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+%--------------------------------------------
+%
+% Package pgfplots, library for smith charts.
+%
+% Copyright 2010 by Christian Feuersänger.
+%
+% This program is free software: you can redistribute it and/or modify
+% it under the terms of the GNU General Public License as published by
+% the Free Software Foundation, either version 3 of the License, or
+% (at your option) any later version.
+%
+% This program is distributed in the hope that it will be useful,
+% but WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+% GNU General Public License for more details.
+%
+% You should have received a copy of the GNU General Public License
+% along with this program. If not, see <http://www.gnu.org/licenses/>.
+%
+% A smithchart maps the complex halfplane
+% H subset \C,
+% H := [0,infty] x [-infty,infty]
+% =~ \{ z = a+ j *b | a >=0, b \in \R }
+%
+% to the unit circle.
+%
+% A number z = a+jb is mapped to r(z) = (z-1) / (z+1) which is, per
+% definition, in the 2d unit circle.
+%
+% Grid lines (i.e. a==const or b==const) are mapped on circles.
+%
+% In PGFPlots, the a=Re(z) is the x axis and b = Im(z) is the y axis.
+%
+% - CARTESIAN INPUT
+% - tick/grid coordinates are from
+% - input coordinates can be either from H or (perhaps preferred) from
+% the unit circle.
+% this "preferred" needs to be discussed.
+% - the transformed data range is the unit circle (or a sequeezed variant)
+% - in order to compute limits etc., I should accept data in H. this
+% should simplify the logic to determine ticks etc considerably.
+% problem: this transformation appears to be quite difficult (?)
+% -> r(z) = (z-1)/(z+1)
+% in complex arithmetics (but the G-tutorial.pdf says something
+% about these circle equations!?)
+%
+% www.amanogawa.com/archive/docs/G-tutorial.pdf
+%
+%
+% Idea:
+% - work on H
+% - transform whereever necessary
+% - implement all pgfplots wrinkles in analogy to polar axes
+% - provide support for normalized input coords (combined with
+% untransformed limits or something like that)
+
+\pgfplotsdefineaxistype{smithchart}{%
+ \pgfplots@smithchartaxis@activate
+}%
+
+\newif\ifpgfplotspointisinsmithchartCS
+\newif\ifpgfplots@smithchart@showorigin
+\newif\ifpgfplots@smithchart@mirrored
+
+\pgfplotsset{
+ /pgfplots/xgrid each nth passes y/.initial=,% format: CSV list, each entry of the form '<at> | <at> ':' <eachnth> | <at> 'if <' <xvalue> | <at> ':' <eachnth> 'if <' <xvalue>'
+ /pgfplots/xgrid each nth passes y start/.initial=0,
+ /pgfplots/ygrid each nth passes x/.initial=,
+ /pgfplots/ygrid each nth passes x start/.initial=0,
+ %
+ /pgfplots/xgrid stop at y/.initial=,% individual stop map of the form '<xpos> ':' <stopaty>', separated by white space
+ /pgfplots/ygrid stop at x/.initial=,
+ %
+ % FIXME : this is undocumented:
+ /pgfplots/smithchart mirrored/.is if=pgfplots@smithchart@mirrored,
+ /pgfplots/smithchart mirrored/.default=true,
+ %
+ % this boolean may only be used inside of \addplot. It will be
+ % ignored otherwise.
+ /pgfplots/is smithchart cs/.is if=pgfplotspointisinsmithchartCS,
+ /pgfplots/is smithchart cs/.default=true,
+ /pgfplots/show origin/.is if=pgfplots@smithchart@showorigin,
+ /pgfplots/show origin/.default=true,
+ /pgfplots/show origin code/.code={%
+ \path[draw=black,fill=white] (0pt,0pt) circle (2.5pt);
+ \path[fill=black] (0pt,0pt) circle (0.5pt);
+ },
+ /pgfplots/every smithchart axis/.style={
+ grid=both,
+ xmin=0,
+ xmax=16000,% FIXME : more is not possible because some code uses the \pgfplots@xmin@reg registers... (ticks)
+ ymin=-16000,ymax=16000,
+ scaled ticks=false, % never draw the \cdot 10^4 labels
+ major tick style={draw=black},
+ xtick align=center,
+ ytick align=center,
+ every axis title shift=1.2\baselineskip,
+ legend style={anchor=center},
+ },
+ /pgfplots/default smithchart xtick/.code=,
+ /pgfplots/default smithchart ytick/.code=,
+ /pgfplots/default smithchart xytick/.code=,
+ /pgfplots/smithchart ticks by size/.code 2 args={%
+ \ifdim#1<14cm
+ \pgfkeysalso{/pgfplots/few smithchart ticks}%
+ \else
+ \ifdim#1<20cm
+ \pgfkeysalso{/pgfplots/many smithchart ticks}%
+ \else
+ \pgfkeysalso{/pgfplots/dense smithchart ticks}%
+ \fi
+ \fi
+ },
+ /pgfplots/few smithchart ticks*/.style={
+ default smithchart xtick/.style={
+ xtick={0.2,0.5,1,2,5},
+ },
+ default smithchart ytick/.style={
+ ytick={%
+ 0,%
+ 0.2, 0.5, 1, 2, 5,%
+ -0.2,-0.5,-1,-2,-5},
+ },
+ default smithchart xytick/.style={
+ xgrid each nth passes y={2},
+ ygrid each nth passes x={2},
+ },
+ },
+ /pgfplots/few smithchart ticks/.style={/pgfplots/few smithchart ticks*},
+ /pgfplots/few smithchart ticks*,% use it as initial config
+ /pgfplots/many smithchart ticks*/.style={
+ default smithchart xtick/.style={
+ xtick={
+ 0.1,0.2,0.3,0.4,0.5,1,1.5,2,3,4,5,10,20%
+ },
+ minor xtick={0.6,0.7,0.8,0.9,1.1,1.2,1.3,1.4,1.6,1.7,1.8,1.9,2.2,2.4,2.6,2.8,3.2,3.4,3.6,3.8,4.5,6,7,8,9,50},
+ },
+ default smithchart ytick/.style={
+ ytick={%
+ 0,%
+ 0.1,0.2,...,1,1.5,2,3,4,5,10,20,%
+ -0.1,-0.2,...,-1,-1.5,-2,-3,-4,-5,-10,-20%
+ },
+ minor ytick={%
+ 1.1,1.2,1.3,1.4,1.6,1.7,1.8,1.9,2.2,2.4,2.6,2.8,3.2,3.4,3.6,3.8,4.5,6,7,8,9,50,%
+ -1.1,-1.2,-1.3,-1.4,-1.6,-1.7,-1.8,-1.9,-2.2,-2.4,-2.6,-2.8,-3.2,-3.4,-3.6,-3.8,-4.5,-6,-7,-8,-9,-50%
+ },
+ },
+ default smithchart xytick/.style={
+ xgrid each nth passes y={1,2,4,5,10,20},
+ ygrid each nth passes x={1,2,3,5,10:3,20:3},
+ },
+ },
+ /pgfplots/many smithchart ticks/.style={
+ many smithchart ticks*,
+ every axis title shift=6pt,
+ yticklabel in circle,
+ show origin=true,
+ },
+ /pgfplots/dense smithchart ticks*/.style={
+ default smithchart xtick/.style={
+ %ygrid each nth passes x start=0,
+ xtick={
+ 0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1,1.2,1.4,1.6,1.8,2,3,4,5,10,20%
+ },
+ minor xtick={%
+ 0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,%
+ 0.22,0.24,0.26,0.28,0.32,0.34,0.36,0.38,0.42,0.44,0.46,0.48,%
+ 0.52,%
+ 0.55,0.65,0.75,0.85,0.95,%
+ %0.6,0.7,0.8,0.9,%
+ 1.1,1.3,1.5,1.7,1.9,%
+ 2.2,2.4,2.6,2.8,3.2,3.4,3.6,3.8,4.5,6,7,8,9,50},
+ },
+ default smithchart ytick/.style={
+ ytick={%
+ 0,%
+ 0.1,0.2,...,1,1.2,1.4,1.6,1.8,2,3,4,5,10,20,%
+ -0.1,-0.2,...,-1,-1.2,-1.4,-1.6,-1.8,-2,-3,-4,-5,-10,-20%
+ },
+ minor ytick={%
+ 0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,%
+ 0.22,0.24,0.26,0.28,0.32,0.34,0.36,0.38,0.42,0.44,0.46,0.48,%
+ 0.55,0.65,0.75,0.85,0.95,%
+ 1.1,1.3,1.5,1.7,1.9,2.2,2.4,2.6,2.8,3.2,3.4,3.6,3.8,4.5,6,7,8,9,50,%
+ -0.01,-0.02,-0.03,-0.04,-0.05,-0.06,-0.07,-0.08,-0.09,-0.11,-0.12,-0.13,-0.14,-0.15,-0.16,-0.17,-0.18,-0.19,%
+ -0.22,-0.24,-0.26,-0.28,-0.32,-0.34,-0.36,-0.38,-0.42,-0.44,-0.46,-0.48,%
+ -0.55,-0.65,-0.75,-0.85,-0.95,%
+ -1.1,-1.3,-1.5,-1.7,-1.9,-2.2,-2.4,-2.6,-2.8,-3.2,-3.4,-3.6,-3.8,-4.5,-6,-7,-8,-9,-50%
+ },
+ },
+ default smithchart xytick/.style={
+ xgrid each nth passes y={0.2 if < 0.2001,0.5 if < 0.50001,1 if < 1.001,2,4,5,10,20},
+ ygrid each nth passes x={0.2 if < 0.2001,0.52 if < 0.52001,1 if < 1.001,2,3,5,10:3,20:3},
+ },
+ },
+ /pgfplots/dense smithchart ticks/.style={
+ yticklabel in circle,
+ every axis title shift=6pt,
+ dense smithchart ticks*,
+ show origin=true,
+ every major grid/.style={black!60},
+ },
+ /pgfplots/yticklabel in circle/.style={
+ ytick align=inside,
+ yticklabel style={
+ rotate=90,
+ sloped like y axis={%
+ execute for upside down={\tikzset{anchor=north east}},
+ %allow upside down,
+ reset nontranslations=false},
+ anchor=south west,
+ %font=\tiny,
+ }
+ },
+}
+
+\def\pgfplots@smithchartaxis@activate{%
+ \def\axisdefaultwidth{207pt}%
+ \def\axisdefaultheight{207pt}%
+ \let\pgfplotsqpointxy@cart=\pgfplotsqpointxy
+ \let\pgfplotsqpointxy=\pgfplotsqpointxy@smithchartaxis
+ \let\pgfplotsqpointxy@orthogonal=\pgfplotsqpointxy
+ \def\pgfplotsqpointxyz##1##2##3{\pgfplotsqpointxy{##1}{##2}}% FIXME
+ \let\pgfplotspointouternormalvectorofaxis@=\pgfplotspointouternormalvectorofaxis@smithchartaxis
+ \def\pgfplotspointouternormalvectorofaxis@ifdependson@v##1##2##3{##2}%
+ \def\pgfplots@drawticklines@INSTALLCLIP@onorientedsurf##1{}%
+ \let\pgfplots@drawgridlines@INSTALLCLIP@onorientedsurf=\pgfplots@drawgridlines@INSTALLCLIP@onorientedsurf@smithchartaxis
+ \def\pgfplots@visphase@notify@changeofcanvaslimits##1{}%
+ \def\pgfplots@avoid@empty@axis@range@for##1{}%
+ \def\pgfplotsaxisifcontainspoint##1##2{##1}%
+ \let\pgfplots@set@default@size@options=\pgfplots@set@default@size@options@smithchart%
+ %
+ \def\b@pgfplots@smithchart@defaultticks@x{0}%
+ \def\b@pgfplots@smithchart@defaultticks@y{0}%
+ \let\pgfplots@assign@default@tick@foraxis=\pgfplots@assign@default@tick@foraxis@smithchart
+ \def\pgfplots@checkisuniformLINEARtick##1##2{%
+ % don't do anything here. I suppose it is useless and is a
+ % waste of time for many ticks.
