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y(plane-w)n(a)n(v)n(e)i (basis)h(and)h(uses)g(ultrasoft)g(pseudop)r(oten)n(tials)f([14])2042 5270 y(to)34 b(ac)n(hiev)n(e)e(con)n(v)n(ergence)f(at)j(tolerable)f (cut-o\013)h(energies)e(\(for)2042 5370 y(details)25 b(see)f(Ref.)i([13])e(and)h(refs.)35 b(therein\).)i(The)25 b(quan)n(tum)g(dy-)1946 5645 y(1)p eop %%Page: 2 2 2 1 bop -150 1815 a @beginspecial 72 @llx 72 @lly 540 @urx 720 @ury 2267 @rwi @setspecial %%BeginDocument: TUW_heliPES.ps % Start of procedure set userdict /Mathdict 100 dict dup begin put % The externally visible functions are: % MathPictureStart- start page. % MathPictureEnd - finish off page. % MathSubStart - start a sub-page. % MathSubEnd - finish off a sub-page. % Mdot - draw a dot. % Mtetra - draw a filled tetragon. % Metetra - draw a filled tetragon with black edges. % Mistroke - intermediate stroke of multi-stroke line/curve. % Mfstroke - final stroke of multi-stroke line/curve. % Msboxa - compute coordinates of text bounding box. % Mshowa - plot characters. % MathScale - compute scaling info to contain array of points. %start of ISOLatin1 stuff /ISOLatin1Encoding dup where { pop pop } { [ /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /space /exclam /quotedbl /numbersign /dollar /percent /ampersand /quoteright /parenleft /parenright /asterisk /plus /comma /minus /period /slash /zero /one /two /three /four /five /six /seven /eight /nine /colon /semicolon /less /equal /greater /question /at /A /B /C /D /E /F /G /H /I /J /K /L /M /N /O /P /Q /R /S /T /U /V /W /X /Y /Z /bracketleft /backslash /bracketright /asciicircum /underscore /quoteleft /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o /p /q /r /s /t /u /v /w /x /y /z /braceleft /bar /braceright /asciitilde /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /dotlessi /grave /acute /circumflex /tilde /macron /breve /dotaccent /dieresis /.notdef /ring /cedilla /.notdef /hungarumlaut /ogonek /caron /space /exclamdown /cent /sterling /currency /yen /brokenbar /section /dieresis /copyright /ordfeminine /guillemotleft /logicalnot /hyphen /registered /macron /degree /plusminus /twosuperior /threesuperior /acute /mu /paragraph /periodcentered /cedilla /onesuperior /ordmasculine /guillemotright /onequarter /onehalf /threequarters /questiondown /Agrave /Aacute /Acircumflex /Atilde /Adieresis /Aring /AE /Ccedilla /Egrave /Eacute /Ecircumflex /Edieresis /Igrave /Iacute /Icircumflex /Idieresis /Eth /Ntilde /Ograve /Oacute /Ocircumflex /Otilde /Odieresis /multiply /Oslash /Ugrave /Uacute /Ucircumflex /Udieresis /Yacute /Thorn /germandbls /agrave /aacute /acircumflex /atilde /adieresis /aring /ae /ccedilla /egrave /eacute /ecircumflex /edieresis /igrave /iacute /icircumflex /idieresis /eth /ntilde /ograve /oacute /ocircumflex /otilde /odieresis /divide /oslash /ugrave /uacute /ucircumflex /udieresis /yacute /thorn /ydieresis ] def } ifelse /MFontDict 50 dict def /MStrCat { exch dup length 2 index length add string dup 3 1 roll copy length exch dup 4 2 roll exch putinterval } bind def /MCreateEncoding { 1 index 255 string cvs (-) MStrCat 1 index MStrCat cvn exch (Encoding) MStrCat cvn dup where { exch get } { pop StandardEncoding } ifelse 3 1 roll dup MFontDict exch known not { 1 index findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding 3 index def currentdict end 1 index exch definefont pop MFontDict 1 index null put } if exch pop exch pop } bind def /ISOLatin1 { (ISOLatin1) MCreateEncoding } bind def %end of ISOLatin1 stuff % Set up for the start of a page. /MathPictureStart { /Msaveobj save def /findresource where { pop /WRI-Mathematica-prolog /ProcSet findresource begin } { Mathdict begin } ifelse userdict begin /MathPictureStartHook where { /MathPictureStartHook get exec } if Mtransform Mlmarg Mbmarg translate Mwidth Mlmarg Mrmarg add sub /Mwidth exch def Mheight Mbmarg Mtmarg add sub /Mheight exch def /Mtmatrix matrix currentmatrix def /Mgmatrix matrix currentmatrix def /MathDPSFlag where { pop clientsync } if } def % Finish off a page. /MathPictureEnd { end end Msaveobj restore /MathDPSFlag where { pop } { showpage } ifelse } def %MFill fills the drawing area with the current color. /MFill { 0 0 moveto Mwidth 0 lineto Mwidth Mheight lineto 0 Mheight lineto fill } def %New device-specific optimizing operators /Mfill /.devicefill where { pop /.devicefill load def } { /fill load def } ifelse /Mstroke /.devicestroke where { pop /.devicestroke load def } { /stroke load def } ifelse % xmin xmax ymin ymax MPlotRegion alters the origin, Mwidth and Mheight % so that the picture fills the altered region /MPlotRegion { 3 index Mwidth mul 2 index Mheight mul translate exch sub Mheight mul /Mheight exch def exch sub Mwidth mul /Mwidth exch def } def % Given a rectangle, set it up as a sub-picture. /MathSubStart { Momatrix Mgmatrix Mtmatrix Mwidth Mheight 7 -2 roll moveto Mtmatrix setmatrix currentpoint Mgmatrix setmatrix 9 -2 roll moveto Mtmatrix setmatrix currentpoint 2 copy translate /Mtmatrix matrix currentmatrix def 3 -1 roll exch sub /Mheight exch def sub /Mwidth exch def } def % Restore the saved state left by the matching MathSubStart. % Note, we also leave with the new Mgmatrix as the current matrix. /MathSubEnd { /Mheight exch def /Mwidth exch def /Mtmatrix exch def dup setmatrix /Mgmatrix exch def /Momatrix exch def } def % Given a point, draw a dot. /Mdot { newpath currentlinewidth 2 div 0 360 arc fill } bind def % Given 4 points, draw the corresponding filled tetragon. /Mtetra { moveto lineto lineto lineto Mfill } bind def % Given 4 points, draw the corresponding filled tetragon with black edges. % Note, this leaves the gray level at 0 (for compatibility with the old % C code. /Metetra { moveto lineto lineto lineto closepath gsave Mfill grestore 0 setgray Mstroke } bind def % Mistroke is called to stroke intermediate parts of a path. It makes % sure to resynchronize the dashing pattern and to leave the current point % as the final point of the path. /Mistroke { flattenpath 0 0 0 { 4 2 roll pop pop } { 4 -1 roll 2 index sub dup mul 4 -1 roll 2 index sub dup mul add sqrt 4 -1 roll add 3 1 roll } { stop } { stop } pathforall pop pop currentpoint Mstroke moveto currentdash 3 -1 roll add setdash } bind def % Mfstroke is called to stroke the final parts of a path. It resets % the dashing pattern to compensate for any adjustments made by Mistroke. /Mfstroke { Mstroke currentdash pop 0 setdash } bind def % Mrotsboxa is the same as Msboxa except that it takes an angle % from the stack and the box is calculated for text rendered at this angle. % It gsaves in case we are starting a MathSubStart % save Mrot so that Msboxa can convert bouding box back to the non-rotated % coordinate system % call Mrotcheck to alter the offsets into the rotated system % converts Mtmatrix to render in the rotated system % the calls Msboxa which does all the work % at the end Mtmatrix is restored and Mrot is reset to 0 /Mrotsboxa { gsave dup /Mrot exch def Mrotcheck Mtmatrix dup setmatrix 7 1 roll 4 index 4 index translate rotate 3 index -1 mul 3 index -1 mul translate /Mtmatrix matrix currentmatrix def grestore Msboxa 3 -1 roll /Mtmatrix exch def /Mrot 0 def } bind def % Given an array of strings ([str...]), which represent consecutive lines % of text, a position in graphics coordinates (gx,gy) and a position in % the bounding box coordinates (sx,sy), compute the low and high coordinates % of the resulting text, in the [gx gy tx ty] form, which corresponds to % the point (gx,gy) (in graphics coordinates) plus the offset (tx,ty) (in % text coordinates). % Note, Msboxa assumes that the current matrix is the text matrix. % Mboxout is called in case we are in Mouter to make the box bigger % Mboxrot adjusts the box to account for a rotation to convert the box % into a nonrotated coordinate system % /Msboxa { newpath 5 -1 roll Mvboxa pop Mboxout 6 -1 roll 5 -1 roll 4 -1 roll Msboxa1 5 -3 roll Msboxa1 Mboxrot [ 7 -2 roll 2 copy [ 3 1 roll 10 -1 roll 9 -1 roll ] 6 1 roll 5 -2 roll ] } bind def % Msboxa1 is an internal function which, given a bounding box coordinate % (sz), and the bounding box limits (blz and bhz), computes the actual % offsets (tlz = (blz-bhz)(sz+1)/2, thz = (blz-bhz)(sz-1)/2). /Msboxa1 { sub 2 div dup 2 index 1 add mul 3 -1 roll -1 add 3 -1 roll mul } bind def % Given a (non-empty) array of strings ([str...]) which represent consecutive % lines of text, compute the total bounding box assuming that we start at % (0,0) and the array of y offsets to place the lines correctly. % Note, Mvboxa assumes that the current matrix is the text matrix. % Note, Mvboxa does not alter the current path. % The vertical spacing is set so that the bounding boxes of adjacent lines % are .3 times the width of an `m' apart. /Mvboxa { gsave newpath [ true 3 -1 roll { Mbbox 5 -1 roll { 0 5 1 roll } { 7 -1 roll exch sub (m) stringwidth pop .3 mul sub 7 1 roll 6 -1 roll 4 -1 roll Mmin 3 -1 roll 5 index add 5 -1 roll 4 -1 roll Mmax 4 -1 roll } ifelse false } forall { stop } if counttomark 1 add 4 roll ] grestore } bind def % Given a string, compute the bounding box assuming that we start at (0,0). % Note, the path is assumed to be empty, and we are assumed to be in text % coordinates. Allows for long strings. /Mbbox { 1 dict begin 0 0 moveto /temp (T) def { gsave currentpoint newpath moveto temp 0 3 -1 roll put temp false charpath flattenpath currentpoint pathbbox grestore moveto lineto moveto} forall pathbbox newpath end } bind def % Compute the minimum of two numbers. /Mmin { 2 copy gt { exch } if pop } bind def % Compute the maximum of two numbers. /Mmax { 2 copy lt { exch } if pop } bind def % % Mrotwork saves Mrot (not really needed but saved anyway) % calls Mrotcheck to adjust the offsets into the rotated coordinate system % converts Mtmatrix to render in the rotated system % /Mrotwork { dup /Mrot exch def Mrotcheck Mtmatrix dup setmatrix 7 1 roll 4 index 4 index translate rotate 3 index -1 mul 3 index -1 mul translate /Mtmatrix matrix currentmatrix def Mgmatrix setmatrix } def % % Mrotshowa is the same as Mshowa except that it takes an angle % from the stack and the text is rendered at this angle. % It call Mrotwork to do all the rotation work. % Then it calls Mshowa which does all the drawing work. % At the end Mtmatrix is restored and Mrot is reset to zero. % /Mrotshowa { Mrotwork Mshowa /Mtmatrix exch def /Mrot 0 def } def % % Draws rotated text with a background. % /Mrotback { 7 1 roll dup 8 1 roll Mrotwork 8 -2 roll Mshowback /Mtmatrix exch def /Mrot 0 def } def % % Given an array of strings ([str...]), which represent consecutive lines % of text, a position in graphics coordinates (gx,gy) and a position in % the bounding box coordinates (sx,sy), display the strings. % Mboxout is called in case we are in Mouter % /Mshowa { 4 -2 roll moveto 2 index Mtmatrix setmatrix Mvboxa 7 1 roll Mboxout 6 -1 roll 5 -1 roll 4 -1 roll Mshowa1 4 1 roll Mshowa1 rmoveto currentpoint Mshowax pop pop pop pop Mgmatrix setmatrix } def % % The background box of text is increased by the % size of an "m" % /Madjust { (m) stringwidth pop mul dup 4 -1 roll add 3 1 roll add } def % % % /Mbuildcoord { 7 index 7 index 4 -1 roll 4 -1 roll index exch index Mabsadd } def % % If the text is rotated then translate to the drawing point. % Rotate then translate back. Do not do this if the angle % of rotation is 0. % /Mrotate { 8 index 0 ne { 13 copy 4 -2 roll pop pop 6 -2 roll pop pop 4 -1 roll 3 -1 roll sub 6 -1 roll mul 3 1 roll sub 4 -1 roll mul 3 -1 roll 5 1 roll Mabsadd 2 copy translate 3 -1 roll rotate exch -1 mul exch -1 mul translate } if 9 -1 roll pop } def % % Draw text but into a box with a certain color. % Uses Msboxa to build the box. % /Mshowback { gsave exec 6 copy pop Msboxa aload pop 0.5 Madjust 5 -1 roll aload pop Mrotate -0.5 Madjust 4 -1 roll pop 3 -1 roll pop 3 4 Mbuildcoord moveto 3 4 Mbuildcoord lineto 3 6 Mbuildcoord lineto 5 6 Mbuildcoord lineto 5 4 Mbuildcoord lineto pop pop pop pop pop pop fill grestore Mshowa } def % This is used for fixedwidth fonts % It simply shows each string and advances the y direction by the offset % /Mshowax { 0 1 4 index length -1 add { 2 index 4 index 2 index get 3 index add moveto 4 index exch get Mfixdash { Mfixdashp } if show } for } def % Fix if all dashes and length > 1 /Mfixdashp { dup length 1 gt 1 index true exch { 45 eq and } forall and { gsave (--) stringwidth pop (-) stringwidth pop sub 2 div 0 rmoveto dup length 1 sub { (-) show } repeat grestore } if } bind def % Mshowa1 is an internal routine which, given a bounding box coordinate % (sz), and the bounding box limits if we started drawing at 0 (tlz and thz), % computes the offset at which to start drawing % (relz = (sz-1)tlz/2 - (sz+1)thz/2 = sz(tlz-thz)/2-(tlz+thz)/2). /Mshowa1 { 2 copy add 4 1 roll sub mul sub -2 div } bind def % Given the x and y scaling to user coordinates and an array of points to % fit (xbias xscale ybias yscale [pnts]), set up the scaling. The array % must contain atleast two points, and the last two must be of the form % [gxlow gylow 0 0] and [gxhigh gyhigh 0 0]. % Note, MathScale assumes that we are already scaled so that the active area % is the rectangle [0,Mwidth-Mlmarg-Mrmarg]x[0,Mheight-Mbmarg-Mtmarg]. % also keep bias and scale info for PostScript commands /MathScale { Mwidth Mheight Mlp /MathScaleHook where { /MathScaleHook get exec } if translate scale pop pop pop pop pop pop pop pop /yscale exch def /ybias exch def /xscale exch def /xbias exch def /Momatrix xscale yscale matrix scale xbias ybias matrix translate matrix concatmatrix def /Mgmatrix matrix currentmatrix def } def % Given a non-empty array of points to fit ([p]) and a maximum width (sx) % and height (sy) find the largest scale (Ax and Ay) and offsets (Bx and By) % such that the transformation % [gx gy tx ty] -> (Ax gx + tx + bx, Ay gy + ty + By) % maps the points into the rectangle [0,sx]x[0,sy] /Mlp { 3 copy Mlpfirst { Mnodistort { Mmin dup } if 4 index 2 index 2 index Mlprun 16 -8 roll 21 8 roll 11 index 11 -1 roll 10 -4 roll Mlp1 8 index 9 -5 roll Mlp1 4 -1 roll and { exit } if 15 -8 roll pop pop pop pop pop pop pop pop 3 -1 roll pop pop } loop exch 3 1 roll 7 -3 roll pop pop pop } def % Given an array of points in the [gx gy tx ty] form, with the last two % being [gxlow gylow 0 0] and [gxhigh gyhigh 0 0], and the width and height % (sx and sy) in which to fit them, compute the