From: Martin Mares Date: Mon, 18 Feb 2008 16:25:03 +0000 (+0100) Subject: Snad jiz finalni verze kapitoly o FFT. X-Git-Url: http://mj.ucw.cz/gitweb/?a=commitdiff_plain;h=69363708335681b2f6f321b9f6a4762ebbcd6a70;p=ads2.git Snad jiz finalni verze kapitoly o FFT. --- diff --git a/8-fft/8-fft.tex b/8-fft/8-fft.tex index cd67ba8..b892980 100644 --- a/8-fft/8-fft.tex +++ b/8-fft/8-fft.tex @@ -87,10 +87,8 @@ Pot \s{Definice:} -\>{\I Diskretní Fourierova transformace (DFT)} -je funkce $f: { {\bb C} ^n} \rightarrow { {\bb C} ^n}$ pøiøazující ka¾dému vektoru~$x\in {\bb C}^n$ -vektor~$y\in{\bb C}^n$ takový, ¾e pro ka¾dé~$j$ platí: -$$y_{j} = \sum \limits ^{n-1}_{k=0} x_{k} \cdot \omega ^{jk}.$$ +\>{\I Diskretní Fourierova transformace} $(DFT)$ +je funkce $f: { {\bb C} ^n} \rightarrow { {\bb C} ^n}$, kde $y=f(x) \equiv \forall j \ y_{j} = \sum \limits ^{n-1}_{k=0} x_{k} \cdot \omega ^{k}$. \s{Jak najít inverzní matici?} Víme, ¾e $\Omega =\Omega ^{T}$ proto¾e $\omega ^{jk} = \omega ^{kj}$. @@ -165,19 +163,10 @@ $\O(n \log n)$ pro vyhodnocen \figure{img.eps}{Pøíklad prùbìhu algoritmu na vstupu velikosti 8}{3in} -\>Obrázek ukazuje zapojení kombinaèního obvodu pro DFT pro vstup velikosti 8. Èíslo $\log n$ znaèí poèet hladin, tj. u nás $\log 8 = 3$ hladiny. +\>Obrázek ukazuje zapojení kombinaèního obvodu pro DFT pro vstup velikosti~8. Hladin bude v¾dy $\log_2 n$, tj. v~na¹em pøípadì $\log_2 8 = 3$ hladiny. -\>Základem je kombinaèní obvod tzv. motýlek. (Na obrázku znázornìn dvìma èarami, pøekøí¾enými v jejich støedech). Co motýlek dìlá? Podívejme se na následující obrázek. - -\figure{img2.eps}{Kombinaèní obvod tzv. motýlek}{1in} - -\>Vstup jsou komplexní èísla $x_1$ a $x_2$ a výstup komplexní èísla $y_1$ a $y_2$, taková ¾e -\>$y_1 = x_1 + \omega^j \cdot x_2$ -\>$y_2 = x_1 - \omega^j \cdot x_2$ - -\>kde index $j$ znaèí - -\>V¹imìme si poøadí vstupních hodnot (koeficientù). Èísla jsou v binarním tvaru 0-7 pøeètená pozpátku. +\>Podívejme se na pravou èást obrázku, tedy výstup celého obvodu. Èerná koleèka pøedstavují podobvody, rovnice vedle nich operaci, kterou provádìjí. Hodnoty $y_j$ znaèí hodnotu polynomu $P$ v bodì $\omega^j$ kde $\omega^j$ je $j-tá$ mocnina primitivní $n$-té odmocniny z jednièky. K jejímu spoètení ale potøebujeme znát hodnoty $s_k$ a $l_k$ kde $k$ je z intervalu $[0, {n/2} -1]$ a $s_k$ a $l_k$ jsou hodnoty polynomu stupnì ${n/2}$ v bodì $\omega^{2k}$. V polynomu $s$ jsou sudé koeficienty a v polynomu $l$ liché koeficienty polynomu $P$. Vidíme ze se jedná pøesnì o ná¹ rekurzivní algoritmus pro poèítání FFT a tímto zpùsobem postavíme celou sí». +\>Tímto obvodem jsme tedy získali nerekurzivní algoritmus pro poèítání FFT. V¹imìme si poøadí vstupních hodnot (koeficientù). Èísla jsou v binárním tvaru 0--7 pøeètená pozpátku. Pro pøedstavu jaké koeficienty polynomu $P$ se objevují v rùzných hladinách, na obrázku jsou naznaèena jejich èísla spolu s pøíslu¹nými mocninami primitivní $n$-té odmocniny z jednièky. \s{Z toho:} @@ -189,5 +178,4 @@ a $\O(n)$ hradly na hladin \endlist - \bye diff --git a/8-fft/img.eps b/8-fft/img.eps index 5a4b207..577c491 100644 --- a/8-fft/img.eps +++ b/8-fft/img.eps @@ -1,518 +1,1072 @@ -%!PS-Adobe-2.0 EPSF-1.2 -%%Creator: Xara X -%%For: (Unregistered user) (Unregistered company) -%%Title: (Priklad-prubehu-velikosti-8.xar) -%%CreationDate: (09/12/07) (07:34 PM) -%%BoundingBox: 6 4 265 132 -%%HiResBoundingBox: 6.135 4.944 264.089 131.873 -%%AWColourTable -%%+h (Red) 0.0 100.0 100.0 -%%+h (Orange-Red) 15.0 100.0 100.0 -%%+h (Orange) 30.0 100.0 100.0 -%%+h (Orange-Yellow) 45.0 100.0 100.0 -%%+h (Yellow) 60.0 100.0 100.0 -%%+h (Yellow-Chartreuse) 75.0 100.0 100.0 -%%+h (Chartreuse) 90.0 100.0 100.0 -%%+h (Chartreuse-Green) 105.0 100.0 100.0 -%%+h (Green) 120.0 100.0 100.0 -%%+h 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spconcattransfer iw ih bpc imat [ -setupimageproc/exec load/dup load dup ] cvx nullproc nullproc true -3 colorimage}bd}if not endnoload ncolors 4 eq dup dup not startnoload{ -/stuffclut{cmykindex 3 -1 roll put}bd/ftoint{1 exch sub 255 mul round -cvi}bd/4compute{exch bit4x mul round cvi get 255 div}bd/computecmykclut{setuprgbcluts -/bit4x rgbclut length 3 idiv 4 mul 4 sub def/cmykclut bit4x 4 add -string def/cclut cmykclut def/mclut cclut 1 bit4x defsubclut/yclut -cclut 2 bit4x defsubclut/kclut cclut 3 bit4x defsubclut/cmykindex 0 -def 0 1 bit1x{dup/cmykindex exch bit1x exch sub 4 mul def 3 mul dup -rclut exch get 255 div exch dup gclut exch get 255 div exch bclut exch -get 255 div setrgbcolor currentcmykcolor ftoint kclut stuffclut ftoint -yclut stuffclut ftoint mclut stuffclut ftoint cclut stuffclut}for}bd -/doclutimage{/rgbclut xd pop invalidcolortable?{computecmykclut}if -/4compute cclut mclut yclut kclut spconcattransfer iw ih bpc imat -[ setupimageproc/exec load/dup load dup dup ] cvx nullproc nullproc -nullproc true 4 colorimage}bd}if not endnoload ncolors 0 eq dup dup -not startnoload{/lookupandstore{3 mul 3 getinterval putinterval exch -3 add exch 3 copy}bd/8lookup/lookupandstore ld/4lookup{/byte 1 index -def -4 bitshift lookupandstore byte 15 and lookupandstore}bd/2lookup{ -/byte 1 index def -6 bitshift lookupandstore byte -4 bitshift 3 and -lookupandstore byte -2 bitshift 3 and lookupandstore byte 3 and lookupandstore}bd -/colorexpand{mystringexp 0 rgbclut 3 copy 7 -1 roll/mylookup load -forall pop pop pop pop pop}bd/createexpandstr{/mystringexp exch mystring -length mul string def}bd/doclutimage{/rgbclut xd pop/mylookup bpc 8 -eq{3 createexpandstr/8lookup}{bpc 4 eq{6 createexpandstr/4lookup}{12 -createexpandstr/2lookup}ifelse}ifelse ld iw ih bpc imat [ setupimageproc -/exec load/colorexpand load/exec load] cvx false 3 colorimage}bd}if -not endnoload/colorimage where{pop true}{false}ifelse dup{/do24image{iw -ih 8 imat setupimageproc false 3 colorimage}bd}if dup dup startnoload -not{/rgbtogray{/str xd/len str length def/smlen len 3 idiv def/rstr -str def/gstr str 1 len 1 sub getinterval def/bstr str 2 len 2 sub getinterval -def str dup 0 1 smlen 1 sub{dup 3 mul rstr 1 index get .3 mul gstr -2 index get .59 mul add bstr 3 -1 roll get .11 mul add round cvi put -dup}for pop 0 smlen getinterval}bd/do24image{iw ih 8 imat [ setupimageproc -/exec load/rgbtogray load/exec load ] cvx bind image}bd}if endnoload -/doimage{iw ih 8 imat setupimageproc image}bd level2{dontloadlevel1 -restore}if level2 not{save/dontloadlevel2 xd}if/myappcolorspace/DeviceRGB -def/rgbclut 0 def/doclutimage{/rgbclut xd pop bpc dup 8 eq{pop 255}{4 -eq{15}{3}ifelse}ifelse/hival xd [/Indexed myappcolorspace hival rgbclut] -setcolorspace myimagedict dup begin/Width iw def/Height ih def/Decode -[0 hival] def/ImageMatrix imat def/DataSource setupimageproc def/BitsPerComponent -bpc def/Interpolate smoothflag def end image}bd/do24image{myappcolorspace -setcolorspace myimagedict dup begin/Width iw def/Height ih def/Decode -[0 1 0 1 0 1] def/ImageMatrix imat def/DataSource setupimageproc def -/BitsPerComponent 8 def/Interpolate smoothflag def end image}bd level2 -not{dontloadlevel2 restore}if -/NumSteps{dtransform matrix defaultmatrix idtransform Pythag currentscreen -pop pop 72 exch div div}bd/FindMinSteps{v_ft 4 eq{urx startX sub abs -llx startX sub abs Max ury startY sub abs lly startY sub abs Max Pythag -2 3.14159265 mul mul 0}{v_ft 2 eq{endY startY sub endX startX sub Pythag -endY2 startY sub endX2 startX sub Pythag gt{endY startY sub endX startX -sub}{endY2 startY sub endX2 startX sub}ifelse}{endY startY sub endX -startX sub}ifelse}ifelse NumSteps}bd/cxe{/v_cxe exch def}bd/cxm{pop -/v_cxm exch def}bd/cxmt{pop pop}bd/cxt{pop}bd/S_eoclip{currentflat{{eoclip}stopped{dup -currentflat exch sub 20 gt{([Error: PathTooComplex; OffendingCommand: eoclip]\n)print -flush exit}{currentflat 2 add setflat}ifelse}{exit}ifelse}loop setflat}bd -/S_clip{currentflat{{clip}stopped{dup currentflat exch sub 20 gt{([Error: PathTooComplex; OffendingCommand: clip]\n)print -flush exit}{currentflat 2 add setflat}ifelse}{exit}ifelse}loop setflat}bd -/S_eofill{currentflat{{eofill}stopped{dup currentflat exch sub 20 -gt{([Error: PathTooComplex; OffendingCommand: eofill]\n)print flush -exit}{currentflat 2 add setflat}ifelse}{exit}ifelse}loop setflat}bd -/gpbbx{pathbbox/ury exch def/urx exch def/lly exch def/llx exch def}bd -/lineargfill{initgfill{false initgfx/distance endX startX sub endY -startY sub Pythag def/incD distance Steps div def endY startY sub endX -startX sub atan newpath llx lly urx ury Bx startX startY translate -rotate gpbbx eGy ssg newpath llx lly urx ury Bx S_eofill sGy ssg newpath -llx lly 0 ury Bx S_eofill/fillX 0 def 0 1 Steps 1 sub{stepgfx newpath -fillX lly fillX incD add dup/fillX exch def ury Bx S_eofill pop}for}if}bd -/radialgfill{initgfill{false initgfx/distance endX startX sub endY -startY sub Pythag def/incD distance Steps div def eGy ssg newpath llx -lly urx ury Bx S_eofill/distance 0 def 0 1 Steps 1 sub{stepgfx newpath -startX startY distance 0 360 arc closepath distance incD add dup/distance -exch def 0 rmoveto startX startY distance 0 360 arc closepath S_eofill -pop}for}if}bd/ellipticgfill{initgfill{true initgfx sGy ssg newpath -llx lly urx ury Bx S_eofill [ endX startX sub endY startY sub endX2 -startX sub endY2 startY sub startX startY ] concat Steps 1 sub -1 0{stepgfx -/i exch def 0 0 moveto 0 0 i Steps div 0 360 arc fill}for}if}bd/conicalgfill{initgfill{urx -startX sub abs llx startX sub abs Max ury startY sub abs lly startY -sub abs Max Pythag startY endY sub startX endX sub Pythag div/radius -exch def true initgfx [ endX startX sub endY startY sub startY endY -sub endX startX sub startX startY ] concat/slice 180 Steps div def -/startangle 0 def Steps -1 0{pop stepgfx 0 0 moveto 0 0 radius startangle -neg dup slice add arc fill 0 0 moveto 0 0 radius startangle dup slice -add dup/startangle exch def arc fill}for}if}bd/initgfill{gpbbx{S_eoclip}{S_clip}ifelse -startX endX eq startY endY eq and sGy eGy eq or dup{sGy ssg newpath -llx lly urx ury Bx S_eofill}if not}bd/initgfx{/flag exch def flag{sGy -eGy/sGy exch def/eGy exch def}if eGy sGy sub abs 256 mul FindMinSteps -Min 256 Min ceiling 1 Max/Steps exch def eGy sGy sub Steps div/incGy -exch def sGy/mGy exch def}bd/stepgfx{mGy ssg mGy incGy add/mGy exch -def}bd/linearfill{initfill{false initfx endX startX sub endY startY -sub Pythag/distance exch def/incD distance Steps div def endY startY -sub endX startX sub atan newpath llx lly urx ury Bx startX startY translate -rotate gpbbx v_cxe 0 eq{eR eG eB setgfillrgb}{eH eS eV setgfillhsb}ifelse -newpath llx lly urx ury Bx S_eofill v_cxe 0 eq{sR sG sB setgfillrgb}{sH -sS sV setgfillhsb}ifelse newpath llx lly 0 ury Bx S_eofill/fillX 0 -def 0 1 Steps 1 sub{stepfx newpath fillX lly fillX incD add dup/fillX -exch def ury Bx S_eofill pop}for}if}bd/radialfill{initfill{false initfx -endX startX sub endY startY sub Pythag/distance exch def/incD distance -Steps div def v_cxe 0 eq{eR eG eB setgfillrgb}{eH eS eV setgfillhsb}ifelse -newpath llx lly urx ury Bx S_eofill/distance 0 def 0 1 Steps 1 sub{stepfx -newpath startX startY distance 0 360 arc closepath distance incD add -dup/distance exch def 0 rmoveto startX startY distance 0 360 arc closepath -S_eofill pop}for}if}bind def/ellipticalfill{initfill{true initfx v_cxe -0 eq{sR sG sB setgfillrgb}{sH sS sV setgfillhsb}ifelse newpath llx -lly urx ury Bx S_eofill [ endX startX sub endY startY sub endX2 startX -sub endY2 startY sub startX startY ] concat Steps 1 sub -1 0{stepfx -/i exch def 0 0 moveto 0 0 i Steps div 0 360 arc fill}for v_cxe 0 -eq{sR sG sB eR eG eB/sB exch def/sG exch def/sR exch def/eB exch def -/eG exch def/eR exch def}if}if}bd/conicalfill{initfill{urx startX -sub abs llx startX sub abs Max ury startY sub abs lly startY sub abs -Max Pythag startY endY sub startX endX sub Pythag div/radius exch def -true initfx [ endX startX sub endY startY sub startY endY sub endX -startX sub startX startY ] concat/slice 180 Steps div def/startangle -0 def Steps -1 0{pop stepfx 0 0 moveto 0 0 radius startangle neg dup -slice add arc fill 0 0 moveto 0 0 radius startangle dup slice add dup -/startangle exch def arc fill}for}if}bd/initfill{gpbbx{S_eoclip}{S_clip}ifelse -startX endX eq startY endY eq and v_cxe 2 ne sR eR eq sG eG eq and -sB eB eq and and or dup{sR sG sB setgfillrgb newpath llx lly urx ury -Bx S_eofill}if not}bd/initfx{/flag exch def v_cxe 0 eq{flag{sR sG sB -eR eG eB/sB exch def/sG exch def/sR exch def/eB exch def/eG exch def -/eR exch def}if eR sR sub abs 256 mul eG sG sub abs 256 mul Max eB -sB sub abs 256 mul Max FindMinSteps Min 256 Min ceiling 1 Max/Steps -exch def/incR eR sR sub Steps div def/incG eG sG sub Steps div def -/incB eB sB sub Steps div def sR/mR exch def sG/mG exch def sB/mB -exch def}{sR sG sB rgb2hsb/sV exch def/sS exch def/sH exch def eR eG -eB rgb2hsb/eV exch def/eS exch def/eH exch def eH sH sub abs v_cxe -1 eq{dup 0.5 gt{1 exch sub}if}{dup 0.5 lt{1 exch sub}if}ifelse 256 -mul eS sS sub abs 256 mul Max eV sV sub abs 256 mul Max FindMinSteps -Min 256 Min ceiling 1 Max/Steps exch def v_cxe 1 eq{/incH eH sH sub -dup abs 0.5 gt{dup 0 ge{1 sub}{1 add}ifelse}if Steps div def/incS eS -sS sub Steps div def/incV eV sV sub Steps div def}{/incH eH sH sub -dup abs 0.5 le{dup 0 ge{1 sub}{1 add}ifelse}if Steps div def/incS eS -sS sub Steps div def/incV eV sV sub Steps div def}ifelse flag{/sH eH -/eH sH def def/sS eS/eS sS def def/sV eV/eV sV def def/incH incH neg -def/incS incS neg def/incV incV neg def}if}ifelse}bd/stepfx{v_cxe 0 -eq{mR mG mB setgfillrgb mR incR add/mR exch def mG incG add/mG exch -def mB incB add/mB exch def}{sH sS sV setgfillhsb sH incH add dup 0 -le{1 add}{dup 1 ge{1 sub}if}ifelse/sH exch def sS incS add/sS exch -def sV incV add/sV exch def}ifelse}bd -/ar{}bd/arr{pop pop pop pop pop pop pop}bd/ae{pop pop pop pop pop -pop}bd/aoa{pop}bd/apl{pop}bd/apc{}bd/aof{pop pop}bd/aafs{pop pop pop}bd -/O{pop}bd/R{pop}bd/axop{pop pop pop pop}bd/g{/v_ft 0 def/v_fc 0 def -/v_fm 0 def/v_fy 0 def 1 exch sub/v_fk exch def/v_fct 0 def}bd/G{ -/v_sc 0 def/v_sm 0 def/v_sy 0 def 1 exch sub/v_sk exch def/v_sct 0 -def}bd/k{/v_fk exch def/v_fy exch def/v_fm exch def/v_fc exch def/v_ft -0 def/v_fct 0 def}bd/K{/v_sk exch def/v_sy exch def/v_sm exch def/v_sc -exch def/v_sct 0 def}bd/Xa{/v_fb exch def/v_fg exch def/v_fr exch def -/v_ft 0 def/v_fct 1 def}bd/XA{/v_sb exch def/v_sg exch def/v_sr exch -def/v_sct 1 def}bd/a_tc{exch pop 1 exch sub dup 3 -1 roll exch div -exch dup 4 -1 roll exch div 3 1 roll dup 5 -1 roll exch div 4 1 roll -5 -1 roll exch div 4 1 roll}bd/x{a_tc k}bd/X{a_tc K}bd/Xx{0 eq{x}{pop -pop Xa}ifelse}bd/XX{0 eq{X}{pop pop XA}ifelse}bd/awr{/v_wr exch def}bd -/w{setlinewidth}bd/j{setlinejoin}bd/J{setlinecap}bd/d{setdash}bd/asc{pop -pop J}bd/aec{pop pop J}bd/csah{pop pop pop}bd/ceah{pop pop pop}bd/cst{pop -pop}bd/cdp{pop}bd/m{moveto}bd/l{lineto}bd/c{curveto}bd/Bx{4 copy 5 -1 roll 4 2 roll 5 -1 roll m l l l closepath}bd/Cp{Bx clip newpath}bd -/a_fp{gsave v_wr 0 ne v_ft 0 eq{setfillcolor{eofill}{fill}ifelse}{v_ft -1 eq{linearfill}{v_ft 2 eq{ellipticalfill}{v_ft 3 eq{radialfill}{v_ft -4 eq{conicalfill}{v_ft 8 eq{lineargfill}{v_ft 9 eq{ellipticgfill}{v_ft -10 eq{radialgfill}{conicalgfill}ifelse}ifelse}ifelse}ifelse}ifelse}ifelse}ifelse}ifelse -grestore}bd/*u{/p_count p_count 1 add def}bd/*U{/p_count p_count 1 -sub def p_count 0 eq{vis_flag{p_render}{newpath}ifelse}if}bd/B{/p_render{a_fp -setstrokecolor stroke}bd p_count 0 eq{vis_flag{p_render}{newpath}ifelse}if}bd -/b{closepath B}bd/F{/p_render{a_fp newpath}bd p_count 0 eq{vis_flag{p_render}{newpath}ifelse}if}bd -/f{closepath F}bd/S{/p_render{setstrokecolor stroke}bd p_count 0 eq{vis_flag{p_render}{newpath}ifelse}if}bd -/s{closepath S}bd/H{/p_render{newpath}bd p_count 0 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xd}bd/rgb2gray{0.109 mul exch 0.586 mul add exch 0.305 mul +add}bd/cmyk2rgb{3{dup 5 -1 roll add dup 1 gt{pop 1}if 1 exch sub exch}repeat +pop}bd/rgb2cmyk{3{1.0 exch sub 3 1 roll}repeat 3 copy 2 copy gt{exch}if +pop 2 copy gt{exch}if pop dup 0.5 gt{0.5 sub dup 3{5 1 roll dup 3 1 +roll sub}repeat 5 1 roll pop}{pop 0}ifelse}bd/cmyk2hsb{3{dup 5 -1 roll +add 1 exch sub dup 0 lt{pop 0}if exch}repeat pop rgb2hsb}bd/rgb2hsb{setrgbcolor +currenthsbcolor}bd/readcurve{exch 255.0 mul 0.5 add cvi get 255.0 div}bd +/rgb2devcmyk{3 copy dup 3 1 roll eq 3 1 roll eq v_keyg 1 eq and and{pop +pop 1 exch sub 0 0 0 4 -1 roll}{/ucurve where{pop 3{1.0 exch sub 3 +1 roll}repeat 3 copy 2 copy gt{exch}if pop 2 copy gt{exch}if pop dup +ucurve readcurve exch bcurve readcurve clamp01 3{5 1 roll dup 3 1 roll +sub clamp01}repeat 5 1 roll pop 4 1 roll ycurve readcurve 4 1 roll +mcurve readcurve 4 1 roll ccurve readcurve 4 1 roll}{rgb2cmyk}ifelse}ifelse}def +/rgb2keyG{3 copy dup 3 1 roll eq 3 1 roll eq and{pop pop}{Max3}ifelse +1 exch sub bcurve readcurve clamp01}bd/rgb2key{Max3 1 exch sub bcurve +readcurve clamp01}bd/rgb2cyanG{3 copy dup 3 1 roll eq 3 1 roll eq and{pop +pop pop 0}{rgb2cyan}ifelse}bd/rgb2cyan{3 copy Max3 1 exch sub ucurve +readcurve 4 1 roll pop pop 1 exch sub exch sub ccurve readcurve clamp01}bd +/rgb2magentaG{3 copy dup 3 1 roll eq 3 1 roll eq and{pop pop pop 0}{rgb2magenta}ifelse}bd +/rgb2magenta{3 copy Max3 1 exch sub ucurve readcurve 4 1 roll pop +1 exch sub 3 1 roll pop sub mcurve readcurve clamp01}bd/rgb2yellowG{3 +copy dup 3 1 roll eq 3 1 roll eq and{pop pop pop 0}{rgb2yellow}ifelse}bd +/rgb2yellow{3 copy Max3 1 exch sub ucurve readcurve 4 1 roll 1 exch +sub 4 1 roll pop pop sub ycurve readcurve clamp01}bd/rgb2plategray{v_keyg +0 eq v_plate v_cpky eq{{rgb2key}{rgb2keyG}ifelse}{v_plate v_cpyl eq{{rgb2yellow}{rgb2yellowG}ifelse}{v_plate +v_cpmg eq{{rgb2magenta}{rgb2magentaG}ifelse}{v_plate v_cpcy eq{{rgb2cyan}{rgb2cyanG}ifelse}{{rgb2key}{rgb2keyG}ifelse}ifelse}ifelse}ifelse}ifelse +1 exch sub setgray}bd/dc{0 def}bd/aca{/v_cpnone 0 def/v_cpcy 1 def +/v_cpyl 2 def/v_cpmg 3 def/v_cpky 4 def/v_gseps 0 def/v_keyg 0 def +/v_plate v_cpnone def/v_mono 0 def/v_wr dc/v_fc dc/v_fm dc/v_fy dc +/v_fk dc/v_fg dc/v_fr dc/v_fg dc/v_fb dc/v_sc dc/v_sm dc/v_sy dc/v_sk +dc/v_sg dc/v_sr dc/v_sg dc/v_sb dc/v_sct 0 def/v_fct 0 def/v_ft 0 def +/v_cxe 0 def/v_cxm 0 def/v_sa -1 def/v_ea -1 def/sR dc/sG dc/sB dc +/mR dc/mG dc/mB dc/eR dc/eG dc/eB dc/sC dc/sM dc/sY dc/sK dc/eC dc +/eM dc/eY dc/eK dc/sH dc/sS dc/sV dc/eH dc/eS dc/eV dc/sGy dc/eGy +dc/mGy dc/ci_datasrc dc/ci_matrix dc/ci_dataleft dc/ci_buf dc/ci_dataofs +dc/ci_y dc/rciBuf dc/cbslw dc/cmiBuf dc/cPalette dc/cpci_datasrc dc +/cpci_matrix dc/cpci_bpp dc/cpci_y dc/cpci_sampsleft dc/cpci_nextcol +dc/cpci_buf dc/startX dc/startY dc/endX dc/endY dc/endX2 dc/endY2 dc +/fillX dc/urx dc/ury dc/llx dc/lly dc/incD dc/distance dc/slice dc +/startangle dc/Steps dc/incH dc/incS dc/incV dc/incR dc/incG dc/incB +dc/incGy dc 0.25 setlinewidth [] 0 setdash 0 setlinejoin 0 setlinecap}bd +aca/setplategray{v_plate v_cpky eq{1 exch sub setgray pop pop pop}{v_plate +v_cpyl eq{pop 1 exch sub setgray pop pop}{v_plate v_cpmg eq{pop pop +1 exch sub setgray pop}{v_plate v_cpcy eq{pop pop pop 1 exch sub setgray}{1 +exch sub setgray pop pop pop}ifelse}ifelse}ifelse}ifelse}bd/setplatecolor{v_plate +v_cpky eq{1 exch sub 0 0 0 4 -1 roll setcmykcolor pop pop pop}{v_plate +v_cpyl eq{pop 1 exch sub 0 0 0 4 2 roll setcmykcolor pop pop}{v_plate +v_cpmg eq{pop pop 1 exch sub 0 0 0 4 1 roll setcmykcolor pop}{v_plate +v_cpcy eq{pop pop pop 1 exch sub 0 0 0 setcmykcolor}{1 exch sub 0 0 +0 4 -1 roll setcmykcolor pop pop pop}ifelse}ifelse}ifelse}ifelse}bd +/setcmykcolor where{pop}{/setcmykcolor{cmyk2rgb setrgbcolor}bd}ifelse +/setlogcmykcolor{v_gseps 1 eq{v_mono 1 eq{1 exch sub setgray pop pop +pop}{setcmykcolor}ifelse}{v_mono 1 eq{cmyk2rgb rgb2gray setgray}{setcmykcolor}ifelse}ifelse}bd +/setlogrgbcolor{v_gseps 1 eq{v_mono 1 eq{rgbtoplategray}{rgb2devcmyk +setplatecolor}ifelse}{v_mono 1 eq{rgb2gray setgray}{systemdict begin +setrgbcolor end}ifelse}ifelse}bd/setfillcolor{v_fct 0 eq{v_fc v_fm +v_fy v_fk setlogcmykcolor}{v_fr v_fg v_fb setlogrgbcolor}ifelse}bd +/setstrokecolor{v_sct 0 eq{v_sc v_sm v_sy v_sk setlogcmykcolor}{v_sr +v_sg v_sb setlogrgbcolor}ifelse}bd/setgfillcmyk{v_gseps 1 eq{v_mono +1 eq{cmyk2rgb rgb2plategray}{cmyk2rgb rgb2devcmyk setplatecolor}ifelse}{v_mono +1 eq{cmyk2rgb rgb2gray setgray}{setcmykcolor}ifelse}ifelse}bd/setgfillrgb{v_gseps +1 eq{v_mono 1 eq{rgb2plategray}{rgb2devcmyk setplatecolor}ifelse}{v_mono +1 eq{rgb2gray setgray}{systemdict begin setrgbcolor end}ifelse}ifelse}bd +/setgfillhsb{v_gseps 1 eq{v_mono 1 eq{systemdict begin sethsbcolor +currentrgbcolor end rgb2plategray}{systemdict begin sethsbcolor currentrgbcolor +end rgb2devcmyk setplatecolor}ifelse}{v_mono 1 eq{systemdict begin +sethsbcolor currentgray end setgray}{systemdict begin sethsbcolor end}ifelse}ifelse}bd +/Max{2 copy lt{exch}if pop}bd/Max3{2 copy lt{exch}if pop 2 copy lt{exch}if +pop}bd/Min{2 copy gt{exch}if pop}bd/Min3{2 copy gt{exch}if pop 2 copy +gt{exch}if pop}bd/clamp{3 1 roll Max 2 1 roll Min}bd/clamp01{0 Max +1 Min}bd/Pythag{dup mul exch dup mul add sqrt}bd/ssc{DeviceRGB setcolorspace +setcolor}bd/ssg{setgray}bd/p_render{}def/p_count 0 def/vis_flag true +def/DataString 3 string def/DataSrc{currentfile DataString readhexstring +pop}bd/DataStr1 1 string def/DataStr2 1 string def/DataStr3 1 string +def/DataSrc1{DataStr1}bd/DataSrc2{DataStr2}bd/DataSrc3{DataStr3}bd +/colorimage where{pop/ci{colorimage}bd}{/ci{pop pop/ci_datasrc exch +def matrix invertmatrix/ci_matrix exch def pop/ci_dataleft 0 def/ci_buf()def +/ci_dataofs 0 def 0 1 3 -1 roll 1 sub{/ci_y exch def dup 0 1 3 -1 +roll 1 sub{0 1 2{pop ci_dataleft 0 eq{ci_datasrc dup length/ci_dataleft +exch def/ci_buf exch def/ci_dataofs 0 def}if ci_buf ci_dataofs get +255 div/ci_dataofs ci_dataofs 1 add def/ci_dataleft ci_dataleft 1 sub +def}for setrgbcolor dup ci_y 3 -1 roll 1 add ci_y 1 add 4 copy 5 1 +roll 4 2 roll 5 -1 roll 1 1 4{pop ci_matrix transform 8 2 roll}for +m l l l closepath fill}for}for pop}bd}ifelse/rci{/rciBuf 4 index 3 +index mul 7 add 8 div floor cvi string def{currentfile rciBuf readhexstring +pop}bind false 3 ci}bd/cbsl{2 eq/cbslL2 xd 5 index/cbslw xd translate +scale 8 [ 3 index 0 0 5 index 0 0 ] cbslL2{/DataStr1 cbslw string def +currentfile/ASCII85Decode filter/RunLengthDecode filter DataStr1 readstring +pop pop/DataStr2 cbslw string def currentfile/ASCII85Decode filter +/RunLengthDecode filter DataStr2 readstring pop pop/DataStr3 cbslw +string def currentfile/ASCII85Decode filter/RunLengthDecode filter +DataStr3 readstring pop pop{DataStr1}bind{DataStr2}bind{DataStr3}bind +true}{/DataSrc load false}ifelse 3 ci}bd/gbsl{2 eq/gbslL2 xd 5 index +/gbslw xd translate scale 8 [ 3 index 0 0 5 index 0 0 ] gbslL2{/DataStr1 +gbslw string def currentfile/ASCII85Decode filter/RunLengthDecode filter +DataStr1 readstring pop pop{DataStr1}bind}{/DataStr1 gbslw string def +currentfile DataSrc1 readhexstring pop pop{DataStr1}bind}ifelse image}bd +/cmi{/cmiBuf 4 index 3 index mul 7 