path: root/metapost/context/base/mpiv/mp-tool.mpiv

%D \module
%D   [       file=mp-tool.mpiv,
%D        version=1998.02.15,
%D          title=\CONTEXT\ \METAPOST\ graphics,
%D       subtitle=auxiliary macros,
%D         author=Hans Hagen,
%D           date=\currentdate,
%D      copyright={PRAGMA ADE \& \CONTEXT\ Development Team}]
%C
%C This module is part of the \CONTEXT\ macro||package and is
%C therefore copyrighted by \PRAGMA. See mreadme.pdf for
%C details.

if known context_tool : endinput ; fi ;

boolean context_tool ; context_tool := true ;

let @## = @# ;

let noexpand = quote ;

%D New, version number testing:
%D
%D \starttyping
%D fill fullcircle scaled 2cm withcolor if mpversiongt("0.6") : red  else : green fi ;
%D fill fullcircle scaled 1cm withcolor if mpversionlt(0.6)   : blue else : white fi ;
%D \stoptyping

if not known mpversion : string mpversion ; mpversion := "0.641" ; fi ;

% newinternal metapostversion ; metapostversion := scantokens(mpversion) ;

newinternal metapostversion ; metapostversion := 2.0 ;

%D We always want \EPS\ conforming output, so we say:

prologues    := 1 ;
warningcheck := 0 ;
mpprocset    := 1 ;

%D Handy:

def nothing = enddef ;

%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 ;

string space   ; space   := char 32 ;
string percent ; percent := char 37 ;
string crlf    ; crlf    := char 10 & char 13 ;
string dquote  ; dquote  := char 34 ;

let SPACE   = space ;
let CRLF    = crlf ;
let DQUOTE  = dquote ;
let PERCENT = percent ;

vardef ddecimal primary p =
    decimal xpart p & " " & decimal ypart p
enddef ;

%D Plain compatibility:

string plain_compatibility_data ; plain_compatibility_data := "" ;

def startplaincompatibility =
    begingroup ;
    scantokens plain_compatibility_data ;
enddef ;

def stopplaincompatibility =
    endgroup ;
enddef ;

%D More neutral:

let triplet    = rgbcolor ;
let quadruplet = cmykcolor ;

%D Image redefined, for Alan:

vardef image@#(text t) =
    save currentpicture ;
    picture currentpicture ;
    currentpicture := nullpicture ;
    t ;
    currentpicture
    if str @# <> "" :
        shifted (
              mfun_labxf@#               * lrcorner p
         +                 mfun_labyf@#  * ulcorner p
         + (1-mfun_labxf@#-mfun_labyf@#) * llcorner p
        )
    fi
enddef ;

%D Variables

def dispose suffix s =
    if known s :
        begingroup ;
            save ss ;
            if     numeric   s : numeric   ss
            elseif boolean   s : boolean   ss
            elseif pair      s : pair      ss
            elseif path      s : path      ss
            elseif picture   s : picture   ss
            elseif string    s : string    ss
            elseif transform s : transform ss
            elseif color     s : color     ss
            elseif rgbcolor  s : rgbcolor  ss
            elseif cmykcolor s : cmykcolor ss
            elseif pen       s : pen       ss
            else             s : numeric   ss
            fi ;
            s := ss ;
        endgroup ;
    fi ;
enddef ;

%D Colors:

newinternal nocolormodel   ; nocolormodel   := 1 ;
newinternal greycolormodel ; greycolormodel := 3 ;
newinternal graycolormodel ; graycolormodel := 3 ;
newinternal rgbcolormodel  ; rgbcolormodel  := 5 ;
newinternal cmykcolormodel ; cmykcolormodel := 7 ;

let grayscale = graycolor ;
let greyscale = greycolor ;

vardef colorpart expr c =
    if not picture c :
        0
    elseif colormodel c = greycolormodel :
        greypart c
    elseif colormodel c = rgbcolormodel  :
        (redpart c,greenpart c,bluepart c)
    elseif colormodel c = cmykcolormodel :
        (cyanpart c,magentapart c,yellowpart c,blackpart c)
    else :
        0 % black
    fi
enddef ;

vardef colorlike(text c) text v = % colorlike(a) b, c, d ;
    save _p_ ; picture _p_ ;
    forsuffixes i=v :
        _p_ := image(draw origin withcolor c ;) ; % intercept pre and postscripts
        if (colormodel _p_ = cmykcolormodel) :
            cmykcolor i ;
        elseif (colormodel _p_ = rgbcolormodel) :
            rgbcolor i ;
        else :
            greycolor i ;
        fi ;
    endfor ;
enddef ;

%D Also handy (when we flush colors):

vardef dddecimal primary c =
    decimal redpart c & " " & decimal greenpart c & " " & decimal bluepart c
enddef ;

vardef ddddecimal primary c =
    decimal cyanpart c & " " & decimal magentapart c & " " & decimal yellowpart c & " " & decimal blackpart c
enddef ;

vardef colordecimals primary c =
    if cmykcolor c  :
        decimal cyanpart c & ":" & decimal magentapart c & ":" & decimal yellowpart c & ":" & decimal blackpart c
    elseif rgbcolor c :
        decimal redpart c & ":" & decimal greenpart c & ":" & decimal bluepart c
    elseif string c:
        colordecimals resolvedcolor(c)
    else :
        decimal c
    fi
enddef ;

vardef colordecimalslist(text t) =
    save b ; boolean b ; b := false ;
    for s=t :
        if b : & " " & fi
        colordecimals(s)
        hide(b := true ;)
    endfor
enddef ;

% vardef _ctx_color_spec_ primary c =
%     if cmykcolor c  :
%          "c=" & decimal cyanpart    c &
%         ",m=" & decimal magentapart c &
%         ",y=" & decimal yellowpart  c &
%         ",k=" & decimal blackpart   c
%     elseif rgbcolor c :
%          "r=" & decimal redpart   c &
%         ",g=" & decimal greenpart c &
%         ",b=" & decimal bluepart  c
%     else :
%          "s=" & decimal c
%     fi
% enddef ;
%
% vardef _ctx_color_spec_list_(text t) =
%     save b ; boolean b ; b := false ;
%     for s=t :
%         if b : & " " & fi
%         _ctx_color_spec_(s)
%         hide(b := true ;)
%     endfor
% enddef ;

%D We have standardized data file names:

def job_name =
    jobname
enddef ;

%D Because \METAPOST\ has a hard coded limit of 4~datafiles,
%D we need some trickery when we have multiple files. This will
%D be redone (via \LUA).

boolean savingdata     ; savingdata     := false ;
boolean savingdatadone ; savingdatadone := false ;

def savedata expr txt =
    lua.mp.mf_save_data(txt);
enddef ;

def startsavingdata =
    lua.mp.mf_start_saving_data();
enddef ;

def stopsavingdata =
    lua.mp.mf_stop_saving_data() ;
enddef ;

def finishsavingdata =
    lua.mp.mf_finish_saving_data() ;
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 ;
def newpair      text v = forsuffixes i=v : save i ; pair      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 \starttyping
%D push_boundingbox currentpicture;
%D pop_boundingbox currentpicture;
%D \stoptyping
%D
%D The bounding box can be called with:
%D
%D \starttyping
%D boundingbox currentpicture
%D inner_boundingbox currentpicture
%D outer_boundingbox currentpicture
%D \stoptyping
%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 \starttyping
%D set_outer_boundingbox currentpicture;
%D \stoptyping
%D
%D Its counterpart is:
%D
%D \starttyping
%D set_inner_boundingbox p
%D \stoptyping

path    mfun_boundingbox_stack[] ;
numeric mfun_boundingbox_stack_depth ;

mfun_boundingbox_stack_depth := 0 ;

def pushboundingbox text p =
    mfun_boundingbox_stack_depth := mfun_boundingbox_stack_depth + 1 ;
    mfun_boundingbox_stack[mfun_boundingbox_stack_depth] := boundingbox p ;
enddef ;

def popboundingbox text p =
    setbounds p to mfun_boundingbox_stack[mfun_boundingbox_stack_depth] ;
    mfun_boundingbox_stack[mfun_boundingbox_stack_depth] := origin -- cycle ;
    mfun_boundingbox_stack_depth := mfun_boundingbox_stack_depth - 1 ;
enddef ;

let push_boundingbox = pushboundingbox ; % downward compatible
let pop_boundingbox  = popboundingbox  ; % downward compatible

vardef boundingbox primary p =
    if (path p) or (picture p) :
        llcorner p -- lrcorner p -- urcorner p -- ulcorner p
    else :
        origin
    fi -- cycle
enddef;

vardef innerboundingbox primary p =
    top  rt llcorner p --
    top lft lrcorner p --
    bot lft urcorner p --
    bot  rt ulcorner p -- cycle
enddef;

vardef outerboundingbox primary p =
    bot lft llcorner p --
    bot  rt lrcorner p --
    top  rt urcorner p --
    top lft ulcorner p -- cycle
enddef;

def inner_boundingbox = innerboundingbox enddef ;
def outer_boundingbox = outerboundingbox enddef ;

vardef set_inner_boundingbox text q = % obsolete
    setbounds q to innerboundingbox q;
enddef;

vardef set_outer_boundingbox text q = % obsolete
    setbounds q to outerboundingbox q;
enddef;

% secondarydef a boundedto b = % will this cleanup ?
%     hide(picture mfun_a_b ; mfun_a_b := a ; setbounds mfun_a_b to b;)
%     mfun_a_b
% enddef ;

%D Here are some special ones, cooked up in the process of Alan's mp-node
%D module:

vardef boundingradius primary p =
    if picture p :
        max(
            abs((llcorner p) shifted -center p),
            abs((lrcorner p) shifted -center p),
            abs((urcorner p) shifted -center p),
            abs((ulcorner p) shifted -center p)
        )
    elseif pen p :
        boundingradius image(draw makepath p ;)
    elseif path p :
        boundingradius image(draw p ;)
    fi
enddef ;

vardef boundingcircle primary p =
    fullcircle scaled 2boundingradius p shifted center p
enddef ;

vardef boundingpoint@#(expr p) =
    if picture p : % pen?
        (                 mfun_labxf@# *ulcorner p
         +                mfun_labyf@# *lrcorner p
         +(1-mfun_labxf@#-mfun_labyf@#)*urcorner p)
    elseif path p :
        boundingpoint@#(image(draw p ;))
   %elseif pair p :
   %    p
   %else :
   %    origin
    fi
enddef ;

def mirrored primary a =
    a scaled -1
enddef ;

primarydef a mirroredabout b =
    (a shifted -b) scaled -1 shifted b
enddef ;