maximum scaling (Ax and Ay). /Mlpfirst { 3 -1 roll dup length 2 copy -2 add get aload pop pop pop 4 -2 roll -1 add get aload pop pop pop 6 -1 roll 3 -1 roll 5 -1 roll sub div 4 1 roll exch sub div } bind def % Given a non-empty array of points to fit ([pnts]) and scale factors % for graphics->text (Ax and Ay), compute the limiting points. /Mlprun { 2 copy 4 index 0 get dup 4 1 roll Mlprun1 3 copy 8 -2 roll 9 -1 roll { 3 copy Mlprun1 3 copy 11 -3 roll /gt Mlpminmax 8 3 roll 11 -3 roll /lt Mlpminmax 8 3 roll } forall pop pop pop pop 3 1 roll pop pop aload pop 5 -1 roll aload pop 8 copy exch 6 -1 roll Mlprun2 8 2 roll 4 -1 roll Mlprun2 6 2 roll 3 -1 roll Mlprun2 4 2 roll exch Mlprun2 6 2 roll } bind def % Given scale factors for graphics->text (Ax and Ay) and a point in the % [gx gy tx ty] form, return the text x and y coordinate that results. /Mlprun1 { aload pop exch 6 -1 roll 5 -1 roll mul add 4 -2 roll mul 3 -1 roll add } bind def % Given a low and high coordinate, compute the center and width. /Mlprun2 { 2 copy add 2 div 3 1 roll exch sub } bind def % Given two points stored as [gx gy tx ty] followed by the scaled % result (rx, ry), and a comparison function (lt or gt) leave the % point which is the minimum (or maximum) in each dimension. /Mlpminmax { cvx 2 index 6 index 2 index exec { 7 -3 roll 4 -1 roll } if 1 index 5 index 3 -1 roll exec { 4 1 roll pop 5 -1 roll aload pop pop 4 -1 roll aload pop [ 8 -2 roll pop 5 -2 roll pop 6 -2 roll pop 5 -1 roll ] 4 1 roll pop } { pop pop pop } ifelse } bind def % Given a size (s), graphics->text scale (A), text center (ct), text % width (wt), graphics center (cg) and graphics width (wg), compute % a new graphics->text scale (Anew) and offset (B) and whether or not % we are done. % Note, the mysterious .99999 is magic juju which is supposed to ward % off the possibility that floating point errors would cause this % routine to return the old A and yet claim not-done. /Mlp1 { 5 index 3 index sub 5 index 2 index mul 1 index le 1 index 0 le or dup not { 1 index 3 index div .99999 mul 8 -1 roll pop 7 1 roll } if 8 -1 roll 2 div 7 -2 roll pop sub 5 index 6 -3 roll pop pop mul sub exch } bind def % The following are the workings of the tick, axes and plot labels. % NOTE a possible source of confusion is that for xticks ie tickmarks on % the x axis we keep y information and vice versa for yticks % % When Minner is found then % % assumes that box starts at zero on the left lower side % % 0) if outflag = 1 then intop = 0, inrht = 0 outflag = 0 % 1) Save intop largest top of box % 2) Save inrht largest rht of box % 3) set inflag notifies that inner marks are present % % When Mouter is found then % % if inflag is set then % 1) get vecx and vecy off the stack (points in direcn to move) % 2) vecx < 1 xadrht = inrht*abs(vecx) % 3) vecx > 1 xadlft = inrht*abs(vecx) % 4) vecy < 1 yadtop = intop*abs(vecy) % 5) vecy > 1 yadbot = intop*abs(vecy) % 6) set outflag = 1 % 7) clear inflag, inrht, intop % guaranteed to be zero if no inner is present?? % % % These all have effects in Mrotsboxa and Mrotshowa % check inflag and if set % % 1) increase top of bbox by yadtop % 2) decrease bot of bbox by yadbot % 3) increase rht of bbox by xadrht % 4) increase lft of bbox by xadlft % 5) clear outflag, yadtop, yadbot, % xadrht, xadlft % % % This saves the top right corner of the bounding box as a side effect % This is to allow the adjustment of text placed with Mouter so that % it misses the Minner text. It is assumed that the ang is 0 % in the same way it is assumed that the text of Mouter is 0 or 90 % /Minner { outflag 1 eq { /outflag 0 def /intop 0 def /inrht 0 def } if 5 index gsave Mtmatrix setmatrix Mvboxa pop grestore 3 -1 roll pop dup intop gt { /intop exch def } { pop } ifelse dup inrht gt { /inrht exch def } { pop } ifelse pop /inflag 1 def } def % This takes two number off the stack and uses them as a vector in graphics % coordinates which points in the direction in which the Mouter text is to move % it calculates the bouding box adjustments yadtop yadbot xadrht and xadlft % these are in Mboxout to adjust the bounding box to compensate. /Mouter { /xadrht 0 def /xadlft 0 def /yadtop 0 def /yadbot 0 def inflag 1 eq { dup 0 lt { dup intop mul neg /yadtop exch def } if dup 0 gt { dup intop mul /yadbot exch def } if pop dup 0 lt { dup inrht mul neg /xadrht exch def } if dup 0 gt { dup inrht mul /xadlft exch def } if pop /outflag 1 def } { pop pop} ifelse /inflag 0 def /inrht 0 def /intop 0 def } def % % This adjusts the bounding box to account for adjacent text % This allows the two text strings to avoid each other % current matrix is the text matrix /Mboxout { outflag 1 eq { 4 -1 roll xadlft leadjust add sub 4 1 roll 3 -1 roll yadbot leadjust add sub 3 1 roll exch xadrht leadjust add add exch yadtop leadjust add add /outflag 0 def /xadlft 0 def /yadbot 0 def /xadrht 0 def /yadtop 0 def } if } def /leadjust { (m) stringwidth pop .5 mul } bind def % The offsets sx and sy refer to the graphics coordinate system % thus they must be altered if a rotation has taken place. % We must also change the bounding box computations for Minner % /Mrotcheck { dup 90 eq { % % Mouter only applies to strings which are either at 0 or 90 % sort out the box adjust factors % % xadrht -> yadbot % xadlft -> yadtop % yadtop -> xadrht % yadbot -> xadlft yadbot /yadbot xadrht def /xadrht yadtop def /yadtop xadlft def /xadlft exch def } if dup cos 1 index sin Checkaux dup cos 1 index sin neg exch Checkaux 3 1 roll pop pop } def % % Checkaux is an auxilliary function for Mrotcheck it multiplies a % row vector by a column vector % /Checkaux { 4 index exch 4 index mul 3 1 roll mul add 4 1 roll } bind def % % Mboxrot converts the bounding box back from the rotated coordinate % system to the Mgmatrix system to compensate for a rotation % It has the opposite functionality of Mrotcheck % This is not the most neatest or most efficient implementation but it works % /Mboxrot { Mrot 90 eq { % old tlx thx tly thy % new -thy -tly tlx thx % brotaux 4 2 roll } if Mrot 180 eq { % old tlx thx tly thy % new -thx -tlx -thx -tly % 4 2 roll brotaux 4 2 roll brotaux } if Mrot 270 eq { % old tlx thx tly thy % new tly thy -thx -tlx % 4 2 roll brotaux } if } def % % auxilliary function negate and reverse /brotaux { neg exch neg } bind def % % Mabsproc takes a measurement in the default user units and converts % it to the present units. This allows absolute thickness and dashing % to work. It works by using a {0, x} vector and using the RMS of the result. /Mabsproc { 0 matrix defaultmatrix dtransform idtransform dup mul exch dup mul add sqrt } bind def % % Mabswid allows the linewidth to be specified in absolute coordinates % It does this by recording the graphics transformation matrix at the % begining of the plot. % This will break if the scaling in the x and y directions is % different. This is the case if Mnodistort is false % /Mabswid { Mabsproc setlinewidth } bind def % Mabsdash allows the dashing pattern to be specified in absolute coordinates % It does this by recording the graphics transformation matrix at the % begining of the plot. % This will break if the scaling in the x and y directions is % different. This is