add 8 div floor cvi string def{currentfile +cmiBuf readhexstring pop}bind image}bd/cpal{4 mul string/cPalette exch +def currentfile cPalette readhexstring pop}bd/cpci{/cpci_datasrc exch +def matrix invertmatrix/cpci_matrix exch def/cpci_bpp exch def cpci_init +0 1 3 -1 roll 1 sub{/cpci_y exch def dup cpci_bpp 4 eq{cpci_sampsleft +1 eq{/cpci_sampsleft 0 def}if}if 0 1 3 -1 roll 1 sub{cpci_nextcol dup +cpci_y 3 -1 roll 1 add cpci_y 1 add 4 copy 5 1 roll 4 2 roll 5 -1 roll +1 1 4{pop cpci_matrix transform 8 2 roll}for m l l l closepath fill}for}for +pop}bd/cpci_init{/cpci_sampsleft 0 def}bd/cpci_buf 1 string def/cpci_nextcol{cpci_bpp +1 eq{cpci_sampsleft 0 eq{currentfile cpci_buf readhexstring pop pop +/cpci_sampsleft 8 def}if cpci_buf dup 0 get dup 1 and setgray -1 bitshift +1 exch put/cpci_sampsleft cpci_sampsleft 1 sub def}{cpci_bpp 4 eq{cpci_sampsleft +0 eq{currentfile cpci_buf readhexstring pop pop/cpci_sampsleft 2 def}if +cpci_buf 0 get dup 15 and exch -4 bitshift cpci_buf 0 3 -1 roll put +/cpci_sampsleft cpci_sampsleft 1 sub def}{currentfile cpci_buf readhexstring +pop 0 get}ifelse 4 mul dup 2 add cPalette exch get 255 div exch dup +1 add cPalette exch get 255 div exch cPalette exch get 255 div setrgbcolor}ifelse}bd +/setup1asciiproc{[ currentfile mystring/readhexstring cvx/pop cvx +] cvx bind}bd/setup1binaryproc{[ currentfile mystring/readstring cvx +/pop cvx ] cvx bind}bd level2{save/dontloadlevel1 xd}if/iw 0 def/ih +0 def/im_save 0 def/setupimageproc 0 def/polarity 0 def/smoothflag +0 def/mystring 0 def/bpc 0 def/beginimage{/im_save save def dup 0 eq{pop +/setup1binaryproc}{1 eq{/setup1asciiproc}{(error, can't use level2 data acquisition procs for level1)print +flush}ifelse}ifelse/setupimageproc exch ld/polarity xd/smoothflag xd +/imat xd/mystring exch string def/bpc xd/ih xd/iw xd}bd/endimage{im_save +restore}bd/1bitbwcopyimage{1 setgray 0 0 moveto 0 1 rlineto 1 0 rlineto +0 -1 rlineto closepath fill 0 setgray iw ih polarity imat setupimageproc +imagemask}bd/1bitcopyimage{setrgbcolor 0 0 moveto 0 1 rlineto 1 0 rlineto +0 -1 rlineto closepath fill setrgbcolor iw ih polarity imat setupimageproc +imagemask}bd/1bitmaskimage{setrgbcolor iw ih polarity [iw 0 0 ih 0 +0] setupimageproc imagemask}bd level2{dontloadlevel1 restore}if level2 +not{save/dontloadlevel2 xd}if/setup2asciiproc{currentfile/ASCII85Decode +filter/RunLengthDecode filter}bd/setup2binaryproc{currentfile/RunLengthDecode +filter}bd/myimagedict 9 dict dup begin/ImageType 1 def/MultipleDataSource +false def end def/im_save 0 def/setupimageproc 0 def/polarity 0 def +/smoothflag 0 def/mystring 0 def/bpc 0 def/ih 0 def/iw 0 def/beginimage{ +/im_save save def dup 2 eq{pop/setup2binaryproc}{dup 3 eq{pop/setup2asciiproc}{0 +eq{/setup1binaryproc}{/setup1asciiproc}ifelse}ifelse}ifelse/setupimageproc +exch ld{[ 1 0 ]}{[ 0 1 ]}ifelse/polarity xd/smoothflag xd/imat xd/mystring +exch string def/bpc xd/ih xd/iw xd}bd/endimage{im_save restore}bd/1bitbwcopyimage{1 +ssg 0 0 moveto 0 1 rlineto 1 0 rlineto 0 -1 rlineto closepath fill +0 ssg myimagedict dup begin/Width iw def/Height ih def/Decode polarity +def/ImageMatrix imat def/DataSource setupimageproc def/BitsPerComponent +1 def/Interpolate smoothflag def end imagemask}bd/1bitcopyimage{ssc +0 0 moveto 0 1 rlineto 1 0 rlineto 0 -1 rlineto closepath fill ssc +myimagedict dup begin/Width iw def/Height ih def/Decode polarity def +/ImageMatrix imat def/DataSource setupimageproc def/BitsPerComponent +1 def/Interpolate smoothflag def end imagemask}bd/1bitmaskimage{ssc +myimagedict dup begin/Width iw def/Height ih def/Decode polarity def +/ImageMatrix imat def/DataSource setupimageproc def/BitsPerComponent +1 def/Interpolate smoothflag def end imagemask}bd level2 not{dontloadlevel2 +restore}if +level2{save/dontloadlevel1 xd}if/startnoload{{/noload save def}if}bd +/endnoload{{noload restore}if}bd/testsystemdict{where{systemdict eq{true}{false}ifelse}{false}ifelse}bd +/ncolors 1 def/colorimage where{pop true}{false}ifelse{/ncolors 0 +statusdict begin/processcolors where{pop pop processcolors}{/deviceinfo +where{pop deviceinfo/Colors known{pop{deviceinfo/Colors get}}if}if}ifelse +end def ncolors 0 ne{/colorimage testsystemdict/setcolortransfer testsystemdict +/currentcolortransfer testsystemdict/currentcmykcolor testsystemdict +and and and not{/ncolors 0 def}if}if}if ncolors dup 1 ne exch dup 3 +ne exch 4 ne and and{/ncolors 0 def}if ncolors 1 eq dup dup not startnoload{ +/expandbw{expandfactor mul round cvi bwclut exch get 255 div}bd/doclutimage{bwclut +colorclut pop/bwclut xd bpc dup 8 eq{pop 255}{4 