%!PS-Adobe-2.0 %%Creator: dvips(k) 5.98 Copyright 2009 Radical Eye Software %%Title: article.dvi %%CreationDate: Fri Apr 01 15:58:06 2011 %%Pages: 17 %%PageOrder: Ascend %%BoundingBox: 0 0 595 842 %%DocumentFonts: Times-Bold Times-Roman CMSY10 Symbol Times-Italic CMR10 %%+ CMMI10 CMEX10 rsfs10 rsfs7 CMTT9 CMTT8 MSBM10 CMITT10 %%DocumentPaperSizes: a4 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips.exe article.dvi %DVIPSParameters: dpi=600 %DVIPSSource: TeX output 2011.04.01:1557 %%BeginProcSet: tex.pro 0 0 %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round 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RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: pstricks.pro 0 0 % $Id: pstricks.pro 90 2009-01-30 10:58:51Z herbert $ % %% PostScript prologue for pstricks.tex. %% Version 1.06, 2009/01/30 %% %% This program can be redistributed and/or modified under the terms %% of the LaTeX Project Public License Distributed from CTAN archives %% in directory macros/latex/base/lppl.txt. % % % Define the follwing gs-functions if not known, eg when using distiller % systemdict /.setopacityalpha known not {/.setopacityalpha { pop } def } if systemdict /.setblendmode known not {/.setblendmode { pop } def } if systemdict /.setshapealpha known not {/.setshapealpha { pop } def } if % /tx@Dict 200 dict def % the main PSTricks dictionary tx@Dict begin /ADict 25 dict def % The arrow dictionaray /CM { matrix currentmatrix } bind def /SLW /setlinewidth load def /CLW /currentlinewidth load def /CP /currentpoint load def /ED { exch def } bind def /L /lineto load def /T /translate load def /TMatrix { } def /RAngle { 0 } def /Sqrt { dup 0 lt { pop 0 } { sqrt } ifelse } def % return 0 for negative arguments /Atan { /atan load stopped { pop pop 0 } if } def % return 0 if atan not known /ATAN1 {neg -1 atan 180 sub } def % atan(x) (only one parameter) /Div { dup 0 eq { pop } { div } ifelse } def % control the division /tan { dup cos abs 1.e-10 lt { pop 1.e10 } % return 1.e10 as infinit { dup sin exch cos div } ifelse % default sin/cos } def /Tan { dup sin exch cos Div } def % sin(x)/cos(x) x in degrees /Acos {dup dup mul neg 1 add dup 0 lt { % arc cos, returns 0 when negative root pop pop 0 }{ sqrt exch atan} ifelse } def /NET { neg exch neg exch T } def % change coordinate system to the negative one /Pyth { dup mul exch dup mul add sqrt } def % Pythagoras, expects 2 parameter /Pyth2 { % Pythagoras, xA yA xB yB 3 -1 roll % xA xB yB yA sub % xA xB yB-yA 3 1 roll % yB-yA xA xB sub % yB-yA xA-xB Pyth } def /PtoC { 2 copy cos mul 3 1 roll sin mul } def % Polar to Cartesian /Rand { rand 4294967295 div } def % a real random number %----------------- hv added 20050516 --------------- /PiDiv2 1.57079632680 def /Pi 3.14159265359 def /TwoPi 6.28318530718 def /Euler 2.71828182846 def %/e Euler bind def % /RadtoDeg { 180 mul Pi div } bind def % convert from radian to degrees /DegtoRad { Pi mul 180 div } bind def % viceversa %----------------- hv end--------------------------- /PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } def % /PathLength { flattenpath /z 0 def { /y1 ED /x1 ED /y2 y1 def /x2 x1 def } { /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ } /pathforall load stopped { pop pop pop pop } if z } def % /STP { .996264 dup scale } def % BP/PT scaling /STV { SDict begin normalscale end STP } def % % %%-------------- DG begin patch 15 ---------------%% %/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def %PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y %mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul %/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ] %0 } ifelse setdash stroke } def /DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } ifelse /b ED /x1 ED /y1 ED /x ED /y ED /z y x add y1 add x1 add def /Coef b a .5 sub 2 mul y mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div def /y y Coef mul def /x x Coef mul def /y1 y1 Coef mul def /x1 x1 Coef mul def x1 0 gt y1 0 gt or x 0 gt or y 0 gt and { [ y x y1 x1 ] 1 a sub y mul } { [ 1 0 ] 0 } ifelse setdash stroke } def %%-------------- DG end patch 15 ---------------%% /DotLine { /b PathLength def /a ED /z ED /y CLW def /z y z add def a 0 gt { /b b a div def }{ a 0 eq { /b b y sub def }{ a -3 eq { /b b y add def } if } ifelse } ifelse [ 0 b b z Div round Div dup 0 le { pop 1 } if ] a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse setdash 1 setlinecap stroke } def % /LineFill { % hv ------------ patch 7 ------------- gsave abs /hatchWidthInc ED abs /hatchSepInc ED abs CLW add /a ED a 0 dtransform round exch round exch 2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict /setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add hatchWidthInc 0 gt { CLW add } if def hatchSepInc 0 gt hatchWidthInc 0 gt or { /a a hatchSepInc add def CLW hatchWidthInc add SLW } if } repeat grestore pop pop } def % /PenroseFill {% on stack: scaling factor dup dup scale 1 exch div round /penroseFactor ED a 0 dtransform round exch round exch 2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a Div cvi /x1 ED /y2 y2 y1 sub def clip newpath systemdict /setstrokeadjust known { true setstrokeadjust } if /I/S/L/W/G/+/Z/F/E/D[/def/exch/for{E D}/add{s E get mul} { Z -36.2001 1 33 }{25 E S rlineto}{/q Z dup q G E q 1 + G}{Z 2 2}]{cvx def}forall [0 72 1008 {dup sin E cos }F ]1 setlinejoin/s W{/a W{/b I 10{/i I 4{/m I moveto i m +/j I 10{/l Z b m l + G a l G sub s m get div .2 + floor .3 + 25 mul j l + S rmoveto}F i L j L stroke }F}F}F}F grestore pop pop } def % %gsave abs CLW add /a ED a 0 dtransform round exch round exch %2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 %% DG/SR modification begin - Dec. 12, 1997 - Patch 2 %%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a %itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a %% DG/SR modification end %Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict %/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 %% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) %% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } %% def %a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore %pop pop } def %% DG/SR modification end % /BeginArrow { ADict begin % hold it local, for end see EndArrow /@mtrx CM def gsave 2 copy T 2 index sub neg exch 3 index sub exch Atan rotate newpath } def % /EndArrow { @mtrx setmatrix CP grestore end } def % end the ADict % /Arrow { CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0 h T 1 -1 scale } if w neg h moveto 0 0 L w h L w neg a neg rlineto gsave fill grestore } def % /ArrowD { % the sides are drawn as curves (hv 20071211) CLW mul add dup 2 div /w ED mul dup /h ED mul /Inset ED { 0 h T 1 -1 scale } if % changes the direction % we use y=w/h^2 * x^2 as equation for the control points % for the coordinates the arrow is seen from top to bottom % the bottom (tip) is (0;0) w neg h moveto % lower left of > w 9 div 4 mul neg h 3 div 2 mul w 9 div neg h 3 div 0 0 curveto % tip of > w 9 div h 3 div w 9 div 4 mul h 3 div 2 mul w h curveto % upper left of > w neg Inset neg rlineto % move to x=0 and inset gsave fill grestore } def % /Tbar { CLW mul add /z ED z -2 div CLW 2 div moveto z 0 rlineto stroke 0 CLW moveto } def % /Bracket { CLW mul add dup CLW sub 2 div /x ED mul CLW add /y ED /z CLW 2 div def x neg y moveto x neg CLW 2 div L x CLW 2 div L x y L stroke 0 CLW moveto } def % /RoundBracket { CLW mul add dup 2 div /x ED mul /y ED /mtrx CM def 0 CLW 2 div T x y mul 0 ne { x y scale } if 1 1 moveto .85 .5 .35 0 0 0 curveto -.35 0 -.85 .5 -1 1 curveto mtrx setmatrix stroke 0 CLW moveto } def % /SD { 0 360 arc fill } def % /EndDot { % DS is the dot size { /z DS def } { /z 0 def } ifelse /b ED 0 z DS SD b { 0 z DS CLW sub SD } if 0 DS z add CLW 4 div sub moveto } def % /Shadow { [ { /moveto load } { /lineto load } { /curveto load } { /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto load } if ] cvx newpath 3 1 roll T exec } def % %/NArray { % aload length 2 div dup dup cvi eq not { exch pop } if /n exch % cvi def %} def % /NArray { % holds the coordinates and on top of stack the showpoints boolean /showpoints ED counttomark 2 div dup cvi /n ED n eq not { exch pop } if showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def % /Line { NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def n { Lineto } repeat CP 4 2 roll ArrowB L pop pop } if } def % /Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } ifelse { pop } repeat a } def % /CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq and { pop pop /n n 1 sub def } if } def /Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto Lineto pop pop closepath } ifelse } def /Diamond { /mtrx CM def T rotate /h ED /w ED dup 0 eq { pop } { CLW mul neg /d ED /a w h Atan def /h d a sin Div h add def /w d a cos Div w add def } ifelse mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx setmatrix } def % DG modification begin - Jan. 15, 1997 %/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { %pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 %div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 %d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx %setmatrix } def % /Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx % DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) % setmatrix } def setmatrix pop } def % DG/SR modification end % /CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth def } def % /CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def /y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul m mul neg def } def % /IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } def % /BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def /NC { CC x1 y1 x2 y2 x y curveto } def /EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def /BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def /NAC { x2 y2 x y curveto CC x1 y1 } def /EAC { x2 y2 x y ArrowB curveto pop pop } def % /OpenCurve { NArray n 3 lt { n { pop pop } repeat } { BOC /n n 3 sub def n { NC } repeat EOC } ifelse } def % /AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload /Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def % /ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } repeat closepath pop pop } ifelse } def % /SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def /ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def /SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } def % /FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix rotate matrix concatmatrix exch findfont exch makefont setfont } def % /Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto x1 y1 lineto closepath } def % /OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse /b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } ifelse } def % /Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add /y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { pop