+ \global\pgfplots@isuniformtickfalse
+ }%
+ \let\pgfplots@clippath@prepare@for@axistype=\pgfplots@clippath@prepare@for@axistype@smithchartaxis
+ %
+ % invalid range: do not clear plots. simply assign default limits.
+ \let\pgfplots@handle@invalid@range@defaultlimits=\pgfplots@handle@invalid@range@defaultlimits@smithchart%
+ \def\pgfplots@handle@invalid@range{\pgfplots@handle@invalid@range@defaultlimits}%
+ %
+ \let\pgfplotspointonorientedsurfaceabwithbshift=\pgfplotspointonorientedsurfaceabwithbshift@smithchartaxis
+ \let\pgfplots@draw@axis@is@prepared=\pgfplots@draw@axis@is@prepared@smithchartaxis
+ \let\pgfplots@drawgridlines@onorientedsurf@fromto=\pgfplots@drawgridlines@onorientedsurf@fromto@smithchart
+ \let\pgfplots@drawaxis@innerlines@onorientedsurf=\pgfplots@drawaxis@innerlines@onorientedsurf@smithchart
+ \let\pgfplots@drawaxis@outerlines@separate@onorientedsurf=\pgfplots@drawaxis@outerlines@separate@onorientedsurf@smithchartaxis
+ \let\pgfplotspoint@initialisation@axes=\pgfplotspoint@initialisation@axes@smithchart%
+ \let\pgfplotspoint@initialisation@units=\pgfplotspoint@initialisation@units@smithchart
+ \expandafter\def\expandafter\pgfplots@create@axis@descriptions@\expandafter{%
+ \pgfplots@create@axis@descriptions@
+ \ifpgfplots@smithchart@showorigin
+ \pgfkeysvalueof{/pgfplots/show origin code/.@cmd}\pgfeov%
+ \fi
+ }%
+ \def\axisdefaultheight{\axisdefaultwidth}%
+ \let\pgfplots@initsizes=\pgfplots@initsizes@smithchart
+ %\let\pgfplots@limits@ready=\pgfplots@limits@ready@smithchart
+ %\let\pgfplots@show@ticklabel@=\pgfplots@show@ticklabel@@smithchart
+ %\def\pgfplots@xtick@disable@last@tick{0}%
+ \let\pgfplots@xtick@check@tickshow=\pgfplots@xtick@check@tickshow@smithchart%
+ \let\pgfplots@ytick@check@tickshow=\pgfplots@ytick@check@tickshow@smithchart%
+ \let\pgfplots@set@options@sanitize=\relax
+ \let\pgfplots@set@options@sanitizemode=\relax
+ \let\pgfplotscoordmathnotifydatascalesetfor=\pgfplotscoordmathnotifydatascalesetfor@smithchart
+ %
+ \expandafter\def\expandafter\pgfplots@notify@options@are@set\expandafter{%
+ \pgfplots@notify@options@are@set
+ \pgfplotsset{%
+ separate axis lines,%
+ is smithchart cs=false,%
+ xtick pos=left,
+ ytick pos=left,
+ axis x line*=center,
+ disabledatascaling,
+ }%
+ \def\pgfplots@xtickposnum{2}%
+ %
+ \ifx\pgfplots@xtick\pgfutil@empty
+ \def\b@pgfplots@smithchart@defaultticks@x{1}%
+ \fi
+ \ifx\pgfplots@ytick\pgfutil@empty
+ \def\b@pgfplots@smithchart@defaultticks@y{1}%
+ \fi
+ \pgfplotscoordmath{default}{parsenumber}{0.002}%
+ \let\pgfplots@almost@zero@thresh=\pgfmathresult
+ }%
+ \def\pgfplots@xticklabel@pos{}%
+ \def\pgfplots@yticklabel@pos{}%
+ \def\pgfplots@zticklabel@pos{}%
+ \def\pgfplots@init@ticklabelaxisspecfor##1##2{}%
+ \def\pgfplots@init@ticklabelaxisspec@twodim@for##1##2{}%
+ \def\pgfplotspointonorientedsurfaceabmatchaxisline@warn##1{}% clear warning. It works for smith charts.
+ \def\pgfplots@xticklabelaxisspec{v20}%
+ \def\pgfplots@yticklabelaxisspec{0v0}%
+ \def\pgfplots@zticklabelaxisspec{00v}%
+ %
+ % cartesian cs
+ \tikzdeclarecoordinatesystem{cartesian}{\edef\pgfplots@loc@TMPa{##1}\expandafter\pgfplotspointcartesian@\pgfplots@loc@TMPa\pgfplots@coord@end}%
+ %
+ %
+ % Special treatment for
+ % \pgfplots@prepare@tick@coordlists@for: make sure we don't need
+ % to use the register arithmetics in \pgfplots@xmin@reg and its
+ % variants! I want an UNRESTRICTED max data range!
+ \def\pgfplots@prepare@tick@coordlists@for@assign##1=##2{\edef##1{##2}}%
+ \def\pgfplots@prepare@tick@coordlists@for@advance##1by##2{%
+ % THIS IS NEVER USED (at the time of this writing).
+ \edef\pgfplots@loc@TMPa{##2}%
+ \pgfplotscoordmath{default}{parsenumber}{##1}%
+ \pgfplotscoordmath{default}{op}{add}{{\pgfmathresult}{\pgfplots@loc@TMPa}}%
+ \pgfplotscoordmath{default}{tofixed}{\pgfmathresult}%
+ \let##1=\pgfmathresult
+ }%
+ \def\pgfplots@prepare@tick@coordlists@for@tofixed##1{\edef\pgfmathresult{##1}}%
+ \def\pgfplots@prepare@tick@coordlists@for@handletolerance##1{}% does not apply to smithcharts.
+ \def\pgfplots@prepare@tick@coordlists@for@checktickmin##1{%
+ \pgfplotscoordmath{default}{parsenumber}{\pgfplots@tmpa}%
+ \let\pgfplots@loc@TMPa=\pgfmathresult
+ \pgfplotscoordmath{default}{parsenumber}{\csname pgfplots@##1tickmin\endcsname}%
+ \let\pgfplots@loc@TMPb=\pgfmathresult
+ \pgfplotscoordmath{default}{if less than}{\pgfplots@loc@TMPa}{\pgfplots@loc@TMPb}{%
+ \pgfplots@tickshowfalse
+ }{%
+ }%
+ }%
+ \def\pgfplots@prepare@tick@coordlists@for@checktickmax##1{%
+ \pgfplotscoordmath{default}{parsenumber}{\pgfplots@tmpa}%
+ \let\pgfplots@loc@TMPa=\pgfmathresult
+ \pgfplotscoordmath{default}{parsenumber}{\csname pgfplots@##1tickmin\endcsname}%
+ \let\pgfplots@loc@TMPb=\pgfmathresult
+ \pgfplotscoordmath{default}{if less than}{\pgfplots@loc@TMPb}{\pgfplots@loc@TMPa}{%
+ \pgfplots@tickshowfalse
+ }{%
+ }%
+ }%
+ \def\pgfplots@prepare@tick@coordlists@for@checkdatalimits##1{}% I won't do this here. Smithcharts are somewhat special.
+}%
+
+\def\pgfplotspointcartesian@#1,#2\pgfplots@coord@end{%
+ \pgfpointxy@orig{#1}{#2}%
+}%
+\def\pgfplotscoordmathnotifydatascalesetfor@smithchart#1{%
+ \def\pgfplotscoordmathnotifydatascalesetfor##1{}%
+ \edef\pgfplotscoordmathnotifydatascalesetfor@{#1}%
+ \def\pgfplotscoordmathnotifydatascalesetfor@@{x}%
+ \ifx\pgfplotscoordmathnotifydatascalesetfor@@\pgfplotscoordmathnotifydatascalesetfor@
+ \pgfplotscoordmath{#1}{datascaletrafo set params}{0}{0}%
+ \else
+ \def\pgfplotscoordmathnotifydatascalesetfor@@{y}%
+ \ifx\pgfplotscoordmathnotifydatascalesetfor@@\pgfplotscoordmathnotifydatascalesetfor@
+ \pgfplotscoordmath{#1}{datascaletrafo set shift}{0}%
+ \fi
+ \fi
+ \let\pgfplotscoordmathnotifydatascalesetfor=\pgfplotscoordmathnotifydatascalesetfor@smithchart
+}%
+
+% #1: the "a" value on the oriented surf
+% #2: the "b" value.
+% #3: the shift along the normal.
+%
+\def\pgfplotspointonorientedsurfaceabwithbshift@smithchartaxis#1#2#3{%
+ % implement the shift in "b" direction explicitly:
+ \pgfpointadd
+ {\pgfplotspointonorientedsurfaceab{#1}{#2}}%
+ {%
+ \pgfplotspointonorientedsurfaceabtolinespec{v}{0}%
+ \afterassignment\pgfplots@gobble@until@relax
+ \pgf@xa=-#3\relax
+ \edef\pgfplots@shift@no@unit{\pgf@sys@tonumber\pgf@xa}%
+ \pgfqpointscale
+ {\pgfplots@shift@no@unit}
+ {\expandafter\pgfplotspointouternormalvectorofaxis\expandafter{\pgfplotsretval}}%
+ }%
+}
+
+
+% Computes the complex division
+% (A + j B) / (C + j D) = (A C + B D + j (B C - A D) ) / (C^2 + D^2)
+% and assigns the result to \pgfmathresult and \pgfmathresultim . Here
+% 'j = sqrt{-1}' is the imaginary unit.
