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{\nprt@sign@+ }[0]{{\ensuremath {+}}} \newcommand {\nprt@sign@-}[0]{{\ensuremath {-}}} \newcommand {\nprt@sign@+-}[0]{{\ensuremath {\pm }}} \newcommand {\nprt@printsign }[2]{\nprt@debug {\string \nprt@printsign : ‘##2’}\edef \nprt@marg {##2}\csname ifnprt@addplus@##1\endcsname \ifx \nprt@marg \@empty \edef \nprt@marg {+}\fi \fi \ifx \nprt@marg \@empty \else \@ifundefined {nprt@sign@\nprt@marg }{\PackageWarning {numprint}{Unknown sign ‘\nprt@marg ’. 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\expandafter \nprt@printone \nprt@numbertoprint \@empty \else \ifnum \thenprt@digitsfirstblock =2 \expandafter \nprt@printtwo \nprt@numbertoprint \@empty \else \ifnum \thenprt@digitsfirstblock =3 \expandafter \nprt@printthree \nprt@numbertoprint \@empty \else \ifnum \thenprt@digitsfirstblock =0 \else \PackageError {numprint}{internal error}{}\fi \fi \fi \fi \fi \endgroup } \newcommand {\nprt@printafter }[1]{\csname ifnprt@##1@decimalfound\endcsname \ifnprt@addmissingzero \ifnum \csname thenprt@##1@digitsafter\endcsname =0 \expandafter \edef \csname nprt@##1@after\endcsname {0}\advance \csname c@nprt@##1@digitsafter\endcsname by 1\relax \fi \fi \ifx \nprt@replacenull \@empty \else \ifnum \csname thenprt@##1@digitsafter\endcsname =0 \expandafter \edef \csname nprt@##1@after\endcsname {0}\advance \csname c@nprt@##1@digitsafter\endcsname by 1\relax \fi \fi \fi \begingroup \edef \nprt@numbertoprint {\csname nprt@##1@after\endcsname }\ifx \nprt@numbertoprint \@empty \else \ifnprt@numsepfour \else \ifnum \csname thenprt@##1@digitsbefore\endcsname <5 \ifnum \csname thenprt@##1@digitsafter\endcsname <5 \nprt@shortnumbertrue \fi \fi \fi \ifx \nprt@replacenull \@empty \else \ifnum \nprt@numbertoprint =0 \nprt@shortnumbertrue \edef \nprt@numbertoprint {\nprt@replacenull }\fi \fi \ifnprt@shortnumber \nprt@numbertoprint \else \expandafter \nprt@printthree@after \nprt@numbertoprint \@empty \@empty \@empty \fi \fi \endgroup } \newcommand {\npdefunit }[3]{\if ##3* \else \expandafter \def \csname nprt@factor@##1\endcsname {##3}\fi \expandafter \def \csname nprt@unit@##1\endcsname {##2}} \newcommand {\nprt@ifundefined }[1]{\begingroup \expandafter \expandafter \expandafter \endgroup \expandafter \ifx \csname ##1\endcsname \relax \expandafter \@firstoftwo \else \expandafter \@secondoftwo \fi } \newcommand {\nprt@addto }[2]{\expandafter \nprt@ifundefined {##1}{}{\expandafter \addto \expandafter {\csname ##1\endcsname }{##2}}} \newcommand {\npaddtolanguage }[2]{\nprt@addto {extras##1}{\csname npstyle##2\endcsname }\nprt@addto {noextras##1}{\npstyledefault }} \newcommand {\npstyledefault }[0]{\npthousandsep {\,}\npdecimalsign {,}\npproductsign {\cdot }\npunitseparator {\,}\npdegreeseparator {}\npcelsiusseparator {\nprt@unitsep }\nppercentseparator {\nprt@unitsep }} \newcommand {\npstylegerman }[0]{\npthousandsep {\,}\npdecimalsign {,}\npproductsign {\cdot }\npunitseparator {\,}\npdegreeseparator {}\npcelsiusseparator {\nprt@unitsep }\nppercentseparator {\nprt@unitsep }} \newcommand {\npstyleenglish }[0]{\npthousandsep {,}\npdecimalsign {.}\npproductsign {\times }\npunitseparator {\,}\npdegreeseparator {}\npcelsiusseparator {\nprt@unitsep }\nppercentseparator {\nprt@unitsep }} \newcommand {\npstyleportuguese }[0]{\npthousandsep {.}\npdecimalsign {,}\npproductsign {\cdot }\npunitseparator {\,}\npdegreeseparator {}\npcelsiusseparator {\nprt@unitsep }\nppercentseparator {\nprt@unitsep }} \newcommand {\npstyledutch }[0]{\npthousandsep {\,}\npdecimalsign {,}\npproductsign {\cdot }\npunitseparator {\,}\npdegreeseparator {}\npcelsiusseparator {\nprt@unitsep }\nppercentseparator {}} \newcommand {\npstylefrench }[0]{\npthousandsep {~}\npdecimalsign {,}\npproductsign {\cdot }\npunitseparator {\,}\npdegreeseparator {}\npcelsiusseparator {\nprt@unitsep }\nppercentseparator {\nprt@unitsep }} \newcommand {\nprt@renameerror }[1]{\expandafter \def \csname ##1\endcsname {\PackageError {numprint}{This command has been renamed to\MessageBreak \string \np ##1}{In order to avoid problems with other packages and for consistency,this\MessageBreak command has been renamed in this version.}}} \newcommand {\tkz@getdecimal }[1]{\expandafter \@getdecimal ##1.\@nil } \newcommand {\CountToken }[1]{\c@pgfmath@countb 0 \expandafter \C@untToken ##1\@nil } \newcommand {\C@untToken }[0]{\afterassignment \C@untT@ken \let \CurrT@ken = } \newcommand {\C@untT@ken }[0]{\ifx \CurrT@ken \@nil \else \advance \c@pgfmath@countb by1 \expandafter \C@untToken \fi } \newcommand {\tdplotsinandcos }[3]{\pgfmathsetmacro {##1}{sin(##3)}\pgfmathsetmacro {##2}{cos(##3)}} \newcommand {\tdplotmult }[3]{\pgfmathsetmacro {##1}{##2*##3}} \newcommand {\tdplotdiv }[3]{\pgfmathsetmacro {##1}{##2/##3}} \newcommand {\tdplotcheckdiff }[5]{\par \par \pgfmathparse { abs(##2 -##1)<##3 } \par \ifthenelse {\equal {\pgfmathresult }{1}}{##4}{##5} } \newcommand {\tdplotsetmaincoords }[2]{\pgfmathsetmacro {\tdplotmaintheta }{##1} \pgfmathsetmacro {\tdplotmainphi }{##2} \tdplotcalctransformmainscreen \tikzset {tdplot_main_coords/.style={x={(\raarot cm,\rbarot cm)},y={(\rabrot cm,\rbbrot cm)},z={(\racrot cm,\rbcrot cm)}}}} \newcommand {\tdplotcalctransformmainscreen }[0]{\tdplotsinandcos {\sintheta }{\costheta }{\tdplotmaintheta }\tdplotsinandcos {\sinphi }{\cosphi }{\tdplotmainphi }\tdplotmult {\stsp }{\sintheta }{\sinphi }\tdplotmult {\stcp }{\sintheta }{\cosphi }\tdplotmult {\ctsp }{\costheta }{\sinphi }\tdplotmult {\ctcp }{\costheta }{\cosphi }\pgfmathsetmacro {\raarot }{\cosphi }\pgfmathsetmacro {\rabrot }{\sinphi }\pgfmathsetmacro {\racrot }{0}\pgfmathsetmacro {\rbarot }{-\ctsp }\pgfmathsetmacro {\rbbrot }{\ctcp }\pgfmathsetmacro {\rbcrot }{\sintheta }\pgfmathsetmacro {\rcarot }{\stsp }\pgfmathsetmacro {\rcbrot }{-\stcp }\pgfmathsetmacro {\rccrot }{\costheta }} \newcommand {\tdplotcalctransformrotmain }[0]{\tdplotsinandcos {\sinalpha }{\cosalpha }{\tdplotalpha } \tdplotsinandcos {\sinbeta }{\cosbeta }{\tdplotbeta } \tdplotsinandcos {\singamma }{\cosgamma }{\tdplotgamma } \tdplotmult {\sasb }{\sinalpha }{\sinbeta } \tdplotmult {\sbsg }{\sinbeta }{\singamma } \tdplotmult {\sasg }{\sinalpha }{\singamma } \tdplotmult {\sasbsg }{\sasb }{\singamma } \tdplotmult {\sacb }{\sinalpha }{\cosbeta } \tdplotmult {\sacg }{\sinalpha }{\cosgamma } \tdplotmult {\sbcg }{\sinbeta }{\cosgamma } \tdplotmult {\sacbsg }{\sacb }{\singamma } \tdplotmult {\sacbcg }{\sacb }{\cosgamma } \tdplotmult {\casb }{\cosalpha }{\sinbeta } \tdplotmult {\cacb }{\cosalpha }{\cosbeta } \tdplotmult {\cacg }{\cosalpha }{\cosgamma } \tdplotmult {\casg }{\cosalpha }{\singamma } \tdplotmult {\cacbsg }{\cacb }{\singamma } \tdplotmult {\cacbcg }{\cacb }{\cosgamma } \pgfmathsetmacro {\raaeul }{\cacbcg -\sasg } \pgfmathsetmacro {\rabeul }{-\cacbsg -\sacg } \pgfmathsetmacro {\raceul }{\casb } \pgfmathsetmacro {\rbaeul }{\sacbcg + \casg } \pgfmathsetmacro {\rbbeul }{-\sacbsg + \cacg } \pgfmathsetmacro {\rbceul }{\sasb } \pgfmathsetmacro {\rcaeul }{-\sbcg } \pgfmathsetmacro {\rcbeul }{\sbsg } \pgfmathsetmacro {\rcceul }{\cosbeta } } \newcommand {\tdplotcalctransformmainrot }[0]{\tdplotsinandcos {\sinalpha }{\cosalpha }{\tdplotalpha } \tdplotsinandcos {\sinbeta }{\cosbeta }{\tdplotbeta } \tdplotsinandcos {\singamma }{\cosgamma }{\tdplotgamma } \tdplotmult {\sasb }{\sinalpha }{\sinbeta } \tdplotmult {\sbsg }{\sinbeta }{\singamma } \tdplotmult {\sasg }{\sinalpha }{\singamma } \tdplotmult {\sasbsg }{\sasb }{\singamma } \tdplotmult {\sacb }{\sinalpha }{\cosbeta } \tdplotmult {\sacg }{\sinalpha }{\cosgamma } \tdplotmult {\sbcg }{\sinbeta }{\cosgamma } \tdplotmult {\sacbsg }{\sacb }{\singamma } \tdplotmult {\sacbcg }{\sacb }{\cosgamma } \tdplotmult {\casb }{\cosalpha }{\sinbeta } \tdplotmult {\cacb }{\cosalpha }{\cosbeta } \tdplotmult {\cacg }{\cosalpha }{\cosgamma } \tdplotmult {\casg }{\cosalpha }{\singamma } \tdplotmult {\cacbsg }{\cacb }{\singamma } \tdplotmult {\cacbcg }{\cacb }{\cosgamma } \pgfmathsetmacro {\raaeul }{\cacbcg -\sasg } \pgfmathsetmacro {\rabeul }{\sacbcg + \casg } \pgfmathsetmacro {\raceul }{-\sbcg } \pgfmathsetmacro {\rbaeul }{-\cacbsg -\sacg } \pgfmathsetmacro {\rbbeul }{-\sacbsg + \cacg } \pgfmathsetmacro {\rbceul }{\sbsg } \pgfmathsetmacro {\rcaeul }{\casb } \pgfmathsetmacro {\rcbeul }{\sasb } \pgfmathsetmacro {\rcceul }{\cosbeta } } \newcommand {\tdplottransformmainrot }[3]{\tdplotcalctransformmainrot \par \pgfmathsetmacro {\tdplotresx }{\raaeul * ##1 + \rabeul * ##2 + \raceul * ##3} \pgfmathsetmacro {\tdplotresy }{\rbaeul * ##1 + \rbbeul * ##2 + \rbceul * ##3} \pgfmathsetmacro {\tdplotresz }{\rcaeul * ##1 + \rcbeul * ##2 + \rcceul * ##3} } \newcommand {\tdplottransformrotmain }[3]{\tdplotcalctransformrotmain \par \pgfmathsetmacro {\tdplotresx }{\raaeul * ##1 + \rabeul * ##2 + \raceul * ##3} \pgfmathsetmacro {\tdplotresy }{\rbaeul * ##1 + \rbbeul * ##2 + \rbceul * ##3} \pgfmathsetmacro {\tdplotresz }{\rcaeul * ##1 + \rcbeul * ##2 + \rcceul * ##3} } \newcommand {\tdplottransformmainscreen }[3]{\tdplotcalctransformmainscreen \par \pgfmathsetmacro {\tdplotresx }{\raarot * ##1 + \rabrot * ##2 + \racrot * ##3} \pgfmathsetmacro {\tdplotresy }{\rbarot * ##1 + \rbbrot * ##2 + \rbcrot * ##3} } \newcommand {\tdplotsetrotatedcoords }[3]{\pgfmathsetmacro {\tdplotalpha }{##1} \pgfmathsetmacro {\tdplotbeta }{##2} \pgfmathsetmacro {\tdplotgamma }{##3} \tdplotcalctransformrotmain \par \tdplotmult {\raaeaa }{\raarot }{\raaeul } \tdplotmult {\rabeba }{\rabrot }{\rbaeul } \tdplotmult {\raceca }{\racrot }{\rcaeul } \tdplotmult {\raaeab }{\raarot }{\rabeul } \tdplotmult {\rabebb }{\rabrot }{\rbbeul } \tdplotmult {\racecb }{\racrot }{\rcbeul } \tdplotmult {\raaeac }{\raarot }{\raceul } \tdplotmult {\rabebc }{\rabrot }{\rbceul } \tdplotmult {\racecc }{\racrot }{\rcceul } \tdplotmult {\rbaeaa }{\rbarot }{\raaeul } \tdplotmult {\rbbeba }{\rbbrot }{\rbaeul } \tdplotmult {\rbceca }{\rbcrot }{\rcaeul } \tdplotmult {\rbaeab }{\rbarot }{\rabeul } \tdplotmult {\rbbebb }{\rbbrot }{\rbbeul } \tdplotmult {\rbcecb }{\rbcrot }{\rcbeul } \tdplotmult {\rbaeac }{\rbarot }{\raceul } \tdplotmult {\rbbebc }{\rbbrot }{\rbceul } \tdplotmult {\rbcecc }{\rbcrot }{\rcceul } \pgfmathsetmacro {\raarc }{\raaeaa + \rabeba + \raceca } \pgfmathsetmacro {\rabrc }{\raaeab + \rabebb + \racecb } \pgfmathsetmacro {\racrc }{\raaeac + \rabebc + \racecc } \pgfmathsetmacro {\rbarc }{\rbaeaa + \rbbeba + \rbceca } \pgfmathsetmacro {\rbbrc }{\rbaeab + \rbbebb + \rbcecb } \pgfmathsetmacro {\rbcrc }{\rbaeac + \rbbebc + \rbcecc } \tikzset {tdplot_rotated_coords/.append style={x={(\raarc cm,\rbarc cm)},y={(\rabrc cm,\rbbrc cm)},z={(\racrc cm,\rbcrc cm)}}}} \newcommand {\tdplotsetrotatedcoordsorigin }[1]{\tikzset {tdplot_rotated_coords/.append style={shift=##1}}} \newcommand {\tdplotresetrotatedcoordsorigin }[0]{\tikzset {tdplot_rotated_coords/.append style={shift={(0,0,0)}}}} \newcommand {\tdplotsetthetaplanecoords }[1]{\tdplotresetrotatedcoordsorigin \tdplotsetrotatedcoords {270 + ##1}{270}{0}} \newcommand {\tdplotsetrotatedthetaplanecoords }[1]{\tdplotsetrotatedcoords {\tdplotalpha }{\tdplotbeta }{\tdplotgamma + ##1}\tikzset {tdplot_rotated_coords/.append style={y={(\raarc cm,\rbarc cm)},z={(\rabrc cm,\rbbrc cm)},x={(\racrc cm,\rbcrc cm)}}}} \newcommand {\tdplotsetcoord }[4]{\tdplotsinandcos {\sinthetavec }{\costhetavec }{##3}\tdplotsinandcos {\sinphivec }{\cosphivec }{##4}\tdplotmult {\stcpv }{\sinthetavec }{\cosphivec }\tdplotmult {\stspv }{\sinthetavec }{\sinphivec }\coordinate (##1) at ($##2*(\stcpv ,\stspv ,\costhetavec )$); \coordinate (##1xy) at ($##2*(\stcpv ,\stspv ,0)$); \coordinate (##1xz) at ($##2*(\stcpv ,0,\costhetavec )$); \coordinate (##1yz) at ($##2*(0,\stspv ,\costhetavec )$); \coordinate (##1x) at ($##2*(\stcpv ,0,0)$); \coordinate (##1y) at ($##2*(0,\stspv ,0)$); \coordinate (##1z) at ($##2*(0,0,\costhetavec )$); } \newcommand {\tdplotsimplesetcoord }[4]{\tdplotsinandcos {\sinthetavec }{\costhetavec }{##3}\tdplotsinandcos {\sinphivec }{\cosphivec }{##4}\tdplotmult {\stcpv }{\sinthetavec }{\cosphivec }\tdplotmult {\stspv }{\sinthetavec }{\sinphivec }\coordinate (##1) at ($##2*(\stcpv ,\stspv ,\costhetavec )$); } \newcommand {\tdplotsetpolarplotrange }[4]{\pgfmathsetmacro {\tdplotlowerphi }{##3} \pgfmathsetmacro {\tdplotupperphi }{##4} \pgfmathsetmacro {\tdplotlowertheta }{##1} \pgfmathsetmacro {\tdplotuppertheta }{##2} } \newcommand {\tdplotresetpolarplotrange }[0]{\pgfmathsetmacro {\tdplotlowerphi }{0} \pgfmathsetmacro {\tdplotupperphi }{360} \pgfmathsetmacro {\tdplotlowertheta }{0} \pgfmathsetmacro {\tdplotuppertheta }{180} } \newcommand {\tdplotdosurfaceplot }[6]{\par \pgfmathsetmacro {\nextphi }{\curphi + \tdplotsuperfudge *\viewphistep } \par \begin {scope}[opacity=1] \par \par \tdplotcheckdiff {\nextphi }{360}{\origviewphistep }{##2}{} \tdplotcheckdiff {\nextphi }{0}{\origviewphistep }{##2}{} \par \tdplotcheckdiff {\nextphi }{90}{\origviewphistep }{##3}{} \tdplotcheckdiff {\nextphi }{450}{\origviewphistep }{##3}{} \end {scope} \par \foreach \curtheta in{\viewthetastart ,\viewthetainc ,...,\viewthetaend } { \par \pgfmathsetmacro {\curlongitude }{90 -\curphi } \pgfmathsetmacro {\curlatitude }{90 -\curtheta } \par \ifthenelse {\equal {\leftright }{-1.0}}{\pgfmathsetmacro {\curphi }{\curphi -\origviewphistep } }{} \par \pgfmathsetmacro {\tdplottheta }{mod(\curtheta ,360)} \pgfmathsetmacro {\tdplotphi }{mod(\curphi ,360)} \par \pgfmathparse {\tdplotphi <0} \ifthenelse {\equal {\pgfmathresult }{1}}{ \pgfmathsetmacro {\tdplotphi }{\tdplotphi + 360} }{}\par \pgfmathparse {\tdplottheta >\tdplotuppertheta } \pgfmathsetmacro {\logictest }{1 -\pgfmathresult } \par \pgfmathparse {\tdplottheta <\tdplotlowertheta } \pgfmathsetmacro {\logictest }{\logictest * (1 -\pgfmathresult )} \par \pgfmathsetmacro {\tdplottheta }{\tdplottheta + \viewthetastep } \pgfmathparse {\tdplottheta >\tdplotuppertheta } \pgfmathsetmacro {\logictest }{\logictest * (1 -\pgfmathresult )} \par \pgfmathparse {\tdplottheta <\tdplotlowertheta } \pgfmathsetmacro {\logictest }{\logictest * (1 -\pgfmathresult )} \par \pgfmathparse {\tdplotphi >\tdplotupperphi } \pgfmathsetmacro {\logictest }{\logictest * (1 -\pgfmathresult )} \par \pgfmathparse {\tdplotphi <\tdplotlowerphi } \pgfmathsetmacro {\logictest }{\logictest * (1 -\pgfmathresult )} \par \pgfmathsetmacro {\tdplotphi }{\tdplotphi + \viewphistep } \par \pgfmathparse {\tdplotphi <0} \ifthenelse {\equal {\pgfmathresult }{1}}{ \pgfmathsetmacro {\tdplotphi }{\tdplotphi + 360} }{}\par \pgfmathparse {\tdplotphi >\tdplotupperphi } \pgfmathsetmacro {\logictest }{\logictest * (1 -\pgfmathresult )} \par \pgfmathparse {\tdplotphi <\tdplotlowerphi } \pgfmathsetmacro {\logictest }{\logictest * (1 -\pgfmathresult )} \par \par \pgfmathsetmacro {\tdplottheta }{\curtheta } \pgfmathsetmacro {\tdplotphi }{\curphi } \par \ifthenelse {\equal {##6}{parametricfill}}{\ifthenelse {\equal {\logictest }{1.0}}{\pgfmathsetmacro {\radius }{##1} \pgfmathsetmacro {\tdplotr }{\radius *360} \par \pgfmathlessthan {\radius }{0} \pgfmathsetmacro {\phaseshift }{180 * \pgfmathresult } \par \pgfmathsetmacro {\colorarg }{##5} \pgfmathsetmacro {\colorarg }{\colorarg + \phaseshift } \pgfmathsetmacro {\colorarg }{mod(\colorarg ,360)} \par \pgfmathlessthan {\colorarg }{0} \pgfmathsetmacro {\colorarg }{\colorarg + 360*\pgfmathresult } \par \pgfmathdivide {\colorarg }{360} \definecolor {tdplotfillcolor}{hsb}{\pgfmathresult ,1,1} \color {tdplotfillcolor} }{}}{\pgfsetfillcolor {##5} } \pgfsetstrokecolor {##4} \par \ifthenelse {\equal {\leftright 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{\tdplothuestep }{5} \pgfmathsetmacro {\tdplotxsize }{##3} \pgfmathsetmacro {\tdplotysize }{##4} \par \pgfmathsetmacro {\tdplotyscale }{\tdplotysize /360} \par \foreach \tdplotphi in {0,\tdplothuestep ,...,360} { \pgfmathdivide {\tdplotphi }{360} \definecolor {tdplotfillcolor}{hsb}{\pgfmathresult ,1,1} \color {tdplotfillcolor} \par \pgfmathsetmacro {\tdplotstarty }{\tdploty + \tdplotphi * \tdplotyscale } \pgfmathsetmacro {\tdplotstopy }{\tdplotstarty + \tdplothuestep * \tdplotyscale } \pgfmathsetmacro {\tdplotstartx }{\tdplotx } \pgfmathsetmacro {\tdplotstopx }{\tdplotx + \tdplotxsize } \filldraw [tdplot_screen_coords] (\tdplotstartx ,\tdplotstarty ) rectangle (\tdplotstopx ,\tdplotstopy ); } \par \pgfmathsetmacro {\tdplotstopy }{\tdploty + (360+\tdplothuestep )*\tdplotyscale } \pgfmathsetmacro {\tdplotstopx }{\tdplotx + \tdplotxsize } \par \draw [tdplot_screen_coords] (\tdplotx ,\tdploty ) rectangle (\tdplotstopx ,\tdplotstopy ); \par \node 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