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diff --git a/Master/texmf-dist/tex/generic/pst-bspline/pst-bspline.tex b/Master/texmf-dist/tex/generic/pst-bspline/pst-bspline.tex new file mode 100644 index 00000000000..55949e9310b --- /dev/null +++ b/Master/texmf-dist/tex/generic/pst-bspline/pst-bspline.tex @@ -0,0 +1,288 @@ +%% BEGIN pst-bspline.tex +%% Author: Michael Sharpe (msharpe@ucsd.edu) +\def\fileversion{1.12} +\def\filedate{2008/11/28} +%% +\message{ v\fileversion, \filedate} +\csname PSTBsplineLoaded\endcsname +\let\PSTBsplineLoaded\endinput +\ifx\PSTnodesLoaded\endinput\else\input pst-node.tex \fi\relax +\edef\TheAtCode{\the\catcode`\@}\catcode`\@=11 +% +% Utility macros +% Build the linear combination #3[1]]*#1+#3[[2]]*#2=#4 +% #4 can be same as #1, #2 or #3--eg, \psLCNodeVar(A)(B)(3,4){A}. +% #3 may use Postscript code +\def\psLCNodeVar(#1)(#2)(#3)#4{% +\pst@getcoor{#1}\pst@tempA% +\pst@getcoor{#2}\pst@tempB% +\pnode(#3){tmpLCn@de}% +\pnode(!% + \pst@tempA /YA exch \pst@number\psyunit div def + /XA exch \pst@number\psxunit div def + \pst@tempB /YB exch \pst@number\psyunit div def + /XB exch \pst@number\psxunit div def %stack now empty + \psGetNodeCenter{tmpLCn@de}\space + XA tmpLCn@de.x mul XB tmpLCn@de.y mul add + YA tmpLCn@de.x mul YB tmpLCn@de.y mul add){tmpLCn@deA}% +\pnode(tmpLCn@deA){#4}% +} +% Useful for debugging a node location +\def\shownode(#1){%display node user coords in console +\pnode(! /nodecoors 2 array def \psGetNodeCenter{#1} + nodecoors 1 #1.y put nodecoors 0 #1.x put end nodecoors == #1.x #1.y ){temp@} +} +% Use to construct a sequence of nodes +% Eg, \pnodes{P}(0,1)(2;5)(3,4) defines nodes P0, P1, P2 with respective locations +\def\pnodes#1{% +\newcount\bsp@args\bsp@args=0\relax% +\def\bsp@root{#1}% +\next@Node}% +% +\def\next@Node{\@ifnextchar({\next@Node@i}{\advance\bsp@args by -1\typeout{Defined nodes \bsp@root0 .. \bsp@root\the\bsp@args.}}}% +% +\def\next@Node@i(#1){% +\pnode(#1){\bsp@root\the\bsp@args}% +\advance\bsp@args by 1\relax% +\next@Node} +% +%\def\nextpt#1#2#3{\typeout{Next points:#1:#2:#3:}} +\def\nextfour#1#2#3#4{\newwrite\foo \immediate\openout\foo=foo.txt \immediate\write\foo{Next chars:#1:#2:#3:#4:}\closeout\foo} +%end utility macros +\newcount\bsp@args +\newcount\bsp@cntA +\newcount\bsp@cntB +\newif\ifbsp@omitends +\newif\ifbsp@closed +\newif\ifbsp@showpoints +\newif\ifbsp@doubleline +\newif\ifbsp@seq +% +\def\bsp@init{%these items are used only within the plotting macros +\def\bsp@arrowA{}% +\def\bsp@arrowB{}% +}% +\def\refreshbspopts{% +\bsp@doublelinefalse +\bsp@closedfalse +\bsp@showpointsfalse +\bsp@omitendsfalse +\bsp@seqfalse +}% +\def\saveparams{ +\let\save@linecolor\pslinecolor +% \let\save@arrowA\psk@arrowA +% \let\save@arrowB\psk@arrowB + \let\save@linestyle\pslinestyle} +\def\restoreparams{% settings for linestyle, arrows, linecolor may have changed + \let\pslinecolor\save@linecolor +% \let\psk@arrowA\save@arrowA +% \let\psk@arrowB\save@arrowB + \let\pslinestyle\save@linestyle} +% showframe key and its default are global +\newif\ifshowframe +\def\psset@showframe#1{\@nameuse{showframe#1}} +\psset@showframe{false} +% +%Bspline drawing macros +\def\psBsplineNodes{\pst@object{psBsplineNodes}}% +\def\psBsplineNodesC{\pst@object{psBsplineCNodes}}% +\def\psBsplineNodesE{\pst@object{psBsplineENodes}}% +\def\psBsplineC{\pst@object{psBsplineC}}% +\def\psBsplineE{\pst@object{psBsplineE}}% +\def\psBspline{\pst@object{psBspline}}% +%Bspline internal macros, level 1 +\def\psBsplineC@i{\bsp@init\refreshbspopts\bsp@closedtrue\ps@bspline} +\def\psBsplineE@i{\bsp@init\refreshbspopts\bsp@omitendstrue\ps@bspline} +\def\psBspline@i{\bsp@init\refreshbspopts\ps@bspline} +\def\psBsplineNodes@i{\bsp@init\refreshbspopts\bsp@seqtrue\ps@bsplineNodes} +\def\psBsplineCNodes@i{\bsp@init\refreshbspopts\bsp@seqtrue\bsp@closedtrue\ps@bsplineNodes} +\def\psBsplineENodes@i{\bsp@init\refreshbspopts\bsp@seqtrue\bsp@omitendstrue\ps@bsplineNodes} +%Bspline internal macros, level 2 +\def\ps@bsplineNodes#1#2{%noderoot, endindex +\def\bsp@root{#1} +\bsp@args=#2 +\psBsplineMain} +% +\def\ps@bspline{\bsp@args=0\relax% +\@ifnextchar({\psBspline@read{pn@de}}{\psBspline@read}} +% +\def\psBspline@read#1{% +\def\bsp@root{#1}% +%\show\bsp@root +\psBsplineMain}% +% +\def\psBsplineMain{% + \ifshowpoints \bsp@showpointstrue \fi% +\ifbsp@closed\begin@ClosedObj \else \begin@OpenObj \fi% +% \ifshowpoints \bsp@showpointstrue \showpointsfalse \fi +\ifpsdoubleline \bsp@doublelinetrue \fi% +\let\bsp@linecolor\pslinecolor% +\let\bsp@arrowA\psk@arrowA% +\let\bsp@arrowB\psk@arrowB% +\let\bsp@linestyle\pslinestyle% +\tracingcommands=2\tracingmacros=2 +%\ifbsp@seq\next@Point@ii \else +\next@Point%omit the \fi or it becomes the nextchar +}% +% +\def\next@Point{\@ifnextchar({\next@Point@i}{\next@Point@ii}}% +\def\next@Point@i(#1){% +\pnode(#1){\bsp@root\the\bsp@args} +\advance\bsp@args by 1 \relax +\next@Point} +\def\next@Point@ii{%done reading nodes +\tracingcommands=0\tracingmacros=0 +\ifbsp@seq\advance\bsp@args by 1\fi +\ifbsp@closed + \psset{doubleline=false} + \pnode(\bsp@root0){\bsp@root\the\bsp@args} + \advance\bsp@args by 1 \relax + \pnode(\bsp@root1){\bsp@root\the\bsp@args} + \advance\bsp@args by 1 \relax +\fi +\advance\bsp@args by -1 +% Define the left and right bezier control points in each