+%
+% #1 : A
+% #2 : B
+% #3 : C
+% #4 : D
+%
+% The arithmetics is performed in \pgfplotscoordmath{default} (which
+% uses the floating point unit in the initial configuration)
+%
+% Numbers are expected to be already parsed (i.e. you need to invoke
+% \pgfplotscoordmath{default}{parsenumber}{#1}%
+% \let\A=\pgfmathresult
+% before)
+\def\pgfplotscoordmathcomplexdivision#1#2#3#4{%
+ \begingroup
+ \edef\pgfplots@A{#1}%
+ \edef\pgfplots@B{#2}%
+ \edef\pgfplots@C{#3}%
+ \edef\pgfplots@D{#4}%
+ %
+ %
+ % ok, compute it:
+ \pgfplotscoordmath{default}{op}{multiply}{{\pgfplots@A}{\pgfplots@C}}%
+ \let\pgfplots@AC=\pgfmathresult
+ \pgfplotscoordmath{default}{op}{multiply}{{\pgfplots@A}{\pgfplots@D}}%
+ \let\pgfplots@AD=\pgfmathresult
+ \pgfplotscoordmath{default}{op}{multiply}{{\pgfplots@B}{\pgfplots@D}}%
+ \let\pgfplots@BD=\pgfmathresult
+ \pgfplotscoordmath{default}{op}{multiply}{{\pgfplots@B}{\pgfplots@C}}%
+ \let\pgfplots@BC=\pgfmathresult
+ %
+ \pgfplotscoordmath{default}{op}{multiply}{{\pgfplots@C}{\pgfplots@C}}%
+ \let\pgfplots@CC=\pgfmathresult
+ \pgfplotscoordmath{default}{op}{multiply}{{\pgfplots@D}{\pgfplots@D}}%
+ \let\pgfplots@DD=\pgfmathresult
+ \pgfplotscoordmath{default}{op}{add}{{\pgfplots@CC}{\pgfplots@DD}}%
+ \pgfplotscoordmath{default}{op}{reciprocal}{{\pgfmathresult}}%
+ \let\pgfplots@scale=\pgfmathresult
+ %
+ %
+ \pgfplotscoordmath{default}{op}{add}{{\pgfplots@AC}{\pgfplots@BD}}%
+ \pgfplotscoordmath{default}{op}{multiply}{{\pgfmathresult}{\pgfplots@scale}}%
+ \let\pgfplots@x=\pgfmathresult
+ %
+ \pgfplotscoordmath{default}{op}{subtract}{{\pgfplots@BC}{\pgfplots@AD}}%
+ \pgfplotscoordmath{default}{op}{multiply}{{\pgfmathresult}{\pgfplots@scale}}%
+ \let\pgfplots@y=\pgfmathresult
+ %
+ \xdef\pgfplots@glob@TMPa{%
+ \noexpand\def\noexpand\pgfmathresult{\pgfplots@x}%
+ \noexpand\def\noexpand\pgfmathresultim{\pgfplots@y}%
+ }%
+ \endgroup
+ \pgfplots@glob@TMPa
+}%
+
+\def\pgfplotsqpointxy@smithchartaxis#1#2{%
+ \pgf@process{%
+ \ifpgfplotspointisinsmithchartCS
+ \def\pgfplots@x{#1}%
+ \def\pgfplots@y{#2}%
+ \else
+ % compute rx + j* ry = (#1 + j * #2 -1) / (#1 + j*#2 + 1)
+ %
+ % I write
+ % #1 - 1 + j * #2 = A + j * B
+ % 1 + #1 + j * #2 = C + j * D
+ %
+ % -> rx + j * ry = (A + j B) / (C + j D) = (A C + B D + j (B C - A D) ) / (C^2 + D^2)
+ \pgfplotscoordmath{default}{parsenumber}{#1}%
+ \let\pgfplots@x=\pgfmathresult
+ %
+ \pgfplotscoordmath{default}{parsenumber}{#2}%
+ \let\pgfplots@D=\pgfmathresult
+ %
+ \pgfplotscoordmath{default}{one}%
+ \let\pgfplots@one=\pgfmathresult
+ %
+ \pgfplotscoordmath{default}{op}{add}{{\pgfplots@one}{\pgfplots@x}}%
+ \let\pgfplots@C=\pgfmathresult
+ %
+ \pgfplotscoordmath{default}{op}{subtract}{{\pgfplots@x}{\pgfplots@one}}%
+ \let\pgfplots@A=\pgfmathresult
+ %
+ \let\pgfplots@B=\pgfplots@D
+ %
+ \pgfplotscoordmathcomplexdivision\pgfplots@A\pgfplots@B\pgfplots@C\pgfplots@D
+ \pgfplotscoordmath{default}{tofixed}{\pgfmathresult}%
+ \let\pgfplots@x=\pgfmathresult
+ \pgfplotscoordmath{default}{tofixed}{\pgfmathresultim}%
+ \let\pgfplots@y=\pgfmathresult
+ \fi
+ %
+ \pgfplotsqpointxy@smithchart@canvas\pgfplots@x\pgfplots@y
+%\message{pgfplotsqpointxy{#1}{#2} ---> (\pgfplots@x,\pgfplots@y) ---> (\the\pgf@x,\the\pgf@y)}%
+ }%
+}%
+
+\def\pgfplotsqpointxy@smithchart@canvas#1#2{%
+ \ifpgfplots@smithchart@mirrored
+ \pgfqpointxy@orig{-#1}{#2}%
+ \else
+ \pgfqpointxy@orig{#1}{#2}%
+ \fi
+}%
+
+\def\pgfplots@clippath@prepare@for@axistype@smithchartaxis{%
+ \def\pgfplots@clippath@install##1{%
+ \pgfpathellipse
+ {\pgfplotsqpointxy@smithchart@canvas{0}{0}}
+ {\pgfplotsqpointxy@smithchart@canvas{1}{0}}
+ {\pgfplotsqpointxy@smithchart@canvas{0}{1}}%
+ \pgfplots@clippath@use@{##1}%
+ }%
+}%
+
+\def\pgfplotspointouternormalvectorofaxis@smithchartaxis#1#2#3\relax{%
+ \if v#1%
+ \pgfqpoint{0pt}{1pt}%
+ \else
+ \if v#2%
+ \pgfplotspointouternormalvectorofaxisgetv{#1#2#3}%
+ \ifx\pgfplotsretval\pgfutil@empty
+ \def\pgfplotsretval{0}%
+ \fi
+ \pgfpointdiff
+ {\pgfplotsqpointxy@smithchart@canvas{0}{0}}%
+ {\pgfplotsqpointxy{0}{\pgfplotsretval}}%
+ \pgfpointnormalised{}%
+ \else
+ \pgfqpoint{0pt}{1pt}%
+ \fi
+ \fi
+ \pgf@process{}%
+ \endgroup
+}%
+
+\def\pgfplotspoint@initialisation@axes@smithchart{%
+ \begingroup
+ %\pgfplotsqpointxy{\pgfplots@xmin}{\pgfplots@ymin}%
+ \gdef\pgfplotspointminminmin{\pgfplotsqpointxy@smithchart@canvas{0}{0}}%
+ %
+ % the "x" axis is the diameter of the circle (for fixed y=0)
+ \pgf@x=2\pgf@xx
+ \pgf@y=0pt
+ \xdef\pgfplotspointxaxis{\noexpand\pgf@x=\the\pgf@x\space\noexpand\pgf@y=\the\pgf@y\space}%
+ \pgfmathveclen{\pgf@x}{\pgf@y}%
+ \xdef\pgfplotspointxaxislength{\pgfmathresult pt}%
+ %
+ \pgfplotsqpointxy{\pgfplots@xmax}{\pgfplots@ymax}%
+ \xdef\pgfplotspointyaxis{\noexpand\pgf@x=\the\pgf@x\space\noexpand\pgf@y=\the\pgf@y\space}%
+ %
+ % the length of the "y" axis is 2*pi*r (for fixed x=0, the outer
+ % circle).
+ % The radius is the length of (0,1) which is (0pt,\pgf@xx1):
+ \pgfmath@basic@multiply@{\pgf@sys@tonumber\pgf@xx}{1}%
+ \pgfmathmultiply@{\pgfmathresult}{6.28318530717959}% 2*pi * r
+ \xdef\pgfplotspointyaxislength{\pgfmathresult pt}%
+ %
+ \global\let\pgfplotspointzaxis=\pgfpointorigin
+ \gdef\pgfplotspointzaxislength{0pt}%
+ \endgroup
+ %
+ \edef\pgfplots@loc@TMPa{\pgf@sys@tonumber\pgf@xx}%
+ \pgfmathdivide@{16000}{\pgfplots@loc@TMPa}%
+ \let\pgfplots@smithchart@axis@max@xradius@for@ycircle=\pgfmathresult
+ %
+ \ifdim\pgf@xx=\pgf@yy
+ \def\pgfplots@smithchart@axis@ratioxy{1}%
+ \def\pgfplots@smithchart@axis@ratioyx{1}%
+ \let\pgfplots@smithchart@axis@max@yradius@for@ycircle=\pgfplots@smithchart@axis@max@xradius@for@ycircle
+ \else
+ \edef\pgfplots@loc@TMPb{\pgf@sys@tonumber\pgf@yy}%
+ \pgfmathdivide@\pgfplots@loc@TMPa\pgfplots@loc@TMPb
+ \let\pgfplots@smithchart@axis@ratioxy=\pgfmathresult
+ \pgfmathdivide@\pgfplots@loc@TMPb\pgfplots@loc@TMPa
+ \let\pgfplots@smithchart@axis@ratioyx=\pgfmathresult
+ %
+ \pgfmathdivide@{16000}{\pgfplots@loc@TMPb}%
+ \let\pgfplots@smithchart@axis@max@yradius@for@ycircle=\pgfmathresult
+ \fi
+}
+\let\pgfplotspoint@initialisation@units@orig=\pgfplotspoint@initialisation@units
+\def\pgfplotspoint@initialisation@units@smithchart{%
+ \pgfplotspoint@initialisation@units@orig
+ \def\pgfplotspointunity{%
+ \pgfplotspointouternormalvectorofaxisgetv{0v0}% x=0 (outer circle) and v varies (the yticks)
+ \ifx\pgfplotsretval\pgfutil@empty
+ \def\pgfplotsretval{0}%
+ \fi
+ \pgfpointnormalised{\pgfplotsqpointxy{0}{\ifx\pgfplotsretval\pgfutil@empty 0\else\pgfplotsretval\fi}}%
+ \pgf@xa=-\pgf@y
+ \global\pgf@y=\pgf@x
+ \global\pgf@x=\pgf@xa
+ }%
+ \def\pgfplotsunitylength{1}%
+ \def\pgfplotsunityinvlength{1}%
+}%
+
+\def\pgfplots@drawgridlines@INSTALLCLIP@onorientedsurf@smithchartaxis#1{%
+ %\pgfplots@clippath@install{\pgfusepath{clip}}%
+}%
+
+% At this time, the minor/major tick lists are initialised.
+\def\pgfplots@draw@axis@is@prepared@smithchartaxis{%
+ \pgfplots@gridlines@init@grid@stop@points@for xy%
+ \pgfplots@gridlines@init@grid@stop@points@for yx%
+ %
+ % and finalize x:
+ \def\pgfplots@finalize@constraints{1}%
+ \pgfplots@gridlines@init@grid@stop@points@for@computethem{x}{y}{\pgfplots@finalize@constraints}%
+}%
+
+
+% Initialises the '#1grid each nth passes #2' and '#1grid stop at #2'
+% features. All it does is to prepare the
+% method \pgfplots@get@current@grid@stop@point.
+%
+% The method is quite involved. Please refer to the manual for what it
+% is supposed to do, and refer to the code comments below for
+% implementational details.
+%
+% #1 either x or y
+% #2 either x or y
+\def\pgfplots@gridlines@init@grid@stop@points@for#1#2{%
+ %
+ \expandafter\let\csname pgfplots@#1grid@stop@points\endcsname=\relax
+ %
+ \pgfkeysgetvalue{/pgfplots/#1grid each nth passes #2}\pgfplots@loc@TMPa
+ \ifx\pgfplots@loc@TMPa\pgfutil@empty
+ \else
+ % we have no "xticknum -> xtickpos" lookup table yet.
+ \expandafter\def\csname b@pgfplots@#2ticknum@to@pos@lookup\endcsname{0}%
+ %
+ \pgfplotslistnewempty\pgfplots@loc@TMPd
+ % normalise the argument for 'ygrid each nth passes x': each list element
+ % should be of the form '<xtickpos>:<n>' where <n> means that each
+ % <n>th arc can pass.
+ \expandafter\pgfplotsutilforeachcommasep\pgfplots@loc@TMPa\as\entry{%
+ \expandafter\pgfplots@gridlines@init@grid@stop@points@for@normalise\entry\relax#1#2%
+ \expandafter\pgfplotslistpushback\entry\to\pgfplots@loc@TMPd
+ }%
+ \expandafter\let\csname pgfplots@#1grid@stop@points\endcsname=\pgfplots@loc@TMPd
+ %
+ % Ok.
+ %
+ % Now, the 'ygrid each nth passes x' feature relies *crucially* on grid line
+ % indices (for the 'each nth' feature).
+ %
+ % I sort the arcs according to their absolute magnitude and assign
+ % indices into the resulting arrays to normalize that stuff.
+ %
+ % The array is of the form
+ % A[i] = entry of \pgfplots@prepared@tick@positions@*
+ % and contains *both*, major and minor grid lines.
+ \pgfplotsarraynewempty\pgfplots@gridlines
+ \pgfplotscoordmath{default}{zero}%
+ \edef\elem{{-1}{\pgfmathresult}}% require 0 to be zero for symmetry even if there is no such tick pos
+ \expandafter\pgfplotsarraypushback\elem\to\pgfplots@gridlines
+ \pgfplots@if{pgfplots@#1majorgrids}{%
+ % insert all major tick positions, using their absolute value.
+ \expandafter
+ \pgfplotslistforeachungrouped\csname pgfplots@prepared@tick@positions@major@#1\endcsname\as\elem{%
+ \expandafter\pgfplots@prepared@tick@pos@unpack\elem
+ \pgfplotscoordmath{default}{parsenumber}{\pgfplots@tick}%
+ \pgfplotscoordmath{default}{op}{abs}{{\pgfmathresult}}%
+ \edef\elem{{\pgfplots@ticknum}{\pgfmathresult}}%
+ \expandafter\pgfplotsarraypushback\elem\to\pgfplots@gridlines
+ }%
+ }{}%
+ \pgfplots@if{pgfplots@#1minorgrids}{%
+ % now the same for minor grid positions:
+ \expandafter
+ \pgfplotslistforeachungrouped\csname pgfplots@prepared@tick@positions@minor@#1\endcsname\as\elem{%
+ \expandafter\pgfplots@prepared@tick@pos@unpack\elem
+ \pgfplotscoordmath{default}{parsenumber}{\pgfplots@tick}%
+ \pgfplotscoordmath{default}{op}{abs}{{\pgfmathresult}}%
+ \edef\elem{{\pgfplots@ticknum}{\pgfmathresult}}%
+ \expandafter\pgfplotsarraypushback\elem\to\pgfplots@gridlines
+ }%
+ }{}%
+ % sort the array!
+ \pgfkeysgetvalue{/pgfplots/smithchart@sortlt/.@cmd}\pgfplots@loc@TMPa
+ \pgfkeyslet{/pgfplots/iflessthan/.@cmd}\pgfplots@loc@TMPa
+ \pgfplotsarraysort\pgfplots@gridlines
+ %
+ % ok. Now it is sorted.
+ %
+ % I finally need a lookup
+ % \pgfplots@ticknum --> sort index.
+ % If the associated values have the same absolute value, the same
+ % sort index should be assigned.
+ %
+ % For example, the array might be associated to the following tick
+ % positions, sorted by absolute value:
+ % 0.0, 1.0, -1.0, 3.0, -3.0, 4.0, -4.0, 5.0, -5.0
+ % What I want is that
+ % 0.0 gets sort index 0
+ % 1.0 and -1.0 get sort index 1
+ % 3.0 and -3.0 get sort index 2
+ % 4.0 and -4.0 get sort index 3
+ % and so on. The array contains only absolute values, so that's
+ % not too difficult to check.
+ %
+ % Since each of the tick positions can be (uniquely) identified by
+ % its associated \pgfplots@ticknum value, I map \pgfplots@ticknum
+ % to the sort index.
+ \countdef\c@sortindex=\c@pgf@counta
+ \c@sortindex=\pgfkeysvalueof{/pgfplots/#1grid each nth passes #2 start} % this is assigned to the '0.0' gridline (if any)
+ \def\pgfplots@lasttickpos{}%
+ \pgfplotsarrayforeachungrouped\pgfplots@gridlines\as\elem{%
+ \expandafter\pgfplots@prepared@tick@pos@unpack\elem
+ \ifx\pgfplots@lasttickpos\pgfutil@empty
+ \else
+ \ifx\pgfplots@lasttickpos\pgfplots@tick
+ \else
+ \advance\c@sortindex by1
+ \fi
+ \fi
+ \expandafter\edef\csname pgfplots@#1tickpos@to@sortidx@\pgfplots@ticknum\endcsname{\the\c@sortindex}%
+%\message{\pgfplots@ticknum\space(abs(tickpos) = \pgfplots@tick)---> sort index \csname pgfplots@#1tickpos@to@sortidx@\pgfplots@ticknum\endcsname^^J}%
+ \let\pgfplots@lasttickpos=\pgfplots@tick
+ }%
+ %
+ % unfortunately, I can't free the \pgfplots@gridlines array
+ % without extensive overhead :-(
+ \fi
+ %
+ \expandafter\let\csname b@pgfplots@#1gridline@stopmap\endcsname\relax
+ \pgfkeysgetvalue{/pgfplots/#1grid stop at #2}\pgfplots@loc@TMPa
+ \ifx\pgfplots@loc@TMPa\pgfutil@empty
+ \else
+ \edef\pgfplots@loc@TMPa{\pgfplots@loc@TMPa,}% this inserts the final comma and handles any active ':' sign (for french babel)
+ \def\pgfplots@loc@TMPb{\pgfplots@gridlines@init@stop@maps #1#2}%
+ \expandafter\pgfplots@loc@TMPb\pgfplots@loc@TMPa\pgfplots@EOI%
+ \fi
+ %
+ %
+ % Now, compute all final stop positions. Also prepare the cross
+ % dependencies between x grids and y grids here (such that there
+ % is no grid line stopping in white space)
+ %
+ \if#1x%
+ \def\pgfplots@finalize@constraints{0}% we have to wait until y stop points are known.
+ \else
+ \def\pgfplots@finalize@constraints{1}%
+ \fi
+ \pgfplots@gridlines@init@grid@stop@points@for@computethem{#1}{#2}{\pgfplots@finalize@constraints}%
+}%
+% #1,#2,#3 the arguments for
+% \pgfplots@gridlines@preparation@get@current@grid@stop@point
+\def\pgfplots@gridlines@init@grid@stop@points@for@computethem#1#2#3{%
+ %
+ \expandafter\pgfplotslistforeachungrouped\csname pgfplots@prepared@tick@positions@major@#1\endcsname\as\elem{%
+ \expandafter\pgfplots@prepared@tick@pos@unpack\elem
+ \pgfplotscoordmath{default}{parsenumber}{\pgfplots@tick}\let\pgfplots@tick=\pgfmathresult
+ \pgfplots@gridlines@preparation@get@current@grid@stop@point{#1}{#2}{\pgfplots@tick}{#3}%
+ \if1#3%
+ \pgfplots@gridlines@let{#1}{\pgfplots@tick@prepared}=\pgfplotsretval
+ \fi
+ }%
+ \expandafter\pgfplotslistforeachungrouped\csname pgfplots@prepared@tick@positions@minor@#1\endcsname\as\elem{%
+ \expandafter\pgfplots@prepared@tick@pos@unpack\elem
+ \pgfplotscoordmath{default}{parsenumber}{\pgfplots@tick}\let\pgfplots@tick=\pgfmathresult
+ \pgfplots@gridlines@preparation@get@current@grid@stop@point{#1}{#2}{\pgfplots@tick}{#3}%
+ \if1#3%
+ \pgfplots@gridlines@let{#1}{\pgfplots@tick@prepared}=\pgfplotsretval
+ \fi
+ }%
+ \expandafter\def\csname b@pgfplots@#1gridline@stopmap\endcsname{1}%
+}
+
+\def\pgfplots@gridlines@init@stop@maps#1#2{%
+ \pgfutil@ifnextchar\pgfplots@EOI{%
+ \pgfutil@gobble
+ }{%
+ \pgfutil@ifnextchar,{%
+ \pgfplots@gridlines@init@stop@maps@next@@#1#2%
+ }{%
+ \pgfplots@gridlines@init@stop@maps@next#1#2%
+ }%
+ }%
+}%
+\def\pgfplots@gridlines@init@stop@maps@next#1#2#3:#4,{%
+ \pgfplotscoordmath{default}{parsenumber}{#4}%
+ \let\pgfplots@loc@TMPa=\pgfmathresult
+ \pgfplots@gridlines@stopmap@prepare{#3}%
+ \pgfplots@gridlines@let{#1}{\pgfmathresult}=\pgfplots@loc@TMPa
+ \expandafter\def\csname b@pgfplots@#1gridline@stopmap\endcsname{1}%
+ %
+ \pgfplots@gridlines@init@stop@maps #1#2%
+}
+% just eat one empty comma:
+\def\pgfplots@gridlines@init@stop@maps@next@@#1#2,{\pgfplots@gridlines@init@stop@maps #1#2}%
+\def\pgfplots@gridlines@let#1#2=#3{%
+ \expandafter\let\csname pgfplots@#1gridline@stopmap@#2\endcsname=#3%
+ \if#1y%
+ % support symmetry:
+ % add -\pgfmathresult to the map.
+ % To disable this symmetry, use 'ygrid stop at x={0.2:4 -0.2:5}
+ % you can also use an empty value '-0.2:{}', that's also ok.
+ \expandafter\let\csname pgfplots@#1gridline@stopmap@-#2\endcsname=#3%
+ \fi
+}%
+
+\def\pgfplots@gridlines@stopmap@prepare@digits{2}%
+\def\pgfplots@gridlines@stopmap@prepare#1{%
+ \begingroup
+ \pgfmathfloatparsenumber{#1}%
+ \let\pgfmathfloat@round@precision=\pgfplots@gridlines@stopmap@prepare@digits%
+ \pgfmathfloatroundzerofill\pgfmathresult
+ \pgfmath@smuggleone\pgfmathresult
+ \endgroup
+}%
+\def\pgfplots@gridlines@stopmap@trunc@#1.#2#3#4\relax{%
+ \def\pgfmathresult{#1.#2#3}%
+}%
+
+\pgfkeysdefargs{/pgfplots/smithchart@sortlt}{#1#2#3#4}{%
+ \expandafter\pgfplots@prepared@tick@pos@unpack#1%
+ \let\pgfplots@A=\pgfplots@tick
+ \expandafter\pgfplots@prepared@tick@pos@unpack#2%
+ \let\pgfplots@B=\pgfplots@tick
+ \pgfplotscoordmath{default}{if less than}{\pgfplots@A}{\pgfplots@B}{#3}{#4}%
+}%
+
+% initialise a lookuptable from ticknumber -> tick position (sort
+% of an array)
+%
+% This is only invoked if it is needed (if 'arc
+% limits={[index]4,[index]2}' or something like that is used, see the
+% manual).
+%
+% #1 either x or y
+% #2 either x or y
+\def\pgfplots@gridlines@init@grid@stop@points@for@init@ticknum@lookup#1#2{%
+ \c@pgf@counta=0
+ \pgfplots@if{pgfplots@#1majorgrids}{%
+ \expandafter
+ \pgfplotslistforeachungrouped\csname pgfplots@prepared@tick@positions@major@#2\endcsname\as\elem{%
+ \expandafter\pgfplots@prepared@tick@pos@unpack\elem
+ \expandafter\let\csname pgfplots@#2tick@num@to@pos@\the\c@pgf@counta\endcsname=\pgfplots@tick
+ \advance\c@pgf@counta by1
+ }%
+ }{}%
+ \pgfplots@if{pgfplots@#1minorgrids}{%
+ \expandafter
+ \pgfplotslistforeachungrouped\csname pgfplots@prepared@tick@positions@minor@#2\endcsname\as\elem{%
+ \expandafter\pgfplots@prepared@tick@pos@unpack\elem
+ \expandafter\let\csname pgfplots@#2tick@num@to@pos@\the\c@pgf@counta\endcsname=\pgfplots@tick
+ \advance\c@pgf@counta by1
+ }%
+ }{}%
+ \expandafter\def\csname b@pgfplots@#2ticknum@to@pos@lookup\endcsname{1}%
+}%
+\def\pgfplots@gridlines@init@grid@stop@points@for@normalise#1\relax#2#3{%
+ \def\b@pgfplots@haslt{0}%
+ %
+ \pgfutil@in@{if <}{#1}%
+ \ifpgfutil@in@
+ % strip the white space between 'if' and '<':
+ \def\pgfplots@loc@TMPa##1if <##2\relax{\edef\entry{##1if<##2}}%
+ \expandafter\pgfplots@loc@TMPa\entry\relax
+ \def\b@pgfplots@haslt{1}%
+ \fi
+ %
+ \pgfutil@in@{if<}{#1}%
+ \ifpgfutil@in@
+ \def\b@pgfplots@haslt{1}%
+ \fi
+ %
+ \pgfutil@in@:{#1}%
+ \ifpgfutil@in@
+ \def\b@pgfplots@hascolon{1}%
+ \else
+ \def\b@pgfplots@hascolon{0}%
+ \fi
+ %
+ \if1\b@pgfplots@hascolon
+ \edef\entry{\entry\if0\b@pgfplots@haslt if<\fi}%
+ \else
+ \if1\b@pgfplots@haslt
+ \expandafter\pgfplots@gridlines@stop@at@unpack@@@\entry\relax
+ \edef\entry{\pgfplots@grid@stop@at:2if<\pgfplots@grid@stop@at@iflt}%
+ \else
+ \edef\entry{\entry:2if<}%
+ \fi%
+ \fi%
+ %
+ \pgfutil@in@{[index]}{#1}%
+ \ifpgfutil@in@
+ \if0\csname b@pgfplots@#3ticknum@to@pos@lookup\endcsname
+ \pgfplots@gridlines@init@grid@stop@points@for@init@ticknum@lookup#2#3%
+ \fi
+ \expandafter\pgfplots@gridlines@stop@at@unpack\entry\relax
+ \pgfutil@ifundefined{pgfplots@#3tick@num@to@pos@\pgfplots@grid@stop@at}{%
+ \pgfplots@warning{There is no #3tick with index '\pgfplots@grid@stop@at'. Skipping it.}%
+ \let\entry=\pgfutil@empty
+ }{%
+ \edef\entry{\csname pgfplots@#3tick@num@to@pos@\pgfplots@grid@stop@at\endcsname:\pgfplots@grid@stop@at@eachnth}%
+ }%
+ \fi
+ %
+ \expandafter\pgfplots@gridlines@stop@at@unpack\entry\relax
+ \pgfplotscoordmath{default}{parsenumber}\pgfplots@grid@stop@at
+ \let\pgfplots@grid@stop@at=\pgfmathresult
+ \ifx\pgfplots@grid@stop@at@iflt\pgfutil@empty
+ \else
+ \pgfplotscoordmath{default}{parsenumber}\pgfplots@grid@stop@at@iflt
+ \let\pgfplots@grid@stop@at@iflt=\pgfmathresult
+ \fi
+ \edef\entry{\pgfplots@grid@stop@at:\pgfplots@grid@stop@at@eachnth if<\pgfplots@grid@stop@at@iflt}%
+}%
+\def\pgfplots@gridlines@stop@at@unpack@@@#1if<#2\relax{%
+ \def\pgfplots@grid@stop@at{#1}%
+ \def\pgfplots@grid@stop@at@iflt{#2}%
+}%
+\def\pgfplots@gridlines@stop@at@unpack#1:#2if<#3\relax{%
+ \def\pgfplots@grid@stop@at{#1}%
+ \def\pgfplots@grid@stop@at@eachnth{#2}%
+ \def\pgfplots@grid@stop@at@iflt{#3}%
+}%
+
+% Returns the xtick position which should end the current arc.