the case if Mnodistort is false % /Mabsdash { exch [ exch { Mabsproc } forall ] exch setdash } bind def % % Mabs takes a pair of coordinates in points % and converts them into a pair of coordinates in % the current drawing scheme % /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def % % Mabs takes a pair of numbers in drawing coordinates % and a pair in points. It converts the points to % drawing coordinates and adds them to the first pair. % /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def % % These two procedures are for using Offset coordinates % with MathScale computations % /Mabsfix1 { 3 -1 roll /ar exch def ar 2 get 3 -1 roll add exch ar 3 get add ar 3 3 -1 roll put ar 2 3 -1 roll put ar } bind def /Mabsfix { 2 copy 6 -1 roll 3 1 roll Mabsfix1 4 1 roll Mabsfix1 } bind def %MBeginOrig start coordinates in user coordinates /MBeginOrig { Momatrix concat} bind def %MEndOrig start coordinates in user coordinates /MEndOrig { Mgmatrix setmatrix} bind def /sampledsound where { pop } { /MathDPSFlag where { pop /sampledsound { clientsync } def } { /sampledsound { exch pop exch 5 1 roll mul 4 idiv mul 2 idiv exch pop exch /Mtempproc exch def { Mtempproc pop } repeat } def } ifelse } ifelse % Define setrgbcolor for those ancient PostScript devices lacking it /setrgbcolor dup where { pop pop } { { .114 mul exch .587 mul add exch .299 mul add setgray } bind def } ifelse % % now simple conversion of cmykcolor to rgbcolor % subtract k and then take complements /setcmykcolor where { pop} { /setcmykcolor { 4 1 roll [ 4 1 roll ] { 1 index sub 1 sub neg dup 0 lt { pop 0 } if dup 1 gt { pop 1 } if exch } forall pop setrgbcolor } bind def } ifelse % Here are the short operators /g /setgray load def /k /setcmykcolor load def /m /moveto load def /p /gsave load def /r /setrgbcolor load def /w /setlinewidth load def /C /curveto load def /F /Mfill load def /L /lineto load def /P /grestore load def /s /Mstroke load def /Mcharproc { currentfile (x) readhexstring pop 0 get exch div } bind def /Mshadeproc { dup 3 1 roll { dup Mcharproc 3 1 roll } repeat 1 eq { setgray } { 3 eq { setrgbcolor } { setcmykcolor } ifelse } ifelse } bind def /Mrectproc { 3 index 2 index moveto 2 index 3 -1 roll lineto dup 3 1 roll lineto lineto Mfill } bind def /Mcolorimage { 7 1 roll pop pop matrix invertmatrix concat 2 exch exp 1 sub 3 1 roll 1 1 2 index { 1 1 4 index { dup 1 sub exch 2 index dup 1 sub exch 7 index 9 index Mshadeproc Mrectproc } for pop } for pop pop pop pop } bind def /Mimage { pop matrix invertmatrix concat 2 exch exp 1 sub 3 1 roll 1 1 2 index { 1 1 4 index { dup 1 sub exch 2 index dup 1 sub exch 7 index Mcharproc setgray Mrectproc } for pop } for pop pop pop } bind def % Default values for variables /Mlmarg 1.0 72 mul def /Mrmarg 1.0 72 mul def /Mbmarg 1.0 72 mul def /Mtmarg 1.0 72 mul def /Mwidth 8.5 72 mul def /Mheight 11 72 mul def /Mtransform { } bind def /Mnodistort true def /Mfixdash false def /Mrot 0 def /intop 0 def /inrht 0 def /inflag 0 def /outflag 0 def /xadrht 0 def /xadlft 0 def /yadtop 0 def /yadbot 0 def /defineresource where { pop /WRI-Mathematica-prolog currentdict /ProcSet defineresource pop } if end %KLUDGE until Mathematica output uses resources directly userdict /MathPictureStart { /findresource where { pop /WRI-Mathematica-prolog /ProcSet findresource } { Mathdict } ifelse /MathPictureStart get exec } put MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def /Helvetica findfont 18 scalefont setfont % Scaling calculations -0.0909091 0.181818 0.188849 0.183362 [ [.09091 -0.0125 -5.4 -23.4 ] [.09091 -0.0125 5.4 0 ] [.27273 -0.0125 -5.4 -23.4 ] [.27273 -0.0125 5.4 0 ] [.45455 -0.0125 -5.4 -23.4 ] [.45455 -0.0125 5.4 0 ] [.63636 -0.0125 -5.4 -23.4 ] [.63636 -0.0125 5.4 0 ] [.81818 -0.0125 -5.4 -23.4 ] [.81818 -0.0125 5.4 0 ] [1 -0.0125 -5.4 -23.4 ] [1 -0.0125 5.4 0 ] [ 0 0 -0.125 0 ] [.5 -0.0125 -21.6 -46.8 ] [.5 -0.0125 21.6 -23.4 ] [-0.0125 .00549 -21.6 -11.7 ] [-0.0125 .00549 0 11.7 ] [-0.0125 .09717 -43.2 -11.7 ] [-0.0125 .09717 0 11.7 ] [-0.0125 .18885 -10.8 -11.7 ] [-0.0125 .18885 0 11.7 ] [-0.0125 .28053 -32.4 -11.7 ] [-0.0125 .28053 0 11.7 ] [-0.0125 .37221 -10.8 -11.7 ] [-0.0125 .37221 0 11.7 ] [-0.0125 .46389 -32.4 -11.7 ] [-0.0125 .46389 0 11.7 ] [ 0 0 -0.125 0 ] [-0.01875 .25 -66.6 -27 ] [-0.01875 .25 -43.2 27 ] [ 0 .5 .125 0 ] [ 1 0 .125 0 ] [ 0 0 0 0 ] [ 1 .5 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .09091 0 m .09091 .00625 L s [(1)] .09091 -0.0125 0 1 Mshowa .27273 0 m .27273 .00625 L s [(2)] .27273 -0.0125 0 1 Mshowa .45455 0 m .45455 .00625 L s [(3)] .45455 -0.0125 0 1 Mshowa .63636 0 m .63636 .00625 L s [(4)] .63636 -0.0125 0 1 Mshowa .81818 0 m .81818 .00625 L s [(5)] .81818 -0.0125 0 1 Mshowa 1 0 m 1 .00625 L s [(6)] 1 -0.0125 0 1 Mshowa .125 Mabswid .12727 0 m .12727 .00375 L s .16364 0 m .16364 .00375 L s .2 0 m .2 .00375 L s .23636 0 m .23636 .00375 L s .30909 0 m .30909 .00375 L s .34545 0 m .34545 .00375 L s .38182 0 m .38182 .00375 L s .41818 0 m .41818 .00375 L s .49091 0 m .49091 .00375 L s .52727 0 m .52727 .00375 L s .56364 0 m .56364 .00375 L s .6 0 m .6 .00375 L s .67273 0 m .67273 .00375 L s .70909 0 m .70909 .00375 L s .74545 0 m .74545 .00375 L s .78182 0 m .78182 .00375 L s .85455 0 m .85455 .00375 L s .89091 0 m .89091 .00375 L s .92727 0 m .92727 .00375 L s .96364 0 m .96364 .00375 L s .05455 0 m .05455 .00375 L s .01818 0 m .01818 .00375 L s .25 Mabswid 0 0 m 1 0 L s [(s[A])] .5 -0.0125 0 -23.4 Mabsadd 0 1 Mshowa 0 .00549 m .00625 .00549 L s [(-1)] -0.0125 .00549 1 0 Mshowa 0 .09717 m .00625 .09717 L s [(-0.5)] -0.0125 .09717 1 0 Mshowa 0 .18885 m .00625 .18885 L s [(0)] -0.0125 .18885 1 0 Mshowa 0 .28053 m .00625 .28053 L s [(0.5)] -0.0125 .28053 1 0 Mshowa 0 .37221 m .00625 .37221 L s [(1)] -0.0125 .37221 1 0 Mshowa 0 .46389 m .00625 .46389 L s [(1.5)] -0.0125 .46389 1 0 Mshowa .125 Mabswid 0 .02382 m .00375 .02382 L s 0 .04216 m .00375 .04216 L s 0 .0605 m .00375 .0605 L s 0 .07883 m .00375 .07883 L s 0 .1155 m .00375 .1155 L s 0 .13384 m .00375 .13384 L s 0 .15218 m .00375 .15218 L s 0 .17051 m .00375 .17051 L s 0 .20719 m .00375 .20719 L s 0 .22552 m .00375 .22552 L s 0 .24386 m .00375 .24386 L s 0 .26219 m .00375 .26219 L s 0 .29887 m .00375 .29887 L s 0 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.92727 .49625 m .92727 .5 L s .96364 .49625 m .96364 .5 L s .05455 .49625 m .05455 .5 L s .01818 .49625 m .01818 .5 L s .25 Mabswid 0 .5 m 1 .5 L s .99375 .00549 m 1 .00549 L s .99375 .09717 m 1 .09717 L s .99375 .18885 m 1 .18885 L s .99375 .28053 m 1 .28053 L s .99375 .37221 m 1 .37221 L s .99375 .46389 m 1 .46389 L s .125 Mabswid .99625 .02382 m 1 .02382 L s .99625 .04216 m 1 .04216 L s .99625 .0605 m 1 .0605 L s .99625 .07883 m 1 .07883 L s .99625 .1155 m 1 .1155 L s .99625 .13384 m 1 .13384 L s .99625 .15218 m 1 .15218 L s .99625 .17051 m 1 .17051 L s .99625 .20719 m 1 .20719 L s .99625 .22552 m 1 .22552 L s .99625 .24386 m 1 .24386 L s .99625 .26219 m 1 .26219 L s .99625 .29887 m 1 .29887 L s .99625 .3172 m 1 .3172 L s .99625 .33554 m 1 .33554 L s .99625 .35387 m 1 .35387 L s .99625 .39055 m 1 .39055 L s .99625 .40888 m 1 .40888 L s .99625 .42722 m 1 .42722 L s .99625 .44556 m 1 .44556 L s .99625 .48223 m 1 .48223 