eq{15}{3}ifelse}ifelse +/expandfactor xd [/expandbw load/exec load dup currenttransfer exch +] cvx bind settransfer iw ih bpc imat setupimageproc image}bd}if not +endnoload ncolors dup 3 eq exch 4 eq or dup dup not startnoload{/nullproc{{}}def +/concatutil{/exec load 7 -1 roll/exec load}bd/defsubclut{1 add getinterval +def}bd/spconcattransfer{/Dclut exch def/Cclut exch def/Bclut exch def +/Aclut exch def/ncompute exch ld currentcolortransfer [{Aclut ncompute}concatutil +] cvx [{Bclut ncompute}concatutil ] cvx [{Cclut ncompute}concatutil +] cvx [{Dclut ncompute}concatutil ] cvx setcolortransfer}bd/setuprgbcluts{ +/bit3x rgbclut length 3 sub def/bit1x bit3x 3 idiv def/rclut rgbclut +def/gclut rclut 1 bit3x defsubclut/bclut rclut 2 bit3x defsubclut}bd}if +not endnoload ncolors 3 eq dup dup not startnoload{/3compute{exch bit3x +mul round cvi get 255 div}bd/doclutimage{/rgbclut xd pop setuprgbcluts +/3compute rclut gclut bclut dup spconcattransfer iw ih bpc imat [ +setupimageproc/exec load/dup load dup ] cvx nullproc nullproc true +3 colorimage}bd}if not endnoload ncolors 4 eq dup dup not startnoload{ +/stuffclut{cmykindex 3 -1 roll put}bd/ftoint{1 exch sub 255 mul round +cvi}bd/4compute{exch bit4x mul round cvi get 255 div}bd/computecmykclut{setuprgbcluts +/bit4x rgbclut length 3 idiv 4 mul 4 sub def/cmykclut bit4x 4 add +string def/cclut cmykclut def/mclut cclut 1 bit4x defsubclut/yclut +cclut 2 bit4x defsubclut/kclut cclut 3 bit4x defsubclut/cmykindex 0 +def 0 1 bit1x{dup/cmykindex exch bit1x exch sub 4 mul def 3 mul dup +rclut exch get 255 div exch dup gclut exch get 255 div exch bclut exch +get 255 div setrgbcolor currentcmykcolor ftoint kclut stuffclut ftoint +yclut stuffclut ftoint mclut stuffclut ftoint cclut stuffclut}for}bd +/doclutimage{/rgbclut xd pop invalidcolortable?{computecmykclut}if +/4compute cclut mclut yclut kclut spconcattransfer iw ih bpc imat +[ setupimageproc/exec load/dup load dup dup ] cvx nullproc nullproc +nullproc true 4 colorimage}bd}if not endnoload ncolors 0 eq dup dup +not startnoload{/lookupandstore{3 mul 3 getinterval putinterval exch +3 add exch 3 copy}bd/8lookup/lookupandstore ld/4lookup{/byte 1 index +def -4 bitshift lookupandstore byte 15 and lookupandstore}bd/2lookup{ +/byte 1 index def -6 bitshift lookupandstore byte -4 bitshift 3 and +lookupandstore byte -2 bitshift 3 and lookupandstore byte 3 and lookupandstore}bd +/colorexpand{mystringexp 0 rgbclut 3 copy 7 -1 roll/mylookup load +forall pop pop pop pop pop}bd/createexpandstr{/mystringexp exch mystring +length mul string def}bd/doclutimage{/rgbclut xd pop/mylookup bpc 8 +eq{3 createexpandstr/8lookup}{bpc 4 eq{6 createexpandstr/4lookup}{12 +createexpandstr/2lookup}ifelse}ifelse ld iw ih bpc imat [ setupimageproc +/exec load/colorexpand load/exec load] cvx false 3 colorimage}bd}if +not endnoload/colorimage where{pop true}{false}ifelse dup{/do24image{iw +ih 8 imat setupimageproc false 3 colorimage}bd}if dup dup startnoload +not{/rgbtogray{/str xd/len str length def/smlen len 3 idiv def/rstr +str def/gstr str 1 len 1 sub getinterval def/bstr str 2 len 2 sub getinterval +def str dup 0 1 smlen 1 sub{dup 3 mul rstr 1 index get .3 mul gstr +2 index get .59 mul add bstr 3 -1 roll get .11 mul add round cvi put +dup}for pop 0 smlen getinterval}bd/do24image{iw ih 8 imat [ setupimageproc +/exec load/rgbtogray load/exec load ] cvx bind image}bd}if endnoload +/doimage{iw ih 8 imat setupimageproc image}bd level2{dontloadlevel1 +restore}if level2 not{save/dontloadlevel2 xd}if/myappcolorspace/DeviceRGB +def/rgbclut 0 def/doclutimage{/rgbclut xd pop bpc dup 8 eq{pop 255}{4 +eq{15}{3}ifelse}ifelse/hival xd [/Indexed myappcolorspace hival rgbclut] +setcolorspace myimagedict dup begin/Width iw def/Height ih def/Decode +[0 hival] def/ImageMatrix imat def/DataSource setupimageproc def/BitsPerComponent +bpc def/Interpolate smoothflag def end image}bd/do24image{myappcolorspace +setcolorspace myimagedict dup begin/Width iw def/Height ih def/Decode +[0 1 0 1 0 1] def/ImageMatrix imat def/DataSource setupimageproc def +/BitsPerComponent 8 def/Interpolate smoothflag def end image}bd level2 +not{dontloadlevel2 restore}if +/NumSteps{dtransform matrix defaultmatrix idtransform Pythag currentscreen +pop pop 72 exch div div}bd/FindMinSteps{v_ft 4 eq{urx startX sub abs +llx startX sub abs Max ury startY sub abs lly startY sub abs Max Pythag +2 3.14159265 mul mul 0}{v_ft 2 eq{endY startY sub endX startX sub Pythag +endY2 startY sub endX2 startX sub Pythag gt{endY startY sub endX startX +sub}{endY2 startY sub endX2 startX sub}ifelse}{endY startY sub endX +startX sub}ifelse}ifelse NumSteps}bd/cxe{/v_cxe exch def}bd/cxm{pop +/v_cxm exch def}bd/cxmt{pop pop}bd/cxt{pop}bd/S_eoclip{currentflat{{eoclip}stopped{dup +currentflat exch sub 20 gt{([Error: PathTooComplex; OffendingCommand: eoclip]\n)print +flush exit}{currentflat 2 add setflat}ifelse}{exit}ifelse}loop setflat}bd +/S_clip{currentflat{{clip}stopped{dup currentflat exch sub 20 gt{([Error: PathTooComplex; OffendingCommand: clip]\n)print +flush exit}{currentflat 2 add setflat}ifelse}{exit}ifelse}loop setflat}bd +/S_eofill{currentflat{{eofill}stopped{dup currentflat exch sub 20 +gt{([Error: PathTooComplex; OffendingCommand: eofill]\n)print flush +exit}{currentflat 2 add setflat}ifelse}{exit}ifelse}loop setflat}bd +/gpbbx{pathbbox/ury exch def/urx exch def/lly exch def/llx exch def}bd +/lineargfill{initgfill{false initgfx/distance endX startX sub endY +startY sub Pythag def/incD distance Steps div def endY startY sub endX +startX sub atan newpath llx lly urx ury Bx startX startY translate +rotate gpbbx eGy ssg newpath llx lly urx ury Bx S_eofill sGy ssg newpath +llx lly 0 ury Bx S_eofill/fillX 0 def 0 1 Steps 1 sub{stepgfx newpath +fillX lly fillX incD add dup/fillX exch def ury Bx S_eofill pop}for}if}bd +/radialgfill{initgfill{false initgfx/distance endX startX sub endY +startY sub Pythag def/incD distance Steps div def eGy ssg newpath llx +lly urx ury Bx S_eofill/distance 0 def 0 1 Steps 1 sub{stepgfx newpath +startX startY distance 0 360 arc closepath distance incD add dup/distance +exch def 0 rmoveto startX startY distance 0 360 arc closepath S_eofill +pop}for}if}bd/ellipticgfill{initgfill{true initgfx sGy ssg newpath +llx lly urx ury Bx S_eofill [ endX startX sub endY startY sub endX2 +startX sub endY2 startY sub startX startY ] concat Steps 1 sub -1 0{stepgfx +/i exch def 0 0 moveto 0 0 i Steps div 0 360 arc fill}for}if}bd/conicalgfill{initgfill{urx +startX sub abs llx startX sub abs Max ury startY sub abs lly startY +sub abs Max Pythag startY endY sub startX endX sub Pythag div/radius +exch def true initgfx [ endX startX sub endY startY sub startY endY +sub endX startX sub startX startY ] concat/slice 180 Steps div def +/startangle 0 def Steps -1 0{pop stepgfx 0 0 moveto 0 0 radius startangle +neg dup slice add arc fill 0 0 moveto 0 0 radius startangle dup slice +add dup/startangle exch def arc fill}for}if}bd/initgfill{gpbbx{S_eoclip}{S_clip}ifelse +startX endX eq startY endY eq and sGy eGy eq or dup{sGy ssg newpath +llx lly urx ury Bx S_eofill}if not}bd/initgfx{/flag exch def flag{sGy +eGy/sGy exch def/eGy exch def}if eGy sGy sub abs 256 mul FindMinSteps +Min 256 Min ceiling 1 Max/Steps exch def eGy sGy sub Steps div/incGy +exch def sGy/mGy exch def}bd/stepgfx{mGy ssg mGy incGy add/mGy exch +def}bd/linearfill{initfill{false initfx endX startX sub endY startY +sub Pythag/distance exch def/incD distance Steps div def endY startY +sub endX startX sub atan newpath llx lly urx ury Bx startX startY translate +rotate gpbbx v_cxe 0 eq{eR eG eB setgfillrgb}{eH eS eV setgfillhsb}ifelse +newpath llx lly urx ury Bx S_eofill v_cxe 0 eq{sR sG sB setgfillrgb}{sH +sS sV setgfillhsb}ifelse newpath llx lly 0 ury Bx S_eofill/fillX 0 +def 0 1 Steps 1 sub{stepfx newpath fillX lly fillX incD add dup/fillX +exch def ury Bx S_eofill pop}for}if}bd/radialfill{initfill{false initfx +endX startX sub endY startY sub Pythag/distance exch def/incD distance +Steps div def v_cxe 0 eq{eR eG eB setgfillrgb}{eH eS eV setgfillhsb}ifelse +newpath llx lly urx ury Bx S_eofill/distance 0 def 0 1 Steps 1 sub{stepfx +newpath startX startY distance 0 360 arc closepath distance incD add +dup/distance exch def 0 rmoveto startX startY distance 0 360 arc closepath +S_eofill pop}for}if}bind def/ellipticalfill{initfill{true initfx v_cxe +0 eq{sR sG sB setgfillrgb}{sH sS sV setgfillhsb}ifelse newpath llx +lly urx ury Bx S_eofill [ endX startX sub endY startY sub endX2 startX +sub endY2 startY sub startX startY ] concat Steps 1 sub -1 0{stepfx +/i exch def 0 0 moveto 0 0 i Steps div 0 360 arc fill}for v_cxe 0 +eq{sR sG sB eR eG eB/sB exch def/sG exch def/sR exch def/eB exch def +/eG exch def/eR exch def}if}if}bd/conicalfill{initfill{urx startX +sub abs llx startX sub abs Max ury startY sub abs lly startY sub abs +Max Pythag startY endY sub startX endX sub Pythag div/radius exch def +true initfx [ endX startX sub endY startY sub startY endY sub endX +startX sub startX startY ] concat/slice 180 Steps div def/startangle +0 def Steps -1 0{pop stepfx 0 0 moveto 0 0 radius startangle 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