+%
+% This is an INTERNAL preparation method. See
+% \pgfplots@get@current@grid@stop@point for the final one.
+%
+% Note that arcs correspond to ygrid lines.
+%
+% #1 either x or y
+% #2 either x or y
+% #3 the value of the current grid line
+% #4 a boolean which expands either to 0 or to 1.
+% The \pgfplots@get@current@grid@stop@point@handle@constraints method
+% will be invoked if and only if #4=1
+%
+% @POSTCONDITION On output,
+% - \pgfplotsretval will be filled with the
+% result. If the result is empty, no restriction is imposed.
+% Otherwise, it contains the #2tick value at which the current #1grid shall end.
+% The result is already processed with
+% \pgfplotscoordmath{default}{parsenumber}{<value>}
+% - \pgfplots@tick@prepared contains a rounded representation of #3.
+%
+% The method relies on the 'ygrid each nth passes x' feature, more specifically the
+% stuff prepared by \pgfplots@gridlines@init@grid@stop@points@for
+\def\pgfplots@gridlines@preparation@get@current@grid@stop@point#1#2#3#4{%
+ \def\pgfplotsretval{}%
+ %
+ \pgfplots@gridlines@stopmap@prepare{#3}%
+ \let\pgfplots@tick@prepared=\pgfmathresult
+ \pgfmathfloatabs@\pgfplots@tick@prepared
+ \let\pgfplots@tick@prepared@abs=\pgfmathresult
+ %
+ \pgfplotscoordmath{default}{op}{abs}{{#3}}%
+ \let\pgfplots@tick@abs=\pgfmathresult
+ %
+ % first: check the '#1grid stop at #2':
+ \expandafter\ifx\csname b@pgfplots@#1gridline@stopmap\endcsname\relax%
+ % ok. there is no such thing.
+ \else
+ % ah - process it!
+ \pgfutil@ifundefined{pgfplots@#1gridline@stopmap@\pgfplots@tick@prepared}{%
+ }{%
+ \edef\pgfplotsretval{\csname pgfplots@#1gridline@stopmap@\pgfplots@tick@prepared\endcsname}%
+ }%
+ \fi
+ %
+ \ifx\pgfplotsretval\pgfutil@empty
+ % the individual map failed. Ok, then check for the '#1grid each nth passes #2'
+ \expandafter\ifx\csname pgfplots@#1grid@stop@points\endcsname\relax
+ \else
+ % \pgfplots@ticknum is defined in this context here.
+ \pgfutil@ifundefined{pgfplots@#1tickpos@to@sortidx@\pgfplots@ticknum}{%
+ \pgfplots@warning{Sorry, I can't get the current arc limit for #1grid no \#\pgfplots@ticknum\space(value \pgfplots@tick). This seems like an internal error!?}%
+ }{%
+ % get the sort index for the current tick (which is
+ % uniquely identified by its \pgfplots@ticknum)
+ \expandafter\let\expandafter\pgfplots@k\csname pgfplots@#1tickpos@to@sortidx@\pgfplots@ticknum\endcsname
+ %
+ \expandafter\pgfplotslistforeachungrouped\csname pgfplots@#1grid@stop@points\endcsname\as\pgfplots@loc@TMPa{%
+ \ifx\pgfplotsretval\pgfutil@empty
+ % we found no final limit so far. proceed.
+ \expandafter\pgfplots@gridlines@stop@at@unpack\pgfplots@loc@TMPa\relax
+ \ifx\pgfplots@grid@stop@at@iflt\pgfutil@empty
+ \pgfplots@loop@CONTINUEtrue
+ \else
+ \pgfplotscoordmath{default}{if less than}{\pgfplots@tick@abs}{\pgfplots@grid@stop@at@iflt}{%
+ \pgfplots@loop@CONTINUEtrue
+ }{%
+ \pgfplots@loop@CONTINUEfalse
+ }%
+ \fi
+ %
+ \ifpgfplots@loop@CONTINUE
+ \pgfplotsmathmodint\pgfplots@k\pgfplots@grid@stop@at@eachnth
+ \ifnum\pgfmathresult=0
+ \c@pgf@counta=\pgfplots@k
+ \divide\c@pgf@counta by\pgfplots@grid@stop@at@eachnth\relax
+ \edef\pgfplots@k{\the\c@pgf@counta}%
+ \else
+ % found the final limit.
+ %
+ % Now, check the constraints which couple
+ % X and Y.
+ \let\pgfplotsretval=\pgfplots@grid@stop@at
+ \if1#4%
+ \pgfplots@get@current@grid@stop@point@handle@constraints #1#2{#3}%
+ \fi
+ \fi
+ \fi
+ \fi
+ }%
+ }%
+ \fi
+ \fi
+ \ifx\pgfplotsretval\pgfutil@empty
+ \else
+ \expandafter\let\csname pgfplots@final@stop@point@for@#1tick@\pgfplots@tick@prepared\endcsname=\pgfplotsretval
+%\message{#1 grid line: storing end value for '#3' END[\pgfplots@tick@prepared] = \pgfplotsretval.^^J}%
+ \fi
+}%
+
+% PRECONDITION
+% \pgfplotsretval contains a non-zero constraint for the ygrid at #1.
+%
+% POSTCONDITION
+% either \pgfplotsretval is unchanged, or it is reset to
+% \pgfutil@empty if constraints are violated.
+%
+% The constraints are ONLY effective if BOTH, incomplete x- and y grid
+% lines are in effect. In that case, it should never happen that a
+% single grid line ends in a dead-end somewhere in white space.
+%
+% I enforce two constraints which apply only to ygrid to fix this
+% issue (this may be improved later).
+%
+% The idea is simple:
+% 1. suppose the grid line 'x=1' stops at 'y=5'.
+% Suppose further that the y grid line 'y=0.95' should stop at 'x=1'.
+% Is that acceptable? Yes, because |y| < 5.
+% Now, suppose an y grid line with |y| > 5 should stop at 'x=1'.
+% Is this allowed? NO! Because it would become a dead end since
+% the 'x=1' line ends at 'y=5'!
+%
+% So, whenever we consider ygrids and stop point candidates "x=X",
+% acquire the value Q where the x (!) grid line "x=X" stops.
+% If |y| > Q, the candidate "x=X" is rejected.
+%
+% 2. There might still be the case that x grid lines have dead-ends.
+% The current solution applies the idea first to all y grid lines,
+% and once the y grid lines are ready, it applies the same idea to
+% x grid lines.
+%
+% Uncomment the routine(s) and run the test cases to see what happens.
+\def\pgfplots@get@current@grid@stop@point@handle@constraints#1#2#3{%
+ \ifx\pgfplotsretval\pgfutil@empty
+ \else
+ \pgfplots@gridlines@stopmap@prepare{\pgfplotsretval}%
+ \let\pgfplots@loc@TMPa=\pgfmathresult
+ %
+%\message{checking ending '#1=#3' at '#2=\pgfplotsretval'. '#2=\pgfplots@loc@TMPa' stops}%
+ \pgfutil@ifundefined{pgfplots@final@stop@point@for@#2tick@\pgfplots@loc@TMPa}{%
+ % no constraint. Ok.
+%\message{ nowhere. No constraint.^^J}%
+ }{%
+%\message{ at \pgfplots@loc@TMPa. Feasible: }%
+ % Oh, a constraint. That means
+ % further work.
+ \expandafter\let\expandafter\pgfplots@loc@TMPa\csname pgfplots@final@stop@point@for@#2tick@\pgfmathresult\endcsname
+ \pgfplotscoordmath{default}{op}{abs}{{#3}}%
+ \pgfplotscoordmath{default}{if less than}{\pgfmathresult}{\pgfplots@loc@TMPa}{%
+ % ok, we can use the found
+ % stop value.
+%\message{YES.^^J}%
+ }{%
+%\message{NO.^^J}%
+ % no, the stop value is
+ % invalid; it would stop in
+ % white space!
+ \let\pgfplotsretval=\pgfutil@empty
+ }%
+ }%
+ \fi
+}%
+
+% Returns the xtick position which should end the current arc.
+%
+% Note that arcs correspond to ygrid lines.
+%
+% #1 either x or y
+% #2 either x or y
+% #3 the value of the current grid line
+%
+% @POSTCONDITION On output, \pgfplotsretval will be filled with the
+% result. If the result is empty, no restriction is imposed.
+% Otherwise, it contains the #2tick value at which the current #1grid shall end.
+% The result is already processed with
+% \pgfplotscoordmath{default}{parsenumber}{<value>}
+%
+% The method relies on the 'ygrid each nth passes x' feature, more specifically the
+% stuff prepared by \pgfplots@gridlines@init@grid@stop@points@for
+%
+% Note that all work has already been done by
+% \pgfplots@gridlines@init@grid@stop@points@for. We only need to query
+% the result at this point.
+% @see \pgfplots@gridlines@init@grid@stop@points@for
+% @see \pgfplots@gridlines@preparation@get@current@grid@stop@point
+\def\pgfplots@get@current@grid@stop@point#1#2#3{%
+ \def\pgfplotsretval{}%
+ %
+ % check the '#1grid stop at #2':
+ \expandafter\ifx\csname b@pgfplots@#1gridline@stopmap\endcsname\relax%
+ % ok. there is no such thing.
+ \else
+ %
+ \pgfplots@gridlines@stopmap@prepare{#3}%
+ \let\pgfplots@tick@prepared=\pgfmathresult
+ \pgfmathfloatabs@\pgfplots@tick@prepared
+ \let\pgfplots@tick@prepared@abs=\pgfmathresult
+ %
+ % ah - process it!