L s .25 Mabswid 1 0 m 1 .5 L s 0 .18885 m 1 .18885 L s 0 0 m 1 0 L 1 .5 L 0 .5 L closepath clip newpath .003 w 1 .18383 m .98982 .18335 L .96327 .18225 L .93727 .1817 L .91164 .18133 L .88636 .1806 L .86164 .1795 L .83764 .17766 L .814 .17528 L .79127 .17143 L .76891 .16703 L .74745 .16153 L .72673 .15474 L .70673 .14723 L .68745 .13952 L .66891 .13036 L .65127 .12211 L .63436 .11367 L .61836 .1067 L .60327 .10102 L .58891 .0968 L .57545 .09387 L .56273 .09203 L .55091 .09112 L .53982 .09093 L .52964 .09075 L .52018 .09112 L .51145 .09112 L .50364 .09148 L .49636 .09167 L .48982 .09222 L .484 .09258 L .47873 .0924 L .474 .09222 L .46982 .09258 L .46618 .09258 L .46291 .09258 L .46018 .0924 L .45782 .09222 L .45564 .09222 L .45382 .09222 L .45218 .09185 L .45073 .09203 L .44927 .09203 L .448 .09185 L .44655 .09185 L .44527 .09167 L .44382 .09185 L .442 .09148 L .44018 .09112 L Mistroke .43818 .0913 L .43564 .09075 L .43291 .09038 L .42964 .0902 L .426 .08965 L .42182 .08892 L .41727 .08782 L .412 .08708 L .406 .08562 L .39945 .08433 L .39236 .08232 L 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% MathPictureEnd - finish off page. % MathSubStart - start a sub-page. % MathSubEnd - finish off a sub-page. % Mdot - draw a dot. % Mtetra - draw a filled tetragon. % Metetra - draw a filled tetragon with black edges. % Mistroke - intermediate stroke of multi-stroke line/curve. % Mfstroke - final stroke of multi-stroke line/curve. % Msboxa - compute coordinates of text bounding box. % Mshowa - plot characters. % MathScale - compute scaling info to contain array of points. %start of ISOLatin1 stuff /ISOLatin1Encoding dup where { pop pop } { [ /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /space /exclam /quotedbl /numbersign /dollar /percent /ampersand /quoteright /parenleft /parenright /asterisk /plus /comma /minus /period /slash /zero /one /two /three /four /five /six /seven /eight /nine /colon /semicolon /less /equal /greater /question /at /A /B /C /D /E /F /G /H /I /J /K /L /M /N /O /P /Q /R /S /T /U /V /W /X /Y /Z /bracketleft /backslash /bracketright /asciicircum /underscore /quoteleft /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o /p /q /r /s /t /u /v /w /x /y /z /braceleft /bar /braceright /asciitilde /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /dotlessi /grave /acute /circumflex /tilde /macron /breve /dotaccent /dieresis /.notdef /ring /cedilla /.notdef /hungarumlaut /ogonek /caron /space /exclamdown /cent /sterling /currency /yen /brokenbar /section /dieresis /copyright /ordfeminine /guillemotleft /logicalnot /hyphen /registered /macron /degree /plusminus /twosuperior /threesuperior /acute /mu /paragraph /periodcentered /cedilla /onesuperior /ordmasculine /guillemotright /onequarter /onehalf /threequarters /questiondown /Agrave /Aacute /Acircumflex /Atilde /Adieresis /Aring /AE /Ccedilla /Egrave /Eacute /Ecircumflex /Edieresis /Igrave /Iacute /Icircumflex /Idieresis /Eth /Ntilde /Ograve /Oacute /Ocircumflex /Otilde /Odieresis /multiply /Oslash /Ugrave /Uacute /Ucircumflex /Udieresis /Yacute /Thorn /germandbls /agrave /aacute /acircumflex /atilde /adieresis /aring /ae /ccedilla /egrave /eacute /ecircumflex /edieresis /igrave /iacute /icircumflex /idieresis /eth /ntilde /ograve /oacute /ocircumflex /otilde /odieresis /divide /oslash /ugrave /uacute /ucircumflex /udieresis /yacute /thorn /ydieresis ] def } ifelse /MFontDict 50 dict def /MStrCat { exch dup length 2 index length add string dup 3 1 roll copy length exch dup 4 2 roll exch putinterval } bind def /MCreateEncoding { 1 index 255 string cvs (-) MStrCat 1 index MStrCat cvn exch (Encoding) MStrCat cvn dup where { exch get } { pop StandardEncoding } ifelse 3 1 roll dup MFontDict exch known not { 1 index findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding 3 index def currentdict end 1 index exch definefont pop MFontDict 1 index null put } if exch pop exch pop } bind def /ISOLatin1 { (ISOLatin1) MCreateEncoding } bind def %end of ISOLatin1 stuff % Set up for the start of a page. /MathPictureStart { /Msaveobj save def /findresource where { pop /WRI-Mathematica-prolog /ProcSet findresource begin } { Mathdict begin } ifelse userdict begin /MathPictureStartHook where { /MathPictureStartHook get exec } if Mtransform Mlmarg Mbmarg translate Mwidth Mlmarg Mrmarg add sub /Mwidth exch def Mheight Mbmarg Mtmarg add sub /Mheight exch def /Mtmatrix matrix currentmatrix def /Mgmatrix matrix currentmatrix def /MathDPSFlag where { pop clientsync } if } def % Finish off a page. /MathPictureEnd { end end Msaveobj restore /MathDPSFlag where { pop } { showpage } ifelse } def %MFill fills the drawing area with the current color. /MFill { 0 0 moveto Mwidth 0 lineto Mwidth Mheight lineto 0 Mheight lineto fill } def %New device-specific optimizing operators /Mfill /.devicefill where { pop /.devicefill load def } { /fill load def } ifelse /Mstroke /.devicestroke where { pop /.devicestroke load def } { /stroke load def } ifelse % xmin xmax ymin ymax MPlotRegion alters the origin, Mwidth and Mheight % so that the picture fills the altered region /MPlotRegion { 3 index Mwidth mul 2 index Mheight mul translate exch sub Mheight mul /Mheight exch def exch sub Mwidth mul /Mwidth exch def } def % Given a rectangle, set it up as a sub-picture. /MathSubStart { Momatrix Mgmatrix Mtmatrix Mwidth Mheight 7 -2 roll moveto Mtmatrix setmatrix currentpoint Mgmatrix setmatrix 9 -2 roll moveto Mtmatrix setmatrix currentpoint 2 copy translate /Mtmatrix matrix currentmatrix def 3 -1 roll exch sub /Mheight exch def sub /Mwidth exch def } def % Restore the saved state left by the matching MathSubStart. % Note, we also leave with the new Mgmatrix as the current matrix. /MathSubEnd { /Mheight exch def /Mwidth exch def /Mtmatrix exch def dup setmatrix /Mgmatrix exch def /Momatrix exch def } def % Given a point, draw a dot. /Mdot { newpath currentlinewidth 2 div 0 360 arc fill } bind def % Given 4 points, draw the corresponding filled tetragon. /Mtetra { moveto lineto lineto lineto Mfill } bind def % Given 4 points, draw the corresponding filled tetragon with black edges. % Note, this leaves the gray level at 0 (for compatibility with the old % C code. /Metetra { moveto lineto lineto lineto closepath gsave Mfill grestore 0 setgray Mstroke } bind def % Mistroke is called to stroke intermediate parts of a path. It makes % sure to resynchronize the dashing pattern and to leave the current point % as the final point of the path. /Mistroke { flattenpath 0 0 0 { 4 2 roll pop pop } { 4 -1 roll 2 index sub dup mul 4 -1 roll 2 index sub dup mul add sqrt 4 -1 roll add 3 1 roll } { stop } { stop } pathforall pop pop currentpoint Mstroke moveto currentdash 3 -1 roll add setdash } bind def % Mfstroke is called to stroke the final parts of a path. It resets % the dashing pattern to compensate for any adjustments made by Mistroke. /Mfstroke { Mstroke currentdash pop 0 setdash } bind def % Mrotsboxa is the same as Msboxa except that it takes an angle % from the stack and the box is calculated for text rendered at this angle. % It gsaves in case we are starting a MathSubStart % save Mrot so that Msboxa can convert bouding box back to the non-rotated % coordinate