interval. These are +% denoted (root+) R0, L1, R1, L2, R2, etc +\ifshowframe + \psset{linestyle=dashed,linecolor=gray,arrows=*-*} +\else + \psset{linestyle=none,linecolor=white,arrows=-} +\fi +%2008/9/20---change \ncline{*-*} to just \ncline +\multido{\ia=0+1,\ib=1+1}{\bsp@args}{\ncline{\bsp@root\ia}{\bsp@root\ib}\ncput[npos=.3333]{\pnode{\bsp@root R\ia}}\ncput[npos=.6667]{\pnode{\bsp@root L\ib}}} +%Finally, define the bezier endpoints for each interval +\advance\bsp@args by -1 +\ifshowframe + \psset{linestyle=solid,linecolor=red} +\else + \psset{linestyle=none,linecolor=white} +\fi +%2008/9/20---change \ncline{*-*} to just \ncline +\mmultido{\ia=0+1}{\bsp@args}{\ncline{\bsp@root L\ia}{\bsp@root R\ia}\ncput[npos=.5]{\pnode{\bsp@root S\ia}}\ifshowframe \psdot[linecolor=red](\bsp@root S\ia)\fi +} +% +\ifbsp@closed + \pnode(\bsp@root S\the\bsp@args){\bsp@root S0} + \else + \advance\bsp@args by 1 \relax + \pnode(\bsp@root0){\bsp@root S0} + \pnode(\bsp@root\the\bsp@args){\bsp@root S\the\bsp@args} + \fi +\advance\bsp@args by -1 \relax +%the pieces of bezier curve +\let\pslinecolor\bsp@linecolor +\let\pslinestyle\bsp@linestyle +\ifbsp@closed +\pscustom[arrows=-]{% +\psbezier[showpoints=false](\bsp@root S0)(\bsp@root R0)(\bsp@root L1)(\bsp@root S1) +\multido{\ia=1+1,\ib=2+1}{\bsp@args}{\psbezier(\bsp@root R\ia)(\bsp@root L\ib)(\bsp@root S\ib)}%within \pscustom, \psbezier takes 3 args, using last point of previous +}% +\else %open curve---make arrows, don't use \pscustom + \ifbsp@doubleline \psset{doubleline=true} \fi + \advance\bsp@args by -1 + \ifbsp@omitends \bsp@cntA=2 \bsp@cntB=1 \advance\bsp@args by -2 \else \bsp@cntA=1\bsp@cntB=0 \fi + \psbezier[arrows=-\bsp@arrowA,showpoints=flse](\bsp@root S\the\bsp@cntA)(\bsp@root L\the\bsp@cntA)(\bsp@root R\the\bsp@cntB)(\bsp@root S\the\bsp@cntB) + \mmultido{\ia=\the\bsp@cntA+1,\ib=\the\bsp@cntB+1}{\bsp@args}{\psbezier[arrows=-,showpoints=false](\bsp@root S\ib)(\bsp@root R\ib)(\bsp@root L\ia)(\bsp@root S\ia)} + % + \ifbsp@omitends \advance\bsp@args by 1 \fi + \advance\bsp@args by 1 \relax + \bsp@cntA=\bsp@args + \bsp@cntB=\bsp@cntA + \advance\bsp@cntB by 1 \relax + \psbezier[arrows=-\bsp@arrowB,showpoints=false](\bsp@root S\the\bsp@cntA)(\bsp@root R\the\bsp@cntA)(\bsp@root L\the\bsp@cntB)(\bsp@root S\the\bsp@cntB) + \ifshowframe \psdot[linecolor=red](\bsp@root L\the\bsp@cntB) \fi +\fi % end \ifbsp@closed +\ifshowframe + \psdot[linecolor=red](\bsp@root R0) + \psdot[linecolor=red](\bsp@root L\the\bsp@args) +\fi +\ifshowpoints + \multido{\i=0+1}{\bsp@args}{\psdot(\bsp@root S\i)} +\fi + \ifbsp@closed + \end@ClosedObj% + \else + \end@OpenObj% + \fi +\ifbsp@showpoints \showpointstrue \fi +%\restoreparams +\ignorespaces +} +% +\def\make@mcoeff#1{% +\pstVerb{ /mcoeff #1\space 1 add array def + mcoeff 1 0.25 put + 1 1 #1\space 1 sub + {/j exch def %j is counter + mcoeff j 1 add 1 4 mcoeff j get sub div put } for }} + % + \def\psBsplineInterp#1#2{% + % #1=node name root to interpolate, #2=end index, + % eg, if we want to interpolate S0,..., S100, #1=S, #2=100, +\newcount\top@mone \top@mone=#2\relax%100 +\newcount\top@ndx \top@ndx=\top@mone% +\advance\top@ndx by -1\relax%99 +\advance\top@mone by -2\relax%98 +\newcount\top@mtwo \top@mtwo=\top@mone \advance\top@mtwo by -1\relax%97 +\make@mcoeff{#2}% +\def\noderoot{#1}% +\pnode(\noderoot 0){\noderoot B0}% +\pnode(\noderoot #2){\noderoot B#2}% +\psLCNode(\noderoot 1){6}(\noderoot 0){-1}{\noderoot B1}% 6*S1-S0->SB1 +\multido{\iA=2+1,\iAA=1+1}{\top@mone}{\psLCNodeVar(\noderoot\iA)(\noderoot B\iAA)(! 6 mcoeff \iAA\space get neg ){\noderoot B\iA}}%2 to n-2, 6*S_k-m_{k-1}*SB_{k-1}->SB_k +\psLCNodeVar(\noderoot \the\top@ndx)(S#2)(! mcoeff \the\top@ndx\space get dup 6 mul exch neg ){tmp@node} %m_{99}*(6*S99-S100)->tmp@node +\psLCNodeVar(tmp@node)(\noderoot B\the\top@mone)(! 1 mcoeff \the\top@ndx\space get mcoeff \the\top@mone\space get mul neg ){\noderoot B\the\top@ndx}% temp@node -m_{98}*m_{99}*SB98->SB99 +\multido{\iA=\the\top@mone+-1,\iAA=\the\top@ndx+-1}{\the\top@mone}{\psLCNodeVar(\noderoot B\iA)(\noderoot B\iAA)(! mcoeff \iA\space get dup neg ){\noderoot B\iA}% m_k*SB_k-m_k*SB_{k+1}->SB_k, k=98 downto 1 +}% end multido +}% end def + \def\psBsplineInterpC#1#2{% + % #1=node name root, #2=top index, + % eg, if we want to interpolate S0,..., S100, #1=100, #2=S + % interpolation in this case is periodic (closed curve) +\newcount\top@mone \top@mone=#2 % +\newcount\top@ndx \top@ndx=\top@mone% +\advance\top@ndx by 1\relax%number of nodes to interpolate +\newcount\top@mtwo \top@mtwo=\top@mone \advance\top@mtwo by -1\relax% +% After copying S0 to S101, \top@ndx, \top@mone, \top@mtwo are top index, top index-1, top index-two---101, 100, 99 in the example +\make@mcoeff{\the\top@ndx}% +\def\noderoot{#1}% +\pstVerb{ /bcoeff #2\space 2 add array def /ccoeff #2\space 2 add array def /xcoeff #2\space 2 add array def /ycoeff #2\space 2 add array def +% initialize b, c, x ,y values + 1 1 \the\top@ndx\space %1 add + {/j exch def %j is counter + ccoeff j 0 put bcoeff j 0 put } for +bcoeff 1 1 put bcoeff #2\space 1 put bcoeff #2\space 1 add 4 put +ccoeff 1 0.25 put ccoeff #2\space 1 put }% +%end \pstVerb +\pnode(\noderoot 0){\noderoot\the\top@ndx}%copy node 0 to top end +%\pstVerb{ xcoeff 1 1 put ycoeff 1 1.5 put } +\pnode(! \psGetNodeCenter{\noderoot 1} xcoeff 1 \noderoot 1.x 1.5 mul put ycoeff 1 \noderoot 1.y 1.5 mul put 1 1){temp@}% 1.5=6*0.25 +\multido{\iA=2+1}{\the\top@mone}{\pnode(! ycoeff \iA\space xcoeff \iA\space \psGetNodeCenter{#1\iA} #1\iA.x 6 mul put #1\iA.y 6 mul put 1 1){temp@}}% move x, y coords times 6 to arrays +\multido{\iA=2+1,\iB=1+1}{\the\top@mtwo}{\pstVerb{% + ccoeff \iA\space ccoeff \iA\space get ccoeff \iB\space get sub mcoeff \iA\space get mul put + xcoeff \iA\space xcoeff \iA\space get xcoeff \iB\space get sub mcoeff \iA\space get mul put + ycoeff \iA\space ycoeff \iA\space get ycoeff \iB\space get sub mcoeff \iA\space get mul put +bcoeff \iA\space bcoeff \iA\space get bcoeff \iB\space get mcoeff \iB\space get mul sub put +bcoeff \the\top@ndx\space bcoeff \the\top@ndx\space get bcoeff \iB\space get ccoeff \iB\space get mul sub put +xcoeff \the\top@ndx\space xcoeff \the\top@ndx\space get xcoeff \iB\space get bcoeff \iB\space get mul sub put +ycoeff \the\top@ndx\space ycoeff \the\top@ndx\space get ycoeff \iB\space get bcoeff \iB\space get mul sub put +}% end \pstVerb +}% end \multido +\pstVerb{% + bcoeff \the\top@ndx\space bcoeff \the\top@ndx\space get bcoeff \the\top@mone\space get +ccoeff \the\top@mone\space get mul sub put %b(n)=b(n)-b(n-1)*c(n-1) +xcoeff \the\top@ndx\space xcoeff \the\top@ndx\space get xcoeff \the\top@mone\space get bcoeff \the\top@mone\space get mul sub bcoeff \the\top@ndx\space get div put %x(n)=(x(n)-x(n-1)*b(n-1))/b(n) +ycoeff \the\top@ndx\space ycoeff \the\top@ndx\space get ycoeff \the\top@mone\space get bcoeff \the\top@mone\space get mul sub bcoeff \the\top@ndx\space get div put %y(n)=(y(n)-y(n-1)*b(n-1))/b(n) +xcoeff \the\top@mone\space xcoeff \the\top@mone\space get xcoeff \the\top@ndx\space get ccoeff \the\top@mone\space get mul sub put %x(n-1)=x(n-1)-c(n-1)*x(n) +ycoeff \the\top@mone\space ycoeff \the\top@mone\space get ycoeff \the\top@ndx\space get ccoeff \the\top@mone\space get mul sub put %y(n-1)=y(n-1)-c(n-1)*y(n) +}% end pstVerb +\mmultido{\iA=\the\top@mone+-1,\iB=\the\top@ndx+-1}{\the\top@mtwo}{% +\pstVerb{ xcoeff \iA\space xcoeff \iA\space get mcoeff \iA\space get xcoeff \iB\space get mul sub ccoeff \iA\space get xcoeff \the\top@ndx\space get mul sub put % x(k)=x(k)-m(k)*x(k+1)-c(k)*x(n) +ycoeff \iA\space ycoeff \iA\space get mcoeff \iA\space get ycoeff \iB\space get mul sub ccoeff \iA\space get ycoeff \the\top@ndx\space get mul sub put +}}%y(k)=... +\multido{\iA=1+1}{\the\top@ndx}{\pnode(! xcoeff \iA\space get ycoeff \iA\space get ){\noderoot B\iA}}% +\pnode(\noderoot B\the\top@ndx){\noderoot B0}% +} +\catcode`\@=\TheAtCode\relax +\endinput
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