+ \pgfutil@ifundefined{pgfplots@#1gridline@stopmap@\pgfplots@tick@prepared}{%
+ \let\pgfplotsretval\pgfutil@empty
+ }{%
+ \edef\pgfplotsretval{\csname pgfplots@#1gridline@stopmap@\pgfplots@tick@prepared\endcsname}%
+ }%
+ \fi
+ %
+}%
+
+
+\def\pgfplots@smithchart@draw@xcircle#1{%
+ \pgfplotscoordmath{default}{one}%
+ \let\pgfplots@loc@TMPa=\pgfmathresult
+ %
+ \pgfplotscoordmath{default}{parsenumber}{#1}%
+ \let\pgfplots@x=\pgfmathresult
+ %
+ \pgfplotscoordmath{default}{op}{add}{{\pgfplots@loc@TMPa}{\pgfplots@x}}%
+ \let\pgfplots@radius@inverse=\pgfmathresult
+ \pgfplotscoordmath{default}{op}{reciprocal}{{\pgfmathresult}}%
+ \let\pgfplots@radius=\pgfmathresult
+ \pgfplotscoordmath{default}{op}{multiply}{{\pgfmathresult}{\pgfplots@x}}%
+ \pgfplotscoordmath{default}{tofixed}{\pgfmathresult}%
+ \let\pgfplots@center=\pgfmathresult
+ %
+ \pgfplotscoordmath{default}{tofixed}{\pgfplots@radius}%
+ \let\pgfplots@radius=\pgfmathresult
+ %
+ \pgfplotscoordmath{default}{tofixed}{\pgfplots@radius@inverse}%
+ \let\pgfplots@radius@inverse=\pgfmathresult
+ %
+ % This here would suffice in case 'xgrid each nth passes y={}':
+% \pgfpathellipse
+% {\pgfplotsqpointxy@smithchart@canvas{\pgfplots@center}{0}}
+% {\pgfplotsqpointxy@smithchart@canvas{\pgfplots@radius}{0}}
+% {\pgfplotsqpointxy@smithchart@canvas{0}{\pgfplots@radius}}%
+ %
+ % but we also check for the 'xgrid each nth passes y' feature:
+ \pgfplots@get@current@grid@stop@point xy{\pgfplots@x}%
+ \let\pgfplots@arc@ends@at@y@arc@value\pgfplotsretval%
+ %
+ \ifx\pgfplots@arc@ends@at@y@arc@value\pgfutil@empty
+ % Ok. There is no specific end point -- simply use the
+ % (1,0) point (i.e. draw the full circle).
+ %
+ \pgfmathadd@{\pgfplots@center}{\pgfplots@radius}%
+ \let\pgfplots@start=\pgfmathresult%
+ \def\pgfplots@startim{0}%
+ \def\pgfplots@startangle{0}%
+ \let\pgfplots@end=\pgfplots@start
+ \let\pgfplots@endim=\pgfplots@startim
+ \def\pgfplots@endangle{360}%
+ \else
+ % Ok. The arc should end before it reaches the (1,0)
+ % point. Determine the exact position and the
+ % corresponding arc end angle.
+ %
+ % In general, the intersection between the circle for
+ % fixed x=A and fixed y=B is given by
+ %
+ % p + j * q = (A + j * B -1 ) / ( A + j*B +1)
+ % see http://www.siart.de/lehre/tutorien.xhtml#smishort
+ \pgfplotscoordmath{default}{one}%
+ \let\pgfplots@one=\pgfmathresult
+ \pgfplotscoordmath{default}{parsenumber}{-1}%
+ \let\pgfplots@mone=\pgfmathresult
+ \pgfplotscoordmath{default}{op}{add}{{\pgfplots@x}{\pgfplots@mone}}%
+ \let\pgfplots@A@mone=\pgfmathresult
+ \pgfplotscoordmath{default}{op}{add}{{\pgfplots@x}{\pgfplots@one}}%
+ \let\pgfplots@A@one=\pgfmathresult
+ % oh - we should only draw a partial arc.
+ % Well, then compute its end point and the
+ % corresponding end angle.
+ \pgfplotscoordmathcomplexdivision
+ {\pgfplots@A@mone}{\pgfplots@arc@ends@at@y@arc@value}%
+ {\pgfplots@A@one}{\pgfplots@arc@ends@at@y@arc@value}%
+ \let\pgfplots@start=\pgfmathresult
+ \let\pgfplots@startim=\pgfmathresultim
+ \pgfplotscoordmath{default}{tofixed}{\pgfplots@start}%
+ \let\pgfplots@start=\pgfmathresult
+ \pgfplotscoordmath{default}{tofixed}{\pgfplots@startim}%
+ \let\pgfplots@startim=\pgfmathresult
+ %
+ \pgfplots@compute@angle@of@point@in@circle\pgfplots@start\pgfplots@startim{\pgfplots@center}{\pgfplots@radius}{\pgfplots@radius@inverse}%
+ \let\pgfplots@startangle=\pgfmathresult
+ \pgfmathsubtract@{360}{\pgfplots@startangle}%
+ \let\pgfplots@endangle=\pgfmathresult
+ \let\pgfplots@end=\pgfplots@start
+ \edef\pgfplots@endim{-\pgfplots@startim}%
+ \ifdim\pgfplots@startangle pt>\pgfplots@endangle pt
+ \let\pgfplots@loc@TMPa=\pgfplots@startangle
+ \let\pgfplots@startangle=\pgfplots@endangle
+ \let\pgfplots@endangle=\pgfplots@loc@TMPa
+ \fi
+ \fi
+ %
+%\message{X grid line \#\csname pgfplots@ticknum\endcsname \space at '#1': center = (\pgfplots@center,0); radius = \pgfplots@radius\space(start angle \pgfplots@startangle, end angle = \pgfplots@endangle; stops at y = \pgfplots@arc@ends@at@y@arc@value).^^J}%
+ %
+ % Now, compute the arc.
+ %
+ % first, compute the absolute x/y radii:
+ \pgf@xa=\pgfplots@radius\pgf@xx
+ \pgf@xb=\pgfplots@radius\pgf@yy
+ \edef\pgfplots@mirror@sign{\ifpgfplots@smithchart@mirrored -\fi}%
+ \pgfpathmoveto{\pgfplotsqpointxy@smithchart@canvas{\pgfplots@start}{\pgfplots@startim}}%
+ % note that the case startangle > endangle is
+ % automatically correct; patharc handles that.
+ %\edef\pgfplots@loc@TMPa{{\pgfplots@startangle}{\pgfplots@endangle}{\pgfplots@mirror@sign\the\pgf@xa\space and \the\pgf@xb}}%
+ %\expandafter\pgfpatharc\pgfplots@loc@TMPa
+ %
+ % prefer \pgfpatharctoprecomputed. It is faster and more accurate
+ \edef\pgfplots@loc@TMPa{%
+ {\noexpand\pgfplotsqpointxy@smithchart@canvas{\pgfplots@center}{0}}%
+ {\pgfplots@startangle}%
+ {\pgfplots@endangle}%
+ {\noexpand\pgfplotsqpointxy@smithchart@canvas{\pgfplots@end}{\pgfplots@endim}}%
+ {\pgfplots@mirror@sign\the\pgf@xa}%
+ {\the\pgf@xb}%
+ {\pgfplots@mirror@sign\pgfplots@smithchart@axis@ratioxy}%
+ {\pgfplots@mirror@sign\pgfplots@smithchart@axis@ratioyx}%
+ }%
+ \expandafter\pgfpatharctoprecomputed\pgfplots@loc@TMPa
+}
+
+\def\pgfplots@smithchart@draw@yarc#1{%
+ \pgfplotscoordmath{default}{parsenumber}{#1}%
+ \let\pgfplots@y\pgfmathresult
+ \pgfplotscoordmath{default}{op}{abs}{{\pgfplots@y}}%
+ \pgfplotscoordmath{default}{if less than}{\pgfmathresult}{\pgfplots@almost@zero@thresh}{%
+ \pgfpathmoveto{\pgfplotsqpointxy@smithchart@canvas{-1}{0}}%
+ \pgfpathlineto{\pgfplotsqpointxy@smithchart@canvas{1}{0}}%
+ }{%
+ \pgfplotscoordmath{default}{op}{reciprocal}{{\pgfplots@y}}%
+ \pgfplotscoordmath{default}{tofixed}{\pgfmathresult}%
+ \let\pgfplots@signedradius=\pgfmathresult
+ %
+ \pgfplotscoordmath{default}{tofixed}{\pgfplots@y}%
+ \ifdim\pgfplots@signedradius pt<0pt
+ \def\pgfplots@radius@sign{-}%
+ \edef\pgfplots@radius@inverse{-\pgfmathresult}%
+ \edef\pgfplots@radius{-\pgfplots@signedradius}%
+ \else
+ \def\pgfplots@radius@sign{}%
+ \edef\pgfplots@radius@inverse{\pgfmathresult}%
+ \let\pgfplots@radius=\pgfplots@signedradius
+ \fi
+ % this here is the correct, complete circle -- together
+ % with a clip path, you get what you want:
+ %\pgfpathellipse
+ % {\pgfplotsqpointxy@smithchart@canvas{1}{\pgfplots@signedradius}}
+ % {\pgfplotsqpointxy@smithchart@canvas{\pgfplots@signedradius}{0}}
+ % {\pgfplotsqpointxy@smithchart@canvas{0}{\pgfplots@signedradius}}%
+ % But I only want the arc (probably stopped earlier to
+ % improve qualtity of the chart)
+ %
+ % compute start point for the arc.
+ %
+ % To do so, we need to compute the intersection between
+ % the circle for fixed x=0 and the circle for y=#1.
+ %
+ % In general, the intersection between the circle for
+ % fixed x=A and fixed y=B is given by
+ %
+ % p + j * q = (A + j * B -1 ) / ( A + j*B +1)
+ % see http://www.siart.de/lehre/tutorien.xhtml#smishort
+ %
+ % inserting A = 0 and B = #1 yields the result
+ % p=\pgfplots@start
+ % q=\pgfplots@startim
+ % as follows:
+ \pgfplotscoordmath{default}{one}%
+ \let\pgfplots@one=\pgfmathresult
+ \pgfplotscoordmath{default}{parsenumber}{-1}%
+ \let\pgfplots@mone=\pgfmathresult
+ \pgfplotscoordmathcomplexdivision{\pgfplots@mone}{\pgfplots@y}{\pgfplots@one}{\pgfplots@y}%
+ \let\pgfplots@start=\pgfmathresult
+ \let\pgfplots@startim=\pgfmathresultim
+ \pgfplotscoordmath{default}{tofixed}{\pgfplots@start}%
+ \let\pgfplots@start=\pgfmathresult
+ \pgfplotscoordmath{default}{tofixed}{\pgfplots@startim}%
+ \let\pgfplots@startim=\pgfmathresult
+ %
+ \pgfplots@compute@angle@of@point@in@circle\pgfplots@start\pgfplots@startim{1}{\pgfplots@signedradius}{\pgfplots@radius@inverse}%
+ \let\pgfplots@startangle=\pgfmathresult
+ %
+ %
+ % compute end angle.
+ \pgfplots@get@current@grid@stop@point yx{\pgfplots@y}%
+ \let\pgfplots@arc@ends@at@x@circle@value\pgfplotsretval%
+ %
+ \ifx\pgfplots@arc@ends@at@x@circle@value\pgfutil@empty
+ % Ok. There is no specific end point -- simply use the
+ % (1,0) point (i.e. draw the full arc).
+ %
+ % The "0 degree" angle in my circles is in the direction
+ % of (1,0) .
+ \ifdim\pgfplots@startim pt>0pt
+ % ok; this arc belongs to the upper hemisphere.
+ \def\pgfplots@endangle{270}%
+ \else
+ % ok; this arc belongs to the lower hemisphere.
+ \def\pgfplots@endangle{90}%
+ \fi
+ \def\pgfplots@end{1}%
+ \def\pgfplots@endim{0}%
+ \else
+ % Ok. The arc should end before it reaches the (1,0)
+ % point. Determine the exact position and the
+ % corresponding arc end angle.
+ \pgfplotscoordmath{default}{op}{add}{{\pgfplots@arc@ends@at@x@circle@value}{\pgfplots@mone}}%
+ \let\pgfplots@A@mone=\pgfmathresult
+ \pgfplotscoordmath{default}{op}{add}{{\pgfplots@arc@ends@at@x@circle@value}{\pgfplots@one}}%
+ \let\pgfplots@A@one=\pgfmathresult
+ % oh - we should only draw a partial arc.
+ % Well, then compute its end point and the
+ % corresponding end angle.