pop Rect } { OvalFrame } ifelse } def % /BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop } if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def % /OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } ifelse } def % /ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { 6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def % /BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } def % /Parab { /y0 ED /x0 ED /y1 ED /x1 ED /dx x0 x1 sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 y0 x0 2 mul x1 sub y1 ] def } def % /Grid { newpath /a 4 string def /b ED /c ED /n ED cvi dup 1 lt { pop 1 } if /s ED s div dup 0 eq { pop 1 } if /dy ED s div dup 0 eq { pop 1 } if /dx ED dy div round dy mul /y0 ED dx div round dx mul /x0 ED dy div round cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx div round cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 div add def % /Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 div add def } if systemdict /setstrokeadjust known { true setstrokeadjust /t { } def } { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add exch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if { i dx mul dup y0 moveto b 0 gt { gsave c i a cvs dup stringwidth pop /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse h 0 gt {b neg}{z1} ifelse rmoveto show grestore } if dup t f moveto g t L stroke /i i w add def } repeat grestore gsave n 0 gt % DG/SR modification begin - Nov. 7, 1997 - Patch 1 %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } % DG/SR modification end { 2 setlinecap } ifelse /i y1 def /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvs dup stringwidth pop /z2 ED w 0 gt {z1 z2 add neg} {z1} ifelse h 0 gt {z1} {b neg} ifelse rmoveto show grestore } if dup f exch t moveto g exch t L stroke /i i h add def } repeat grestore } def % /ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 0 1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c mul neg d } def % /Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def % /ArcAdjust { %%%% Vincent Guirardel % given a target length (targetLength) and an initial angle (angle0) [in the stack], % let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). % This computes an angle t such that (x0,y0) is at distance % targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). % NOTE: this an absolute angle, it does not have to be added or substracted to angle0 % contrary to TvZ's code. % To achieve, this, one iterates the following process: start with some angle t, % compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. % Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. % % Another difference with TvZ's code is that we need d (=add/sub) to be defined. % the value of d = add/sub is used to know on which side we have to move. % It is only used in the initialisation of the angle before the iteration. % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Input stack: 1: target length 2: initial angle % variables used : rx, ry, d (=add/sub) % /targetLength ED /angle0 ED /x0 rx angle0 cos mul def /y0 ry angle0 sin mul def % we are looking for an angle t such that (x0,y0) is at distance targetLength % from the point M(t)=(rx*cos(t),ry*sin(t))) %initialisation of angle (using 1st order approx = TvZ's code) targetLength 57.2958 mul angle0 sin rx mul dup mul angle0 cos ry mul dup mul add sqrt div % if initialisation angle is two large (more than 90 degrees) set it to 90 degrees % (if the ellipse is very curved at the point where we draw the arrow, % % the value can be much more than 360 degrees !) % this should avoid going on the wrong side (more than 180 degrees) or go near % a bad attractive point (at 180 degrees) dup 90 ge { pop 90 } if angle0 exch d % add or sub % maximum number of times to iterate the iterative procedure: % iterative procedure: takes an angle t on top of stack, computes a % better angle (and put it on top of stack) 30 { dup % compute distance D between (x0,y0) and M(t) dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt % if D almost equals targetLength, we stop dup targetLength sub abs 1e-5 le { pop exit } if % stack now contains D t % compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: % M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) exch dup cos rx mul x0 sub exch sin ry mul y0 sub % stack contains: y(t)-y0, x(t)-x0, d 2 index Div targetLength mul y0 add ry Div exch 2 index Div targetLength mul x0 add rx Div % stack contains x(t')/rx , y(t')/ry , d % now compute t', and remove D from stack atan exch pop } repeat % we don't look at what happened... in particular, if targetLength is greater % than the diameter of the ellipse... % the final angle will be around /angle0 + 180. maybe we should treat this pathological case... % after iteration, stack contains an angle t such that M(t) is the tail of the arrow % to give back the result as a an angle relative to angle0 we could add the following line: % angle0 sub 0 exch d % % begin bug fix 2006-01-11 % we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 %(we don't want to make the ellipse turn more or less than it should)... dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse % end bug fix } def % /EllipticArcArrow { /d ED % is add or sub /b ED % arrow procedure /a1 ED % angle gsave newpath 0 -1000 moveto clip % Set clippath far from arrow. newpath 0 1 0 0 b % Draw arrow to determine length. grestore % Length of arrow is on top of stack. Next 3 