%D Some missing functions can be implemented rather straightforward (thanks to
%D Taco and others):

% oldpi := 3.14159265358979323846 ; % from <math.h>
pi      := 3.14159265358979323846264338327950288419716939937510 ; % 50 digits
radian  := 180/pi ; % 2pi*radian = 360 ;

% let +++ = ++ ;

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 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 atan   primary x = angle(1,x)       enddef ;

vardef invsin primary x = (asin(x))/radian enddef ;
vardef invcos primary x = (acos(x))/radian enddef ;
vardef invtan primary x = (atan(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 x ; (xx-1/xx)/2 enddef ;
vardef cosh   primary x = save xx ; xx = exp x ; (xx+1/xx)/2 enddef ;
vardef tanh   primary x = save xx ; xx = exp x ; (xx-1/xx)/(xx+1/xx) enddef ;

%D Like mod, but useful for angles, it returns (-.5d,+.5d] and is used
%D in for instance mp-chem.

primarydef a zmod b = (-((b/2 - a) mod b) + b/2) enddef ;

%D Sometimes this is handy:

def undashed =
    dashed nullpicture
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 \starttyping
%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 \stoptyping
%D
%D The a (or angle) alternative supports arbitrary angles and
%D is therefore more versatile.
%D
%D \starttyping
%D stripe_path_a
%D   (withpen pencircle scaled 2 withcolor red)
%D   (draw)
%D   fullcircle xscaled 100 yscaled 40 withcolor blue;
%D \stoptyping
%D
%D We have two alternatives, controlled by arguments or defaults (when arguments
%D are zero).
%D
%D The newer and nicer interface is used as follows (triggered by a question by Mari):
%D
%D \starttyping
%D draw image (draw fullcircle scaled 3cm shifted (0cm,0cm) withcolor green) numberstriped (1,10,3) withcolor red ;
%D draw image (draw fullcircle scaled 3cm shifted (3cm,0cm) withcolor green) numberstriped (2,20,3) withcolor green ;
%D draw image (draw fullcircle scaled 3cm shifted (3cm,3cm) withcolor green) numberstriped (3,10,5) withcolor blue ;
%D draw image (draw fullcircle scaled 3cm shifted (0cm,3cm) withcolor green) numberstriped (4,20,5) withcolor yellow ;
%D
%D draw image (draw fullcircle scaled 3cm shifted (6cm,0cm) withcolor green) anglestriped (1,20,2) withcolor red ;
%D draw image (draw fullcircle scaled 3cm shifted (9cm,0cm) withcolor green) anglestriped (2,40,2) withcolor green ;
%D draw image (draw fullcircle scaled 3cm shifted (9cm,3cm) withcolor green) anglestriped (3,60,2) withcolor blue ;
%D draw image (draw fullcircle scaled 3cm shifted (6cm,3cm) withcolor green) anglestriped (4,80,2) withcolor yellow ;
%D
%D draw image (
%D     draw fullcircle scaled 3cm shifted (0cm,0cm) withcolor green withpen pencircle scaled 2mm ;
%D     draw fullcircle scaled 2cm shifted (0cm,1cm) withcolor blue  withpen pencircle scaled 3mm ;
%D ) shifted (9cm,0cm) numberstriped (1,10,3) withcolor red ;
%D
%D draw image (
%D     draw fullcircle scaled 3cm shifted (0cm,0cm) withcolor green  withpen pencircle scaled 2mm ;
%D     draw fullcircle scaled 2cm shifted (0cm,1cm) withcolor blue   withpen pencircle scaled 3mm ;
%D ) shifted (12cm,0cm) numberstriped (2,10,3) withcolor red ;
%D
%D draw image (
%D     draw fullcircle scaled 3cm shifted (0cm,0cm) withcolor green  withpen pencircle scaled 2mm ;
%D     draw fullcircle scaled 2cm shifted (0cm,1cm) withcolor blue   withpen pencircle scaled 3mm ;
%D ) shifted (9cm,5cm) numberstriped (3,10,3) withcolor red ;
%D
%D draw image (
%D     draw fullcircle scaled 3cm shifted (0cm,0cm) withcolor green  withpen pencircle scaled 2mm ;
%D     draw fullcircle scaled 2cm shifted (0cm,1cm) withcolor blue   withpen pencircle scaled 3mm ;
%D ) shifted (12cm,5cm) numberstriped (4,10,3) withcolor red ;
%D \stoptyping

stripe_n     := 10;
stripe_slot  :=  3;
stripe_gap   :=  5;
stripe_angle := 45;

def mfun_tool_striped_number_action text extra =
    for i = 1/used_n step 1/used_n until 1 :
        draw point (1+i) of bounds -- point (3-i) of bounds withpen pencircle scaled penwidth extra ;
    endfor ;
    for i = 0 step 1/used_n until 1 :
        draw point (3+i) of bounds -- point (1-i) of bounds withpen pencircle scaled penwidth extra ;
    endfor ;
enddef ;

def mfun_tool_striped_set_options(expr option) =
    save isinner, swapped ;
    boolean isinner, swapped ;
    if option = 1 :
        isinner := false ;
        swapped := false ;
    elseif option = 2 :
        isinner := true ;
        swapped := false ;
    elseif option = 3 :
        isinner := false ;
        swapped := true ;
    elseif option = 4 :
        isinner := true ;
        swapped := true ;
    else :
        isinner := false ;
        swapped := false ;
    fi ;
enddef ;

vardef mfun_tool_striped_number(expr option, p, s_n, s_slot) text extra =
    image (
        begingroup ;
        save pattern, shape, bounds, penwidth, used_n, used_slot ;
        picture pattern, shape ; path bounds ; numeric used_s, used_slot ;
        mfun_tool_striped_set_options(option) ;
        used_slot := if s_slot = 0 : stripe_slot else : s_slot fi ;
        used_n := if s_n = 0 : stripe_n else : s_n fi ;
        shape := image(draw p) ;
        bounds := boundingbox shape ;
        penwidth := min(ypart urcorner shape - ypart llcorner shape, xpart urcorner shape - xpart llcorner shape) / (used_slot * used_n) ;
        pattern := image (
            if isinner :
                mfun_tool_striped_number_action extra ;
                for s within shape :
                    if stroked s or filled s :
                        clip currentpicture to pathpart s ;
                    fi
                endfor ;
            else :
                for s within shape :
                    if stroked s or filled s :
                        draw image (
                            mfun_tool_striped_number_action extra ;
                            clip currentpicture to pathpart s ;
                        ) ;
                    fi ;
                endfor ;
            fi ;
        ) ;
        if swapped :
            addto currentpicture also shape ;
            addto currentpicture also pattern ;
        else :
            addto currentpicture also pattern ;
            addto currentpicture also shape ;
        fi ;
        endgroup ;
    )
enddef ;

def mfun_tool_striped_angle_action text extra =
    for i = minimum -.5used_gap step used_gap until maximum :
        draw (minimum,i) -- (maximum,i) extra ;
    endfor ;
    currentpicture := currentpicture rotated used_angle ;
enddef ;

vardef mfun_tool_striped_angle(expr option, p, s_angle, s_gap) text extra =
    image (
        begingroup ;
        save pattern, shape, mask, maximum, minimum, centrum, used_angle, used_gap ;
        picture pattern, shape, mask ; numeric maximum, minimum ; pair centrum ; numeric used_angle, used_gap ;
        mfun_tool_striped_set_options(option) ;
        used_angle := if s_angle = 0 : stripe_angle else : s_angle fi ;
        used_gap := if s_gap = 0 : stripe_gap else : s_gap fi ;
        shape := image(draw p) ;
        centrum := center shape ;
        shape := shape shifted - centrum ;
        mask := shape rotated used_angle ;
        maximum := max (xpart llcorner mask, xpart urcorner mask, ypart llcorner mask, ypart urcorner mask) ;
        minimum := min (xpart llcorner mask, xpart urcorner mask, ypart llcorner mask, ypart urcorner mask) ;
        pattern := image (
            if isinner :
                mfun_tool_striped_angle_action extra ;
                for s within shape :
                    if stroked s or filled s :
                        clip currentpicture to pathpart s ;
                    fi
                endfor ;
            else :
                for s within shape :
                    if stroked s or filled s :
                        draw image (
                            mfun_tool_striped_angle_action extra ;
                            clip currentpicture to pathpart s ;
                        ) ;
                    fi ;
                endfor ;
            fi ;
        ) ;
        if swapped :
            addto currentpicture also shape ;
            addto currentpicture also pattern ;
        else :
            addto currentpicture also pattern ;
            addto currentpicture also shape ;
        fi ;
        currentpicture := currentpicture shifted centrum ;
        endgroup ;
    )
enddef;

newinternal striped_normal_inner  ; striped_normal_inner  := 1 ;
newinternal striped_reverse_inner ; striped_reverse_inner := 2 ;
newinternal striped_normal_outer  ; striped_normal_outer  := 3 ;
newinternal striped_reverse_outer ; striped_reverse_outer := 4 ;

secondarydef p anglestriped s =
    mfun_tool_striped_angle(redpart s,p,greenpart s,bluepart s)
enddef ;

secondarydef p numberstriped s =
    mfun_tool_striped_number(redpart s,p,greenpart s,bluepart s)
enddef ;

% for old times sake:

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 =
    draw image(s_draw s_path s_text) numberstriped(3,0,0) s_spec ;
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 =
    draw image(s_draw s_path s_text) anglestriped(3,0,0) s_spec ;
enddef ;

%D A few normalizing macros:

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 ;

let sized = xysized ;

def xscale_currentpicture(expr w) = % obsolete
    currentpicture := currentpicture xsized w ;
enddef;

def yscale_currentpicture(expr h) = % obsolete
    currentpicture := currentpicture ysized h ;
enddef;

def xyscale_currentpicture(expr w, h) = % obsolete
    currentpicture := currentpicture xysized (w,h) ;
enddef;

def scale_currentpicture(expr w, h) = % obsolete
    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 ; % watch out: it's contrary to what you expect and starts in the origin

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 triangle, uptriangle, downtriangle, lefttriangle, righttriangle ;

triangle      := (1,0) -- (1,0) rotated 120 -- (1,0) rotated -120 -- cycle ;

uptriangle    := triangle rotated  90 ;
downtriangle  := triangle rotated -90 ;
lefttriangle  := triangle rotated 180 ;
righttriangle := triangle ;

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 = % secundarydef does not work out well
    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 Some personal code that might move to another module (todo: save).

def set_grid(expr w, h, nx, ny) =
    boolean grid[][] ; boolean grid_full ;
    numeric grid_w, grid_h, grid_nx, grid_ny, grid_x, grid_y, grid_left ;
    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 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 ;

vardef roundedsquarexy (expr width, height, dx, dy) =
    (dx,0)            -- (width-dx,0)      {right} ..
    (width,dy)        -- (width,height-dy) {up}    ..
    (width-dx,height) -- (dx,height)       {left}  ..
    (0,height-dy)     -- (0,dy)            {down}  .. cycle
enddef ;

%D Some colors.

def resolvedcolor(expr s) =
    .5white
enddef ;

let normalwithcolor = withcolor ;

def withcolor expr c =
     normalwithcolor if string c : resolvedcolor(c) else : c fi
enddef ;

% I don't want a "withcolor black" in case of an empty string ... who knows
% how that can interfere with outer colors. Somehow the next one doesn't
% always work out ok, but why ... must be some parsing issue. Anyway, when
% we cannot do that, we need to fix some chem macros instead as empty strings
% now lead to black while everywhere else in context empty means: leave color
% untouched.