+ \pgfplotscoordmathcomplexdivision{\pgfplots@A@mone}{\pgfplots@y}{\pgfplots@A@one}{\pgfplots@y}%
+ \let\pgfplots@end=\pgfmathresult
+ \let\pgfplots@endim=\pgfmathresultim
+ \pgfplotscoordmath{default}{tofixed}{\pgfplots@end}%
+ \let\pgfplots@end=\pgfmathresult
+ \pgfplotscoordmath{default}{tofixed}{\pgfplots@endim}%
+ \let\pgfplots@endim=\pgfmathresult
+ %
+ \pgfplots@compute@angle@of@point@in@circle\pgfplots@end\pgfplots@endim{1}{\pgfplots@signedradius}{\pgfplots@radius@inverse}%
+ \let\pgfplots@endangle=\pgfmathresult
+ \fi
+ %
+ %
+ %
+ % Now, compute the arc.
+ %
+ % first, compute the absolute x/y radii:
+ %
+ % Note that for small y (like y=0.01), the arc is almost a
+ % straight line. Consequently, the ellipsis radius will be much larger
+ % than 16000, violating TeX's number range.
+ %
+ % To avoid that, I clip it to the highest allowed value.
+ % The final radius is
+ % \pgfplots@radius * \pgf@xx and \pgfplots@radius * \pgf@yy.
+ % the clipped value thus needs to respect the magnitude of \pgf@xx and \pgf@yy.
+ \ifdim\pgfplots@radius pt<\pgfplots@smithchart@axis@max@xradius@for@ycircle pt
+ \let\pgfplots@radius@x\pgfplots@radius
+ \else
+ \let\pgfplots@radius@x=\pgfplots@smithchart@axis@max@xradius@for@ycircle
+ \fi
+ \ifdim\pgfplots@radius pt<\pgfplots@smithchart@axis@max@yradius@for@ycircle pt
+ \let\pgfplots@radius@y\pgfplots@radius
+ \else
+ \let\pgfplots@radius@y=\pgfplots@smithchart@axis@max@yradius@for@ycircle
+ \fi
+%\message{Y grid line \#\csname pgfplots@ticknum\endcsname\space at '#1': center = (1,\pgfplots@signedradius); signedradius = \pgfplots@signedradius\space clipped radii = \pgfplots@radius@x*\the\pgf@xx\space and \pgfplots@radius@y*\the\pgf@yy\space ( start angle \pgfplots@startangle, end angle \pgfplots@endangle, arc limit: \ifx\pgfplots@arc@ends@at@x@circle@value\pgfutil@empty NONE\else \pgfplots@arc@ends@at@x@circle@value\fi)^^J}%
+ \pgf@xa=\pgfplots@radius@x\pgf@xx
+ \pgf@xb=\pgfplots@radius@y\pgf@yy
+ \edef\pgfplots@mirror@sign{\ifpgfplots@smithchart@mirrored -\fi}%
+ \pgfpathmoveto{\pgfplotsqpointxy@smithchart@canvas{\pgfplots@start}{\pgfplots@startim}}%
+ % note that the case startangle > endangle is
+ % automatically correct; patharc handles that.
+ %\edef\pgfplots@loc@TMPa{{\pgfplots@startangle}{\pgfplots@endangle}{\pgfplots@mirror@sign\the\pgf@xa\space and \the\pgf@xb}}%
+ %\expandafter\pgfpatharc\pgfplots@loc@TMPa
+ %
+ % prefer \pgfpatharctoprecomputed. It is faster and more accurate
+ \ifdim\pgfplots@startangle pt>\pgfplots@endangle pt
+ \let\pgfplots@loc@TMPa=\pgfplots@startangle
+% \let\pgfplots@startangle=\pgfplots@endangle
+% \let\pgfplots@endangle=\pgfplots@loc@TMPa
+ \fi
+ \edef\pgfplots@loc@TMPa{%
+ {\noexpand\pgfplotsqpointxy@smithchart@canvas{1}{\pgfplots@radius@sign\pgfplots@radius@y}}%
+ {\pgfplots@startangle}%
+ {\pgfplots@endangle}%
+ {\noexpand\pgfplotsqpointxy@smithchart@canvas{\pgfplots@end}{\pgfplots@endim}}%
+ {\pgfplots@mirror@sign\the\pgf@xa}%
+ {\the\pgf@xb}%
+ {\pgfplots@mirror@sign\pgfplots@smithchart@axis@ratioxy}%
+ {\pgfplots@mirror@sign\pgfplots@smithchart@axis@ratioyx}%
+ }%
+ \expandafter\pgfpatharctoprecomputed\pgfplots@loc@TMPa
+ }%
+}
+
+\def\pgfplots@drawgridlines@onorientedsurf@fromto@smithchart#1{%
+ \if x\pgfplotspointonorientedsurfaceA
+ \pgfplots@smithchart@draw@xcircle{#1}%
+ \else
+ \pgfplots@smithchart@draw@yarc{#1}%
+ \fi
+}%
+
+% Given a circle with center point (#3,#4), we search for the angle
+% of the point (#1,#2). The point is expected to be on the circle.
+% The resulting angle is returned in \pgfmathresult
+%
+% #1 x coordinate of the point for which an angle is searched
+% #2 y coordinate of the point for which an angle is searched
+% #3 x coordinate of the circle's center point
+% #4 y coordinate of the circle's center point
+% #5 is either empty or it is expected to contain the inverse radius, 1/r
+% this information is available in my context, so I don't recompute
+% it.
+%
+% All coordinates are expected in standard TeX precision (numbers
+% without unit)
+\def\pgfplots@compute@angle@of@point@in@circle#1#2#3#4#5{%
+ %
+ % 1. compute diff vector from center=(1,\pgfplots@signedradius) to start:
+ \pgfmathsubtract@{#1}{#3}%
+ \let\pgfplots@D\pgfmathresult
+ \pgfmathsubtract@{#2}{#4}%
+ \let\pgfplots@Dim\pgfmathresult
+ %
+ % 2. compute the start angle.
+ % It is related to the angle between the point (1,0) and
+ % diff, which, in turn is given by
+ % < (1,0), (D,Dim) > = cos(alpha) ||(D,Dim)||
+ % < (1,0), (D,Dim) > = D
+ %
+ % Note that ||(D,Dim)|| = r, the radius of the involved circle
+ % around (#3,#4). If 1/r is already available, use it! Saves a lot
+ % of time.
+ %
+ \def\pgfplots@loc@TMPa{#5}%
+ \ifx\pgfplots@loc@TMPa\pgfutil@empty
+ \pgfmathveclen\pgfplots@D\pgfplots@Dim
+ \let\pgfplots@veclen=\pgfmathresult
+ \pgfmathreciprocal@\pgfplots@veclen
+ \let\pgfplots@inverseveclen=\pgfmathresult
+ \else
+ % oh, good -- we already have 1/||(D,Dim)||. Use it.
+ \def\pgfplots@inverseveclen{#5}%
+%\message{using already available inverseveclen '#5' }%
+ \fi
+ \pgfmathmultiply@{\pgfplots@D}{\pgfplots@inverseveclen}%
+%\message{D= (\pgfplots@D,\pgfplots@Dim).. acos(\pgfplots@D * \pgfplots@inverseveclen) = acos(\pgfmathresult)}%
+ \pgfmathacos@{\pgfmathresult}% the '-' comes from D<0 .
+%\message{= \pgfmathresult^^J}%
+ \let\pgfplots@tmpangle\pgfmathresult%
+ % ok. tmpangle is per definition less than 180; it is the
+ % smaller angle between (1,0) and (D,Dim).
+ %
+ % compute the angle relative to (1,0):
+ \ifdim\pgfplots@Dim pt<0pt
+ \pgfmathsubtract@{360}{\pgfplots@tmpangle}%
+ \fi
+}%
+
+\def\pgfplots@drawaxis@innerlines@onorientedsurf@smithchart#1#2#3{%
+ \if2\csname pgfplots@#1axislinesnum\endcsname
+ \draw[/pgfplots/every inner #1 axis line,%
+ decorate,%
+ #1discont,%
+ decoration={pre length=\csname #1disstart\endcsname, post length=\csname #1disend\endcsname}]
+ \pgfextra
+ \csname pgfplotspointonorientedsurfaceabsetupforset#3\endcsname{\csname pgfplots@logical@ZERO@#3\endcsname}{2}%
+ \if#1x%
+ \pgfplotspointonorientedsurfaceabsetupfor{#2}{#1}{\pgfplotspointonorientedsurfaceN}%
+ \pgfplots@drawgridlines@onorientedsurf@fromto{0}%
+ \else
+ \pgfpathmoveto{\pgfplotspointonorientedsurfaceab{\csname pgfplots@#1min\endcsname}{\csname pgfplots@logical@ZERO@#2\endcsname}}%
+ \pgfpathlineto{\pgfplotspointonorientedsurfaceab{\csname pgfplots@#1max\endcsname}{\csname pgfplots@logical@ZERO@#2\endcsname}}%
+ \fi
+ \endpgfextra
+ ;
+ \fi
+}%
+\def\pgfplots@drawaxis@outerlines@separate@onorientedsurf@smithchartaxis#1#2{%
+ \if2\csname pgfplots@#1axislinesnum\endcsname
+ % centered axis lines handled elsewhere.
+ \else
+ \scope[/pgfplots/every outer #1 axis line,
+ #1discont,decoration={pre length=\csname #1disstart\endcsname, post length=\csname #1disend\endcsname}]
+ \if#1x
+ \draw decorate {
+ \pgfextra
+ % exchange roles of A <-> B axes:
+ \pgfplotspointonorientedsurfaceabsetupfor{#2}{#1}{\pgfplotspointonorientedsurfaceN}%
+ \pgfplots@drawgridlines@onorientedsurf@fromto{0}%
+ \endpgfextra
+ };
+ \else
+ \pgfplots@ifaxisline@B@onorientedsurf@should@be@drawn{0}{%
+ \draw decorate {
+ \pgfextra
+ % exchange roles of A <-> B axes:
+ \pgfplotspointonorientedsurfaceabsetupfor{#2}{#1}{\pgfplotspointonorientedsurfaceN}%
+ \pgfplots@drawgridlines@onorientedsurf@fromto{\csname pgfplots@#2min\endcsname}%
+ \endpgfextra
+ };
+ }{}%
+ %--------------------------------------------------
+ % \pgfplots@ifaxisline@B@onorientedsurf@should@be@drawn{1}{%
+ % \draw decorate {
+ % \pgfextra
+ % % exchange roles of A <-> B axes:
+ % \pgfplotspointonorientedsurfaceabsetupfor{#2}{#1}{\pgfplotspointonorientedsurfaceN}%
+ % \pgfplots@drawgridlines@onorientedsurf@fromto{\csname pgfplots@#2max\endcsname}%
+ % \endpgfextra
+ % };
+ % }{}%
+ %--------------------------------------------------
+ \fi
+ \endscope
+ \fi
+}%
+
+\def\pgfplots@initsizes@smithchart{%
+ % I copy-pasted most of this code, up to just one position where
+ % I introduced the modified scaling for smithchart axes
+ %----------------------------------
+ % INIT.