numbers are junk. % a1 exch ArcAdjust % Angular position of base of arrow. /a2 ED pop pop pop a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig a1 cos rx mul xOrig add % a1 sin ry mul yOrig add % % Now arrow tip coor and base coor are on stack. b pop pop pop pop % Draw arrow, and discard coordinates. a2 CLW 8 div % change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse ArcAdjust % resets original value of d 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. } def %%------------------ tvz/DG/hv (2004-05-10) end -------------------%% % /Rot { CP CP translate 3 -1 roll neg rotate NET } def % /RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngle dup a add ] cvx def } def % /RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def % /PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def /PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def /PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def % /Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs }{ h1 abs h sub dup s mul abs } ifelse } def % /UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt }{ x c div s mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q { x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add exch } def % /BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible /IfVisible true def } if } { IfVisible { Invisible /IfVisible false def } if } ifelse } def % /InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def /Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def /IfVisible true def } def % end %-----------------------------------------------------------------------------% % % END pstricks.pro %%EndProcSet %%BeginProcSet: pst-algparser.pro 0 0 % $Id: pst-algparser.pro 26 2008-06-14 11:50:02Z herbert $ %% %% PostScript prologue for PSTricks algorithm parser %% Version 0.01, 2008/01/01 %% %% This program can be redistributed and/or modified under the terms %% of the LaTeX Project Public License Distributed from CTAN archives %% in directory macros/latex/base/lppl.txt. %% %%-----------------------------------------------------------------------------% % /AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez % /tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin % % PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 % E->T|E+T % T->FS|T*FS % FS -> F | +FS | -FS % F->P|F^SF % P->(E)|literal % literal->number|var|var[E]|func(params) % params->E|E,param % number->TOBEFINISHED % %% E expression, T term, SF signed factor, F factor, P power % %% parser % %% str % %% C->EE %% STR index -> STR index+lenExpr /AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def % %% analyze Expression List (separator , or | ) %% STR index -> STR index+lenExpr %% /AnalyzeListOfE { %% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar %% NextNonBlankChar dup 0 eq { pop exit } if %% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if %% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop %% AnalyzeListOfEPostHook %% } def /AnalyzeListOfE { /NotFirst false def { NextNonBlankChar pop AnalyzeExpr NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse dup Strlen eq { exit } if NextNonBlankChar dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if pop 1 add } loop AnalyzeListOfEPostHook } def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% E->T|E+T %% STR index -> STR index+lenExpr /AnalyzeExpr { AnalyzePreHook AnalyzeTerm IsEndingExpr { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } ifelse AnalyzePostHook } def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% T->FS|T*FS %% STR index /AnalyzeTerm { AnalyzePreHook AnalyzeSignedFactor IsEndingTerm { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } ifelse AnalyzePostHook } def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% FS -> F | +FS | -FS %% STR index /AnalyzeSignedFactor { AnalyzePreHook 2 copy get dup IsUnaryOp { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } { pop AnalyzeFactor } ifelse AnalyzePostHook } def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% F->P|F^P %% STR index /AnalyzeFactor { AnalyzePreHook AnalyzePower IsEndingFactor { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } ifelse AnalyzePostHook } def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% P->(E)|literal %% STR index /AnalyzePower { %% depending of first char either a number, or a literal 2 copy get dup 40 eq%%an open par { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } { AnalyzeLiteral } ifelse } def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% STR index STR[index] -> STR index %/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def /AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% recognize + or - %% chr -> T/F /IsUnaryOp { dup 43 eq exch 45 eq or } bind def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% a number can contain only : 0123456789. %% chr -> T/F /IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% STR index -> STR index number %% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? %% STR index -> STR index' number /ReadNumber { exch dup 3 -1 roll dup 3 1 roll %%read mantissa { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop dup 101 eq exch 69 eq or %%% there is a "e" or "E" -> read exponant { 1 add 2 copy get dup IsUnaryOp { pop 1 add 2 copy get } if { IsNumber not { exit } if 1 add 2 copy get } loop } if dup 4 1 roll 3 -1 roll exch 1 index sub getinterval } def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% a