ save s, p, q, l ; picture s ; path p, q ; pair l ;
+ interim labeloffset := freelabeloffset ;
+ s := if string str : thelabel(str,loc) else : str shifted -center str shifted loc fi ;
+ setbounds s to boundingbox s enlarged freelabeloffset ;
+ p := fullcircle scaled (2*length(loc-ori)) shifted ori ;
+ q := freesquare xyscaled (urcorner s - llcorner s) ;
+% l := point (xpart (p intersectiontimes (ori--loc))) of q ;
+ l := point xpart (p intersectiontimes
+ (ori--((1+eps)*arclength(ori--loc)*unitvector(loc-ori)))) of q ;
+ setbounds s to boundingbox s enlarged -freelabeloffset ; % new
+ %draw boundingbox s shifted -l withpen pencircle scaled .5pt withcolor red ;
+ (s shifted -l)
+enddef ;
+
+% better?
+
+vardef thefreelabel (expr str, loc, ori) =
+ save s, p, q, l ; picture s ; path p, q ; pair l ;
+ interim labeloffset := freelabeloffset ;
+ s := if string str : thelabel(str,loc) else : str shifted -center str shifted loc fi ;
+ setbounds s to boundingbox s enlarged freelabeloffset ;
+ p := fullcircle scaled (2*length(loc-ori)) shifted ori ;
+ q := freesquare xyscaled (urcorner s - llcorner s) ;
+ l := point xpart (p intersectiontimes (ori--loc shifted (loc-ori))) of q ;
+ setbounds s to boundingbox s enlarged -freelabeloffset ; % new
+ %draw boundingbox s shifted -l withpen pencircle scaled .5pt withcolor red ;
+ (s shifted -l)
+enddef ;
+
+vardef freelabel (expr str, loc, ori) =
+ draw thefreelabel(str,loc,ori) ;
+enddef ;
+
+vardef freedotlabel (expr str, loc, ori) =
+ interim linecap:=rounded ;
+ draw loc withpen pencircle scaled freedotlabelsize ;
+ draw thefreelabel(str,loc,ori) ;
+enddef ;
+
+%D \starttypen
+%D drawarrow anglebetween(line_a,line_b,somelabel) ;
+%D \stoptypen
+
+% angleoffset ; angleoffset := 0pt ;
+numeric anglelength ; anglelength := 20pt ;
+numeric anglemethod ; anglemethod := 1 ;
+
+% vardef anglebetween (expr a, b, str) = % path path string
+% save pointa, pointb, common, middle, offset ;
+% pair pointa, pointb, common, middle, offset ;
+% save curve ; path curve ;
+% save where ; numeric where ;
+% if round point 0 of a = round point 0 of b :
+% common := point 0 of a ;
+% else :
+% common := a intersectionpoint b ;
+% fi ;
+% pointa := point anglelength on a ;
+% pointb := point anglelength on b ;
+% where := turningnumber (common--pointa--pointb--cycle) ;
+% middle := ((common--pointa) rotatedaround (pointa,-where*90))
+% intersectionpoint
+% ((common--pointb) rotatedaround (pointb, where*90)) ;
+% if anglemethod = 0 :
+% curve := pointa{unitvector(middle-pointa)}.. pointb;
+% middle := point .5 along curve ;
+% curve := common ;
+% elseif anglemethod = 1 :
+% curve := pointa{unitvector(middle-pointa)}.. pointb;
+% middle := point .5 along curve ;
+% elseif anglemethod = 2 :
+% middle := common rotatedaround(.5[pointa,pointb],180) ;
+% curve := pointa--middle--pointb ;
+% elseif anglemethod = 3 :
+% curve := pointa--middle--pointb ;
+% elseif anglemethod = 4 :
+% curve := pointa..controls middle..pointb ;
+% middle := point .5 along curve ;
+% fi ;
+% draw thefreelabel(str, middle, common) withcolor black ;
+% curve
+% enddef ;
+
+vardef anglebetween (expr a, b, str) = % path path string
+ save pointa, pointb, common, middle, offset ;
+ pair pointa, pointb, common, middle, offset ;
+ save curve ; path curve ;
+ save where ; numeric where ;
+ if round point 0 of a = round point 0 of b :
+ common := point 0 of a ;
+ else :
+ common := a intersectionpoint b ;
+ fi ;
+ pointa := point anglelength on a ;
+ pointb := point anglelength on b ;
+ where := turningnumber (common--pointa--pointb--cycle) ;