+ %
+ %
+ \def\pgfplots@minmax@reg@forbidden{\pgfplots@error{Sorry, an internal logic error occured during smithchart processing (a routine tried to access \string\pgfplots@xmin@reg\space or its variants). Please report this as bug, sorry}}%
+ \iffalse
+ \pgfplots@xmin@reg=\pgfplots@xmin pt %
+ \pgfplots@xmax@reg=\pgfplots@xmax pt %
+ \pgfplots@ymin@reg=\pgfplots@ymin pt %
+ \pgfplots@ymax@reg=\pgfplots@ymax pt %
+ \ifpgfplots@threedim
+ \pgfplots@zmin@reg=\pgfplots@zmin pt %
+ \pgfplots@zmax@reg=\pgfplots@zmax pt %
+ \fi
+ \else
+ \let\pgfplots@xmin@reg=\pgfplots@minmax@reg@forbidden
+ \let\pgfplots@xmax@reg=\pgfplots@minmax@reg@forbidden
+ \let\pgfplots@ymin@reg=\pgfplots@minmax@reg@forbidden
+ \let\pgfplots@ymax@reg=\pgfplots@minmax@reg@forbidden
+ \let\pgfplots@zmin@reg=\pgfplots@minmax@reg@forbidden
+ \let\pgfplots@zmax@reg=\pgfplots@minmax@reg@forbidden
+ \fi
+ %
+ %
+ %-----------------------------------------
+ % PROCESS THE 'width' and 'height' options
+ %-----------------------------------------
+ %
+ %
+ \pgfkeysgetvalue{/pgfplots/view/az}{\pgfplots@view@az}%
+ \pgfkeysgetvalue{/pgfplots/view/el}{\pgfplots@view@el}%
+ \ifpgfplots@threedim
+ \def\pgfplots@tmpZscale{1pt}%
+ \else
+ \def\pgfplots@tmpZscale{0pt}%
+ \let\pgfplots@view@el=\pgfutil@empty
+ \let\pgfplots@view@az=\pgfutil@empty
+ \fi
+ \ifx\pgfplots@view@az\pgfutil@empty
+ %\let\pgfplots@rectangle@width=\pgfutil@empty
+ %\let\pgfplots@rectangle@height=\pgfutil@empty
+ \def\pgfplots@view@dir@threedim@x{0}%
+ \def\pgfplots@view@dir@threedim@y{0}%
+ \def\pgfplots@view@dir@threedim@z{1}%
+ %
+ % FIXME HERE COMES THE smithchart MODIFICATION
+ %--------------------------------------------------
+ % \pgfpointdiff
+ % {\pgfplotsqpointxy{\pgfplots@xmin}{\pgfplots@ymin}}
+ % {\pgfplotsqpointxy{\pgfplots@xmax}{\pgfplots@ymax}}%
+ %--------------------------------------------------
+ % instead of scaling from (min) (max), we only need the UPPER
+ % bound -- in both, x and y directions (since we have a cycle.
+ % Furthermore, we need it twice since we are interested in the
+ % diameter, not the radius.
+ \global\pgf@x=2 pt % radius
+ \global\pgf@y=\pgf@x % same for y
+ %
+ % only used temporarily in this macro to compute the correct
+ % length for unit vectors:
+ \edef\pgfplots@initsizes@axisdiag@x{\the\pgf@x}%
+ \edef\pgfplots@initsizes@axisdiag@y{\the\pgf@y}%
+ %
+ \ifx\pgfplots@x\pgfutil@empty
+ \ifx\pgfplots@width\pgfutil@empty
+ \pgfplots@error{INTERNAL LOGIC ERROR! WIDTH NOT SET}%
+ \fi
+ \pgfplots@initsizes@getXscale\pgfplots@initsizes@axisdiag@x\into\pgfplots@tmpXscale
+ %\ifpgfplots@scale@only@axis
+ % \let\pgfplots@rectangle@width=\pgfplots@width
+ %\fi
+ \else
+ \def\pgfplots@tmpXscale{1}%
+ \fi
+ %
+ \ifx\pgfplots@y\pgfutil@empty
+ \ifx\pgfplots@height\pgfutil@empty
+ \pgfplots@error{INTERNAL LOGIC ERROR! HEIGHT NOT SET}%
+ \fi
+ \pgfplots@initsizes@getYscale\pgfplots@initsizes@axisdiag@y\into\pgfplots@tmpYscale
+ %\ifpgfplots@scale@only@axis
+ % \let\pgfplots@rectangle@height=\pgfplots@height
+ %\fi
+ \else
+ \def\pgfplots@tmpYscale{1}%
+ \fi
+ %
+ \edef\pgfplots@tmpXscale{\pgfplots@tmpXscale pt}%
+ \edef\pgfplots@tmpYscale{\pgfplots@tmpYscale pt}%
+ %
+ \pgfplots@initsizes@setunitvector{x}{0}{\pgfplots@tmpXscale}{\pgfplots@tmp@xisaxisparallel}%
+ \pgfplots@initsizes@setunitvector{y}{1}{\pgfplots@tmpYscale}{\pgfplots@tmp@yisaxisparallel}%
+ \pgfplots@initsizes@setunitvector{z}{2}{\pgfplots@tmpZscale}{\pgfplots@loc@TMPc}%
+ \else
+ % 3D case is currently always initialised by `view':
+ \let\pgfplots@x=\pgfutil@empty
+ \let\pgfplots@y=\pgfutil@empty
+ \let\pgfplots@z=\pgfutil@empty
+ \pgfplotssetaxesfromazel{\pgfplots@view@az}{\pgfplots@view@el}{\pgfplots@tmp@xisaxisparallel}%
+ \if1\pgfplots@tmp@xisaxisparallel%
+ \def\pgfplots@tmp@yisaxisparallel{1}%
+ \fi
+ \fi
+%\message{Pgfplots debug: initialised unit vectors to x=(\the\pgf@xx,\the\pgf@xy), y=(\the\pgf@yx,\the\pgf@yy), z=(\the\pgf@zx,\the\pgf@zy). }%
+ %
+ \let\pgfplotsmathfloatviewdepthxyz@=\pgfplotsmathfloatviewdepthxyz@infigure
+ \let\pgfplotsmathviewdepthxyz@=\pgfplotsmathviewdepthxyz@infigure
+ %
+ \pgfplotsmath@ifzero{\pgfplots@x@veclength}{\pgfplots@hide@xtrue\pgfplots@shownothingof@xtrue}{}%
+ \pgfplotsmath@ifzero{\pgfplots@y@veclength}{\pgfplots@hide@ytrue\pgfplots@shownothingof@ytrue}{}%
+ \ifpgfplots@threedim
+ \pgfplotsmath@ifzero{\pgfplots@z@veclength}{\pgfplots@hide@ztrue\pgfplots@shownothingof@ztrue}{}%
+ \else
+ \if1\pgfplots@tmp@xisaxisparallel%
+ \if1\pgfplots@tmp@yisaxisparallel%
+ % Optimize for axis-parallel case!
+ % puh. Did not make any measureable difference!? Ok...
+ \let\pgfplotsqpointxy=\pgfplotsqpointxy@orthogonal
+ \fi
+ \fi
+ \fi
+ %
+ % FIXME : unit vector ratio / axis equal
+ %
+}
+
+\def\pgfplots@handle@invalid@range@defaultlimits@smithchart{%
+ \pgfplotscoordmath{x}{parsenumber}{0}%
+ \global\let\pgfplots@xmin=\pgfmathresult
+ \pgfplotscoordmath{x}{parsenumber}{16000}%
+ \global\let\pgfplots@xmax=\pgfmathresult
+ \global\let\pgfplots@data@xmin=\pgfplots@xmin
+ \global\let\pgfplots@data@xmax=\pgfplots@xmax
+ %
+ \pgfplotscoordmath{y}{parsenumber}{0}%
+ \global\let\pgfplots@ymin=\pgfmathresult
+ \pgfplotscoordmath{y}{parsenumber}{16000}%
+ \global\let\pgfplots@ymax=\pgfmathresult
+ \global\let\pgfplots@data@ymin=\pgfplots@ymin
+ \global\let\pgfplots@data@ymax=\pgfplots@ymax
+ \pgfplotsset{enlargelimits=false}%
+}
+
+\let\pgfplots@set@default@size@options@standard=\pgfplots@set@default@size@options
+\def\pgfplots@set@default@size@options@smithchart{%
+ \pgfplots@set@default@size@options@standard
+ \pgfplotsset{smithchart ticks by size={\pgfkeysvalueof{/pgfplots/width}}{\pgfkeysvalueof{/pgfplots/height}}}%
+ %
+ \if1\b@pgfplots@smithchart@defaultticks@x
+ \if1\b@pgfplots@smithchart@defaultticks@y
+ \pgfplotsset{default smithchart xytick}%
+ \fi
+ \fi
+}
+\def\pgfplots@assign@default@tick@foraxis@smithchart#1{%
+ % do nothing here. I don't know the algorithm yet... but for
+ % smithcharts, it may be sufficient to simply predefine several
+ % sets of ticks, depending on the final size.
+ %
+ % This is realized in
+ % \pgfplots@set@default@size@options@smithchart (which is invoked
+ % before the ticks are processed).
+ \pgfplots@determinedefaultvalues@needs@check@uniformtickfalse
+ \expandafter\let\csname pgfplots@tick@distance@#1\endcsname=\pgfutil@empty
+ %
+ \pgfplotsset{default smithchart #1tick}%
+ % ok, I expect the '#1tick' key to be set now. Process it.
+ % Note that the earlier processing of pgfplots has been bypassed
+ % at this point -- we need to preprocess the tick list *here*:
+ \expandafter\let\expandafter\pgfplots@loc@TMPa\csname pgfplots@#1tick\endcsname
+ \expandafter\pgfplots@assign@default@tick@foraxis@smithchart@\expandafter{\pgfplots@loc@TMPa}%
+ \expandafter\let\csname pgfplots@#1tick\endcsname=\pgfplotsretval
+ %
+ \pgfkeysgetvalue{/pgfplots/minor #1tick}\pgfplots@loc@TMPa
+ \ifx\pgfplots@loc@TMPa\pgfutil@empty
+ \else
+ \expandafter\pgfplots@assign@default@tick@foraxis@smithchart@\expandafter{\pgfplots@loc@TMPa}%
+ \pgfkeyslet{/pgfplots/minor #1tick}\pgfplotsretval
+ \fi
+ %
+}%
+% #1: a \foreach list
+% on output, \pgfplotsretval contains a parsed list of positions
+\def\pgfplots@assign@default@tick@foraxis@smithchart@#1{%
+ \pgfplotsapplistXXglobalnewempty
+ \gdef\pgfplots@loc@TMPd{1}%
+ \foreach \pgfplots@loc@TMPb in {#1} {%
+ \ifx\pgfplots@loc@TMPb\pgfutil@empty
+ \else
+ \pgfplotscoordmath{default}{parsenumber}{\pgfplots@loc@TMPb}%
+ \pgfplotscoordmath{default}{tofixed}{\pgfmathresult}% per convention...
+ \edef\pgfmathresult{\if0\pgfplots@loc@TMPd,\fi\pgfmathresult}%
+ \gdef\pgfplots@loc@TMPd{0}%
+ \expandafter\pgfplotsapplistXXglobalpushback\expandafter{\pgfmathresult}%
+ \fi
+ }%
+ \pgfplotsapplistXXgloballet\pgfplotsretval
+ \pgfplotsapplistXXglobalclear
+}%
+
+\let\pgfplots@show@ticklabel@@orig=\pgfplots@show@ticklabel@
+\def\pgfplots@show@ticklabel@@smithchart#1#2{%
+ \def\pgfmathresult{#2}%
+ \if#1x%
+ \ifdim#2pt>360pt
+ \pgfmath@basic@mod@{#2}{360}%
+ \fi
+ \fi
+ \def\pgfplots@loc@TMPa{\pgfplots@show@ticklabel@@orig{#1}}%
+ \expandafter\pgfplots@loc@TMPa\expandafter{\pgfmathresult}%
+}%
+
+\def\pgfplots@xtick@check@tickshow@smithchart{%
+ \pgfplots@tickshowtrue
+}
+\def\pgfplots@ytick@check@tickshow@smithchart{%
+ \pgfplots@tickshowtrue
+}
+
+\let\pgfplots@limits@ready@orig=\pgfplots@limits@ready
+\def\pgfplots@limits@ready@smithchart{%
+ \pgfplots@limits@ready@orig
+ %
+ % Avoid tick labels at upper *and* lower angle range if both are the
+ % same:
+ \pgfmath@basic@sin@{\pgfplots@xmin}%
+ \let\pgfplots@loc@TMPa=\pgfmathresult
+ \pgfmath@basic@sin@{\pgfplots@xmax}%
+ \pgfplotsmath@ifapproxequal@dim
+ {\pgfmathresult pt}{\pgfplots@loc@TMPa pt}%
+ {0.002pt}
+ {%
+ \def\pgfplots@xtick@disable@last@tick{1}%
+ }{%
+ }%
+}%
+
+\def\smithchart{\smithchartaxis}
+\def\endsmithchart{\endsmithchartaxis}
+
+\def\startsmithchart{\smithchart}%
+\def\stopsmithchart{\endsmithchart}%
+\endinput