number can contain only : 0123456789. %% chr -> T/F /IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% STR index -> STR index number %% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? %% STR index -> STR index' number /ReadCondOp { NextNonBlankChar 1 index 4 1 roll { IsCondOp not { exit } if 1 add 2 copy get } loop 2 copy 5 -1 roll exch 1 index sub getinterval 3 1 roll } def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% a literal can contain only : 0123456789. %% chr -> T/F /IsLiteral {% dup 48 ge exch dup 57 le 3 -1 roll and exch dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch dup 97 ge exch 122 le and or } bind def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? %% STR index -> literal STR index' nextchr /ReadLiteral { exch dup 3 -1 roll dup 3 1 roll %%read literal core { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll } def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% expr is ended by end of str or a clpar %% STR index -> STR index STR[index] T/F /IsEndingExpr {% 2 copy dup Strlen eq %% if end of str is reached -> end ! { pop pop 0 true } %% ending chr -> clpar, comma, |, <, >, =, !, {get dup dup 41 eq exch dup 124 eq exch dup 93 eq exch dup 44 eq exch dup 30 eq exch dup 60 ge exch 62 le and or or or or or} ifelse } def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% expr is ended by end of str or a +- %% STR index -> STR index STR[index] T/F /IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% expr is ended by end of str or */ %% STR index -> STR index STR[index] T/F /IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% expr is ended by end of str or ^ %% STR index -> STR index STR[index] T/F /IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% STR index -> STR index STR[index] /NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def /neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def %%%%%%%%%%%%%%%%%%%%%%%% %% DEBUG /BRK {false} def /BRKtrue {/BRK true def} def /BRKStop {BRK {BRKtoto} if } def /BRKEvalStop {BRK exch if } def /BRKBRK2true {BRK {BRK2true} if } def /BRK2 {false} def /BRK2true {/BRK2 true def} def /BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def end % %-------------------------------------------------------------------------------% % /tx@AlgToPs 12 dict def tx@AlgToPs begin % %% algExpr -> PSVector /AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def /EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def /InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def /Strlen 0 def /EvalListOfExpr {} def% /EvalNumber {% ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx exch 1 add array astore def NextNonBlankChar pop } def /EvalAddSub {% /ExpressionVector ExpressionVector aload length dup 5 add -1 roll 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def } def /EvalMulDiv {% /ExpressionVector ExpressionVector aload length dup 5 add -1 roll 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def } def /EvalPower {% /ExpressionVector ExpressionVector aload length dup 5 add -1 roll pop /exp cvx exch 1 add array astore def } def /EvalLiteral {% ReadLiteral dup 40 eq%%% there is an open par -> function call { pop 2 index dup (Sum) eq { EvalSum } { dup (IfTE) eq { EvalCond } { dup (Derive) eq { pop EvalDerive } { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def dup 91 eq%%% there is an open bracket -> vector element { pop 1 add NextNonBlankChar pop AnalyzeExpr /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } { pop NextNonBlankChar pop } ifelse} ifelse } def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% the derive function : Derive(n,f(x)) %% firstparindex lastparindex -> /EvalDerive { %% manage the function descripiton 1 add ReadNumber 3 1 roll NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if 1 add NextNonBlankChar pop 3 -1 roll cvi dup 0 eq { pop AnalyzeExpr 3 -1 roll pop 1 add } { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll { (x) tx@Derive begin Derive end } repeat ExpressionVector exch /ExpressionVector [] def AlgToPs aload length /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add 1 index length /Strlen exch def } ifelse } def /EvalSum {% pop 1 add NextNonBlankChar pop %% read the variable name ReadLiteral pop NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if %% read the initial value 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if %% read the increment value 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if %% read the limit value 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll 5 -1 roll 4 add array astore def %% keep ExpressionVector for later and create a new one for internal Sum computation ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def 1 add NextNonBlankChar pop AnalyzeExpr %% add each term /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add array astore def 3 -1 roll pop 1 add } def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Convert to radians if trigo function call %% (name) -> /TrigoFunc { dup (cos) eq 1 index (sin) eq or exch (tan) eq or { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add array astore def } if } def /EvalCond {% pop 1 add AnalyzeCond NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if ExpressionVector 3 1 roll /ExpressionVector [] def 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if 1 add AnalyzeExpr NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if ExpressionVector /ExpressionVector 6 -1 roll aload length dup 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def 1 add 3 -1 roll pop } def %% CondOp STR index /EvalCondOp {% 3 -1 roll dup (=) eq { /eq } {% dup (<) eq { /lt } {% dup (>) eq { /gt } {% dup (>=) eq { /ge } {% dup (<=) eq { /ge } {% dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } ifelse } ifelse } ifelse } ifelse } ifelse } ifelse cvx exch pop /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def /EvalUnaryOp { 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if } def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% H O O K S /AnalyzePreHook {} bind def /PreEvalHook {} bind def /AnalyzeListOfEPostHook {} bind def /AnalyzePostHook {} def /RollOp { 3 1 roll } bind def end %tx@CoreAnalyzerDict % %--------------------------------------------------------------------% % /tx@Derive 41 dict def tx@Derive begin %%increase ^^ for each function added %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% algExpr variable -> PSVector /Derive {% 10240 string 3 1 roll 0 3 1 roll /Variable exch def tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end } def /Strlen 0 def /InitParser { dup length /Strlen exch def 0 } def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% algExpr variable index -> PSVector /DeriveIndexed {% 3 1 roll 10240 string 3 1 roll 0 3 1 roll /Variable exch def tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end } def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% (u,v)'=-(u',v') /EvalListOfExpr {% 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe 2 copy 7 -1 roll dup length 4 1 roll putinterval add 6 -2 roll pop pop 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% (-u)'=-(u') /EvalUnaryOp { 4 -2 roll 4 index (0) eq { (0) StrConcat 7 -1 roll pop } { 7 -1 roll 45 eq { AddSub AddOpPar true } { false } ifelse 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse 2 copy pop 0 6 2 roll GetIntervalNewStr 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll } def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% (number)'=0 /EvalNumber { ReadNumber (0) 6 2 roll } def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% (u+v)'=u'+v' /EvalAddSub {% 7 index dup (0) eq { pop true }%% du=0 nothing added { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } ifelse 5 index dup (0) eq { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 { exch { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added { 5 -2 roll 7 index 43 eq%%something yet added { AddAdd false } { AddSub AddOpPar true } ifelse } ifelse 11 1 roll 3 -1 roll StrConcat 10 -1 roll { AddClPar } if 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll } def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% (u*v)' or (u/v)' /EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% (u*v)'=u'*v+u*v' /EvalMul {% 4 -2 roll 7 index dup (0) eq { pop false }%%du=0 { (1) eq%%du=1 { false } { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if true }%%du!=0 ifelse 5 1 roll 5 index (0) eq { 5 -1 roll not { (0) StrConcat } if }%%dv=0 { 5 -1 roll { AddAdd } if 4 index (1) eq { 8 index StrConcat } { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } ifelse }%%dv!=0 ifelse 2 copy pop 0 6 2 roll GetIntervalNewStr mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll } def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% (u/v)'=(u'*v-u*v')/v^2 /EvalDiv {% 4 -2 roll 4 index (0) eq%%dv=0 -> u'/v { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } { 7 index dup (0) eq { pop }%%du=0 { (1) eq%%du=1 { false } { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 ifelse AddSub 4 index (1) eq { 8 index StrConcat } { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } ifelse %}%%dv!=0 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } ifelse 2 copy pop 0 6 2 roll GetIntervalNewStr mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll } def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% str1 index str2 -> str1 index /StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def /GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) /EvalPower {% 4 -2 roll 7 index (0) eq {%%if du=0 then (u^v)'=v'ln(u)u^v 4 index (0) eq { (0) StrConcat }%%if dv=0 then (u^v)'=0 { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse } {%%du!=0 4 index (0) eq {%%if dv=0 then (u^v)'=vu'u^(v-1) 5 index dup IsStrNumber { dup (0) eq { StrConcat } { dup dup (1) eq exch (1.0) eq or { StrConcat } { StrConcat 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 (*\() StrConcat 8 index StrConcat (\)) StrConcat 5 index dup dup (2) eq exch (2.0) eq or { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat 5 index StrConcat (-1\)) StrConcat } ifelse } {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat 5 index StrConcat (-1\)+\() StrConcat 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if 8 index StrConcat (\)^\() StrConcat 5 index StrConcat (\)*ln\() StrConcat 8 index StrConcat AddClPar } ifelse } ifelse 2 copy pop 0 6 2 roll GetIntervalNewStr mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll } def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% str -> true/false /IsStrNumber {% true exch { dup 48 lt exch dup 57 gt 3 -1 roll or exch dup 46 ne%%. exch dup 43 ne%%+ exch 45 ne%%- and and and { pop false } if } forall } def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% literal switch -> func call, vector, variables /EvalLiteral {% ReadLiteral dup 40 eq%%% there is an open par -> function call { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } { dup 91 eq%%% there is an open bracket -> vector element { ERROR_vector_not_yet_implemented } { pop EvalVariable } ifelse } ifelse } def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% first last parpos Expr[first:parpos-1] -> /EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% (f(u))'=u'f'(u) /EvalFunc { 4 2 roll 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec 2 copy pop 0 6 2 roll GetIntervalNewStr mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll } def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Func derivative -> Eval /EvalFunc_sin {% PreCommonFunc { (cos\() StrConcat 5 index StrConcat AddClPar } if PostCommonFunc } def /EvalFunc_cos {% PreCommonFunc { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if PostCommonFunc } def /EvalFunc_tan {% PreCommonFunc { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if PostCommonFunc } def /EvalFunc_asin {% PreCommonFunc { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if PostCommonFunc } def /EvalFunc_acos {% PreCommonFunc { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if PostCommonFunc } def /EvalFunc_atg {% PreCommonFunc { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if PostCommonFunc } def /EvalFunc_ln {% PreCommonFunc { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if PostCommonFunc } def /EvalFunc_exp {% PreCommonFunc { (exp\() StrConcat 5 index StrConcat AddClPar } if PostCommonFunc } def /EvalFunc_sqrt {% PreCommonFunc { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if PostCommonFunc } def /EvalFunc_Fact {% PreCommonFunc { ERROR_no_variable_expression_in_Fact } if PostCommonFunc } def /EvalFunc_sh {% PreCommonFunc { (ch\() StrConcat 5 index StrConcat AddClPar } if PostCommonFunc } def /EvalFunc_ch {% PreCommonFunc { (sh\() StrConcat 5 index StrConcat AddClPar } if PostCommonFunc } def /EvalFunc_th {% PreCommonFunc { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if PostCommonFunc } def /EvalFunc_Argsh {% PreCommonFunc { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if PostCommonFunc } def /EvalFunc_Argch {% PreCommonFunc { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if PostCommonFunc } def /EvalFunc_Argth {% PreCommonFunc { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if PostCommonFunc } def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% /PreCommonFunc { 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop 4 2 roll 4 index (0) eq { (0) StrConcat false } { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse } def /PostCommonFunc { 2 copy pop 0 6 2 roll GetIntervalNewStr mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll } def /EvalFunc_Derive {% 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll } def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% literal switch -> func call, vector, variables /EvalFunc_Sum {% 1 add NextNonBlankChar pop %% read the variable name ReadLiteral pop 3 -1 roll pop NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if %% read the initial value 1 add NextNonBlankChar pop ReadNumber pop 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if %% read the increment value 1 add NextNonBlankChar pop ReadNumber pop 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if %% read the limit value 1 add NextNonBlankChar pop ReadNumber pop 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat 4 index StrConcat AddClPar 2 copy pop 0 6 2 roll GetIntervalNewStr mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll } def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% literal switch -> func call, vector, variables /EvalFunc_IfTE {% 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if 1 add NextNonBlankChar pop dup 5 1 roll AnalyzeExpr NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar 2 copy pop 0 6 2 roll GetIntervalNewStr mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll } def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% advance in str until a comma is found (no error detection!) %% str index -> str index' /SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Convert to radians if trigo function call %% (name) -> /TrigoFunc { dup (cos) eq 1 index (sin) eq or exch (tan) eq or { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add array astore def } if } def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% No derivative for condition.... /EvalCondOp { 3 -1 roll pop } bind def /PutIntervalOneAdd {putinterval 1 add} bind def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Add open parenthesis in string at the given index %% str index -> str index+1 /AddOpPar {2 copy (\() PutIntervalOneAdd} bind def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Add close parenthesis in string at the given index %% str index -> str index+1 /AddClPar {2 copy (\)) PutIntervalOneAdd} bind def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Add 0 in string at the given index %% str index -> str index+1 /AddZero {2 copy (0) PutIntervalOneAdd} bind def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Add open parenthesis in string at the given index %% str index -> str index+1 /AddMul {2 copy (*) PutIntervalOneAdd} bind def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Add open parenthesis in string at the given index %% str index -> str index+1 /AddDiv {2 copy (/) PutIntervalOneAdd} bind def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Add a plus sign in string at the given index %% str index -> str index+1 /AddAdd {2 copy (+) PutIntervalOneAdd} bind def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Add a minus sign in string at the given index %% str index -> str index+1 /AddSub {2 copy (-) PutIntervalOneAdd} bind def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Add a pipe sign in string at the given index %% str index -> str index+1 /AddPipe {2 copy (|) PutIntervalOneAdd} bind def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% H O O K S /AnalyzePreHook { dup 5 1 roll } bind def /PreEvalHook {} def /AnalyzePostHook { 7 -1 roll pop } bind def /AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def /RollOp { 5 1 roll } bind def end%%%tx@CoreAnalyzerDict /tx@AddMathFunc 12 dict def tx@AddMathFunc begin %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% NEW FUNC %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) %% x -> theta /asin {% dup abs 1 gt { EQDFasinrangeerror } if dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad } def %% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) %% x -> theta /acos {% dup abs 1 gt { EQDFacosrangeerror } if dup dup mul 1 exch sub sqrt exch atan DegtoRad } def %% function arctangent in radians %% x -> theta /atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def %% HYPERBOLIC FUNCTIONS /sh { dup Ex exch neg Ex sub 2 div } def /ch { dup Ex exch neg Ex add 2 div } def /th { dup sh exch ch div } def /Argsh { dup dup mul 1 add sqrt add ln } def /Argch { dup dup mul 1 sub sqrt add ln } def /Argth { dup 1 add exch 1 exch sub div ln 2 div } def %% modified exponential funtion for 0 %% x n -> x^n /Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def %% modified exponential funtion for 0 %% x -> e^x /Ex { Euler exch exp } bind def %% %% factorial function %% n -> n! /Fact { 1 exch 2 exch 1 exch { mul } for } bind def /fact { Fact } bind def end % END pstricks.pro %%EndProcSet %%BeginProcSet: pst-dots.pro 0 0 % $Id: pst-dots.pro 26 2008-06-14 11:50:02Z herbert $ % %% PostScript prologue for pstricks.tex. %% Version 2.02, 2008/04/18 %% %% For distribution, see pstricks.tex. %% %% Timothy Van Zandt %% %% This program can be redistributed and/or modified under the terms %% of the LaTeX Project Public License Distributed from CTAN archives %% in directory macros/latex/base/lppl.txt. %% %% Modified by Etienne Riga - Dec. 16, 1999 %% Modified by Etienne Riga - 2005/01/01 (er) %% to add /Diamond, /SolidDiamond and /BoldDiamond %% Modified by Herbert Voss (hv) - 2008/04/17 % 10 dict dup begin % hold local /FontType 3 def /FontMatrix [.001 0 0 .001 0 0] def /FontBBox [-571.5 -742.5 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dup (a) 0 get /Add put dup (A) 0 get /BoldAdd put % 65 dup (x) 0 get /Mul put dup (X) 0 get /BoldMul put dup (m) 0 get /Oplus put dup (M) 0 get /BOplus put dup (e) 0 get /SolidOplus put dup (n) 0 get /Otimes put dup (N) 0 get /BOtimes put dup (E) 0 get /SolidOtimes put dup (i) 0 get /Bar put dup (I) 0 get /BoldBar put dup (l) 0 get /SolidDiamond put dup (d) 0 get /Diamond put (D) 0 get /BoldDiamond put %%% /CharProcs 47 dict def CharProcs begin /CirclePath {0 0 500 0 360 arc closepath} def /Bullet {CirclePath fill} def /Circle {CirclePath .9 .9 scale CirclePath eofill} def /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath} def /SolidTriangle {TrianglePath fill} def /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto closepath} def /SolidSquare 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Jones %Copyright: Copyright (c) 1997, 2009 American Mathematical Society %Copyright: (), with Reserved Font Name CMTT8. % This Font Software is licensed under the SIL Open Font License, Version 1.1. % This license is in the accompanying file OFL.txt, and is also % available with a FAQ at: http://scripts.sil.org/OFL. %%EndComments FontDirectory/CMTT8 known{/CMTT8 findfont dup/UniqueID known{dup /UniqueID get 5000830 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 11 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def /FontName /CMTT8 def /FontBBox {-5 -232 545 699 }readonly def /UniqueID 5000830 def /PaintType 0 def /FontInfo 9 dict dup begin /version (003.002) readonly def /Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMTT8.) readonly def /FullName (CMTT8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def 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266.013763 cm 390.66 243.293 m 390.66 251.293 l S Q q 1 0 0 -1 0 266.013763 cm 358.66 243.293 m 358.66 251.293 l S Q q 1 0 0 -1 0 266.013763 cm 326.66 243.293 m 326.66 251.293 l S Q Q Q showpage %%Trailer count op_count sub {pop} repeat countdictstack dict_count sub {end} repeat cairo_eps_state restore %%EOF %%EndDocument @endspecial 116 x Fr(Fig)o(.)h(2)33 b FZ(Creating)21 b(ne)n(w)e(nodes)g(from)g(an)f Fo(OUTAGE)i FZ(node)f Fw(n)g FZ(in)g(graph)g Fw(G)1833 1932 y Ft(i)1869 1922 y FZ(inside)h(the)f(beam)g(of)f(possible)i(stock)g(interv)n(als.)g (Stars)f(\002gure)g(out)g Fo(OUTAGE)150 1999 y FZ(nodes,)j(circles)h (are)g Fo(BO)f FZ(nodes.)f(Note)i(that)g(no)e Fo(BO)h FZ(node)g(is)g(created)i(at)e(week)h Fo(TA)2105 2010 y Ft(k)q Fe(+)p Fl(1)2196 1999 y FZ(,)e(because)i(the)g(paths)f(that)h (w)o(ould)g(go)e(through)i(such)f(a)g(node)150 2075 y(w)o(ould)c(break) g(constraint)i Fo(CT13bis)p FZ(.)p 0 TeXcolorgray 0 TeXcolorgray 195 2328 a F5(\226)p 0 TeXcolorgray 37 w FU(C)322 2341 y FV(i)p 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