% def withcolor expr c =
%     if not string c :
%         normalwithcolor c
%     elseif c <> "" :
%         normalwithcolor resolvedcolor(c)
%     fi
% enddef ;

% So why does this work better than the above:
%
% def withcolor expr c =
%     if string c :
%         if c <> "" :
%             normalwithcolor resolvedcolor(c)
%         fi
%     else :
%         normalwithcolor c
%     fi
% enddef ;

vardef colortype expr c =
        if cmykcolor c : cmykcolor
    elseif rgbcolor  c : rgbcolor
    elseif numeric   c : grayscale
        fi
enddef ;

vardef whitecolor expr c =
        if cmykcolor c : (0,0,0,0)
    elseif rgbcolor  c : (1,1,1)
    elseif numeric   c : 1
    elseif string    c : whitecolor resolvedcolor(c)
        fi
enddef ;

vardef blackcolor expr c =
        if cmykcolor c : (0,0,0,1)
    elseif rgbcolor  c : (0,0,0)
    elseif numeric   c : 0
    elseif string    c : blackcolor resolvedcolor(c)
        fi
enddef ;

vardef complementary expr c =
        if cmykcolor c : (1,1,1,1) - c
    elseif rgbcolor  c : (1,1,1) - c
    elseif pair      c : (1,1) - c
    elseif numeric   c :  1 - c
    elseif string    c : complementary resolvedcolor(c)
        fi
enddef ;

vardef complemented expr c =
    save m ;
        if cmykcolor c : m := max(cyanpart c, magentapart c, yellowpart c, blackpart c) ;
                         (m,m,m,m) - c
    elseif rgbcolor  c : m := max(redpart c, greenpart c, bluepart c) ;
                         (m,m,m) - c
    elseif pair      c : m := max(xpart c, ypart c) ;
                         (m,m) - c
    elseif numeric   c : m - c
    elseif string    c : complemented resolvedcolor(c)
        fi
enddef ;

%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 ;
    mfun_do_drawfill
enddef ;

def mfun_do_drawfill text t =
    draw _c_ t ;
    fill _c_ t ;
enddef;

def undrawfill expr c =
    drawfill c withcolor background % rather useless
enddef ;

%D Moved from mp-char.mp

vardef paired primary d =
    if pair d : d else : (d,d) fi
enddef ;

vardef tripled primary d =
    if color d : d else : (d,d,d) fi
enddef ;

% maybe secondaries:

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 Handy as stepper:

vardef rotation(expr i, n) =
    if (n == 0) : 0 else : i * 360 / n fi
enddef ;

%D Handy for testing/debugging:

primarydef p crossed d = (
    if pair p :
        p shifted (-d, 0) -- p --
        p shifted ( 0,-d) -- p --
        p shifted (+d, 0) -- p --
        p shifted ( 0,+d) -- p -- cycle
    else :
        center p shifted (-d, 0) -- llcorner p --
        center p shifted ( 0,-d) -- lrcorner p --
        center p shifted (+d, 0) -- urcorner p --
        center p shifted ( 0,+d) -- ulcorner p -- cycle
    fi
) enddef ;

%D Also handy (math ladders):

vardef laddered primary p = % was expr
    point 0 of p
    for i=1 upto length(p) :
        -- (xpart (point i of p), ypart (point (i-1) of p)) -- (point i of p)
    endfor
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 ;

vardef mfun_randomized_path(expr p,s) =
    for i=0 upto length(p)-1 :
         (point       i    of p) .. 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)
    fi
enddef;

vardef mfun_randomized_picture(expr p,s)(text rnd) =
    save currentpicture ;
    picture currentpicture ;
    currentpicture := nullpicture ;
    for i within p :
        addto currentpicture
            if stroked i :
                doublepath pathpart i rnd s
                dashed dashpart i
                withpen penpart i
                withcolor colorpart i
                withprescript prescriptpart i
                withpostscript postscriptpart i
            elseif filled i :
                contour pathpart i rnd s
                withpen penpart i
                withcolor colorpart i
                withprescript prescriptpart i
                withpostscript postscriptpart i
            else :
                also i
            fi
        ;
    endfor ;
    currentpicture
enddef ;

primarydef p randomizedcontrols s = (
    if path p :
        mfun_randomized_path(p,s)
    elseif picture p :
        mfun_randomized_picture(p,s)(randomizedcontrols)
    else :
        p randomized s
    fi
) 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 cmykcolor p :
        if color s :
           ((uniformdeviate cyanpart    s) * cyanpart    p,
            (uniformdeviate magentapart s) * magentapart p,
            (uniformdeviate yellowpart  s) * yellowpart  p,
            (uniformdeviate blackpart   s) * blackpart   p)
        elseif pair s :
            ((xpart s + (uniformdeviate (ypart s - xpart s))) * p)
        else :
            ((uniformdeviate s) * p)
        fi
    elseif rgbcolor 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
    elseif color p :
        if color s :
            ((uniformdeviate greypart s) * greypart p)
        elseif pair s :
            ((xpart s + (uniformdeviate (ypart s - xpart s))) * p)
        else :
            ((uniformdeviate s) * p)
        fi
    elseif string p :
        (resolvedcolor(p)) randomized s
    elseif picture p :
        mfun_randomized_picture(p,s)(randomized)
    else :
      % p - s/2 + uniformdeviate s % would have been better but we want to be positive
        p + uniformdeviate s
    fi
) enddef ;

%D Not perfect (alternative for interpath)

vardef interpolated(expr s, p, q) =
    save m ; numeric 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 paralleled d = (
%     p shifted if d < 0 : - fi ((point abs(d) on (p rotatedaround(point 0 of p,90))) - point 0 of p)
% ) enddef ;
%
% primarydef p paralleled d = (
%     p shifted ((d*unitvector(direction 0 of p) - point 0 of p) rotated 90)
% ) enddef ;
%
% Alan came up with an improved version and stepwise we ended up with (or
% might up with a variant of):

vardef perpendicular expr t of p =
    unitvector((direction t of p) rotated 90)
enddef ;

def istextext(expr p) =
    (picture p and ((substring(0,3) of prescriptpart p) = "tx_"))
enddef ;

primarydef p paralleled d = (
    if path p :
        begingroup ;
        save dp ; pair dp ;
        for i=0 upto length p if cycle p : -1 fi :
            hide(dp := d * perpendicular i of p)
            if i > 0 : .. fi
            (point i of p + dp)
            if i < length p :
                .. controls (postcontrol i    of p + dp) and
                            (precontrol (i+1) of p + dp)
            fi
        endfor
        if cycle p : .. cycle fi
        endgroup
    elseif picture p :
        image(
            for i within p :
                draw (pathpart i)
                if not istextext(i) : % dirty trick
                    paralleled d
                fi
                mfun_decoration_i i ;
            endfor ;
        )
    elseif pair p :
        p
    fi
) 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.

% not yet ok

vardef leftrightpath(expr p, l) = % used in s-pre-19
    save q, r, t, b ; path q, r ; pair t, b ;
    t := (ulcorner p -- urcorner p) intersection_point p ;
    b := (llcorner p -- lrcorner p) intersection_point p ;
    r := if xpart directionpoint t of p < 0 : reverse p else : p fi ; % r is needed, else problems when reverse is fed
    q := r cutbefore if l: t else: b fi ;
    q := q if xpart point 0 of r > 0 : & r 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. (not yet in lexer)

let normaldraw = draw ;
let normalfill = fill ;

% bugged in mplib so ...

def normalfill expr c = addto currentpicture contour c _op_ enddef ;
def normaldraw expr p = addto currentpicture if picture p: also p else: doublepath p withpen currentpen fi _op_ enddef ;

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 ;

numeric drawoptionsfactor ; drawoptionsfactor := pt ;

def resetdrawoptions =
    drawlineoptions   (withpen pencircle scaled 1.0 drawoptionsfactor withcolor .5white) ;
    drawpointoptions  (withpen pencircle scaled 4.0 drawoptionsfactor withcolor   black) ;
    drawcontroloptions(withpen pencircle scaled 2.5 drawoptionsfactor withcolor   black) ;
    drawlabeloptions  () ;
    draworiginoptions (withpen pencircle scaled 1.0 drawoptionsfactor withcolor .5white) ;
    drawboundoptions  (dashed evenly _ori_opt_) ;
    drawpathoptions   (withpen pencircle scaled 5.0 drawoptionsfactor withcolor .8white) ;
enddef ;

resetdrawoptions ;

%D Path.

def drawpath expr p =
    normaldraw p _pth_opt_
enddef ;

%D Arrow.

newinternal ahvariant ; ahvariant := 0 ;
newinternal ahdimple  ; ahdimple  := 1/5 ;
newinternal ahscale   ; ahscale   := 3/4 ;

vardef arrowhead expr p =
     save q, e, r ;
     pair e ; e = point length p of p ;
     path q ; q = gobble(p shifted -e cutafter makepath(pencircle scaled (2ahlength))) cuttings ;
     if ahvariant > 0:
         path r ; r = gobble(p shifted -e cutafter makepath(pencircle scaled ((1-ahdimple)*2ahlength))) cuttings ;
     fi
     (q rotated (ahangle/2) & reverse q rotated -(ahangle/2)
         if ahvariant = 1 :
             -- point 0 of r --
         elseif ahvariant = 2 :
             ... point 0 of r ...
         else :
         --
         fi
         cycle
     ) shifted e
enddef ;

vardef drawarrowpath expr p =
    save autoarrows ; boolean autoarrows ; autoarrows := true ;
    drawarrow p _pth_opt_
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 ;
    set_ahlength(scaled ahfactor) ; % added
    arrowhead p if s < 1 : cutafter (point (s*arclength(p) + (ahlength/2)) on p) fi
enddef ;

def resetarrows =
    hide (
        ahlength  := 4 ;
        ahangle   := 45 ;
        ahvariant := 0 ;
        ahdimple  := 1/5 ;
        ahscale   := 3/4 ;
)
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 ; mfun_draw_points        enddef ;
def drawcontrolpoints expr c = path _c_ ; _c_ := c ; mfun_draw_controlpoints enddef ;
def drawcontrollines  expr c = path _c_ ; _c_ := c ; mfun_draw_controllines  enddef ;
def drawpointlabels   expr c = path _c_ ; _c_ := c ; mfun_draw_pointlabels   enddef ;

def mfun_draw_points text t =
    for _i_=0 upto length(_c_) if cycle _c_ : -1 fi :
        normaldraw point _i_ of _c_ _pnt_opt_ t ;
    endfor ;
enddef;

def mfun_draw_controlpoints 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 mfun_draw_controllines 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 ;
numeric pointlabelscale ; pointlabelscale := 0 ;
string  pointlabelfont  ; pointlabelfont  := "" ;

def mfun_draw_pointlabels text t =
    for _i_=0 upto length(_c_) if cycle _c_ : -1 fi :
        pair _u_ ; _u_ := unitvector(direction _i_ of _c_) rotated if swappointlabels : - fi 90 ;
        pair _p_ ; _p_ := (point _i_ of _c_) ;
        begingroup ;
        if pointlabelscale > 0 :
            save defaultscale ; numeric defaultscale ;
            defaultscale := pointlabelscale ;
        fi ;
        if pointlabelfont <> "" :
            save defaultfont ; string defaultfont ;
            defaultfont := pointlabelfont ;
        fi ;
        _u_ := 10 * drawoptionsfactor * defaultscale * _u_ ;
        normaldraw thelabel ( decimal _i_, _p_ shifted if cycle _c_ and (_i_=0) : - fi _u_ ) _lab_opt_ t ;
        endgroup ;
    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 ; mfun_draw_xticks enddef ;
def drawyticks expr c = path _c_ ; _c_ := c ; mfun_draw_yticks enddef ;
def drawticks  expr c = path _c_ ; _c_ := c ; mfun_draw_ticks  enddef ;

% Adding eps prevents disappearance due to rounding errors.

def mfun_draw_xticks 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 mfun_draw_yticks 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 mfun_draw_ticks 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 ;

def drawpathonly expr p =
    drawpath          p ;
    drawcontrollines  p ;
    drawcontrolpoints p ;
    drawpoints        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 detaileddraw expr c =
    if picture c : normaldraw c else : path _c_ ; _c_ := c ; do_detaileddraw fi
enddef ;

def do_detaileddraw text t =
    drawpath          _c_ t ;
    drawcontrollines  _c_ ;
    drawcontrolpoints _c_ ;
    drawpoints        _c_ ;
  % % for labels we need an third run (as the second will mark the numbers); i could preroll them
  % % but then the hash needs to handle that as well (as now we keep numbering)
  % drawpointlabels   _c_ ;
enddef ;

def visualizepaths =
    let fill = visualizedfill ;
    let draw = visualizeddraw ;
enddef ;

def detailpaths =
    let draw = detaileddraw ;
enddef ;

def naturalizepaths =
    let fill = normalfill ;
    let draw = normaldraw ;
enddef ;

extra_endfig := extra_endfig & " naturalizepaths ; " ;

%D Nice tracer:

def drawboundary primary p =
    draw p dashed evenly withcolor white ;
    draw p dashed oddly  withcolor black ;
    draw (- llcorner p) withpen pencircle scaled 3   withcolor white ;
    draw (- llcorner p) withpen pencircle scaled 1.5 withcolor black ;
enddef ;

%D Also handy:

extra_beginfig := extra_beginfig & " truecorners :=  0 ; "   ; % restores
extra_beginfig := extra_beginfig & " miterlimit  := 10 ; "   ; % restores
extra_beginfig := extra_beginfig & " linejoin := rounded ; " ; % restores
extra_beginfig := extra_beginfig & " linecap  := rounded ; " ; % restores

%D Normally, arrowheads don't scale well. So we provide a hack.

boolean autoarrows ; autoarrows := false ;
numeric ahfactor   ; ahfactor   := 2.5 ;

def set_ahlength (text t) = % called to often
  % ahlength := (ahfactor*pen_size(_op_ t)) ; % _op_ added
  % problem: _op_ can contain color so a no-go, we could apply the transform
  % but i need to figure out the best way (fakepicture and take components).
    ahlength := (ahfactor*pen_size(t)) ;
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.

vardef arrowpath expr p = % patch by Peter Rolf: supports squared pen and shifting (hh: maybe just use center of head as first)
    (p cutafter makepath(pencircle
        scaled (if ahvariant > 0 : (1-ahdimple)* fi 2ahlength*cosd(ahangle/2))
        shifted point length p of p
    ))
enddef;

% New experimental extension: also handling pictures:
%
% drawarrow fullsquare scaled 2cm withcolor green ;
% drawarrow fullcircle scaled 3cm withcolor green ;
% drawarrow image (
%     draw fullsquare scaled 4cm withcolor red ;
%     draw fullcircle scaled 5cm withcolor blue ;
% ) ;
% currentpicture := currentpicture shifted (-bbwidth(currentpicture)-1cm,0) ;
% drawdblarrow fullsquare scaled 2cm withcolor green ;
% drawdblarrow fullcircle scaled 3cm withcolor green ;
% drawdblarrow image (
%     draw fullsquare scaled 4cm withcolor red ;
%     draw fullcircle scaled 5cm withcolor blue ;
% ) ;

vardef stroked_paths(expr p) =
    save n ; numeric n ; n := 0 ;
    for i within p :
        if stroked i :
            n := n + 1 ;
        fi
    endfor ;
    n
enddef ;

def mfun_decoration_i expr i =
    withpen penpart i
    withcolor colorpart i
    withprescript prescriptpart i
    withpostscript postscriptpart i
enddef ;

% We could collapse all in one helper but in context we nowaways don't want
% the added obscurity. Tokens come cheap.

numeric mfun_arrow_snippets ;
numeric mfun_arrow_count ;

def drawarrow expr p =
    begingroup ;
    save mfun_arrow_path ;
    path mfun_arrow_path ;
    if path p :
        mfun_arrow_path := p ;
        expandafter mfun_draw_arrow_path
    elseif picture p :
        save mfun_arrow_picture ;
        picture mfun_arrow_picture ;
        mfun_arrow_picture := p ;
        expandafter mfun_draw_arrow_picture
    else :
        expandafter mfun_draw_arrow_nothing
    fi
enddef ;

def drawdblarrow expr p =
    begingroup ;
    save mfun_arrow_path ;
    path mfun_arrow_path ;
    if path p :
        mfun_arrow_path := p ;
        expandafter mfun_draw_arrow_path_double
    elseif picture p :
        save mfun_arrow_picture ;
        picture mfun_arrow_picture ;
        mfun_arrow_picture := p ;
        expandafter mfun_draw_arrow_picture_double
    else :
        expandafter mfun_draw_arrow_nothing
    fi
enddef ;

def mfun_draw_arrow_nothing text t =
enddef ;

% The path is shortened so that the arrow head extends it to the original
% length. In case of a double arrow the path gets shortened twice.

def mfun_draw_arrow_path text t =
    if autoarrows :
        set_ahlength(t) ;
    fi
    draw arrowpath mfun_arrow_path t ;
    fillup arrowhead mfun_arrow_path t ;
    endgroup ;
enddef ;

def mfun_draw_arrow_path_double text t =
    if autoarrows :
        set_ahlength(t) ;
    fi
    draw arrowpath (reverse arrowpath mfun_arrow_path) t ;
    fillup arrowhead mfun_arrow_path t ;
    fillup arrowhead reverse mfun_arrow_path t ;
    endgroup ;
enddef ;

% The picture variant is not treating each path but only the first and
% last path. This can be somewhat counterintuitive but is needed for Alan's
% macros. So here the last and in case of a double path first paths in a
% picture get the shortening.

def mfun_with_arrow_picture (text t) =
    mfun_arrow_count := 0 ;
    mfun_arrow_snippets := stroked_paths(mfun_arrow_picture) ;
    for i within mfun_arrow_picture :
        if istextext(i) :
            draw i
        else :
            mfun_arrow_count := mfun_arrow_count + 1 ;
            mfun_arrow_path := pathpart i ;
            t
        fi ;
    endfor ;
enddef ;

def mfun_draw_arrow_picture text t =
    if autoarrows :
        set_ahlength(t) ;
    fi
    mfun_with_arrow_picture (
        if mfun_arrow_count = mfun_arrow_snippets :
            draw arrowpath mfun_arrow_path mfun_decoration_i i t ;
            fillup arrowhead mfun_arrow_path mfun_decoration_i i t ;
        else :
            draw mfun_arrow_path mfun_decoration_i i t ;
        fi ;
    )
    endgroup ;
enddef ;

def mfun_draw_arrow_picture_double text t =
    if autoarrows :
        set_ahlength(t) ;
    fi
    mfun_with_arrow_picture (
        draw
        if mfun_arrow_count = 1 :
            arrowpath reverse
        elseif mfun_arrow_count = mfun_arrow_snippets :
            arrowpath
        fi
        mfun_arrow_path mfun_decoration_i i t ;
        if mfun_arrow_count = 1 :
            fillup arrowhead reverse mfun_arrow_path mfun_decoration_i i t ;
        fi
        if mfun_arrow_count = mfun_arrow_snippets :
            fillup arrowhead mfun_arrow_path mfun_decoration_i i t ;
        fi
    )
    endgroup ;
enddef ;

%D Some more arrow magic, by Alan:

def drawdoublearrows expr p =
    begingroup ;
    save mfun_arrow_path ;
    path mfun_arrow_path ;
    save mfun_arrow_path_parallel ;
    path mfun_arrow_path_parallel ;
    if path p :
        mfun_arrow_path := p ;
        expandafter mfun_draw_arrow_paths
    elseif picture p :
        save mfun_arrow_picture ;
        picture mfun_arrow_picture ;
        mfun_arrow_picture := p ;
        expandafter mfun_draw_arrow_pictures
    else :
        expandafter mfun_draw_arrow_nothing
    fi
enddef ;

def mfun_draw_arrow_paths text t =
    if autoarrows :
        set_ahlength(t) ;
    fi
    save d ; d := ahscale*ahlength*sind(ahangle/2) ;
    mfun_arrow_path_parallel := mfun_arrow_path paralleled d ;
    draw   arrowpath mfun_arrow_path_parallel t ;
    fillup arrowhead mfun_arrow_path_parallel t ;
    mfun_arrow_path_parallel := (reverse mfun_arrow_path) paralleled d ;
    draw   arrowpath mfun_arrow_path_parallel t ;
    fillup arrowhead mfun_arrow_path_parallel t ;
    endgroup ;
enddef ;

def mfun_draw_arrow_pictures text t =
    if autoarrows :
        set_ahlength(t) ;
    fi
    save d ; d := ahscale*ahlength*sind(ahangle/2) ;
    mfun_with_arrow_picture(
        if mfun_arrow_count = 1 :
            draw (mfun_arrow_path  paralleled d)          mfun_decoration_i i t ;
            mfun_arrow_path_parallel := (reverse mfun_arrow_path) paralleled d ;
            draw   arrowpath mfun_arrow_path_parallel     mfun_decoration_i i t ;
            fillup arrowhead mfun_arrow_path_parallel     mfun_decoration_i i t ;
        elseif mfun_arrow_count = mfun_arrow_snippets :
            draw ((reverse mfun_arrow_path) paralleled d) mfun_decoration_i i t ;
            mfun_arrow_path_parallel := mfun_arrow_path paralleled d ;
            draw   arrowpath mfun_arrow_path_parallel     mfun_decoration_i i t ;
            fillup arrowhead mfun_arrow_path_parallel     mfun_decoration_i i t ;
        else :
            draw (         mfun_arrow_path  paralleled d) mfun_decoration_i i t ;
            draw ((reverse mfun_arrow_path) paralleled d) mfun_decoration_i i t ;
        fi
    )
    endgroup ;
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 ;
    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 as follows:
%D
%D \starttyping
%D drawdot point .5  along somepath ;
%D drawdot point 3cm on    somepath ;
%D \stoptyping
%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 = % no outer ( ) .. somehow fails
    (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 (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 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 \starttyping
%D drawarrow anglebetween(line_a,line_b,somelabel) ;
%D \stoptyping

newinternal angleoffset ; angleoffset :=  0pt ;
newinternal anglelength ; anglelength := 20pt ;
newinternal 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 := (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 mfun_current_picture_stack[] ;
numeric mfun_current_picture_depth   ;

mfun_current_picture_depth := 0 ;

def pushcurrentpicture =
    mfun_current_picture_depth := mfun_current_picture_depth + 1 ;
    mfun_current_picture_stack[mfun_current_picture_depth] := currentpicture ;
    currentpicture := nullpicture ;
enddef ;

def popcurrentpicture text t = % optional text
    if mfun_current_picture_depth > 0 :
        addto mfun_current_picture_stack[mfun_current_picture_depth] also currentpicture t ;
        currentpicture := mfun_current_picture_stack[mfun_current_picture_depth] ;
        mfun_current_picture_stack[mfun_current_picture_depth] := nullpicture ;
        mfun_current_picture_depth := mfun_current_picture_depth - 1 ;
    fi ;
enddef ;

%D colorcircle(size, red, green, blue) ;

vardef colorcircle (expr size, red, green, blue) = % might move
    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 = % not complete ... needs text and scripts and ...
    if color p :
        c - p
    else :
        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 ;
        )
  fi
enddef ;

vardef inverted primary p =
    p uncolored white
enddef ;

primarydef p softened c =
    begingroup
    save cc ; color cc ; cc := tripled(c) ;
    if color p :
        (redpart cc * redpart p,greenpart cc * greenpart p, bluepart cc * bluepart p)
    else :
        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 (redpart cc * redpart i, greenpart cc * greenpart i, bluepart cc * bluepart i) ;
            endfor ;
        )
    fi
    endgroup
enddef ;

vardef grayed primary p =
    if rgbcolor p :
        tripled(.30redpart p+.59greenpart p+.11bluepart p)
    elseif cmykcolor p :
        tripled(.30*(1-cyanpart i)+.59*(1-magentapart i)+.11*(1-yellowpart i)+blackpart i)
    elseif greycolor p :
        p
    elseif string p :
        grayed resolvedcolor(p)
    elseif picture 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
                if unknown colorpart i :
                    % nothing
                elseif rgbcolor colorpart i :
                    withcolor tripled(.30redpart i+.59greenpart i+.11bluepart i) ;
                elseif cmykcolor colorpart i :
                    withcolor tripled(.30*(1-cyanpart i)+.59*(1-magentapart i)+.11*(1-yellowpart i)+blackpart i) ;
                else :
                    withcolor colorpart i ;
                fi
            endfor ;
        )
    else :
        p
    fi
enddef ;

let greyed = grayed ;

vardef hsvtorgb(expr h,s,v) =
    save H, S, V, x ;
    H = h mod 360 ;
    S = if s < 0 : 0 elseif s > 1 : 1 else: s fi ;
    V = if v < 0 : 0 elseif v > 1 : 1 else: v fi ;
    x = 1 - abs(H mod 120 - 60)/60 ;
    V * ( (1-S) * (1,1,1) + S *
        if     H <  60 : (1,x,0)
        elseif H < 120 : (x,1,0)
        elseif H < 180 : (0,1,x)
        elseif H < 240 : (0,x,1)
        elseif H < 300 : (x,0,1)
        else           : (1,0,x)
    fi )
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 xyscaled s ;
    (pp shifted ((point 0 of p) - (point 0 of pp)))
    endgroup
enddef ;

primarydef p enlonged len =
    begingroup
    if pair p :
        save q ; path q ; q := origin -- p ;
        save al ; al := arclength(q) ;
        if al > 0 :
            point 1 of (q stretched ((al+len)/al))
        else :
            p
        fi
    else :
        save al ; al := arclength(p) ;
        if al > 0 :
            p stretched ((al+len)/al)
        else :
            p
        fi
    fi
    endgroup
enddef ;

% path p ; p := (0,0) -- (10cm,5cm) ;
% drawarrow p withcolor red ;
% drawarrow p shortened 1cm withcolor green ;

primarydef p shortened d =
    reverse ( ( reverse (p enlonged -d) ) enlonged -d )
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 ;
%
% this sometimes fails on the elseif, so :
%

def readfile (expr name) =
    begingroup ; save ok ; boolean ok ;
    if (readfrom (name) <> EOF) :
        ok := false ;
    elseif (readfrom (name) <> EOF) :
        ok := false ;
    else :
        ok := true ;
    fi ;
    if not ok :
        scantokens("input " & name & " ") ;
    fi ;
    closefrom (name) ;
    endgroup ;
enddef ;

% permits redefinition of end in macro

inner end ;

% this will be redone (when needed) using scripts and backend handling

let mfun_remap_colors_normalwithcolor = normalwithcolor ;

def remapcolors =
    def normalwithcolor primary c =
        mfun_remap_colors_normalwithcolor remappedcolor(c)
    enddef ;
enddef ;

def normalcolors =
    let normalwithcolor = mfun_remap_colors_normalwithcolor ;
enddef ;

def resetcolormap =
    color color_map[][][] ;
    normalcolors ;
enddef ;

resetcolormap ;

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[redpart old][greenpart old][bluepart old] := new ;
enddef ;

def remappedcolor(expr c) =
    if known color_map[redpart c][greenpart c][bluepart c] :
        color_map[redpart c][greenpart c][bluepart c]
    else :
        c
    fi
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) ;

def restroke  suffix p = p := repathed (21,p) enddef ; % keep attributes
def reprocess suffix p = p := repathed (22,p) enddef ; % no attributes

% also 11 and 12

vardef repathed (expr mode, p) text t =
    begingroup ;
    if mode = 0 :
        save normalwithcolor ;
        remapcolors ;
    fi ;
    save _p_, _pp_, _ppp_, _f_, _b_, _t_ ;
    picture _p_, _pp_, _ppp_ ; 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 :
            if mode=21 :
                _ppp_ := i ; % indirectness is needed
                addto _p_ also image(scantokens(t & " pathpart _ppp_")
                    dashed dashpart i withpen penpart i
                    withcolor _f_ ; ) ;
            elseif mode=22 :
                _ppp_ := i ; % indirectness is needed
                addto _p_ also image(scantokens(t & " pathpart _ppp_")) ;
            else :
                addto _p_ doublepath pathpart i
                    dashed dashpart i withpen penpart i
                    withcolor _f_ % (redpart i, greenpart i, bluepart i)
                    if mode = 2 :
                        t
                    fi ;
            fi ;
        elseif filled  i :
            if mode=11 :
                _ppp_ := i ; % indirectness is needed
                addto _p_ also image(scantokens(t & " pathpart _ppp_")
                    withcolor _f_ ; ) ;
            elseif mode=12 :
                _ppp_ := i ; % indirectness is needed
                addto _p_ also image(scantokens(t & " pathpart _ppp_")) ;
            else :
                addto _p_ contour pathpart i
                    withcolor _f_
                    if (mode=1) and (_f_<>refillbackground) :
                        t
                    fi ;
            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) = % elsewhere
%     (1-c-k,1-m-k,1-y-k)
% enddef ;

% handy

% vardef bbwidth (expr p) = % vardef width_of primary p =
%     if known p :
%         if path p or picture p :
%             xpart (lrcorner p - llcorner p)
%         else :
%             0
%         fi
%     else :
%         0
%     fi
% enddef ;

vardef bbwidth primary p =
    if unknown p :
        0
    elseif path p or picture p :
        xpart (lrcorner p - llcorner p)
    else :
        0
    fi
enddef ;

% vardef bbheight (expr p) = % vardef heigth_of primary p =
%     if known p :
%         if path p or picture p :
%             ypart (urcorner p - lrcorner p)
%         else :
%             0
%         fi
%     else :
%         0
%     fi
% enddef ;

vardef bbheight primary p =
    if unknown p :
        0
    elseif path p or picture p :
        ypart (urcorner p - lrcorner p)
    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 ;

let == = = ;

% added

picture oddly ; % evenly already defined

evenly := dashpattern(on  3 off 3) ;
oddly  := dashpattern(off 3 on  3) ;

% not perfect, but useful since it removes redundant points.

vardef mfun_straightened(expr sign, p) =
    save _p_, _q_ ; path _p_, _q_ ;
    _p_ := p ;
    forever :
        _q_ := mfun_do_straightened(sign, _p_) ;
        exitif length(_p_) = length(_q_) ;
        _p_ := _q_ ;
    endfor ;
    _q_
enddef ;

% vardef mfun_straightened(expr sign, p) =
%     save lp, lq, q ; path q ; q := p ;
%     lp := length(p) ;
%     forever :
%         q := mfun_do_straightened(sign,q) ;
%         lq := length(q) ;
%         exitif lp = lq ;
%         lp := lq ;
%     endfor ;
%     q
% enddef ;

% can be optimized:

vardef mfun_do_straightened(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 :
                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 ;

vardef simplified expr p = (
    reverse mfun_straightened(+1,mfun_straightened(+1,reverse p))
) enddef ;

vardef unspiked expr p = (
    reverse mfun_straightened(-1,mfun_straightened(-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 % hm, abs origin is just origin
enddef;

% also new

% vardef anchored@#(expr p, z) = % maybe use the textext variant
%     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
enddef ;

% for metafun

if unknown darkred     : color darkred     ; darkred     := .625(1,0,0) fi ;
if unknown darkgreen   : color darkgreen   ; darkgreen   := .625(0,1,0) fi ;
if unknown darkblue    : color darkblue    ; darkblue    := .625(0,0,1) fi ;
if unknown darkcyan    : color darkcyan    ; darkcyan    := .625(0,1,1) fi ;
if unknown darkmagenta : color darkmagenta ; darkmagenta := .625(1,0,1) 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   := .850(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, b ; picture p ; path b ;
    b := boundingbox currentpicture ;
    p := currentpicture ; currentpicture := nullpicture ;
    fill b t ;
    setbounds currentpicture to b ;
    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) .. will go away

string mfun_clean_ascii[] ;

def register_dirty_chars(expr str) =
    for i = 0 upto length(str)-1 :
        mfun_clean_ascii[ASCII substring(i,i+1) of str] := "_" ;
    endfor ;
enddef ;

register_dirty_chars("+-*/:;., ") ;

vardef cleanstring (expr s) =
    save ss ; string ss, si ; ss = "" ; save i ;
    for i=0 upto length(s) :
        si := substring(i,i+1) of s ;
        ss := ss & if known mfun_clean_ascii[ASCII si] : mfun_clean_ascii[ASCII si] else : si fi ;
    endfor ;
    ss
enddef ;

vardef asciistring (expr s) =
    save ss ; string ss, si ; ss = "" ; save i ;
    for i=0 upto length(s) :
        si := substring(i,i+1) of s ;
        if (ASCII si >= ASCII "0") and (ASCII si <= ASCII "9") :
            ss := ss & char(scantokens(si) + ASCII "A") ;
        else :
            ss := ss & si ;
        fi ;
    endfor ;
    ss
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 ;

% for david arnold:

% showgrid(-5,10,1cm,-10,10,1cm);

def showgrid (expr MinX, MaxX, DeltaX, MinY, MaxY, DeltaY) = % will move
    begingroup
    save size ; numeric size ; size := 2pt ;
    for x=MinX upto MaxX :
        for y=MinY upto MaxY :
            draw (x*DeltaX, y*DeltaY) withpen pencircle scaled
                if (x mod 5 = 0) and (y mod 5 = 0) :
                    1.5size withcolor .50white
                else :
                       size withcolor .75white
                fi ;
        endfor ;
    endfor ;
    for x=MinX upto MaxX:
        label.bot(textext("\infofont " & decimal x), (x*DeltaX,-size)) ;
    endfor ;
    for y=MinY upto MaxY:
        label.lft(textext("\infofont " & decimal y), (-size,y*DeltaY)) ;
    endfor ;
    endgroup
enddef;

% new, handy for:
%
% \startuseMPgraphic{map}{n}
%   \includeMPgraphic{map:germany} ;
%   c_phantom (\MPvar{n}<1) (
%     fill map_germany withcolor \MPcolor{lightgray} ;
%     draw map_germany withpen pencircle scaled 1pt withcolor \MPcolor{darkgray} ;
%   ) ;
%   \includeMPgraphic{map:austria} ;
%   c_phantom (\MPvar{n}<2) (
%     fill map_austria withcolor \MPcolor{lightgray} ;
%     draw map_austria withpen pencircle scaled 1pt withcolor \MPcolor{darkgray} ;
%   ) ;
%   c_phantom (\MPvar{n}<3) (
%   \includeMPgraphic{map:swiss} ;
%     fill map_swiss withcolor \MPcolor{lightgray} ;
%     draw map_swiss withpen pencircle scaled 1pt withcolor \MPcolor{darkgray}  ;
%   ) ;
%   c_phantom (\MPvar{n}<4) (
%   \includeMPgraphic{map:luxembourg} ;
%     fill map_luxembourg withcolor \MPcolor{lightgray} ;
%     draw map_luxembourg withpen pencircle scaled 1pt withcolor \MPcolor{darkgray}  ;
%   ) ;
% \stopuseMPgraphic
%
% \useMPgraphic{map}{n=3}

vardef phantom (text t) = % to be checked
    picture _p_ ;
    _p_ := image(t) ;
    addto _p_ also currentpicture ;
    setbounds currentpicture to boundingbox _p_ ;
enddef ;

vardef c_phantom (expr b) (text t) =
    if b :
        picture _p_ ;
        _p_ := image(t) ;
        addto _p_ also currentpicture ;
        setbounds currentpicture to boundingbox _p_ ;
    else :
        t ;
    fi ;
enddef ;

%D Handy:

def break =
    exitif true ; % fi
enddef ;

%D New too:

primarydef p xstretched w = (
    p if (bbwidth (p)>0) and (w>0) : xscaled (w/bbwidth (p)) fi
) enddef ;

primarydef p ystretched h = (
    p if (bbheight(p)>0) and (h>0) : yscaled (h/bbheight(p)) fi
) enddef ;

%D Newer:

vardef area expr p =
    % we could calculate the boundingbox once
    (xpart llcorner boundingbox p,0) -- p --
    (xpart lrcorner boundingbox p,0) -- cycle
enddef ;

vardef basiccolors[] =
    if @ = 0 :
        white
    else :
        save n ; n := @ mod 7 ;
        if     n = 1 : red
        elseif n = 2 : green
        elseif n = 3 : blue
        elseif n = 4 : cyan
        elseif n = 5 : magenta
        elseif n = 6 : yellow
        else         : black
        fi
    fi
enddef ;


% vardef somecolor = (1,1,0,0) enddef ;

% fill OverlayBox withcolor (rcomponent somecolor,gcomponent somecolor,bcomponent somecolor) ;
% fill OverlayBox withcolor (ccomponent somecolor,mcomponent somecolor,ycomponent somecolor,bcomponent somecolor) ;

% This could be standard mplib 2 behaviour:

% vardef rcomponent expr p = if rgbcolor  p : redpart     elseif cmykcolor p : 1 - cyanpart    fi p enddef ;

vardef rcomponent expr p = if rgbcolor  p : redpart     p elseif cmykcolor p : 1 - cyanpart    p else : p fi enddef ;
vardef gcomponent expr p = if rgbcolor  p : greenpart   p elseif cmykcolor p : 1 - magentapart p else : p fi enddef ;
vardef bcomponent expr p = if rgbcolor  p : bluepart    p elseif cmykcolor p : 1 - yellowpart  p else : p fi enddef ;
vardef ccomponent expr p = if cmykcolor p : cyanpart    p elseif rgbcolor  p : 1 - redpart     p else : p fi enddef ;
vardef mcomponent expr p = if cmykcolor p : magentapart p elseif rgbcolor  p : 1 - greenpart   p else : p fi enddef ;
vardef ycomponent expr p = if cmykcolor p : yellowpart  p elseif rgbcolor  p : 1 - bluepart    p else : p fi enddef ;
vardef kcomponent expr p = if cmykcolor p : blackpart   p elseif rgbcolor  p : 0                 else : p fi enddef ;

% draw image       (...) ... ; % prescripts prepended to first, postscripts appended to last
% draw decorated   (...) ... ; % prescripts prepended to each,  postscripts appended to each
% draw redecorated (...) ... ; % prescripts assigned  to each,  postscripts assigned to each
% draw undecorated (...) ... ; % following properties are ignored, existing properties are kept
%
% draw decorated (
%     draw fullcircle scaled 20cm withpen pencircle scaled 20mm withcolor red   withtransparency (1,.40) ;
%     draw fullcircle scaled 15cm withpen pencircle scaled 15mm withcolor green withtransparency (1,.30) ;
%     draw fullcircle scaled 10cm withpen pencircle scaled 10mm withcolor blue  withtransparency (1,.20) ;
% )
%     withcolor blue
%     withtransparency (1,.125) % selectively applied
%     withpen pencircle scaled 10mm
% ;

% vardef image (text imagedata) = % already defined
%     save currentpicture ;
%     picture currentpicture ;
%     currentpicture := nullpicture ;
%     imagedata ;
%     currentpicture
% enddef ;

vardef undecorated (text imagedata) text decoration =
    save currentpicture ;
    picture currentpicture ;
    currentpicture := nullpicture ;
    imagedata ;
    currentpicture
enddef ;

% if metapostversion < 1.770  :
%
%     vardef decorated (text imagedata) text decoration =
%         save mfun_decorated_path, currentpicture ;
%         picture mfun_decorated_path, currentpicture ;
%         currentpicture := nullpicture ;
%         imagedata ;
%         mfun_decorated_path := currentpicture ;
%         currentpicture := nullpicture ;
%         for i within mfun_decorated_path :
%             addto currentpicture
%                 if stroked i :
%                     doublepath pathpart i
%                     dashed dashpart i
%                     withpen penpart i
%                     withcolor colorpart i
%                     decoration
%                 elseif filled i :
%                     contour pathpart i
%                     withpen penpart i
%                     withcolor colorpart i
%                     decoration
%                 elseif textual i :
%                     also i
%                     withcolor colorpart i
%                     decoration
%                 else :
%                     also i
%                 fi
%             ;
%         endfor ;
%         currentpicture
%     enddef ;
%
% else:

    vardef decorated (text imagedata) text decoration =
        save mfun_decorated_path, currentpicture ;
        picture mfun_decorated_path, currentpicture ;
        currentpicture := nullpicture ;
        imagedata ;
        mfun_decorated_path := currentpicture ;
        currentpicture := nullpicture ;
        for i within mfun_decorated_path :
            addto currentpicture
                if stroked i :
                    doublepath pathpart i
                    dashed dashpart i
                    withpen penpart i
                    withcolor colorpart i
                    withprescript prescriptpart i
                    withpostscript postscriptpart i
                    decoration
                elseif filled i :
                    contour pathpart i
                    withpen penpart i
                    withcolor colorpart i
                    withprescript prescriptpart i
                    withpostscript postscriptpart i
                    decoration
                elseif textual i :
                    also i
                    withcolor colorpart i
                    withprescript prescriptpart i
                    withpostscript postscriptpart i
                    decoration
                else :
                    also i
                fi
            ;
        endfor ;
        currentpicture
    enddef ;

% fi ;

vardef redecorated (text imagedata) text decoration =
    save mfun_decorated_path, currentpicture ;
    picture mfun_decorated_path, currentpicture ;
    currentpicture := nullpicture ;
    imagedata ;
    mfun_decorated_path := currentpicture ;
    currentpicture := nullpicture ;
    for i within mfun_decorated_path :
        addto currentpicture
            if stroked i :
                doublepath pathpart i
                dashed dashpart i
                withpen penpart i
                decoration
            elseif filled i :
                contour pathpart i
                withpen penpart i
                decoration
            elseif textual i :
                also i
                decoration
            else :
                also i
            fi
        ;
    endfor ;
    currentpicture
enddef ;

% path mfun_bleed_box ;

% primarydef p bleeded d =
%     image (
%         mfun_bleed_box := boundingbox p ;
%         if pair d :
%             draw p xysized (bbwidth(p)+2*xpart d,bbheight(p)+2*ypart d) shifted -d ;
%         else :
%             draw p xysized (bbwidth(p)+2d,bbheight(p)+2d) shifted (-d,-d) ;
%         fi ;
%         setbounds currentpicture to mfun_bleed_box ;
%     )
% enddef ;

vardef mfun_snapped(expr p, s) =
    if p < 0 : - ( - else : ( fi p div s) * s % the less tokens the better
enddef ;

vardef mfun_applied(expr p, s)(suffix a) =
    if path p :
        if pair s :
            for i=0 upto length(p)-1 :
                (a(xpart point i of p,xpart s),a(ypart point i of p,ypart s)) --
            endfor
            if cycle p :
                cycle
            else :
                (a(xpart point length(p) of p,xpart s),a(ypart point length(p) of p,ypart s))
            fi
        else :
            for i=0 upto length(p)-1 :
                (a(xpart point i of p,s),a(ypart point i of p,s)) --
            endfor
            if cycle p :
                cycle
            else :
                (a(xpart point length(p) of p,s),a(ypart point length(p) of p,s))
            fi
        fi
    elseif pair p :
        if pair s :
            (a(xpart p,xpart s),a(ypart p,ypart s))
        else :
            (a(xpart p,s),a(ypart p,s))
        fi
    elseif cmykcolor p :
       (a(cyanpart p,s),a(magentapart p,s),a(yellowpart p,s),a(blackpart p,s))
    elseif rgbcolor p :
       (a(redpart p,s),a(greenpart p,s),a(bluepart p,s))
    elseif graycolor p :
        a(p,s)
    elseif numeric p :
        a(p,s)
    else
        p
    fi
enddef ;

primarydef p snapped s =
    mfun_applied(p,s)(mfun_snapped) % so we can play with variants
enddef ;

%D New helpers:

newinternal charscale ; charscale := 1 ; % persistent so one needs to 'reset' it to 0 or 1

def beginglyph(expr unicode, width, height, depth) =
    beginfig(unicode) ; % the number is irrelevant
    charcode := unicode ;
    charwd   := width ;
    charht   := height ;
    chardp   := depth ;
  % charscale := 1 ; % can be set for a whole font, so no reset here
enddef ;

def endglyph =
    setbounds currentpicture to (boundingbox unitsquare xscaled charwd yscaled (charht + chardp) shifted (0,-chardp)) ;
    if known charscale : if (charscale > 0) and (charscale <> 1) :
        currentpicture := currentpicture scaled charscale ;
    fi ; fi ;
    endfig ;
enddef ;

%D Dimensions have never been an issue as traditional MP can't make that large
%D pictures, but with double mode we need a catch:

newinternal maxdimensions ; maxdimensions := 14000 ;

def mfun_apply_max_dimensions = % not a generic helper, we want to protect this one
    if bbwidth currentpicture > maxdimensions :
        currentpicture := currentpicture if bbheight currentpicture  > bbwidth currentpicture : ysized else : xsized fi maxdimensions ;
    elseif bbheight currentpicture  > maxdimensions :
        currentpicture := currentpicture ysized maxdimensions ;
    fi ;
enddef;

extra_endfig := extra_endfig & "mfun_apply_max_dimensions ;" ;

%D Bonus shapes (need along):

path unittriangle, fulltriangle ; % not really units but circle based

unittriangle := point 0   along unitcircle
             -- point 1/3 along unitcircle
             -- point 2/3 along unitcircle
             -- cycle ;
fulltriangle := point 0   along fullcircle
             -- point 1/3 along fullcircle
             -- point 2/3 along fullcircle
             -- cycle ;

%D Kind of special and undocumented. On Wikipedia one can find examples
%D of quick sort routines. Here we have a variant that permits a
%D method.

% vardef listsize(suffix list) =
%     numeric len ; len := 0 ;
%     forever :
%         exitif unknown list[len+1] ;
%         len := len + 1 ;
%     endfor ;
%     len
% enddef ;

vardef listsize(suffix list) =
    numeric len ; len := 1 ;
    forever :
        exitif unknown list[len] ;
        len := len + 1 ;
    endfor ;
    len if unknown list[0] : - 1 fi
enddef ;

vardef listlast(suffix list) =
    numeric len ; len := if known list[0] : 0 else : 1 fi  ;
    forever :
        len := len + 1 ;
        exitif unknown list[len] ;
    endfor ;
    len - 1
enddef ;

vardef mfun_quick_sort(suffix list)(expr _min_, _max_)(text what) =
    save l, r, m ;
    numeric l ; l := _min_ ;
    numeric r ; r := _max_ ;
    numeric m ; m := floor(.5[_min_,_max_]) ;
    _mid_ := what list[m] ;
    forever :
        exitif l >= r ;
        forever :
            exitif l > _max_ ;
          % exitif (what list[l]) >= (what list[m]) ;
            exitif (what list[l]) >= _mid_ ;
            l := l + 1 ;
        endfor ;
        forever :
            exitif r < _min_ ;
          % exitif (what list[m]) >= (what list[r]) ;
            exitif _mid_ >= (what list[r]) ;
            r := r - 1 ;
        endfor ;
        if l <= r :
          temp := list[l] ;
          list[l] := list[r] ;
          list[r] := temp ;
          l := l + 1 ;
          r := r - 1 ;
        fi ;
    endfor ;
    if _min_ < r :
        mfun_quick_sort(list)(_min_,r)(what) ;
    fi ;
    if l < _max_ :
        mfun_quick_sort(list)(l,_max_)(what) ;
    fi ;
enddef ;

vardef sortlist(suffix list)(text what) =
    save _max_ ; numeric _max_ ;
    save _mid_ ; numeric _mid_ ;
    save temp ;
  % _max_ := listsize(list) ;
    _max_ := listlast(list) ;
    if pair list[_max_] :
        pair temp ;
    else :
        numeric temp ;
    fi ;
    if pair what list[_max_] :
        pair _mid_ ;
    else :
        numeric _mid_ ;
    fi ;
    if _max_ > 1 :
      % mfun_quick_sort(list)(1,_max_)(what) ;
        mfun_quick_sort(list)(if known list[0] : 0 else : 1 fi,_max_)(what) ;
    fi ;
enddef ;

vardef uniquelist(suffix list) =
    % this one will be defined later
enddef ;

vardef copylist(suffix list, target) =
    save i ; i := 1 ;
    forever :
        exitif unknown list[i] ;
        target[i] := list[i] ;
        i := i + 1 ;
    endfor ;
enddef ;

vardef listtolines(suffix list) =
    list[1] for i=2 upto listsize(list) : -- list[i] endfor
enddef ;

vardef listtocurves(suffix list) =
    list[1] for i=2 upto listsize(list) : .. list[i] endfor
enddef ;

%D The sorter is used in:

% not yet ok

vardef shapedlist(suffix p) = % takes a list of paths
    save l ; pair l[] ;
    save r ; pair r[] ;
    save i ; i := 1 ;
    save n ; n := 0 ;
    forever :
        exitif unknown p[i] ;
        n := n + 1 ;
        l[n] := ulcorner p[i] ;
        r[n] := urcorner p[i] ;
        n := n + 1 ;
        l[n] := llcorner p[i] ;
        r[n] := lrcorner p[i] ;
        i := i + 1 ;
    endfor ;
    for i = 3 upto n :
        if xpart r[i] < xpart r[i-1] :
            r[i] := (xpart r[i],ypart r[i-1]) ;
        elseif xpart r[i] > xpart r[i-1] :
            r[i-1] := (xpart r[i-1],ypart r[i]) ;
        fi ;
        if xpart l[i] < xpart l[i-1] :
            l[i-1] := (xpart l[i-1],ypart l[i]) ;
        elseif xpart l[i] > xpart l[i-1] :
            l[i] := (xpart l[i],ypart l[i-1]) ;
        fi ;
    endfor ;
    if n > 0 :
        simplified (
            for i = 1 upto   n : r[i] -- endfor
            for i = n downto 1 : l[i] -- endfor
            cycle
        )
    else :
        origin -- cycle
    fi
enddef ;

%D Dumping is fake anyway but let's keep this:

let dump = relax ;

%D Loading modules can be done with:

def loadmodule expr name = % no vardef
    % input can't be used directly in a macro
    if unknown scantokens("context_" & name) :
        save s ; string s ;
      % s := "mp-" & name & ".mpiv" ;
      % message("loading module",s) ;
      % s := "input " & s ;
        s := "input " & "mp-" & name & ".mpiv" ;
        expandafter scantokens expandafter s
    fi ;
enddef ;

def loadfile  (expr filename) =       scantokens("input " & filename)   enddef ;
def loadimage (expr filename) = image(scantokens("input " & filename);) enddef ;

%D Handy for backgrounds:

def drawpathwithpoints expr p =
    do_drawpathwithpoints(p)
enddef ;

def do_drawpathwithpoints(expr p) text t =
    draw p t ;
    if length(p) > 2 :
        begingroup ;
        save _c_ ; path _c_ ;
        save _p_; picture _p_ ;
        _p_ := image (
            _c_ := if cycle p : fullsquare else : fullcircle fi scaled 6pt ;
            for i=0 upto length(p) if cycle p : -1 fi :
                fill _c_ shifted point i of p withcolor white ;
                draw _c_ shifted point i of p withcolor white/2 withpen pencircle scaled .5pt ;
                if (i = 0) and cycle p :
                    _c_ := fullcircle scaled 6pt ;
                fi ;
            endfor ;
            for i=0 upto length(p) if cycle p : -1 fi :
                draw textext("\infofont " & decimal i) ysized 2pt shifted point i of p ;
            endfor ;
        ) ;
        setbounds _p_ to boundingbox p ;
        draw _p_ ;
    fi ;
enddef ;

%D These new helpers are by Alan and are used in for instance the mp-node
%D module.

newinternal crossingdebug     ; crossingdebug     := 0 ;
newinternal crossingscale     ; crossingscale     := 10 ;
newinternal crossingnumbermax ; crossingnumbermax := 1000 ;

% primary, secondary or tertiary? always hard to decide but primary makes sense

vardef infotext@#(expr txt, ysize) =
    textext@#("\infofont " & if numeric txt : decimal fi txt) ysized ysize
enddef ;

primarydef p crossingunder q =
    begingroup
    save pic ; picture pic ; pic := nullpicture ;
    if picture p :
        for i within p :
            if stroked i :
                addto pic also image(draw pathpart i crossingunder q) ;
            fi
        endfor
    elseif path p :
        save n, t, a, b, c, r, bcuttings, hold ;
        numeric n, t[], hold ;
        path a, b, c, r, bcuttings, hold[] ;
        c := makepath(currentpen scaled crossingscale) ;
        r := if picture q : boundingbox fi q ;
        t[0] := n := hold := 0 ;
        a := p ;
        % The cutbefore/cutafter using c below prevents endless loops!
       %forever : % find all intersections
        for i=1 upto crossingnumbermax : % safeguard
            clearxy ; z = a intersectiontimes r ;
            if x < 0 :
                exitif hold < 1 ;
                a := hold[hold] ; hold := hold - 1 ;
                clearxy ; z = a intersectiontimes r ;
            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 r ;
                if x < 0 :
                    a := b ;
                    cuttings := bcuttings ;
                else :
                    if length bcuttings > 0 :
                        clearxy ; z = b intersectiontimes r ;
                        if x >= 0 :
                            hold[incr hold] := b ;
                        fi
                    fi
                fi
            fi
            if length cuttings = 0 : % a single point: nothing cut
                exitif hold < 1 ;
                a := hold[hold] ; hold := hold - 1 ;
            fi
            if i = crossingnumbermax :
                message("crossingunder reached maximum " & decimal i & " intersections.");
            fi
        endfor

        if n = 0 : % No crossings, we return the PATH
            save pic ; path pic ; pic := p ;
        else : % n>0
            sortlist(t,) ;
            % we add too much, maybe a test is needed
            t[incr n] = length p if cycle p : + t[1] fi ;
% save tt[] ; numeric tt[] ; uniquelist(t,tt) ; t := tt ;
            % Now, n>1 !
            % t[0] is the first point of the path and t[n] is the last point
            % (or the first intersection beyond the length if cyclic)
            save m ; m := 0 ;
            for i=if cycle p: 2 else: 1 fi upto n :
                % skip the first segment if cyclic
                % as it gets repeated (fully) at the end.
                if crossingdebug > 0 :
                    if crossingdebug = 1 :
                        addto pic doublepath c shifted point t[i] of p
                        withpen currentpen withtransparency(1,.5) ;
                    elseif crossingdebug = 2 :
                        addto pic also
                        infotext (incr m,crossingscale/5)
                        shifted point t[i] of p ;
                    fi
                fi
                a := subpath (t[i-1],t[i]) of p
                    if i > 1 :
                        cutbefore (c shifted point t[i-1] of p)
                    fi
                    if (i < n) or (cycle p) :
                        cutafter  (c shifted point t[i]   of p)
                    fi ;
                if (not picture q) or (a outsideof q) :
                    addto pic doublepath a withpen currentpen ;
                fi
            endfor
        fi
    fi
    pic
    endgroup
enddef ;

primarydef p insideof q =
    begingroup
        save pth, pic, t ;
        path pth ; picture pic ;
        pic := if path q : image(draw q;) else : q fi ;
        pth := p -- center pic ;
        (t, whatever) = pth intersectiontimes boundingbox pic ;
        t < 0
    endgroup
enddef ;

% primarydef p insideof q =
%     if (path q or picture q) :
%         if (path p or picture p) :
%             (xpart llcorner p > xpart llcorner q) and
%             (xpart urcorner p < xpart urcorner q) and
%             (ypart llcorner p > ypart llcorner q) and
%             (ypart urcorner p < ypart urcorner q)
%         elseif pair p  :
%             (xpart p > xpart llcorner q) and
%             (xpart p < xpart urcorner q) and
%             (ypart p > ypart llcorner q) and
%             (ypart p < ypart urcorner q)
%         fi
%     elseif (numeric p and pair q) :
%         % range check
%         (p >= xpart q) and (p <= ypart q)
%     else : % maybe triplets and such
%         false
%     fi
% enddef ;

primarydef p outsideof q =
    not (p insideof q)
enddef ;

%D Also handy:

vardef circularpath primary n =
    reverse (for i=0 step 2/n until 8-2/n+2eps: point i of fullcircle .. endfor cycle) rotated 90
enddef ;

vardef squarepath primary n =
    for i=0 step 1/n until 4-1/n + 2eps: point i of fullsquare -- endfor cycle
enddef ;

vardef linearpath primary n =
    origin for i=1/n step 1/n until 1-1/n + 2eps: -- point i of (origin--(1,0)) endfor
enddef ;

%D  A nice tracing helper:

color       pensilcolor ; pensilcolor := .5red ;
newinternal pensilstep  ; pensilstep  := 1/25 ;

vardef pensilled(expr p, q) =
    image (
        draw p withcolor pensilcolor withpen q ;
        for i = 0 step pensilstep until length(p) + eps:
            draw point i of p withcolor white withtransparency (1,.5) withpen q ;
        endfor ;
    )
enddef ;

%D Easy to forget but handy for manuals:

vardef tolist(suffix l)(text t) =
    save n ; n := 1 ;
    for p = t :
        if numeric p :
            n := p ;
            dispose(l[n])
        elseif pair p :
            l[n] := p ;
            n := n + 1 ;
        elseif path p :
            for i=0 step 1 until length(p) :
                l[n] := point i of p ;
                n := n + 1 ;
            endfor ;
        else :
            % ignore
        fi ;
    endfor ;
    forever :
        exitif unknown l[n] ;
        dispose(l[n])
        n := n + 1 ;
    endfor ;
enddef ;

vardef topath(suffix p)(text t) =
    save i ; i := if known p[1] : 2 ; p[1] elseif known p[0] : 1 ; p[0] else : 0 ; origin fi
    forever :
        exitif unknown p[i] ;
        t p[i]
        hide(i := i + 1)
    endfor
enddef ;

vardef tocycle(suffix p)(text t) =
    topath(p,t) t cycle
enddef ;

% reimplemented to support paths and pictures

def drawdot expr p =
    if pair p :
        addto currentpicture doublepath p
            withpen currentpen _op_
    elseif path p :
        draw image (
            for i=0 upto length p :
                addto currentpicture doublepath point i of p
                    withpen currentpen _op_ ;
            endfor ;
        )
    elseif picture p :
        draw image (
            save pp ; path pp ;
            for i within p :
                if stroked i or filled i :
                    pp := pathpart i ;
                    for j=0 upto length pp :
                        addto currentpicture doublepath point j of pp
                            withpen currentpen _op_ ;
                    endfor ;
                fi ;
            endfor ;
        )
    fi
enddef ;

% vardef textlength(text t) =
%     save n ; n := 0 ;
%     for i = t :
% 		n := n + 1 ;
% 	endfor;
%     n
% enddef;

vardef mfun_timestamp =
    decimal year                        & "-" &
    decimal month                       & "-" &
    decimal day                         & " " &
    if ((time div 60) < 10)           :   "0" & fi
    decimal (time div 60)               & ":" &
    if ((time-(time div 60)*60) < 10) :   "0" & fi
    decimal (time-(time div 60)*60)
enddef ;

vardef totransform(expr x, y, xx, xy, yx, yy) =
    save t ; transform t ;
    xxpart t = xx ; yypart t = yy ;
    xypart t = xy ; yxpart t = yx ;
    xpart  t = x  ; ypart  t = y  ;
    t
enddef ;

vardef bymatrix(expr rx, sx, sy, ry, tx, ty) =
    save t ; transform t ;
    xxpart t = rx ; yypart t = ry ;
    xypart t = sx ; yxpart t = sy ;
    xpart  t = tx ; ypart  t = ty ;
    t
enddef ;

let xslanted = slanted ;

def yslanted primary s =
    transformed
        begingroup
            save t ; transform t ;
            xxpart t = 1 ; yypart t = 1 ;
            xypart t = 0 ; yxpart t = s ;
            xpart  t = 0 ; ypart  t = 0 ;
            t
        endgroup
enddef ;