+ middle := (reverse(common--pointa) rotatedaround (pointa,-where*90))
+ intersection_point
+ (reverse(common--pointb) rotatedaround (pointb, where*90)) ;
+ if not intersection_found :
+ middle := point .5 along
+ ((reverse(common--pointa) rotatedaround (pointa,-where*90)) --
+ ( (common--pointb) rotatedaround (pointb, where*90))) ;
+ fi ;
+ if anglemethod = 0 :
+ curve := pointa{unitvector(middle-pointa)}.. pointb;
+ middle := point .5 along curve ;
+ curve := common ;
+ elseif anglemethod = 1 :
+ curve := pointa{unitvector(middle-pointa)}.. pointb;
+ middle := point .5 along curve ;
+ elseif anglemethod = 2 :
+ middle := common rotatedaround(.5[pointa,pointb],180) ;
+ curve := pointa--middle--pointb ;
+ elseif anglemethod = 3 :
+ curve := pointa--middle--pointb ;
+ elseif anglemethod = 4 :
+ curve := pointa..controls middle..pointb ;
+ middle := point .5 along curve ;
+ fi ;
+ draw thefreelabel(str, middle, common) ; % withcolor black ;
+ curve
+enddef ;
+
+% Stack
+
+picture currentpicturestack[] ;
+numeric currentpicturedepth ; currentpicturedepth := 0 ;
+
+def pushcurrentpicture =
+ currentpicturedepth := currentpicturedepth + 1 ;
+ currentpicturestack[currentpicturedepth] := currentpicture ;
+ currentpicture := nullpicture ;
+enddef ;
+
+def popcurrentpicture text t = % optional text
+ if currentpicturedepth > 0 :
+ addto currentpicturestack[currentpicturedepth] also currentpicture t ;
+ currentpicture := currentpicturestack[currentpicturedepth] ;
+ currentpicturedepth := currentpicturedepth - 1 ;
+ fi ;
+enddef ;
+
+%D colorcircle(size, red, green, blue) ;
+
+% vardef colorcircle (expr size, red, green, blue) =
+% save r, g, b, rr, gg, bb, cc, mm, yy ; save radius ;
+% path r, g, b, rr, bb, gg, cc, mm, yy ; numeric radius ;
+%
+% radius := 5cm ; pickup pencircle scaled (radius/25) ;
+%
+% r := g := b := fullcircle scaled radius shifted (0,radius/4) ;
+%
+% r := r rotatedaround (origin, 15) ;
+% g := g rotatedaround (origin,135) ;
+% b := b rotatedaround (origin,255) ;
+%
+% r := r rotatedaround(center r,-90) ;
+% g := g rotatedaround(center g, 90) ;
+%
+% gg := buildcycle(buildcycle(reverse r,b),g) ;
+% cc := buildcycle(buildcycle(b,reverse g),r) ;
+%
+% rr := gg rotatedaround(origin,120) ;
+% bb := gg rotatedaround(origin,240) ;
+%
+% yy := cc rotatedaround(origin,120) ;
+% mm := cc rotatedaround(origin,240) ;
+%
+% pushcurrentpicture ;
+%
+% fill fullcircle scaled radius withcolor white ;
+%
+% fill rr withcolor red ; fill cc withcolor white-red ;
+% fill gg withcolor green ; fill mm withcolor white-green ;
+% fill bb withcolor blue ; fill yy withcolor white-blue ;
+%
+% for i = rr,gg,bb,cc,mm,yy : draw i withcolor .5white ; endfor ;
+%
+% currentpicture := currentpicture xsized size ;
+%
+% popcurrentpicture ;
+% enddef ;
+
+% vardef colorcircle (expr size, red, green, blue) =
+% save r, g, b, rr, gg, bb, cc, mm, yy ; save radius ;
+% path r, g, b, rr, bb, gg, cc, mm, yy ; numeric radius ;
+%
+% radius := 5cm ; pickup pencircle scaled (radius/25) ;
+%
+% transform t ; t := identity rotatedaround(origin,120) ;
+%
+% r := fullcircle scaled radius
+% shifted (0,radius/4) rotatedaround(origin,15) ;
+%
+% g := r transformed t ; b := g transformed t ;
+%
+% r := r rotatedaround(center r,-90) ;
+% g := g rotatedaround(center g, 90) ;
+%
+% gg := buildcycle(buildcycle(reverse r,b),g) ;
+% cc := buildcycle(buildcycle(b,reverse g),r) ;
+%
+% rr := gg transformed t ; bb := rr transformed t ;
+% yy := cc transformed t ; mm := yy transformed t ;
+%
+% pushcurrentpicture ;
+%
+% fill fullcircle scaled radius withcolor white ;
+%
+% fill rr withcolor red ; fill cc withcolor white-red ;