system % call Mrotcheck to alter the offsets into the rotated system % converts Mtmatrix to render in the rotated system % the calls Msboxa which does all the work % at the end Mtmatrix is restored and Mrot is reset to 0 /Mrotsboxa { gsave dup /Mrot exch def Mrotcheck Mtmatrix dup setmatrix 7 1 roll 4 index 4 index translate rotate 3 index -1 mul 3 index -1 mul translate /Mtmatrix matrix currentmatrix def grestore Msboxa 3 -1 roll /Mtmatrix exch def /Mrot 0 def } bind def % Given an array of strings ([str...]), which represent consecutive lines % of text, a position in graphics coordinates (gx,gy) and a position in % the bounding box coordinates (sx,sy), compute the low and high coordinates % of the resulting text, in the [gx gy tx ty] form, which corresponds to % the point (gx,gy) (in graphics coordinates) plus the offset (tx,ty) (in % text coordinates). % Note, Msboxa assumes that the current matrix is the text matrix. % Mboxout is called in case we are in Mouter to make the box bigger % Mboxrot adjusts the box to account for a rotation to convert the box % into a nonrotated coordinate system % /Msboxa { newpath 5 -1 roll Mvboxa pop Mboxout 6 -1 roll 5 -1 roll 4 -1 roll Msboxa1 5 -3 roll Msboxa1 Mboxrot [ 7 -2 roll 2 copy [ 3 1 roll 10 -1 roll 9 -1 roll ] 6 1 roll 5 -2 roll ] } bind def % Msboxa1 is an internal function which, given a bounding box coordinate % (sz), and the bounding box limits (blz and bhz), computes the actual % offsets (tlz = (blz-bhz)(sz+1)/2, thz = (blz-bhz)(sz-1)/2). /Msboxa1 { sub 2 div dup 2 index 1 add mul 3 -1 roll -1 add 3 -1 roll mul } bind def % Given a (non-empty) array of strings ([str...]) which represent consecutive % lines of text, compute the total bounding box assuming that we start at % (0,0) and the array of y offsets to place the lines correctly. % Note, Mvboxa assumes that the current matrix is the text matrix. % Note, Mvboxa does not alter the current path. % The vertical spacing is set so that the bounding boxes of adjacent lines % are .3 times the width of an `m' apart. /Mvboxa { gsave newpath [ true 3 -1 roll { Mbbox 5 -1 roll { 0 5 1 roll } { 7 -1 roll exch sub (m) stringwidth pop .3 mul sub 7 1 roll 6 -1 roll 4 -1 roll Mmin 3 -1 roll 5 index add 5 -1 roll 4 -1 roll Mmax 4 -1 roll } ifelse false } forall { stop } if counttomark 1 add 4 roll ] grestore } bind def % Given a string, compute the bounding box assuming that we start at (0,0). % Note, the path is assumed to be empty, and we are assumed to be in text % coordinates. Allows for long strings. /Mbbox { 1 dict begin 0 0 moveto /temp (T) def { gsave currentpoint newpath moveto temp 0 3 -1 roll put temp false charpath flattenpath currentpoint pathbbox grestore moveto lineto moveto} forall pathbbox newpath end } bind def % Compute the minimum of two numbers. /Mmin { 2 copy gt { exch } if pop } bind def % Compute the maximum of two numbers. /Mmax { 2 copy lt { exch } if pop } bind def % % Mrotwork saves Mrot (not really needed but saved anyway) % calls Mrotcheck to adjust the offsets into the rotated coordinate system % converts Mtmatrix to render in the rotated system % /Mrotwork { dup /Mrot exch def Mrotcheck Mtmatrix dup setmatrix 7 1 roll 4 index 4 index translate rotate 3 index -1 mul 3 index -1 mul translate /Mtmatrix matrix currentmatrix def Mgmatrix setmatrix } def % % Mrotshowa is the same as Mshowa except that it takes an angle % from the stack and the text is rendered at this angle. % It call Mrotwork to do all the rotation work. % Then it calls Mshowa which does all the drawing work. % At the end Mtmatrix is restored and Mrot is reset to zero. % /Mrotshowa { Mrotwork Mshowa /Mtmatrix exch def /Mrot 0 def } def % % Draws rotated text with a background. % /Mrotback { 7 1 roll dup 8 1 roll Mrotwork 8 -2 roll Mshowback /Mtmatrix exch def /Mrot 0 def } def % % Given an array of strings ([str...]), which represent consecutive lines % of text, a position in graphics coordinates (gx,gy) and a position in % the bounding box coordinates (sx,sy), display the strings. % Mboxout is called in case we are in Mouter % /Mshowa { 4 -2 roll moveto 2 index Mtmatrix setmatrix Mvboxa 7 1 roll Mboxout 6 -1 roll 5 -1 roll 4 -1 roll Mshowa1 4 1 roll Mshowa1 rmoveto currentpoint Mshowax pop pop pop pop Mgmatrix setmatrix } def % % The background box of text is increased by the % size of an "m" % /Madjust { (m) stringwidth pop mul dup 4 -1 roll add 3 1 roll add } def % % % /Mbuildcoord { 7 index 7 index 4 -1 roll 4 -1 roll index exch index Mabsadd } def % % If the text is rotated then translate to the drawing point. % Rotate then translate back. Do not do this if the angle % of rotation is 0. % /Mrotate { 8 index 0 ne { 13 copy 4 -2 roll pop pop 6 -2 roll pop pop 4 -1 roll 3 -1 roll sub 6 -1 roll mul 3 1 roll sub 4 -1 roll mul 3 -1 roll 5 1 roll Mabsadd 2 copy translate 3 -1 roll rotate exch -1 mul exch -1 mul translate } if 9 -1 roll pop } def % % Draw text but into a box with a certain color. % Uses Msboxa to build the box. % /Mshowback { gsave exec 6 copy pop Msboxa aload pop 0.5 Madjust 5 -1 roll aload pop Mrotate -0.5 Madjust 4 -1 roll pop 3 -1 roll pop 3 4 Mbuildcoord moveto 3 4 Mbuildcoord lineto 3 6 Mbuildcoord lineto 5 6 Mbuildcoord lineto 5 4 Mbuildcoord lineto pop pop pop pop pop pop fill grestore Mshowa } def % This is used for fixedwidth fonts % It simply shows each string and advances the y direction by the offset % /Mshowax { 0 1 4 index length -1 add { 2 index 4 index 2 index get 3 index add moveto 4 index exch get Mfixdash { Mfixdashp } if show } for } def % Fix if all dashes and length > 1 /Mfixdashp { dup length 1 gt 1 index true exch { 45 eq and } forall and { gsave (--) stringwidth pop (-) stringwidth pop sub 2 div 0 rmoveto dup length 1 sub { (-) show } repeat grestore } if } bind def % Mshowa1 is an internal routine which, given a bounding box coordinate % (sz), and the bounding box limits if we started drawing at 0 (tlz and thz), % computes the offset at which to start drawing % (relz = (sz-1)tlz/2 - (sz+1)thz/2 = sz(tlz-thz)/2-(tlz+thz)/2). /Mshowa1 { 2 copy add 4 1 roll sub mul sub -2 div } bind def % Given the x and y scaling to user coordinates and an array of points to % fit (xbias xscale ybias yscale [pnts]), set up the scaling. The array % must contain atleast two points, and the last two must be of the form % [gxlow gylow 0 0] and [gxhigh gyhigh 0 0]. % Note, MathScale assumes that we are already scaled so that the active area % is the rectangle [0,Mwidth-Mlmarg-Mrmarg]x[0,Mheight-Mbmarg-Mtmarg]. % also keep bias and scale info for PostScript commands /MathScale { Mwidth Mheight Mlp /MathScaleHook where { /MathScaleHook get exec } if translate scale pop pop pop pop pop pop pop pop /yscale exch def /ybias exch def /xscale exch def /xbias exch def /Momatrix xscale yscale matrix scale xbias ybias matrix translate matrix concatmatrix def /Mgmatrix matrix currentmatrix def } def % Given a non-empty array of points to fit ([p]) and a maximum width (sx) % and height (sy) find the largest scale (Ax and Ay) and offsets (Bx and By) % such that the transformation % [gx gy tx ty] -> (Ax gx + tx + bx, Ay gy + ty + By) % maps the points into the rectangle [0,sx]x[0,sy] /Mlp { 3 copy