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+% Macros for drawing graphs
+
+% begingraph(width,height) begin a new graph
+% setcoords(xtype,ytype) sets up a new coordinate system (log,-linear..)
+% setrange(lo,hi) set coord ranges (numeric and string args OK)
+% gdraw <file or path> [with...] draw a line in current coord system
+% gfill <file or path> [with...] fill a region using current coord system
+% gdrawarrow .., gdrawdblarrow.. like gdraw, but with 1 or 2 arrowheads
+% Mreadpath(<filename>) read path from file and return it in Mlog form
+% augment<path name>(loc) append given coordinates to a polygonal path
+% glabel<suffix>(pic,loc) place label pic near graph coords or time loc
+% gdotlabel<suffix>(pic,loc) same with dot
+% OUT loc value for labels relative to whole graph
+% gdata(file,s,text) read coords from file; evaluate t w/ tokens s[]
+% auto.<x or y> default x or y tick locations (for interation)
+% itick.<bot|top|..>(fmt,u) draw inward tick from given side at u w/ format
+% otick.<bot|top|..>(fmt,u) draw outward tick at coord u; label format fmt
+% grid.<bot|top|..>(fmt,u) draw grid line at u with given side labelled
+% autogrid([itick|.. bot|..],..) iterate over auto.x, auto.y, drawing tick/grids
+% frame.[bot|top..] draw frame (or one side of the frame)
+% endgraph end of graph--the result is a picture
+
+% option `plot <picture>' draws picture at each path knot, turns off pen
+% Gtemplate.<tickcmd> template paths for tick marks and grid lines
+% Gmargin.low, Gmargin.high fractions determining margins when no setrange
+% Glmarks[], Gumarks, Gemarks loop text strings used by auto.<x or y>
+% Gmarks, Gminlog numeric parameters used by auto.<x or y>
+% Gpaths tells how to interpret paths: log or linear
+% Autoform is the format string used by autogrid
+
+% Other than the above-documented user interface, all externally visible names
+% are of the form X_.<suffix>, Y_.<suffix>, or Z_.<suffix>, or they start
+% with `G' and end with `_'.
+
+
+if unknown Mzero:
+ begingroup interim % marith.mp starts with `warningcheck:=0'
+ input marith
+ endgroup; % restore warningcheck; we zero it when necessary
+fi
+if unknown mant_font:
+ input format
+fi
+
+
+vardef Gerr_(expr x,s) =
+ interim showstopping:=0;
+ show x; errmessage s;
+enddef;
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%% Data structures, begingraph %%%%%%%%%%%%%%%%%%%%%%%%
+
+vardef Z_@# = (X_@#,Y_@#) enddef; % used in place of plain.mp's z convention
+
+def Gsuf_(suffix $) = % convert from x or y to X_ or Y_
+ if str$="x": X_ else: Y_ fi
+enddef;
+
+
+def begingraph(expr w, h) =
+ begingroup
+ save X_, Y_, Gfin_, Gcur_, Gcbb_, Gneedgr_, Gneedfr_, Gdidsc_;
+ save Gdpic_, Gppic_, Ggl_, Garw_;
+ picture Gfin_, Gcur_, Gcbb_, Gdpic_, Gppic_, Ggl_[];
+ boolean Gneedgr_, Gneedfr_, Gdidsc_;
+ Gfin_ = nullpicture; % the finished part of the graph
+ Gcur_ = nullpicture; % what has been drawn in current coords
+ Gcbb_ = nullpicture; % picture whose bbox is Gcur_'s w/ linewidths 0
+ X_.ctyp = Y_.ctyp = linear; % coordinate system for each axis
+ Z_.gdim = (w,h); % dimensions of graph not counting axes etc.
+ X_.sc = Y_.sc = 0; % Mlog(the amount Gcur_ has been descaled by)
+ Gneedgr_ = true; % whether autogrid is needed
+ Gneedfr_ = true; % whether frame needs to be drawn
+ Gdidsc_ = false; % set when Glinsc_ rescales coordinates
+ Gdpic_ = nullpicture; % result of last gdraw or gfill
+ Garw_ = 0; % number of arrowheads for next gdraw
+enddef;
+
+% Additional variables not explained above:
+% Z_.low, Z_.high user-specified coordinate ranges in units used in Gcur_
+% Gppic_ a picture from the `plot' option known when plot allowed
+% Gmll_, Gmhh_ pairs giving bounds used in auto<x or y>
+% Gme_, Gcma_ variables and macros used in auto<x or y>
+% Gc_ temporary macro used in auto<x or y>
+% Gbias_ an offset to Gmll_ and Gmhh_ to ease computing exponents
+% Ggl_[] labels to place around the whole graph when it is done
+% Some additional variables function as constants. Most can be modified by the
+% user to alter the behavior of these macros.