+% fill gg withcolor green ; fill mm withcolor white-green ;
+% fill bb withcolor blue ; fill yy withcolor white-blue ;
+%
+% for i = rr,gg,bb,cc,mm,yy : draw i withcolor .5white ; endfor ;
+%
+% currentpicture := currentpicture xsized size ;
+%
+% popcurrentpicture ;
+% enddef ;
+
+vardef colorcircle (expr size, red, green, blue) =
+ save r, g, b, c, m, y, w ; save radius ;
+ path r, g, b, c, m, y, w ; numeric radius ;
+
+ radius := 5cm ; pickup pencircle scaled (radius/25) ;
+
+ transform t ; t := identity rotatedaround(origin,120) ;
+
+ r := fullcircle rotated 90 scaled radius
+ shifted (0,radius/4) rotatedaround(origin,135) ;
+
+ b := r transformed t ; g := b transformed t ;
+
+ c := buildcycle(subpath(1,7) of g,subpath(1,7) of b) ;
+ y := c transformed t ; m := y transformed t ;
+
+ w := buildcycle(subpath(3,5) of r, subpath(3,5) of g,subpath(3,5) of b) ;
+
+ pushcurrentpicture ;
+
+ fill r withcolor red ;
+ fill g withcolor green ;
+ fill b withcolor blue ;
+ fill c withcolor white-red ;
+ fill m withcolor white-green ;
+ fill y withcolor white-blue ;
+ fill w withcolor white ;
+
+ for i = r,g,b,c,m,y : draw i withcolor .5white ; endfor ;
+
+ currentpicture := currentpicture xsized size ;
+
+ popcurrentpicture ;
+enddef ;
+
+% penpoint (i,2) of somepath -> inner / outer point
+
+vardef penpoint expr pnt of p =
+ save n, d ; numeric n, d ;
+ (n,d) = if pair pnt : pnt else : (pnt,1) fi ;
+ (point n of p shifted ((penoffset direction n of p of currentpen) scaled d))
+enddef ;
+
+% nice: currentpicture := inverted currentpicture ;
+
+primarydef p uncolored c =
+ image
+ (for i within p :
+ addto currentpicture
+ if stroked i or filled i :
+ if filled i : contour else : doublepath fi pathpart i
+ dashed dashpart i withpen penpart i
+ else :
+ also i
+ fi
+ withcolor c-(redpart i, greenpart i, bluepart i) ;
+ endfor ; )
+enddef ;
+
+vardef inverted primary p =
+ (p uncolored white)
+enddef ;
+
+primarydef p softened c =
+ image
+ (save cc ; color cc ; cc := tripled(c) ;
+ for i within p :
+ addto currentpicture
+ if stroked i or filled i :
+ if filled i : contour else : doublepath fi pathpart i
+ dashed dashpart i withpen penpart i
+ else :
+ also i
+ fi
+ withcolor (redpart cc * redpart i,
+ greenpart cc * greenpart i,
+ bluepart cc * bluepart i) ;
+ endfor ;)
+enddef ;
+
+vardef grayed primary p =
+ image
+ (for i within p :
+ addto currentpicture
+ if stroked i or filled i :
+ if filled i : contour else : doublepath fi pathpart i
+ dashed dashpart i withpen penpart i
+ else :
+ also i
+ fi
+ withcolor tripled(.30redpart i+.59greenpart i+.11bluepart i) ;
+ endfor ; )
+enddef ;
+
+% yes or no: "text" infont "cmr12" at 24pt ;
+
+% let normalinfont = infont ;
+%
+% numeric lastfontsize ; lastfontsize = fontsize defaultfont ;
+%
+% def infont primary name = % no vardef, no expr
+% hide(lastfontsize := fontsize name) % no ;
+% normalinfont name
+% enddef ;
+%
+% def scaledat expr size =
+% scaled (size/lastfontsize)
+% enddef ;
+%
+% let at = scaledat ;
+
+% like decimal
+
+def condition primary b = if b : "true" else : "false" fi enddef ;
+
+% undocumented
+
+primarydef p stretched s =
+ begingroup
+% save pp ; path pp ; pp := p scaled s ;
+ save pp ; path pp ; pp := p xyscaled s ;
+ (pp shifted ((point 0 of p) - (point 0 of pp)))
+ endgroup
+enddef ;
+
+% yes or no, untested -)
+
+def xshifted expr dx = shifted(dx,0) enddef ;
+def yshifted expr dy = shifted(0,dy) enddef ;
+
+% also handy
+
+% right: str = readfrom ("abc" & ".def" ) ;
+% wrong: str = readfrom "abc" & ".def" ;
+
+% Every 62th read fails so we need to try again!
+
+def readfile (expr name) =
+ if (readfrom (name) <> EOF) :
+ scantokens("input " & name & " ") ;
+ elseif (readfrom (name) <> EOF) :
+ scantokens("input " & name & " ") ;
+ fi
+ closefrom (name) ;
+enddef ;
+
+% permits redefinition of end in macro
+
+inner end ;
+
+% real fun
+
+let normalwithcolor = withcolor ;
+
+def remapcolors =
+ def withcolor primary c = normalwithcolor remappedcolor(c) enddef ;
+enddef ;
+
+def normalcolors =
+ let withcolor = normalwithcolor ;
+enddef ;
+
+def resetcolormap =
+ color color_map[][][] ;
+ normalcolors ;
+enddef ;
+
+resetcolormap ;
+
+% color_map_resolution := 1000 ;
+%
+% def r_color primary c = round(color_map_resolution*redpart c) enddef ;
+% def g_color primary c = round(color_map_resolution*greenpart c) enddef ;
+% def b_color primary c = round(color_map_resolution*bluepart c) enddef ;
+
+def r_color primary c = redpart c enddef ;
+def g_color primary c = greenpart c enddef ;
+def b_color primary c = bluepart c enddef ;
+
+def remapcolor(expr old, new) =
+ color_map[r_color old][g_color old][b_color old] := new ;
+enddef ;
+
+def remappedcolor(expr c) =
+ if known color_map[r_color c][g_color c][b_color c] :
+ color_map[r_color c][g_color c][b_color c]
+ else :
+ c
+ fi
+enddef ;
+
+% def refill suffix c = do_repath (1) (c) enddef ;
+% def redraw suffix c = do_repath (2) (c) enddef ;
+% def recolor suffix c = do_repath (0) (c) enddef ;
+%
+% color refillbackground ; refillbackground := (1,1,1) ;
+%
+% def do_repath (expr mode) (suffix c) text t = % can it be stroked and filled at the same time ?
+% begingroup ;
+% if mode=0 : save withcolor ; remapcolors ; fi ;
+% save _c_, _cc_, _f_, _b_ ; picture _c_, _cc_ ; color _f_ ; path _b_ ;
+% _c_ := c ; _b_ := boundingbox c ; c := nullpicture ;
+% for i within _c_ :
+% _f_ := (redpart i, greenpart i, bluepart i) ;
+% if bounded i :
+% setbounds c to pathpart i ;
+% elseif clipped i :
+% clip c to pathpart i ;
+% elseif stroked i :
+% addto c doublepath pathpart i
+% dashed dashpart i withpen penpart i
+% withcolor _f_ % (redpart i, greenpart i, bluepart i)
+% if mode=2 : t fi ;
+% elseif filled i :
+% addto c contour pathpart i
+% withcolor _f_
+% if (mode=1) and (_f_<>refillbackground) : t fi ;
+% else :
+% addto c also i ;
+% fi ;
+% endfor ;
+% setbounds c to _b_ ;
+% endgroup ;
+% enddef ;
+
+% Thanks to Jens-Uwe Morawski for pointing out that we need
+% to treat bounded and clipped components as local pictures.
+
+def recolor suffix p = p := repathed (0,p) enddef ;
+def refill suffix p = p := repathed (1,p) enddef ;
+def redraw suffix p = p := repathed (2,p) enddef ;
+def retext suffix p = p := repathed (3,p) enddef ;
+def untext suffix p = p := repathed (4,p) enddef ;
+
+primarydef p recolored t = repathed(0,p) t enddef ;
+primarydef p refilled t = repathed(1,p) t enddef ;
+primarydef p redrawn t = repathed(2,p) t enddef ;
+primarydef p retexted t = repathed(3,p) t enddef ;
+primarydef p untexted t = repathed(4,p) t enddef ;
+
+color refillbackground ; refillbackground := (1,1,1) ;
+
+vardef repathed (expr mode, p) text t =
+ begingroup ;
+ if mode=0 : save withcolor ; remapcolors ; fi ;
+ save _p_, _pp_, _f_, _b_, _t_ ;
+ picture _p_, _pp_ ; color _f_ ; path _b_ ; transform _t_ ;
+ _b_ := boundingbox p ; _p_ := nullpicture ;
+ for i within p :
+ _f_ := (redpart i, greenpart i, bluepart i) ;
+ if bounded i :
+ _pp_ := repathed(mode,i) t ;
+ setbounds _pp_ to pathpart i ;
+ addto _p_ also _pp_ ;
+ elseif clipped i :
+ _pp_ := repathed(mode,i) t ;
+ clip _pp_ to pathpart i ;
+ addto _p_ also _pp_ ;
+ elseif stroked i :
+ addto _p_ doublepath pathpart i
+ dashed dashpart i withpen penpart i
+ withcolor _f_ % (redpart i, greenpart i, bluepart i)
+ if mode=2 : t fi ;
+ elseif filled i :
+ addto _p_ contour pathpart i
+ withcolor _f_
+ if (mode=1) and (_f_<>refillbackground) : t fi ;
+ elseif textual i : % textpart i <> "" :
+ if mode <> 4 :
+ % transform _t_ ;
+ % (xpart _t_, xxpart _t_, xypart _t_) = (xpart i, xxpart i, xypart i) ;
+ % (ypart _t_, yypart _t_, yxpart _t_) = (ypart i, yypart i, yxpart i) ;
+ % addto _p_ also
+ % textpart i infont fontpart i % todo : other font
+ % transformed _t_
+ % withpen penpart i
+ % withcolor _f_
+ % if mode=3 : t fi ;
+ addto _p_ also i if mode=3 : t fi ;
+ fi ;
+ else :
+ addto _p_ also i ;
+ fi ;
+ endfor ;
+ setbounds _p_ to _b_ ;
+ _p_
+ endgroup
+enddef ;
+
+
+
+
+% After a question of Denis on how to erase a z variable, Jacko
+% suggested to assign whatever to x and y. So a clearz
+% variable can be defined as:
+%
+% vardef clearz@# =
+% x@# := whatever ;
+% y@# := whatever ;
+% enddef ;
+%
+% but Jacko suggested a redefinition of clearxy:
+%
+% def clearxy text s =
+% clearxy_index_:=0;
+% for $:=s:
+% clearxy_index_:=clearxy_index_+1; endfor;
+% if clearxy_index_=0:
+% save x,y;
+% else:
+% forsuffixes $:=s: x$:=whatever; y$:=whatever; endfor;
+% fi
+% enddef;
+%
+% which i decided to simplify to:
+
+def clearxy text s =
+ if false for $ := s : or true endfor :
+ forsuffixes $ := s : x$ := whatever ; y$ := whatever ; endfor ;
+ else :
+ save x, y ;
+ fi
+enddef ;
+
+% so now we can say: clearxy ; as well as clearxy 1, 2, 3 ;
+
+% show x0 ; z0 = (10,10) ;
+% show x0 ; x0 := whatever ; y0 := whatever ;
+% show x0 ; z0 = (20,20) ;
+% show x0 ; clearxy 0 ;
+% show x0 ; z0 = (30,30) ;
+
+primarydef p smoothed d =
+ (p llmoved (-xpart paired(d),0) -- p lrmoved (-xpart paired(d),0) {right} ..
+ p lrmoved (0,-ypart paired(d)) -- p urmoved (0,-ypart paired(d)) {up} ..
+ p urmoved (-xpart paired(d),0) -- p ulmoved (-xpart paired(d),0) {left} ..
+ p ulmoved (0,-ypart paired(d)) -- p llmoved (0,-ypart paired(d)) {down} .. cycle)
+enddef ;
+
+primarydef p cornered c =
+ ((point 0 of p) shifted (c*(unitvector(point 1 of p - point 0 of p))) --
+ for i=1 upto length(p) :
+ (point i-1 of p) shifted (c*(unitvector(point i of p - point i-1 of p))) --
+ (point i of p) shifted (c*(unitvector(point i-1 of p - point i of p))) ..
+ controls point i of p ..
+ endfor cycle)
+enddef ;
+
+% cmyk color support
+
+vardef cmyk(expr c,m,y,k) =
+ (1-c-k,1-m-k,1-y-k)
+enddef ;
+
+% handy
+
+vardef bbwidth (expr p) =
+ (if known p :
+ if path p or picture p :
+ xpart (lrcorner p - llcorner p)
+ else : 0 fi else : 0
+ fi )
+enddef ;
+
+vardef bbheight (expr p) =
+ (if known p : if path p or picture p :
+ ypart (urcorner p - lrcorner p)
+ else : 0 fi else : 0
+ fi)
+enddef ;
+
+color nocolor ; numeric noline ; % both unknown signals
+
+def dowithpath (expr p, lw, lc, bc) =
+ if known p :
+ if known bc :
+ fill p withcolor bc ;
+ fi ;
+ if known lw and known lc :
+ draw p withpen pencircle scaled lw withcolor lc ;
+ elseif known lw :
+ draw p withpen pencircle scaled lw ;
+ elseif known lc :
+ draw p withcolor lc ;
+ fi ;
+ fi ;
+enddef ;
+
+% result from metafont discussion list (denisr/boguslawj)
+
+def ]] = ] ] enddef ; def ]]] = ] ] ] enddef ;
+def [[ = [ [ enddef ; def [[[ = [ [ [ enddef ;
+
+% not prefect, but useful since it removes redundant points.
+
+vardef dostraightened(expr sign, p) =
+ if length(p)>2 : % was 1, but straight lines are ok
+ save pp ; path pp ;
+ pp := point 0 of p ;
+ for i=1 upto length(p)-1 :
+ if round(point i of p) <> round(point length(pp) of pp) :
+ pp := pp -- point i of p ;
+ fi ;
+ endfor ;
+ save n, ok ; numeric n ; boolean ok ;
+ n := length(pp) ; ok := false ;
+if n>2 :
+ for i=0 upto n : % evt hier ook round
+
+ if unitvector(round(point i of pp -
+ point if i=0 : n else : i-1 fi of pp)) <>
+ sign * unitvector(round(point if i=n : 0 else : i+1 fi of pp -
+ point i of pp)) :
+ if ok : -- else : ok := true ; fi point i of pp
+ fi
+
+ endfor
+ if ok and (cycle p) : -- cycle fi
+else :
+ pp
+fi
+ else :
+ p
+ fi
+enddef ;
+
+% simplified : remove same points as well as redundant points
+% unspiked : remove same points as well as areas with zero distance
+
+% vardef simplified expr p = dostraightened(+1,p) enddef ;
+% vardef unspiked expr p = dostraightened(-1,p) enddef ;
+
+vardef simplified expr p =
+ (reverse dostraightened(+1,dostraightened(+1,reverse p)))
+enddef ;
+
+vardef unspiked expr p =
+ (reverse dostraightened(-1,dostraightened(-1,reverse p)))
+enddef ;
+
+% path p ;
+% p := (2cm,1cm) -- (2cm,1cm) -- (2cm,1cm) -- (3cm,1cm) --
+% (4cm,1cm) -- (4cm,2cm) -- (4cm,2.5cm) -- (4cm,3cm) --
+% (3cm,3cm) -- (2cm,3cm) -- (1cm,3cm) -- (-1cm,3cm) --
+% .5[(-1cm,3cm),(1cm,1cm)] -- (1cm,1cm) -- cycle ;
+%
+% p := unitcircle scaled 4cm ;
+%
+% drawpath p ; drawpoints p ; drawpointlabels p ;
+% p := p shifted (4cm,0) ; p := straightened p ;
+% drawpath p ; drawpoints p ; drawpointlabels p ;
+% p := p shifted (4cm,0) ; p := straightened p ;
+% drawpath p ; drawpoints p ; drawpointlabels p ;
+
+% new
+
+path originpath ; originpath := origin -- cycle ;
+
+vardef unitvector primary z =
+ if abs z = abs origin : z else : z/abs z fi
+enddef;
+
+% also new
+
+vardef anchored@#(expr p, z) =
+ p shifted (z + (labxf@#*lrcorner p + labyf@#*ulcorner p
+ + (1-labxf@#-labyf@#)*llcorner p))
+enddef ;
+
+% epsed(1.2345)
+
+vardef epsed (expr e) =
+ e if e>0 : + eps elseif e<0 : - eps fi
+enddef ;
+
+% handy
+
+def withgray primary g =
+ withcolor (g,g,g)
+enddef ;
+
+% for metafun
+
+if unknown darkred : color darkred ; darkred := .625(1,0,0) fi ;
+if unknown darkyellow : color darkyellow ; darkyellow := .625(1,1,0) fi ;
+if unknown darkgray : color darkgray ; darkgray := .625(1,1,1) fi ;
+if unknown lightgray : color lightgray ; lightgray := .875(1,1,1) fi ;
+
+% an improved plain mp macro
+
+vardef center primary p =
+ if pair p : p else : .5[llcorner p, urcorner p] fi
+enddef;
+
+% new, yet undocumented
+
+vardef rangepath (expr p, d, a) =
+ (if length p>0 :
+ (d*unitvector(direction 0 of p) rotated a)
+ shifted point 0 of p
+ -- p --
+ (d*unitvector(direction length(p) of p) rotated a)
+ shifted point length(p) of p
+ else :
+ p
+ fi)
+enddef ;
+
+% under construction
+
+vardef straightpath(expr a, b, method) =
+ if (method<1) or (method>6) :
+ (a--b)
+ elseif method = 1 :
+ (a --
+ if xpart a > xpart b :
+ if ypart a > ypart b :
+ (xpart b,ypart a) --
+ elseif ypart a < ypart b :
+ (xpart a,ypart b) --
+ fi
+ elseif xpart a < xpart b :
+ if ypart a > ypart b :
+ (xpart a,ypart b) --
+ elseif ypart a < ypart b :
+ (xpart b,ypart a) --
+ fi
+ fi
+ b)
+ elseif method = 3 :
+ (a --
+ if xpart a > xpart b :
+ (xpart b,ypart a) --
+ elseif xpart a < xpart b :
+ (xpart a,ypart b) --
+ fi
+ b)
+ elseif method = 5 :
+ (a --
+ if ypart a > ypart b :
+ (xpart b,ypart a) --
+ elseif ypart a < ypart b :
+ (xpart a,ypart b) --
+ fi
+ b)
+ else :
+ (reverse straightpath(b,a,method-1))
+ fi
+enddef ;
+
+% handy for myself
+
+def addbackground text t =
+ begingroup ; save p ; picture p ;
+ p := currentpicture ; currentpicture := nullpicture ;
+ fill boundingbox p t ; addto currentpicture also p ;
+ endgroup ;
+enddef ;
+
+% makes a (line) into an infinite one (handy for calculating
+% intersection points
+
+vardef infinite expr p =
+ (-infinity*unitvector(direction 0 of p)
+ shifted point 0 of p
+ -- p --
+ +infinity*unitvector(direction length(p) of p)
+ shifted point length(p) of p)
+enddef ;
+
+% obscure macros: create var from string and replace - and :
+% (needed for process color id's)
+
+string _clean_ascii[] ;
+
+_clean_ascii[ASCII "-"] := "_" ;
+_clean_ascii[ASCII ":"] := "_" ;
+_clean_ascii[ASCII "."] := "_" ;
+
+vardef cleanstring (expr s) =
+ save ss ; string ss, si ; ss = "" ;
+ for i=0 upto length(s) :
+ si := substring(i,i+1) of s ;
+ ss := ss & if known _clean_ascii[ASCII si] : _clean_ascii[ASCII si] else : si fi ;
+ endfor ;
+ ss
+enddef ;
+
+vardef setunstringed (expr s, v) =
+ scantokens(cleanstring(s)) := v ;
+enddef ;
+
+vardef setunstringed (expr s, v) =
+ scantokens(cleanstring(s)) := v ;
+enddef ;
+
+vardef getunstringed (expr s) =
+ scantokens(cleanstring(s))
+enddef ;
+
+vardef unstringed (expr s) =
+ expandafter known scantokens(cleanstring(s))
+enddef ;
+
+% new
+
+vardef colorpart(expr i) =
+ (redpart i, greenpart i,bluepart i)
+enddef ;
+
+
+% done
+
+endinput ;
generated by cgit v1.2.3 (git 2.25.1) at 2024-07-08 00:24:54 +0000