Mlpfirst { Mnodistort { Mmin dup } if 4 index 2 index 2 index Mlprun 16 -8 roll 21 8 roll 11 index 11 -1 roll 10 -4 roll Mlp1 8 index 9 -5 roll Mlp1 4 -1 roll and { exit } if 15 -8 roll pop pop pop pop pop pop pop pop 3 -1 roll pop pop } loop exch 3 1 roll 7 -3 roll pop pop pop } def % Given an array of points in the [gx gy tx ty] form, with the last two % being [gxlow gylow 0 0] and [gxhigh gyhigh 0 0], and the width and height % (sx and sy) in which to fit them, compute the maximum scaling (Ax and Ay). /Mlpfirst { 3 -1 roll dup length 2 copy -2 add get aload pop pop pop 4 -2 roll -1 add get aload pop pop pop 6 -1 roll 3 -1 roll 5 -1 roll sub div 4 1 roll exch sub div } bind def % Given a non-empty array of points to fit ([pnts]) and scale factors % for graphics->text (Ax and Ay), compute the limiting points. /Mlprun { 2 copy 4 index 0 get dup 4 1 roll Mlprun1 3 copy 8 -2 roll 9 -1 roll { 3 copy Mlprun1 3 copy 11 -3 roll /gt Mlpminmax 8 3 roll 11 -3 roll /lt Mlpminmax 8 3 roll } forall pop pop pop pop 3 1 roll pop pop aload pop 5 -1 roll aload pop 8 copy exch 6 -1 roll Mlprun2 8 2 roll 4 -1 roll Mlprun2 6 2 roll 3 -1 roll Mlprun2 4 2 roll exch Mlprun2 6 2 roll } bind def % Given scale factors for graphics->text (Ax and Ay) and a point in the % [gx gy tx ty] form, return the text x and y coordinate that results. /Mlprun1 { aload pop exch 6 -1 roll 5 -1 roll mul add 4 -2 roll mul 3 -1 roll add } bind def % Given a low and high coordinate, compute the center and width. /Mlprun2 { 2 copy add 2 div 3 1 roll exch sub } bind def % Given two points stored as [gx gy tx ty] followed by the scaled % result (rx, ry), and a comparison function (lt or gt) leave the % point which is the minimum (or maximum) in each dimension. /Mlpminmax { cvx 2 index 6 index 2 index exec { 7 -3 roll 4 -1 roll } if 1 index 5 index 3 -1 roll exec { 4 1 roll pop 5 -1 roll aload pop pop 4 -1 roll aload pop [ 8 -2 roll pop 5 -2 roll pop 6 -2 roll pop 5 -1 roll ] 4 1 roll pop } { pop pop pop } ifelse } bind def % Given a size (s), graphics->text scale (A), text center (ct), text % width (wt), graphics center (cg) and graphics width (wg), compute % a new graphics->text scale (Anew) and offset (B) and whether or not % we are done. % Note, the mysterious .99999 is magic juju which is supposed to ward % off the possibility that floating point errors would cause this % routine to return the old A and yet claim not-done. /Mlp1 { 5 index 3 index sub 5 index 2 index mul 1 index le 1 index 0 le or dup not { 1 index 3 index div .99999 mul 8 -1 roll pop 7 1 roll } if 8 -1 roll 2 div 7 -2 roll pop sub 5 index 6 -3 roll pop pop mul sub exch } bind def % The following are the workings of the tick, axes and plot labels. % NOTE a possible source of confusion is that for xticks ie tickmarks on % the x axis we keep y information and vice versa for yticks % % When Minner is found then % % assumes that box starts at zero on the left lower side % % 0) if outflag = 1 then intop = 0, inrht = 0 outflag = 0 % 1) Save intop largest top of box % 2) Save inrht largest rht of box % 3) set inflag notifies that inner marks are present % % When Mouter is found then % % if inflag is set then % 1) get vecx and vecy off the stack (points in direcn to move) % 2) vecx < 1 xadrht = inrht*abs(vecx) % 3) vecx > 1 xadlft = inrht*abs(vecx) % 4) vecy < 1 yadtop = intop*abs(vecy) % 5) vecy > 1 yadbot = intop*abs(vecy) % 6) set outflag = 1 % 7) clear inflag, inrht, intop % guaranteed to be zero if no inner is present?? % % % These all have effects in Mrotsboxa and Mrotshowa % check inflag and if set % % 1) increase top of bbox by yadtop % 2) decrease bot of bbox by yadbot % 3) increase rht of bbox by xadrht % 4) increase lft of bbox by xadlft % 5) clear outflag, yadtop, yadbot, % xadrht, xadlft % % % This saves the top right corner of the bounding box as a side effect % This is to allow the adjustment of text placed with Mouter so that % it misses the Minner text. It is assumed that the ang is 0 % in the same way it is assumed that the text of Mouter is 0 or 90 % /Minner { outflag 1 eq { /outflag 0 def /intop 0 def /inrht 0 def } if 5 index gsave Mtmatrix setmatrix Mvboxa pop grestore 3 -1 roll pop dup intop gt { /intop exch def } { pop } ifelse dup inrht gt { /inrht exch def } { pop } ifelse pop /inflag 1 def } def % This takes two number off the stack and uses them as a vector in graphics % coordinates which points in the direction in which the Mouter text is to move % it calculates the bouding box adjustments yadtop yadbot xadrht and xadlft % these are in Mboxout to adjust the bounding box to compensate. /Mouter { /xadrht 0 def /xadlft 0 def /yadtop 0 def /yadbot 0 def inflag 1 eq { dup 0 lt { dup intop mul neg /yadtop exch def } if dup 0 gt { dup intop mul /yadbot exch def } if pop dup 0 lt { dup inrht mul neg /xadrht exch def } if dup 0 gt { dup inrht mul /xadlft exch def } if pop /outflag 1 def } { pop pop} ifelse /inflag 0 def /inrht 0 def /intop 0 def } def % % This adjusts the bounding box to account for adjacent text % This allows the two text strings to avoid each other % current matrix is the text matrix /Mboxout { outflag 1 eq { 4 -1 roll xadlft leadjust add sub 4 1 roll 3 -1 roll yadbot leadjust add sub 3 1 roll exch xadrht leadjust add add exch yadtop leadjust add add /outflag 0 def /xadlft 0 def /yadbot 0 def /xadrht 0 def /yadtop 0 def } if } def /leadjust { (m) stringwidth pop .5 mul } bind def % The offsets sx and sy refer to the graphics coordinate system % thus they must be altered if a rotation has taken place. % We must also change the bounding box computations for Minner % /Mrotcheck { dup 90 eq { % % Mouter only applies to strings which are either at 0 or 90 % sort out the box adjust factors % % xadrht -> yadbot % xadlft -> yadtop % yadtop -> xadrht % yadbot -> xadlft yadbot /yadbot xadrht def /xadrht yadtop def /yadtop xadlft def /xadlft exch def } if dup cos 1 index sin Checkaux dup cos 1 index sin neg exch Checkaux 3 1 roll pop pop } def % % Checkaux is an auxilliary function for Mrotcheck it multiplies a % row vector by a column vector % /Checkaux { 4 index exch 4 index mul 3 1 roll mul add 4 1 roll } bind def % % Mboxrot converts the bounding box back from the rotated coordinate % system to the Mgmatrix system to compensate for a rotation % It has the opposite functionality of Mrotcheck % This is not the most neatest or most efficient implementation but it works % /Mboxrot { Mrot 90 eq { % old tlx thx tly thy % new -thy -tly tlx thx % brotaux 4 2 roll } if Mrot 180 eq { % old tlx thx tly thy % new -thx -tlx -thx -tly % 4 2 roll brotaux 4 2 roll brotaux } if Mrot 270 eq { % old tlx thx tly thy % new tly thy -thx -tlx % 4 2 roll brotaux } if } def % % auxilliary function negate and reverse /brotaux { neg exch neg } bind def % % Mabsproc takes a measurement in the default user units and converts % it to the present units. This allows absolute thickness and dashing % to work. It works by using a {0, x} vector and using the RMS of the result. /Mabsproc { 0 matrix defaultmatrix dtransform idtransform dup mul exch dup mul add sqrt } bind def % % Mabswid allows the linewidth to be specified in absolute coordinates % It does this by recording