+% Not very modifiable: log, linear, Gboff_, Gfra_, Gfrb_, Gmarg_
+% Modifiable: Gtemplate.suffix, Glmarks[], Gumarks, Gemarks, Gmarks,
+% Gminlog, Gpaths, Autoform
+
+
+newinternal log, linear; % coordinate system codes
+newinternal Gpaths; % path interpretation parameter
+log:=1; linear:=2;
+Gpaths := linear;
+
+
+
+%%%%%%%%%%%%%%%%%%%%%% Coordinates: setcoords, setrange %%%%%%%%%%%%%%%%%%%%%%
+
+% Graph-related usr input is `user graph coordinates' as specified by arguments
+% to setcoords.
+% `Internal graph coordinates' are used for Gcur_, Gcbb_, Z_.low, Z_.high.
+% Their meaning depends on the appropriate component of Z_.ctyp:
+% log means internal graph coords = Mlog(user graph coords)
+% -log means internal graph coords = -Mlog(user graph coords)
+% linear means internal graph coords = Mexp(Mlog(user graph coords) Mdiv ?sc)
+% -linear means internal graph coords = -Mexp(Mlog(user graph coords) Mdiv ?sc)
+% (In the last two lines, `?sc' means X_.sc or Y_.sc as appropriate.)
+
+
+vardef Gsetp_ = % Set default Z_.low, Z_.high
+ forsuffixes $=low,high:
+ (if known X_$: whatever else: X_$ fi, if known Y_$: whatever else: Y_$ fi)
+ = Gmargin$[llcorner Gcbb_,urcorner Gcbb_] + Gmarg_$;
+ endfor
+enddef;
+pair Gmarg_.low, Gmarg_.high;
+Gmarg_.high=-Gmarg_.low=(.00002,.00002);
+
+
+% Set $, $$, $$$ so that shifting by $ then transforming by $$ and then $$$
+% maps the essential bounding box of Gcur_ into (0,0)..Z_.gdim. The
+% `essential bounding box' is either what Z_.low and Z_.high imply or the
+% result of ignoring pen widths in Gcur_.
+vardef Gsetsc_(suffix $,$$,$$$) =
+ save p_;
+ Gsetp_;
+ pair p_, $; $=Gboff_-Z_.low;
+ p_ = (max(X_.high-X_.low,.9), max(Y_.high-Y_.low,.9));
+ transform $$, $$$;
+ forsuffixes #=$$,$$$: xpart#=ypart#=xypart#=yxpart#=0; endfor
+ (Z_.high+Gboff_+$) transformed $$ = p_;
+ p_ transformed $$$ = Z_.gdim;
+enddef;
+Gmargin.low=-.07; % bbox fraction for default range start
+Gmargin.high=1.07; % bbox fraction for default range stop
+pair Gboff_; Gboff_=epsilon*(3,3); % allowance to avoid numerical trouble
+
+
+def Gwithpc_(expr q) =
+ withpen penpart q withcolor (redpart q, greenpart q, bluepart q)
+enddef;
+
+
+% Add picture component q to picture @# and change part p to tp, where p is
+% something from q that needs coordinate transformation. The type of p is pair
+% or path.
+% Pair o is the value of p that makes tp (0,0). This implements the trick
+% whereby using 1 instead of 0 for th the width or height or the setbounds path
+% for a label picture supresses shifting in x or y.
+vardef Gpconv_@#(expr q, o)(text tp) =
+ save p;
+ if stroked q:
+ path p; p=pathpart q;
+ addto @# doublepath tp Gwithpc_(q) dashed dashpart q;
+ elseif filled q:
+ path p; p=pathpart q;
+ addto @# contour tp Gwithpc_(q);
+ else:
+ interim truecorners:=0;
+ pair p; p=llcorner q;
+ if urcorner q<>p: p:=p+Gcmul_(o-p,urcorner q-p); fi
+ addto @# also q shifted ((tp)-llcorner q);
+ fi
+enddef;
+def Gcmul_(expr a,b) = (xpart a*xpart b, ypart a*ypart b) enddef;
+
+
+vardef Gclbnds_@# = numeric @#.low, @#.high; enddef;
+
+
+% Finalize anything drawn in the present coordinate system and set up a new
+% system as requested
+vardef setcoords(expr tx, ty) =
+ interim warningcheck:=0;
+ if length Gcur_>0:
+ save s, S, T;
+ Gsetsc_(s, S, T);
+ for q within Gcur_:
+ Gpconv_.Gfin_(q, -s, p shifted s transformed S transformed T);
+ endfor
+ Gcur_ := Gcbb_ := nullpicture;
+ fi
+ Gclbnds_.X_; Gclbnds_.Y_;
+ X_.ctyp:=tx; Y_.ctyp:=ty;
+enddef;
+
+
+% Use scaling command cc to rescale everything in internal graph coords so that
+% if Mlog(user graph coords) is u then the internal graph coord value becomes
+% 10000/128. Assume u>=$sc+4Mten where $ is X_ or Y_, depending on whether cc
+% is xscaled or yscaled.
+vardef Glinsc_@#(expr u)(text cc) =
+ save v, P;
+ v = mexp(4Mten + (@#sc-u));
+ picture P; P=nullpicture;
+ for q within Gcur_: Gpconv_.P(q, origin, p cc v cc 1/128); endfor
+ Gcur_ := P;
+ Gcbb_ := Gcbb_ cc v cc 1/128;
+ forsuffixes $=low, high:
+ if known @#.$: @#.$:=@#.$*v/128; fi
+ endfor
+ @#sc:= Mabs u -1115.72742; % @#sc:=Mabs u+Mlog(128)-4Mten
+ Gdidsc_ := true;
+enddef;
+
+
+% Convert x coordinate u from Mlog(user graph coords) to ctyp=linear internal
+% graph coords. If the result would be uncomfortably large, use Glinsc_ to
+% descale as needed.
+vardef Gxcvlin_ primary u =
+ interim warningcheck:=0;
+ if unknown u: u
+ elseif u>X_.sc+4Mten:
+ Glinsc_.X_(u,xscaled);
+ 78.125
+ else: Mexp(u Mdiv X_.sc)
+ fi
+enddef;
+
+vardef Gycvlin_ primary u = % same as Gxcvlin_ but u is a y coordinate
+ interim warningcheck:=0;
+ if unknown u: u
+ elseif u>Y_.sc+4Mten:
+ Glinsc_.Y_(u,yscaled);
+ 78.125
+ else: Mexp(u Mdiv Y_.sc)
+ fi
+enddef;
+
+
+% Set Z_.low and Z_.high to correspond to given range of user graph
+% coordinates. The text argument should be a sequence of pairs and/or strings
+% with 4 components in all.
+vardef setrange(text t) =
+ interim warningcheck:=0;
+ save r_; r_=0;
+ string r_[]s;
+ for x_=
+ for p_=t: if pair p_: xpart p_, ypart fi p_, endfor:
+ r_[incr r_] if string x_: s fi = x_;
+ if r_>2:
+ Gsetr_ if r_=3: X_(Gxcvlin_) else: Y_(Gycvlin_) fi(
+ r_[r_-2] if unknown r_[r_-2]: s fi, x_);
+ fi
+ exitif r_=4;
+ endfor
+enddef;
+
+
+% @# is X_ or Y_; $ is Gxcvlin_ or Gycvlin_; l and h are numeric or string
+% It would not be OK to set (@#low,@#high) to a pair expression because $ might
+% try to rescale @#low when evaluating the right-hand side for @#high.
+vardef Gsetr_@#(suffix $)(expr l, h) =
+ Gclbnds_@#;
+ if @#ctyp>0:
+ @#low = if abs @#ctyp<>log: $ fi Mlog_Str l;
+ @#high = if abs @#ctyp<>log: $ fi Mlog_Str h;
+ else:
+ -@#high = if abs @#ctyp<>log: $ fi Mlog_Str l;
+ -@#low = if abs @#ctyp<>log: $ fi Mlog_Str h;
+ fi
+enddef;
+
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%% Converting path coordinates %%%%%%%%%%%%%%%%%%%%%%%%%
+
+% Find the result of scanning path p and using macros tx and ty to adjust the
+% x and y parts of each coordinate pair. Boolean paramter c tells whether to
+% force the result to be polygonal.
+vardef Gscan_(expr p, c)(suffix tx, ty) =
+ if (str tx="") and (str ty=""): p
+ else:
+ save r_; path r_;
+ forever:
+ Gdidsc_ := false;
+ r_ := Gpp_(point 0 of p, tx, ty)
+ if path p:
+ for t=1 upto length p:
+ if c: --
+ else: ..controls Gpp_(postcontrol(t-1) of p, tx, ty)
+ and Gpp_(precontrol t of p, tx, ty) ..
+ fi
+ Gpp_(point t of p, tx, ty)
+ endfor
+ if cycle p: &cycle fi
+ fi;
+ exitunless Gdidsc_;
+ endfor
+ if pair p: point 0 of fi r_
+ fi
+enddef;
+vardef Gpp_(expr p)(suffix tx, ty) = (tx xpart p, ty ypart p) enddef;
+
+
+% Convert path p from Mlog(user graph coords) to internal graph coords.
+% Boolean flag f says whether to force the result to be polygonal.
+vardef GMcvi_(expr f) primary p =
+ Gscan_(p, f,
+ if abs X_.ctyp=linear: Gxcvlin_ fi,
+ if abs Y_.ctyp=linear: Gycvlin_ fi)
+ if X_.ctyp<0: xscaled -1 fi
+ if Y_.ctyp<0: yscaled -1 fi
+enddef;
+
+
+% Convert path p from user graph coords to internal graph coords.
+vardef Gucvi_ primary p =
+ if Gpaths=log:
+ GMcvi_((abs X_.ctyp<>log) or (abs Y_.ctyp<>log)) p
+ else:
+ interim warningcheck:=0;
+ save t, u;
+ t=Mexp(-X_.sc); u=Mexp(-Y_.sc);
+ Gscan_(p, (abs X_.ctyp<>linear) or (abs Y_.ctyp<>linear),
+ if abs X_.ctyp=log: Mlog fi,
+ if abs Y_.ctyp=log: Mlog fi)
+ transformed (identity
+ if abs X_.ctyp=linear: xscaled t fi
+ if abs Y_.ctyp=linear: yscaled u fi
+ if X_.ctyp<0: xscaled -1 fi
+ if Y_.ctyp<0: yscaled -1 fi)
+ fi
+enddef;
+
+
+% Convert label location t_ from user graph coords to internal graph coords.
+% The label location should be a pair, or two numbers/strings. If t_ is empty
+% or a single item of non-pair type, just return t_. Unknown coordinates
+% produce unknown components in the result.
+vardef Gtcvi_(text t_) =
+ save n_; n_=0;
+ interim warningcheck:=0;
+ if 0 for x_=t_: +1 if pair x_: +1 fi endfor <= 1:
+ t_
+ else:
+ n_0 = n_1 = 0;
+ point 0 of GMcvi_(true) (
+ for x_=
+ for y_=t_: if pair y_: xpart y_, ypart fi y_, endfor
+ 0, 0:
+ if known x_: Mlog_Str x_
+ else: hide(n_[n_]:=whatever) Mzero
+ fi
+ exitif incr n_=2;
+ ,endfor) + (n_0,n_1)
+ fi
+enddef;
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Reading data files %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+% Read a line from file f, extract whitespace-separated tokens ignoring any
+% initial "%", and return true if at least one token is found. The tokens
+% are stored in @#1, @#2, .. with "" in the last @#[] entry.
+vardef Grdln_@#(expr f) =
+ save n_, s_; string s_;
+ s_ = readfrom f;
+ string @#[];
+ if s_<>EOF:
+ @#1 := loptok s_;
+ n_ = if @#1="%": 0 else: 1 fi;
+ forever:
+ @#[incr n_] := loptok s_;
+ exitif @#[n_]="";
+ endfor
+ @#1<>""
+ else: false
+ fi
+enddef;
+
+
+% Execute c for each line of data read from file f, and stop at the first
+% line with no data. Commands c can use line number i and tokens $1, $2, ...
+def gdata(expr f)(suffix $)(text c) =
+ for i=1 upto infinity:
+ exitunless Grdln_$(f);
+ c
+ endfor
+enddef;
+
+
+% Read a path from file f and return it in Mlog form. The path is terminated
+% by blank line or EOF.
+vardef Mreadpath(expr f) =
+ interim warningcheck:=0;
+ save s;
+ gdata(f, s, if i>1:--fi
+ if s2="": (Mlog i, Mlog_str s1)
+ else: (Mlog_str s1, Mlog_str s2) fi)
+enddef;
+
+
+% Append coordinates t to polygonal path @#. The coordinates can be numerics,
+% strings, or a single pair.
+vardef augment@#(text t) =
+ interim warningcheck := 0;
+ if not path begingroup @# endgroup:
+ Gerr(begingroup @# endgroup, "Cannot augment--not a path");
+ else:
+ def Gcma_= hide(def Gcma_=,enddef) enddef;
+ if known @#: @#:=@#-- else: @#= fi
+ (for p=t:
+ Gcma_ if string p: Mexp Mlog_str fi p
+ endfor);
+ fi
+enddef;
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Drawing and filling %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+% Unknown pair components are set to 0 because glabel and gdotlabel understand
+% unknown coordinates as `0 in absolute units'.
+vardef Gupbb_(expr p) =
+ if known p: addto Gcbb_ doublepath p;
+ else:
+ save x,y;
+ z = llcorner Gcbb_;
+ if unknown xpart p: xpart p= else: x:= fi 0;
+ if unknown ypart p: ypart p= else: y:= fi 0;
+ addto Gcbb_ doublepath (p+z);
+ fi
+ Gcbb_ := image(fill llcorner Gcbb_..urcorner Gcbb_--cycle);
+enddef;
+
+
+% Initiate a gdraw or gfill command. This must be done before scanning the
+% argument, because that could invoke the `if known Gppic_' test in a following
+% plot option .
+def Gaddto_ = Gdpic_:=Gppic_:=nullpicture; addto Gdpic_ enddef;
+
+
+% Handle the part of a Gdraw command that uses path or data file p.
+def Gdraw_ expr p =
+ if string p: GMcvi_(true) Mreadpath(p)
+ elseif path p or pair p: Gucvi_ p
+ else: Gerr_(p,"gdraw argument should be a data file or a path")
+ origin
+ fi
+ withpen currentpen Gwithlist_ _op_
+enddef;
+
+
+% Handle the part of a Gdraw command that uses path or data file p.
+def Gfill_ expr p =
+ if string p: GMcvi_(true) Mreadpath(p) --cycle
+ elseif cycle p: Gucvi_ p
+ else: Gerr_(p,"gfill argument should be a data file or a cyclic path")
+ origin..cycle
+ fi Gwithlist_ _op_
+enddef;
+
+def gdraw = Gaddto_ doublepath Gdraw_ enddef;
+def gfill = Gaddto_ contour Gfill_ enddef;
+
+
+% This is used in Gdraw_ and Gfill_ to allow postprocessing Gdpic_
+def Gwithlist_ text t_ = t_; Gpostdr_; enddef;
+
+
+% Set Gppic_ so the postprocessing step will plot picture p at each path knot.
+% Also select nullpen to supress stroking.
+def plot expr p =
+ if known Gppic_:
+ withpen nullpen
+ hide (Gppic_:=image(
+ if bounded p: for q within p: Gdrw_ q endfor % Save memory
+ else: Gdrw_ p
+ fi Gsetb_ origin..cycle))
+ fi
+enddef;
+
+% This hides a semicolon that could prematurely end Gwithlist_'s text argument
+def Gdrw_ primary p = addto currentpicture also p; enddef;
+def Gsetb_ = setbounds currentpicture to enddef;
+
+
+def gdrawarrow = Garw_:=1; gdraw enddef;
+def gdrawdblarrow = Garw_:=2; gdraw enddef;
+
+
+% Post-process the filled or stroked picture Gdpic_ as follows: (1) update
+% the bounding box information; (2) transfer it to Gcur_ unless the pen has
+% been set to nullpen to disable stroking; (3) plot Gppic at each knot.
+vardef Gpostdr_ =
+ save p;
+ path p; p=pathpart Gdpic_;
+ Gupbb_(p);
+ if filled Gdpic_ or not Gisnull_(penpart Gdpic_):
+ addto Gcur_ also Gdpic_;
+ fi
+ if length Gppic_>0:
+ for i=0 upto length p if cycle p: -1 fi:
+ addto Gcur_ also Gppic_ shifted point i of p;
+ endfor
+ picture Gppic_;
+ fi
+ if Garw_>0:
+ Garwhd_(p, Gwithpc_(Gdpic_));
+ if Garw_>1: Garwhd_(reverse p, Gwithpc_(Gdpic_)); fi
+ Garw_:=0;
+ fi
+enddef;
+vardef Gisnull_(expr p) = (urcorner p=origin) and (llcorner p=origin) enddef;
+
+
+vardef Garwhd_(expr p)(text w) = % Draw arrowhead for path p, with list w
+ addto Gcur_ also
+ image(filldraw arrowhead(
+ Garhwext_(precontrol infinity of p, point infinity of p)) w;
+ Gsetb_ point infinity of p..cycle);
+enddef;
+
+vardef Garhwext_(expr p, q) =
+ if p<>q: (q - 100pt*unitvector(q-p)) -- fi
+ q
+enddef;
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Drawing labels %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+% Argument c is a drawing command that needs an additonal argument p that gives
+% a location in internal graph coords. Draw in Gcur_ enclosed in a setbounds
+% path. Unknown components of p cause the setbounds path to have width or
+% height 1 instead of 0. Then Gupbb_ sets these components to 0 and Gpconv_
+% supresses subsequent repositioning.
+def Glab_(expr p)(suffix $)(text c) =
+ save sdim_; pair sdim_;
+ sdim_ := (if unknown xpart p: 1+ fi 0, if unknown ypart p: 1+ fi 0);
+ Gupbb_(p);
+ addto Gcur_ also
+ image(c(p); Gsetb_ p--p+sdim_--cycle) _op_
+enddef;
+
+
+% Stash the result drawing command c in the Ggl_ table using with list w and
+% an index based on angle laboff$.
+vardef Gglab_(suffix $)(text c) text w =
+ Ggl_[1.5+angle laboff$ /90] = image(c(origin) w);
+enddef;
+
+
+def Glloc_ primary p =
+ if pair p: Glab_(p)
+ elseif numeric p: Glab_(point p of pathpart Gdpic_)
+ else: Gglab_
+ fi
+enddef;
+
+
+% Place label p at user graph coords t using with list w. (t is a time, a pair
+% or 2 numerics or strings).
+vardef glabel@#(expr p)(text t) text w =
+ Glloc_ Gtcvi_(t) (@#,label@#(p)) w; enddef;
+
+
+% Place label p at user graph coords t using with list w and draw a dot there.
+% (t is a time, a pair, or 2 numerics or strings).
+vardef gdotlabel@#(expr p)(text t) text w =
+ Glloc_ Gtcvi_(t) (@#,dotlabel@#(p)) w; enddef;
+
+
+def OUT = enddef; % location text for outside labels
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%% Grid lines, ticks, etc. %%%%%%%%%%%%%%%%%%%%%%%%%%
+
+% Grid lines and tick marks are transformed versions of the templates below.
+% In the template paths, (0,0) is on the edge of the frame and inward is to
+% the right.
+path Gtemplate.itick, Gtemplate.otick, Gtemplate.grid;
+Gtemplate.itick = origin--(7bp,0);
+Gtemplate.otick = (-7bp,0)--origin;
+Gtemplate.grid = origin--(1,0);
+
+vardef itick@#(expr f,u) text w = Gtlab_(@#,@,false,f,u,w); enddef;
+
+vardef otick@#(expr f,u) text w = Gtlab_(@#,@,false,f,u,w); enddef;
+
+vardef grid@#(expr f,u) text w = Gtlab_(@#,@,true,f,u,w); enddef;
+
+
+% Produce a tick or grid mark for label suffix $, Gtemplate suffix $$,
+% coordinate value u, and with list w. Boolean c tells whether Gtemplate$$
+% needs scaling by X_.gdim or Y_.gdim, and f gives a format string or a label
+% picture.
+def Gtlab_(suffix $,$$)(expr c, f, u)(text w) =
+ Glab_(Gtcvi_(Ggpos_($,u)),,draw Ggpic_$($$,c,f,u,w) shifted)
+enddef;
+
+
+% Generate label positioning arguments appropriate for label suffix $ and
+% coordinate u.
+def Ggpos_(suffix $)(expr u) =
+ if xpart laboff.$=0: u,whatever else: whatever,u fi
+enddef;
+
+
+% Generate a picture of a grid line labeled with coordinate value u, picture
+% or format string f, and with list w. Suffix @# is bot, top, lft, or rt,
+% suffix $ identifies entries in the Gtemplate table, and boolean c tells
+% whether to scale Gtemplate$.
+vardef Ggpic_@#(suffix $)(expr c, f, u)(text w) =
+ if unknown u: Gerr_(u,"Label coordinate should be known"); nullpicture
+ else:
+ save p; path p;
+ interim warningcheck:=0;
+ Gneedgr_:=false;
+ p = Gtemplate$ zscaled -laboff@#
+ if c: Gxyscale fi
+ shifted (((.5 + laboff@# dotprod (.5,.5)) * laboff@#) Gxyscale);
+ image(draw p w;
+ label@#(if string f: format(f,u) else: f fi, point 0 of p))
+ fi
+enddef;
+def Gxyscale = xscaled X_.gdim yscaled Y_.gdim enddef;
+
+
+% Draw the frame or the part corresponding to label suffix @# using with list w.
+vardef frame@# text w =
+ Gneedfr_:=false;
+ picture p_;
+ p_ = image(draw
+ if str@#<>"": subpath round(angle laboff@#*Gfra_+Gfrb_) of fi
+ unitsquare Gxyscale w);
+ Glab_((whatever,whatever),,draw p_ shifted);
+enddef;
+pair Gfra_; Gfra_=(1,1)/90; % unitsquare subpath is linear in label angle
+pair Gfrb_; Gfrb_=(.75,2.25);
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%% Automatic grid selection %%%%%%%%%%%%%%%%%%%%%%%%%%
+
+string Glmarks[]; % marking options per decade for logarithmic scales
+string Gumarks; % mark spacing options per decade for linear scales
+string Gemarks; % exponent spacing options for logarithmic scales
+newinternal Gmarks, Gminlog;
+Gmarks := 4; % minimum number marks generated by auto.x or auto.y
+Gminlog := 3.0; % revert to uniform marks when largest/smallest < this
+
+def Gfor(text t) = for i=t endfor enddef; % to shorten the mark templates below
+Glmarks[1]="1,2,5";
+Glmarks[2]="1,1.5,2,3,4,5,7";
+Glmarks[3]="1Gfor(6upto10:,i/5)Gfor(5upto10:,i/2)Gfor(6upto9:,i)";
+Glmarks[4]="1Gfor(11upto20:,i/10)Gfor(11upto25:,i/5)Gfor(11upto19:,i/2)";
+Glmarks[5]="1Gfor(21upto40:,i/20)Gfor(21upto50:,i/10)Gfor(26upto49:,i/5)";
+Gumarks="10,5,2"; % start with 10 and go down; a final `,1' is appended
+Gemarks="20,10,5,2,1";
+
+
+% Determine the X_ or Y_ bounds on the range to be covered by automatic grid
+% marks. Suffix @# is X_ or Y_. The result is log or linear to specify the
+% type of grid spacing to use. Bounds are returned in variables local to
+% begingraph..endgraph: pairs Gmll_ and Gmhh_ are upper and lower bounds in
+% `modified exponential form'. In modified exponential form, (x,y) means
+% (x/1000)*10^y, where 1000<=abs x<10000.
+vardef Gpick_@# =
+ interim warningcheck:=0;
+ save l, h;
+ Gsetp_;
+ if @#ctyp>0: (l,h) else: -(h,l) fi = (@#low, @#high);
+ if abs @#ctyp=log:
+ Gmll_ := Meform(Mabs l)+Gbias_;
+ Gmhh_ := Meform(Mabs h)+Gbias_;
+ if h-l >=mlog Gminlog: log else: linear fi
+ else:
+ Gmll_ := Meform(@#sc + Mlog l)+Gbias_;
+ Gmhh_ := Meform(@#sc + Mlog h)+Gbias_;
+ linear
+ fi
+enddef;
+pair Gbias_; Gbias_=(0,3);
+pair Gmll_, Gmhh_;
+
+
+% Scan Glmarks[k] and evaluate tokens t for each m where l<=m<=h.
+def Gmsc_(expr k, l, h)(text t) =
+ for m=scantokens Glmarks[k]:
+ exitif m>h;
+ if m>=l: t fi
+ endfor
+enddef;
+
+
+% Scan Gmark[k] and evaluate tokens t for each m and e where m*10^e belongs
+% between l and h (inclusive), where both l and h are in modified exponent form.
+def Gmscan_(expr k, l, h)(text t) =
+ for e=ypart l upto ypart h:
+ Gmsc_(k, if e>ypart l: 1 else: xpart l/1000 fi,
+ if e<ypart h: 10 else: xpart h/1000 fi, t)
+ endfor
+enddef;
+
+
+% Select a k for which Gmscan_(k,...) gives enough marks.
+vardef Gkpick_ =
+ save k;
+ k = 0;
+ forever:
+ exitif unknown Glmarks[k+1];
+ exitif 0 Gmscan_(incr k, Gmll_, Gmhh_, +1) >= Gmarks;
+ endfor
+ k
+enddef;
+
+
+% Try to select an exponent spacing from Gemarks. If successful, set @# and
+% return true
+vardef Gempick_@# =
+ numeric @#;
+ for e=scantokens Gemarks:
+ @# = e;
+ exitif floor(ypart Gmhh_/e)-floor(Gey_(Gmll_)/e) >= Gmarks;
+ numeric @#;
+ endfor
+ known @#
+enddef;
+
+vardef Gey_(expr p) = ypart p if xpart p=1000: -1 fi enddef;
+
+
+% Compute the mark spacing d between xpart Gmll_ and xpart Gmhh_.
+vardef Gipick_ =
+ interim warningcheck:=0;
+ save m, n, d;
+ m = Gmarks;
+ n = 1 for i=1 upto mlog(xpart Gmhh_-xpart Gmll_)/Mten - mlog m/(Mten-epsilon):
+ *10 endfor;
+ if n<=1000:
+ for x=scantokens Gumarks:
+ d = n*x;
+ exitif 0 Gigen_(d,+1)>=m;
+ numeric d;
+ endfor
+ fi
+ if known d: d else: n fi
+enddef;
+
+
+def Gigen_(expr d)(text t) =
+ for m = d*ceiling(xpart Gmll_/d) step d until xpart Gmhh_:
+ t
+ endfor
+enddef;
+
+
+% Evaluate tokens t for exponents e in multiples of d in the range determined
+% by Gmll_ and Gmhh_.
+def Gemgen_(expr d)(text t) =
+ for e = d*floor(Gey_(Gmll_)/d+1)
+ step d until d*floor(ypart Gmhh_/d): t
+ endfor
+enddef;
+
+
+% Adjust Gmll_ and Gmhh_ so their exponent parts match and they are in true
+% exponent form ((x,y) means x*10^y). Return the new exponent.
+vardef Gesame_ =
+ interim warningcheck := 0;
+ save e;
+ e+3 = if Gmll_=Gbias_: ypart Gmhh_
+ elseif Gmhh_=Gbias_: ypart Gmll_
+ else: max(ypart Gmll_, ypart Gmhh_) fi;
+ forsuffixes $=Gmll_, Gmhh_:
+ $ := (xpart $ for i=ypart $ upto e+2: /(10) endfor, e);
+ endfor
+ e
+enddef;
+
+
+% Assume e is an integer and either m=0 or 1<=abs(m)<10000. Find m*(10^e)
+% and represent the result as a string if its absolute value would be at least
+% 4096 or less than .1. It is OK to return 0 as a string or a numeric.
+vardef Gpack_(expr m, e) =
+ if (e>3)or(e<-4):
+ decimal m & "e" & decimal e
+ elseif e>=0:
+ if abs m<infinity/Ten_to[e]:
+ m*Ten_to[e]
+ else: decimal m & "e" & decimal e
+ fi
+ else:
+ save x; x=m/Ten_to[-e];
+ if abs x>=.1: x else: decimal m & "e" & decimal e fi
+ fi
+enddef;
+
+
+def auto suffix $ =
+ hide(def Gcma_= hide(def Gcma_=,enddef) enddef)
+ if Gpick_.Gsuf_($)=log:
+ if Gempick_.Gme_: Gemgen_(Gme_, Gcma_ Gpack_(1,e))
+ else:
+ Gmscan_(Gkpick_, Gmll_, Gmhh_, Gcma_ Gpack_(m,e))
+ fi
+ else:
+ hide(Gme_:=Gesame_)
+ Gigen_(Gipick_, Gcma_ Gpack_(m,Gme_))
+ fi
+enddef;
+
+
+string Autoform; Autoform = "%g";
+
+vardef autogrid(suffix tx, ty) text w =
+ Gneedgr_:=false;
+ if str tx<>"": for x=auto.x: tx(Autoform,x) w; endfor fi
+ if str ty<>"": for y=auto.y: ty(Autoform,y) w; endfor fi
+enddef;
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% endgraph %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+def endgraph =
+ if Gneedgr_: autogrid(otick.bot, otick.lft); fi
+ if Gneedfr_: frame; fi
+ setcoords(linear,linear);
+ interim truecorners:=1;
+ for b=bbox Gfin_:
+ setbounds Gfin_ to b;
+ for i=0 step .5 until 3.5:
+ if known Ggl_[i]: addto Gfin_ also Ggl_[i] shifted point i of b; fi
+ endfor
+ endfor
+ Gfin_
+ endgroup
+enddef;