the graphics transformation matrix at the % begining of the plot. % This will break if the scaling in the x and y directions is % different. This is the case if Mnodistort is false % /Mabswid { Mabsproc setlinewidth } bind def % Mabsdash allows the dashing pattern to be specified in absolute coordinates % It does this by recording the graphics transformation matrix at the % begining of the plot. % This will break if the scaling in the x and y directions is % different. This is the case if Mnodistort is false % /Mabsdash { exch [ exch { Mabsproc } forall ] exch setdash } bind def % % Mabs takes a pair of coordinates in points % and converts them into a pair of coordinates in % the current drawing scheme % /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def % % Mabs takes a pair of numbers in drawing coordinates % and a pair in points. It converts the points to % drawing coordinates and adds them to the first pair. % /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def % % These two procedures are for using Offset coordinates % with MathScale computations % /Mabsfix1 { 3 -1 roll /ar exch def ar 2 get 3 -1 roll add exch ar 3 get add ar 3 3 -1 roll put ar 2 3 -1 roll put ar } bind def /Mabsfix { 2 copy 6 -1 roll 3 1 roll Mabsfix1 4 1 roll Mabsfix1 } bind def %MBeginOrig start coordinates in user coordinates /MBeginOrig { Momatrix concat} bind def %MEndOrig start coordinates in user coordinates /MEndOrig { Mgmatrix setmatrix} bind def /sampledsound where { pop } { /MathDPSFlag where { pop /sampledsound { clientsync } def } { /sampledsound { exch pop exch 5 1 roll mul 4 idiv mul 2 idiv exch pop exch /Mtempproc exch def { Mtempproc pop } repeat } def } ifelse } ifelse % Define setrgbcolor for those ancient PostScript devices lacking it /setrgbcolor dup where { pop pop } { { .114 mul exch .587 mul add exch .299 mul add setgray } bind def } ifelse % % now simple conversion of cmykcolor to rgbcolor % subtract k and then take complements /setcmykcolor where { pop} { /setcmykcolor { 4 1 roll [ 4 1 roll ] { 1 index sub 1 sub neg dup 0 lt { pop 0 } if dup 1 gt { pop 1 } if exch } forall pop setrgbcolor } bind def } ifelse % Here are the short operators /g /setgray load def /k /setcmykcolor load def /m /moveto load def /p /gsave load def /r /setrgbcolor load def /w /setlinewidth load def /C /curveto load def /F /Mfill load def /L /lineto load def /P /grestore load def /s /Mstroke load def /Mcharproc { currentfile (x) readhexstring pop 0 get exch div } bind def /Mshadeproc { dup 3 1 roll { dup Mcharproc 3 1 roll } repeat 1 eq { setgray } { 3 eq { setrgbcolor } { setcmykcolor } ifelse } ifelse } bind def /Mrectproc { 3 index 2 index moveto 2 index 3 -1 roll lineto dup 3 1 roll lineto lineto Mfill } bind def /Mcolorimage { 7 1 roll pop pop matrix invertmatrix concat 2 exch exp 1 sub 3 1 roll 1 1 2 index { 1 1 4 index { dup 1 sub exch 2 index dup 1 sub exch 7 index 9 index Mshadeproc Mrectproc } for pop } for pop pop pop pop } bind def /Mimage { pop matrix invertmatrix concat 2 exch exp 1 sub 3 1 roll 1 1 2 index { 1 1 4 index { dup 1 sub exch 2 index dup 1 sub exch 7 index Mcharproc setgray Mrectproc } for pop } for pop pop pop } bind def % Default values for variables /Mlmarg 1.0 72 mul def /Mrmarg 1.0 72 mul def /Mbmarg 1.0 72 mul def /Mtmarg 1.0 72 mul def /Mwidth 8.5 72 mul def /Mheight 11 72 mul def /Mtransform { } bind def /Mnodistort true def /Mfixdash false def /Mrot 0 def /intop 0 def /inrht 0 def /inflag 0 def /outflag 0 def /xadrht 0 def /xadlft 0 def /yadtop 0 def /yadbot 0 def /defineresource where { pop /WRI-Mathematica-prolog currentdict /ProcSet defineresource pop } if end %KLUDGE until Mathematica output uses resources directly userdict /MathPictureStart { /findresource where { pop /WRI-Mathematica-prolog /ProcSet findresource } { Mathdict } ifelse /MathPictureStart get exec } put MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def /Helvetica findfont 18 scalefont setfont % Scaling calculations -0.0909091 0.181818 0.1875 0.208333 [ [.09091 -0.0125 -5.4 -23.4 ] [.09091 -0.0125 5.4 0 ] [.27273 -0.0125 -5.4 -23.4 ] [.27273 -0.0125 5.4 0 ] [.45455 -0.0125 -5.4 -23.4 ] [.45455 -0.0125 5.4 0 ] [.63636 -0.0125 -5.4 -23.4 ] [.63636 -0.0125 5.4 0 ] [.81818 -0.0125 -5.4 -23.4 ] [.81818 -0.0125 5.4 0 ] [1 -0.0125 -5.4 -23.4 ] [1 -0.0125 5.4 0 ] [ 0 0 -0.125 0 ] [.5 -0.0125 -21.6 -46.8 ] [.5 -0.0125 21.6 -23.4 ] [-0.0125 .08333 -43.2 -11.7 ] [-0.0125 .08333 0 11.7 ] [-0.0125 .1875 -10.8 -11.7 ] [-0.0125 .1875 0 11.7 ] [-0.0125 .29167 -32.4 -11.7 ] [-0.0125 .29167 0 11.7 ] [-0.0125 .39583 -10.8 -11.7 ] [-0.0125 .39583 0 11.7 ] [-0.0125 .5 -32.4 -11.7 ] [-0.0125 .5 0 11.7 ] [ 0 0 -0.125 0 ] [-0.01875 .25 -66.6 -27 ] [-0.01875 .25 -43.2 27 ] [ 0 .5 .125 0 ] [ 1 0 .125 0 ] [ 0 0 0 0 ] [ 1 .5 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .09091 0 m .09091 .00625 L s [(1)] .09091 -0.0125 0 1 Mshowa .27273 0 m .27273 .00625 L s [(2)] .27273 -0.0125 0 1 Mshowa .45455 0 m .45455 .00625 L s [(3)] .45455 -0.0125 0 1 Mshowa .63636 0 m .63636 .00625 L s [(4)] .63636 -0.0125 0 1 Mshowa .81818 0 m .81818 .00625 L s [(5)] .81818 -0.0125 0 1 Mshowa 1 0 m 1 .00625 L s [(6)] 1 -0.0125 0 1 Mshowa .125 Mabswid .12727 0 m .12727 .00375 L s .16364 0 m .16364 .00375 L s .2 0 m .2 .00375 L s .23636 0 m .23636 .00375 L s .30909 0 m .30909 .00375 L s .34545 0 m .34545 .00375 L s .38182 0 m .38182 .00375 L s .41818 0 m .41818 .00375 L s .49091 0 m .49091 .00375 L s .52727 0 m .52727 .00375 L s .56364 0 m .56364 .00375 L s .6 0 m .6 .00375 L s .67273 0 m .67273 .00375 L s .70909 0 m .70909 .00375 L s .74545 0 m .74545 .00375 L s .78182 0 m .78182 .00375 L s .85455 0 m .85455 .00375 L s .89091 0 m .89091 .00375 L s .92727 0 m .92727 .00375 L s .96364 0 m .96364 .00375 L s .05455 0 m .05455 .00375 L s .01818 0 m .01818 .00375 L s .25 Mabswid 0 0 m 1 0 L s [(s[A])] .5 -0.0125 0 -23.4 Mabsadd 0 1 Mshowa 0 .08333 m .00625 .08333 L s [(-0.5)] -0.0125 .08333 1 0 Mshowa 0 .1875 m .00625 .1875 L s [(0)] -0.0125 .1875 1 0 Mshowa 0 .29167 m .00625 .29167 L s [(0.5)] -0.0125 .29167 1 0 Mshowa 0 .39583 m .00625 .39583 L s [(1)] -0.0125 .39583 1 0 Mshowa 0 .5 m .00625 .5 L s [(1.5)] -0.0125 .5 1 0 Mshowa .125 Mabswid 0 .10417 m .00375 .10417 L s 0 .125 m .00375 .125 L s 0 .14583 m .00375 .14583 L s 0 .16667 m .00375 .16667 L s 0 .20833 m .00375 .20833 L s 0 .22917 m .00375 .22917 L s 0 .25 m .00375 .25 L s 0 .27083 m .00375 .27083 L s 0 .3125 m .00375 .3125 L s 0 .33333 m .00375 .33333 L s 0 .35417 m .00375 .35417 L s 0 .375 m .00375 .375 L s 0 .41667 m .00375 .41667 L s 0 .4375 m .00375 .4375 L s 0 .45833 m .00375 .45833 L s 0 .47917 m .00375 .47917 L s 0 .0625 m .00375 .0625 L s 0 .04167 m .00375 .04167 L s 0 .02083 m .00375 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b(J.)f(Chem.)e(Ph)n(ys.)h Fl(101)p Fn(,)i(3268)3 556 y(\(1994\).)-150 648 y([28])35 b(D.)25 b(W)-6 b(etzig,)27 b(M.)g(Rutk)n(o)n(wski,)e(W.)h(Ettric)n(h,)h(R.)e(Da)n(vid,)h(and)f(H.) 3 739 y(Zac)n(harias,)i(Surf.)f(Sci.)g Fl(402)p Fn(,)g(232)h(\(1998\).) -150 830 y([29])35 b(A.)18 b(Gross)h(and)f(M.)h(Sc)n(he\017er,)h(Prog.) g(Surf.)e(Sci.)h Fl(53)p Fn(,)h(187)g(\(1996\).)1946 5645 y Fp(6)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF