%%
%% This is file `pst-3dplot.tex',
%%
%% IMPORTANT NOTICE:
%%
%% Package `pst-3dplot.tex'
%%
%% Herbert Voss <voss _at_ perce.de>
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN archives
%% in directory macros/latex/base/lppl.txt.
%%
%% DESCRIPTION:
%%   `pst-3dplot' is a PSTricks package to draw 3d curves,
%%       3d data files  and graphical objects
%%
\csname PSTThreeDplotLoaded\endcsname
\let\PSTThreeDplotLoaded\endinput
% Requires PSTricks, pst-node, pst-plot, multido packages
\ifx\PSTricksLoaded\endinput\else\input pstricks.tex\fi
\ifx\PSTnodesLoaded\endinput\else\input pst-node.tex\fi
\ifx\PSTplotLoaded\endinput\else\input pst-plot.tex\fi% plotpoints
\ifx\PSTVueTroisDLoaded\endinput\else\input pst-vue3d.tex\fi
\ifx\PSTMultidoLoaded\endinput\else\input multido.tex\fi
%
\def\fileversion{1.51}
\def\filedate{2004/12/03}
\message{`PST-3dplot' v\fileversion, \filedate\space (HV)}
%
\edef\PstAtCode{\the\catcode`\@} \catcode`\@=11\relax
\ifx\PSTXKeyLoaded\endinput\else\input pst-xkey \fi
\pst@addfams{pst-3dplot}
\SpecialCoor
%
%%%%%%%%%%%%%%%%%% Macrolist %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% \def\pstThreeDPut
% \def\pstThreeDLine
% \def\pstThreeDDot
% \def\pstThreeDNode
% \def\pstUThreeDPut
% \def\pstThreeDSquare
% \def\pstThreeDBox
% \def\pstThreeDSphere
% \def\pstThreeDEllipse
% \def\pstThreeDPlotFunc
% \def\psplotThreeD
% \def\parametricplotThreeD
% \def\psThreeDPlot
% \def\pstThreeDCoor
% \def\fileplotThreeD
% \def\dataplotThreeD
% \def\listplotThreeD
%
%
\newdimen\pst@dimf
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% ---------------- the if's -----------------
%
\newif\ifPst@drawing%			draw the coordinates?
\define@key[psset]{pst-3dplot}{drawing}[true]{\@nameuse{Pst@drawing#1}}
\newif\ifPst@drawCoor%		draw the coordinates of a dot?
\define@key[psset]{pst-3dplot}{drawCoor}[false]{\@nameuse{Pst@drawCoor#1}}
\newif\ifPst@hiddenLine%	emulate hidden line surface?
\define@key[psset]{pst-3dplot}{hiddenLine}[false]{\@nameuse{Pst@hiddenLine#1}}
\newif\ifPst@SphericalCoor% 	(r,phi,theta)
\define@key[psset]{pst-3dplot}{SphericalCoor}[true]{\@nameuse{Pst@SphericalCoor#1}}
\psset{SphericalCoor=false}
%
% ------- the global definitions for the pspicture frame ------
%
\define@key[psset]{pst-3dplot}{xMin}{\edef\psk@ThreeDplot@xMin{#1}}
\define@key[psset]{pst-3dplot}{xMax}{\edef\psk@ThreeDplot@xMax{#1}}
\define@key[psset]{pst-3dplot}{yMin}{\edef\psk@ThreeDplot@yMin{#1}}
\define@key[psset]{pst-3dplot}{yMax}{\edef\psk@ThreeDplot@yMax{#1}}
\define@key[psset]{pst-3dplot}{zMin}{\edef\psk@ThreeDplot@zMin{#1}}
\define@key[psset]{pst-3dplot}{zMax}{\edef\psk@ThreeDplot@zMax{#1}}
\define@key[psset]{pst-3dplot}{xThreeDunit}{\edef\psk@ThreeDplot@xThreeDunit{#1}}
\define@key[psset]{pst-3dplot}{yThreeDunit}{\edef\psk@ThreeDplot@yThreeDunit{#1}}
\define@key[psset]{pst-3dplot}{zThreeDunit}{\edef\psk@ThreeDplot@zThreeDunit{#1}}
%
% -------------- the angles and the plotpoints -------------
%
\define@key[psset]{pst-3dplot}{Alpha}{\edef\psk@ThreeDplot@Alpha{#1}} %	Horizontal turn
\define@key[psset]{pst-3dplot}{Beta}{\edef\psk@ThreeDplot@Beta{#1}}%	Vertical turn
\def\drawStyle@xLines{xLines}% 0
\def\drawStyle@yLines{yLines}% 1
\def\drawStyle@xyLines{xyLines}% 2
\def\drawStyle@yxLines{yxLines}% 3
\define@key[psset]{pst-3dplot}{drawStyle}{%			how to draw 3D functions
  \def\pst@tempa{#1}	
  \ifx\pst@tempa\drawStyle@xLines\let\psk@ThreeDplot@drawStyle\z@\else
    \ifx\pst@tempa\drawStyle@yLines\let\psk@ThreeDplot@drawStyle\@ne\else
      \ifx\pst@tempa\drawStyle@xyLines\let\psk@ThreeDplot@drawStyle\tw@\else
         \ifx\pst@tempa\drawStyle@yxLines\let\psk@ThreeDplot@drawStyle\thr@@\else
            \@pstrickserr{Bad draw style: `\pst@tempa'}\@ehpa
  \fi\fi\fi\fi%
%  \typeout{drawStyle: \the\psk@ThreeDplot@drawStyle}
  }
\psset[pst-3dplot]{drawStyle=xLines}
%
\define@key[psset]{pst-3dplot}{xPlotpoints}{%		points in x direction
  \edef\psk@ThreeDplot@xPlotpoints{#1}}
\define@key[psset]{pst-3dplot}{yPlotpoints}{%		points in y direction
  \edef\psk@ThreeDplot@yPlotpoints{#1}}
\define@key[psset]{pst-3dplot}{beginAngle}{%		for ellipse/circle arc
  \edef\psk@ThreeDplot@beginAngle{#1}}
\define@key[psset]{pst-3dplot}{endAngle}{%			for ellipse/circle arc
  \edef\psk@ThreeDplot@endAngle{#1}}
\define@key[psset]{pst-3dplot}{linejoin}{%		how lines come together 0,1,2
  \edef\psk@ThreeDplot@linejoin{#1}}
\define@key[psset]{pst-3dplot}{plane}{%			xy,xz,yz
  \edef\psk@ThreeDplot@plane{#1}}
\define@key[psset]{pst-3dplot}{pOrigin}{%			combination of (lr)(tBb)
  \edef\psk@ThreeDplot@pOrigin{#1}}
\def\ThreeDplot@planeXY{xy}
\def\ThreeDplot@planeXZ{xz}
\def\ThreeDplot@planeYZ{yz}
%
% -------------- the length and node definitions -------------
%
\define@key[psset]{pst-3dplot}{XO}{%			the X-offset
  \edef\psk@ThreeDplot@XO{#1}}
\define@key[psset]{pst-3dplot}{YO}{%			the y-offset
  \edef\psk@ThreeDplot@YO{#1}}
\define@key[psset]{pst-3dplot}{angleStep}{%		for circles
  \edef\psk@ThreeDplot@angleStep{#1}}
\define@key[psset]{pst-3dplot}{posStart}{%		where the arrows start
  \edef\psk@ThreeDplot@posStart{#1}}
\define@key[psset]{pst-3dplot}{length}{%		the length of the before|outlines
  \edef\psk@ThreeDplot@length{#1}}
\define@key[psset]{pst-3dplot}{arrowOffset}{%	offset for \arrowLine
  \edef\psk@ThreeDplot@arrowOffset{#1}}
\define@key[psset]{pst-3dplot}{visibleLineStyle}{%	offset for \arrowLine
  \edef\psk@ThreeDplot@visibleLineStyle{#1}}
\define@key[psset]{pst-3dplot}{invisibleLineStyle}{%	offset for \arrowLine
  \edef\psk@ThreeDplot@invisibleLineStyle{#1}}
%
\newif\if@IIIDticks%          draw the ticks?
\define@key[psset]{pst-3dplot}{IIIDticks}[true]{\@nameuse{@IIIDticks#1}}
\define@key[psset]{pst-3dplot}{Dz}{\edef\psk@Dz{#1}}
\define@key[psset]{pst-3dplot}{IIIDxTicksPlane}{\edef\psk@IIIDxTicksPlane{#1}}
\define@key[psset]{pst-3dplot}{IIIDyTicksPlane}{\edef\psk@IIIDyTicksPlane{#1}}
\define@key[psset]{pst-3dplot}{IIIDzTicksPlane}{\edef\psk@IIIDzTicksPlane{#1}}
\define@key[psset]{pst-3dplot}{IIIDticksize}{\edef\psk@IIIDticksize{#1}}
\define@key[psset]{pst-3dplot}{IIIDxticksep}{\edef\psk@IIIDxticksep{#1}}
\define@key[psset]{pst-3dplot}{IIIDyticksep}{\edef\psk@IIIDyticksep{#1}}
\define@key[psset]{pst-3dplot}{IIIDzticksep}{\edef\psk@IIIDzticksep{#1}}
\define@key[psset]{pst-3dplot}{nameX}{%		start of the object arrow
	\edef\psk@ThreeDplot@nameX{#1}}
\define@key[psset]{pst-3dplot}{spotX}{%		where to draw the label
	\edef\psk@ThreeDplot@spotX{#1}}
\define@key[psset]{pst-3dplot}{nameY}{\edef\psk@ThreeDplot@nameY{#1}}
\define@key[psset]{pst-3dplot}{spotY}{\edef\psk@ThreeDplot@spotY{#1}}
\define@key[psset]{pst-3dplot}{nameZ}{\edef\psk@ThreeDplot@nameZ{#1}}
\define@key[psset]{pst-3dplot}{spotZ}{\edef\psk@ThreeDplot@spotZ{#1}}
%
% ###   begin Torsten Suhling
\define@key[psset]{pst-3dplot}{planecorr}{%			make plane tags readable 
	\edef\psk@ThreeDplot@planecorr{#1}} 
\def\ThreeDplot@planecorrOff{off}	% default
\def\ThreeDplot@planecorrNormal{normal}	% make planes readable 
\def\ThreeDplot@planecorrXYrot{xyrot}	% and put tag for xy-plane 
% 					% parallel to the y-axis 
% ###   end Torsten Suhling
%
\def\psds@none{\pst@gdot{}}% define none for the dotstyle
%
\newpsstyle{hiddenStyle}{fillstyle=solid,fillcolor=white}
\newcount\pst@cntx\newcount\pst@cnty\newcount\pst@cntz
\newdimen\pst@dimx\newdimen\pst@dimy\newdimen\pst@dimz
%
\define@key[psset]{pst-3dplot}{planeGrid}{\edef\psk@planeGrid{#1}}
\define@key[psset]{pst-3dplot}{planeGridOffset}{\edef\psk@planeGridOffset{#1}}
\define@key[psset]{pst-3dplot}{subticks}{\edef\psk@xsubticks{#1}\edef\psk@ysubticks{#1}}
\define@key[psset]{pst-3dplot}{xsubticks}{\edef\psk@xsubticks{#1}}
\define@key[psset]{pst-3dplot}{ysubticks}{\edef\psk@ysubticks{#1}}
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                              %
%                        B A S I C S	                       %
%                                                              %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstheader{pst-3dplot.pro}
\def\pst@3ddict{tx@3DPlotDict begin }
\def\tx@saveCoor{\pst@3ddict saveCoor end }
\def\tx@ConvertTo2D{\pst@3ddict ConvertTo2D end }
\def\tx@SphericalCoor{\pst@3ddict SphericalCoor end }
\def\tx@ConvertToCartesian{\pst@3ddict ConvertToCartesian end }
%
\def\setDefaults{%
  \psset[pst-3dplot]{%
  drawing=true,hiddenLine=false,xMin=-1,xMax=4,yMin=-1,yMax=4,zMin=-1,zMax=4,%
  xThreeDunit=1.0,yThreeDunit=1.0,zThreeDunit=1.0,Alpha=45,Beta=30,%
  drawStyle=xLines,xPlotpoints=25,yPlotpoints=25,beginAngle=0,endAngle=360,%
  linejoin=1,XO=0,YO=0,angleStep=1,posStart=0,length=2,arrowOffset=0,%
  visibleLineStyle=solid,invisibleLineStyle=dashed,nameX=$x$,spotX=180,%
  nameY=$y$,spotY=0,nameZ=$z$,spotZ=90,plane=xy,pOrigin=c,SphericalCoor=false,%
  Dz=1,IIIDticks=false,IIIDxTicksPlane=xy,IIIDyTicksPlane=yz,IIIDzTicksPlane=yz,%
  IIIDticksize=0.1,IIIDxticksep=-0.4,IIIDyticksep=-0.2,IIIDzticksep=0.2,
  planecorr=off,%
  planeGrid=xy,planeGridOffset=0,subticks=10%
  }%
}
\setDefaults
%
% (#1) -> #1 #2 #3
\def\getThreeDCoor#1#2{\pst@getThreeDcoor(#1)\let#2\pst@coorIIID}
\def\pst@getThreeDcoor(#1,#2,#3){%
  \edef\pst@coorIIID{#1\space #2\space #3\space}%
}
\def\pst@addThreeDVec(#1)(#2)#3#4#5{%
  \pst@calcThreeDVec(#1)(#2)%
  \let#3\pst@getValueX%
  \let#4\pst@getValueY%
  \let#5\pst@getValueZ%
}
\def\pst@subThreeDVec(#1)(#2,#3,#4)#5#6#7{%
  \pst@calcThreeDVec(#1)(-#2,-#3,-#4)%
  \let#5\pst@getValueX%
  \let#6\pst@getValueY%
  \let#7\pst@getValueZ%
}
\def\pst@calcThreeDVec(#1,#2,#3)(#4,#5,#6){{%
    \pst@dima=#1 pt%
    \pst@dimb=#2 pt%
    \pst@dimc=#3 pt%
    \pst@dimf=#4 pt%
    \pst@dimg=#5 pt%
    \pst@dimh=#6 pt%
    \advance\pst@dima by \pst@dimf%
    \advance\pst@dimb by \pst@dimg%
    \advance\pst@dimc by \pst@dimh%
    \xdef\pst@getValueX{\pst@number\pst@dima}%
    \xdef\pst@getValueY{\pst@number\pst@dimb}%
    \xdef\pst@getValueZ{\pst@number\pst@dimc}%
}}%
%
% the ThreeD coordinate system
%
\def\psxyzlabel#1{\bgroup\footnotesize\textsf{#1}\egroup}
%
\def\pstThreeDCoor{\@ifnextchar[{\pst@ThreeDCoor}{\pst@ThreeDCoor[]}}
\def\pst@ThreeDCoor[#1]{{%
  \pst@killglue%
  \psset{linewidth=0.5pt,linecolor=red,arrows=->,dotstyle=|}%
  \psset{#1}%
  \pstThreeDNode(\psk@ThreeDplot@xMin,0,0){xMin}%
  \pstThreeDNode(\psk@ThreeDplot@xMax,0,0){xMax}%
  \pstThreeDNode(0,\psk@ThreeDplot@yMin,0){yMin}%
  \pstThreeDNode(0,\psk@ThreeDplot@yMax,0){yMax}%
  \pstThreeDNode(0,0,\psk@ThreeDplot@zMin){zMin}%
  \pstThreeDNode(0,0,\psk@ThreeDplot@zMax){zMax}%
  \ifPst@drawing% ThreeDplot axes
    \psline(xMin)(xMax)%
    \psline(yMin)(yMax)%
    \psline(zMin)(zMax)%
    \uput[\psk@ThreeDplot@spotX](xMax){\psk@ThreeDplot@nameX}%
    \uput[\psk@ThreeDplot@spotY](yMax){\psk@ThreeDplot@nameY}%
    \uput[\psk@ThreeDplot@spotZ](zMax){\psk@ThreeDplot@nameZ}%
  \if@IIIDticks%
%    \ifnum\psk@ThreeDplot@Alpha=90\else
    \pst@dimx=\psk@ThreeDplot@xMax\p@%
    \pst@dima=\psk@ThreeDplot@xThreeDunit\p@%
    \divide\pst@dimx by \pst@dima%
    \pst@cntx=\number\pst@dimx\advance\pst@cntx by -1%
    \multido{%
      \rA=\psk@Dx+\psk@Dx,%
      \rB=\psk@ThreeDplot@xThreeDunit+\psk@ThreeDplot@xThreeDunit}{\pst@cntx}{%
      \pstThreeDLine[arrows=-](\rB,-\psk@IIIDticksize,0)(\rB,\psk@IIIDticksize,0)%
      \pstPlanePut[plane=\psk@IIIDxTicksPlane]%
         (\rB,\psk@IIIDxticksep,0){\psxyzlabel{\rA}}%
    }%
    \pst@dimx=\psk@ThreeDplot@xMin\p@%
    \pst@dima=\psk@ThreeDplot@xThreeDunit\p@%
    \divide\pst@dimx by \pst@dima%
    \ifnum\psk@ThreeDplot@xMin<\z@\pst@cntx=-\number\pst@dimx%
    \else\pst@cntx=\number\pst@dimx%
    \fi%
    \multido{\rA=-\psk@Dx+-\psk@Dx,%
       \rB=-\psk@ThreeDplot@xThreeDunit+-\psk@ThreeDplot@xThreeDunit}{\pst@cntx}{%
      \pstThreeDLine[arrows=-](\rB,-\psk@IIIDticksize,0)(\rB,\psk@IIIDticksize,0)%
      \pstPlanePut[plane=\psk@IIIDxTicksPlane](\rB,\psk@IIIDxticksep,0){\psxyzlabel{\rA}}%
    }%
%    \fi%
%    \ifnum\psk@ThreeDplot@Alpha=0\else
    \pst@dimy=\psk@ThreeDplot@yMax\p@%
    \pst@dima=\psk@ThreeDplot@yThreeDunit\p@%
    \divide\pst@dimy by \pst@dima%
    \pst@cnty=\number\pst@dimy\advance\pst@cnty by -1%
    \mmultido{\rA=0.0+\psk@Dy,\rB=0.0+\psk@ThreeDplot@yThreeDunit}{\pst@cnty}{%
      \pstThreeDLine[arrows=-](-\psk@IIIDticksize,\rB,0)(\psk@IIIDticksize,\rB,0)%
      \pstPlanePut[plane=\psk@IIIDyTicksPlane](\psk@IIIDyticksep,\rB,0){\psxyzlabel{\rA}}%
    }%
    \pst@dimy=\psk@ThreeDplot@yMin\p@%
    \pst@dima=\psk@ThreeDplot@yThreeDunit\p@%
    \divide\pst@dimy by \pst@dima%
    \ifnum\psk@ThreeDplot@yMin<\z@\pst@cnty=-\number\pst@dimy%
    \else\pst@cnty=\number\pst@dimy%
    \fi%
    \multido{\rA=-\psk@Dy+-\psk@Dy,%
        \rB=-\psk@ThreeDplot@yThreeDunit+-\psk@ThreeDplot@yThreeDunit}{\pst@cnty}{%
      \pstThreeDLine[arrows=-](-\psk@IIIDticksize,\rB,0)(\psk@IIIDticksize,\rB,0)%
      \pstPlanePut[plane=\psk@IIIDyTicksPlane](\psk@IIIDyticksep,\rB,0){\psxyzlabel{\rA}}%
    }%
%    \fi%
    \pst@dimz=\psk@ThreeDplot@zMax\p@%
    \pst@dima=\psk@ThreeDplot@zThreeDunit\p@%
    \divide\pst@dimz by \pst@dima%
    \pst@cntz=\number\pst@dimz\advance\pst@cntz by -1%
    \mmultido{\rA=0.0+\psk@Dz,\rB=0.0+\psk@ThreeDplot@zThreeDunit}{\pst@cntz}{%
      \pstThreeDLine[arrows=-](0,-\psk@IIIDticksize,\rB)(0,\psk@IIIDticksize,\rB)%
      \pstPlanePut[plane=\psk@IIIDzTicksPlane](0,\psk@IIIDzticksep,\rB){\psxyzlabel{\rA}}%
    }%
    \pst@dimz=\psk@ThreeDplot@zMin\p@%
    \pst@dima=\psk@ThreeDplot@zThreeDunit\p@%
    \divide\pst@dimz by \pst@dima%
    \ifnum\psk@ThreeDplot@zMin<\z@\pst@cntz=-\number\pst@dimz%
    \else\pst@cntz=\number\pst@dimz%
    \fi%
    \multido{\rA=-\psk@Dz+-\psk@Dz,%
       \rB=-\psk@ThreeDplot@zThreeDunit+-\psk@ThreeDplot@zThreeDunit}{\pst@cntz}{%
      \pstThreeDLine[arrows=-](0,-\psk@IIIDticksize,\rB)(0,\psk@IIIDticksize,\rB)%
      \pstPlanePut[plane=\psk@IIIDzTicksPlane](0,\psk@IIIDzticksep,\rB){\psxyzlabel{\rA}}%
    }%
  \fi\fi%
}\ignorespaces}
%
% planeGrids
%
\newdimen\pst@dx\newdimen\pst@dy
\def\pstThreeDPlaneGrid{\pst@object{pstThreeDPlaneGrid}}
\def\pstThreeDPlaneGrid@i(#1,#2)(#3,#4){{%
  \pst@killglue
  \use@par
  \pssetxlength\pst@dima{#1}
  \pssetxlength\pst@dimb{#3}
  \advance\pst@dimb by -\pst@dima
  \divide\pst@dimb by \psk@xsubticks
  \pst@dx=\pst@dimb
%  
  \pssetylength\pst@dima{#2}
  \pssetylength\pst@dimb{#4}
  \advance\pst@dimb by -\pst@dima
  \divide\pst@dimb by \psk@ysubticks
  \pst@dy=\pst@dimb
%  
  \pssetylength\pst@dimx{#2}
  \pssetylength\pst@dimy{#4}
  \pssetylength\pst@dimz{#1}
  \pssetylength\pst@dimf{#3}
  \pst@getlength\psk@planeGridOffset\pst@dima
  \pst@cntx=\psk@xsubticks\advance\pst@cntx by \@ne
  \pst@cnty=\psk@ysubticks\advance\pst@cnty by \@ne
  \psset{unit=1pt,planeGridOffset=\pst@dima}% we need everything in pt
  \ifx\psk@planeGrid\ThreeDplot@planeXY
    \multido{\rA=#1+\strip@pt\pst@dx}{\pst@cntx}{%
      \pstThreeDLine(\rA,\strip@pt\pst@dimx,\psk@planeGridOffset)%
                    (\rA,\strip@pt\pst@dimy,\psk@planeGridOffset)}
    \multido{\rA=#2+\strip@pt\pst@dy}{\pst@cnty}{%
      \pstThreeDLine(\strip@pt\pst@dimz,\rA,\psk@planeGridOffset)%
                    (\strip@pt\pst@dimf,\rA,\psk@planeGridOffset)}
  \else
    \ifx\psk@planeGrid\ThreeDplot@planeXZ
      \multido{\rA=#1+\strip@pt\pst@dx}{\pst@cntx}{%
        \pstThreeDLine(\rA,\psk@planeGridOffset,\strip@pt\pst@dimx)%
	              (\rA,\psk@planeGridOffset,\strip@pt\pst@dimy)}
      \multido{\rA=#2+\strip@pt\pst@dy}{\pst@cnty}{%
        \pstThreeDLine(\strip@pt\pst@dimz,\psk@planeGridOffset,\rA)%
	              (\strip@pt\pst@dimf,\psk@planeGridOffset,\rA)}
    \else
      \multido{\rA=#1+\strip@pt\pst@dx}{\pst@cntx}{%
        \pstThreeDLine(\psk@planeGridOffset,\rA,\strip@pt\pst@dimx)%
	              (\psk@planeGridOffset,\rA,\strip@pt\pst@dimy)}
      \multido{\rA=#2+\strip@pt\pst@dy}{\pst@cnty}{%
        \pstThreeDLine(\psk@planeGridOffset,\strip@pt\pst@dimz,\rA)%
	              (\psk@planeGridOffset,\strip@pt\pst@dimf,\rA)}
    \fi 
  \fi%
}\ignorespaces}
%
% put anything at (#2,#3,#4)
%
\def\pstThreeDPut{\@ifnextchar[{\pst@ThreeDPut}{\pst@ThreeDPut[]}}
\def\pst@ThreeDPut[#1](#2,#3,#4)#5{{%
  \pst@killglue%
  \psset{#1}%
  \pstThreeDNode(#2,#3,#4){temp@pstNode}%
%	\def\@tempa{c}
%	\ifx\pst@ThreeDplot@pOrigin\@tempa%
%	    \rput(temp@pstNode){#5}%
%	\else%
  \rput[\psk@ThreeDplot@pOrigin](temp@pstNode){#5}%
%	\fi%
}\ignorespaces}
%
% draws a 3d line
%
\def\cartesianIIID@coor#1,#2,#3,#4\@nil{\edef\pst@coor{#1 #2 #3 }}
\def\NormalIIIDCoor{%
  \def\pst@@getcoor##1{\pst@expandafter\cartesianIIID@coor{##1}, ,\@nil}%
  \def\pst@@getangle##1{%
    \pst@checknum{##1}\pst@angle%
    \edef\pst@angle{\pst@angle \pst@angleunit}%
  }%
  \def\psput@##1{\pst@@getcoor{##1}\leavevmode\psput@cartesian}%
}%

\def\pstThreeDLine{\NormalIIIDCoor\pst@object{lineIIID}}
\def\lineIIID@i{%
  \pst@killglue%
  \pst@getarrows{%
    \begin@OpenObj%
      \pst@getcoors[\lineIIID@ii%
  }%
}
\def\lineIIID@ii{%
  \addto@pscode{%
    \pst@3ddict
      /dxUnit \psk@ThreeDplot@xThreeDunit\space def
      /dyUnit \psk@ThreeDplot@yThreeDunit\space def
      /dzUnit \psk@ThreeDplot@zThreeDunit\space def 
      /Alpha \psk@ThreeDplot@Alpha\space def %
      /Beta \psk@ThreeDplot@Beta\space def %
      \ifPst@SphericalCoor /SphericalCoor true def 
      \else /SphericalCoor false def
      \fi %
      /xUnit { \pst@number\psxunit\space mul } def
      /yUnit { \pst@number\psyunit\space mul } def
      convertStackTo2D
    end
    \pst@cp\space \psline@iii\space \tx@Line
  }%
  \end@OpenObj%
  \SpecialCoor%
  \ignorespaces
}
%
% set a 3d dot
%
\def\pstThreeDDot{\@ifnextchar[{\pst@ThreeDDot}{\pst@ThreeDDot[]}}
\def\pst@ThreeDDot[#1](#2,#3,#4){{%
  \pst@killglue
  \psset{linestyle=dashed,linewidth=0.5pt}% default
  \psset{#1}%
  \pstThreeDNode[#1](#2,#3,#4){A}%
  \ifx\psk@dotstyle\@none\else\psdots(A)\fi%
  \ifPst@drawCoor%
    \pnode(!%
      \pst@3ddict
        /Alpha \psk@ThreeDplot@Alpha\space def
        /Beta \psk@ThreeDplot@Beta\space def
        \ifPst@SphericalCoor
          #2\space #3\space #4\space
          ConvertToCartesian /z 0 def
        \else
          /x #2\space\psk@ThreeDplot@xThreeDunit\space mul def
	  /y #3\space\psk@ThreeDplot@yThreeDunit\space mul def 
	  /z 0 def
        \fi
        ConvertTo2D x2D y2D 
      end ){B}
    \psline(A)(B)%
    \pnode(!%   y=0, z=0
      \pst@3ddict
        \ifPst@SphericalCoor
          #2\space #3\space #4\space
          ConvertToCartesian /y 0 def /z 0 def
        \else
          /x #2\space\psk@ThreeDplot@xThreeDunit\space mul def 
	  /y 0 def /z 0 def
        \fi
        ConvertTo2D x2D y2D 
      end ){A}%
    \psline(B)(A)%
    \pnode(!%   x=0, z=0
      \pst@3ddict
        \ifPst@SphericalCoor
          #2\space #3\space #4\space
          ConvertToCartesian /x 0 def /z 0 def
        \else
          /x 0 def 
	  /y #3\space\psk@ThreeDplot@yThreeDunit\space mul def 
	  /z 0 def
        \fi
        ConvertTo2D x2D y2D 
      end ){A}%
    \psline(B)(A)%
  \fi%
}\ignorespaces}
%
% transform the 3d coordinates of the node (#1,#2,#3)
% into a 2d node with the name #4
%
\def\pstThreeDNode{\@ifnextchar[{\pst@ThreeDNode}{\pst@ThreeDNode[]}}
\def\pst@ThreeDNode[#1](#2,#3,#4)#5{{%
  \psset{#1}%
  \pnode(!%
    \pst@3ddict
    /Alpha \psk@ThreeDplot@Alpha\space def
    /Beta \psk@ThreeDplot@Beta\space def
    \ifPst@SphericalCoor
      #2\space #3\space #4\space
      ConvertToCartesian
    \else
      /x #2\space\psk@ThreeDplot@xThreeDunit\space mul def 
      /y #3\space\psk@ThreeDplot@yThreeDunit\space mul def 
      /z #4\space\psk@ThreeDplot@zThreeDunit\space mul def
    \fi
    ConvertTo2D x2D y2D end ){#5}%
}\ignorespaces}
%
% a 3d uput[](){}
%
\def\pstUThreeDPut{\@ifnextchar[{\pst@UThreeDPut}{\pst@UThreeDPut[]}}
\def\pst@UThreeDPut[#1](#2,#3,#4)#5{{%
  \uput[#1](!%
    \pst@3ddict
      /Alpha \psk@ThreeDplot@Alpha\space def
      /Beta \psk@ThreeDplot@Beta\space def
      \ifPst@SphericalCoor
        #2\space #3\space #4\space
        ConvertToCartesian
      \else
        /x #2\space\psk@ThreeDplot@xThreeDunit\space mul def 
        /y #3\space\psk@ThreeDplot@yThreeDunit\space mul def 
        /z #4\space\psk@ThreeDplot@zThreeDunit\space mul def
      \fi
      ConvertTo2D x2D y2D 
    end ){#5}%
}\ignorespaces}
%
% Trangle [options](Point1)(Point2)(Point3)
%
\def\pstThreeDTriangle{\@ifnextchar[%
  {\do@ThreeDTriangle}%
  {\do@ThreeDTriangle[]}%
}
\def\do@ThreeDTriangle[#1](#2)(#3)(#4){{%
  \ifx#1\empty\else\psset{#1}\fi%
  \ifPst@drawCoor%
    \pstThreeDDot[drawCoor=true](#2)%
    \pstThreeDDot[drawCoor=true](#3)%
    \pstThreeDDot[drawCoor=true](#4)%
  \fi%
  \pstThreeDNode(#2){A}%
  \pstThreeDNode(#3){B}%
  \pstThreeDNode(#4){C}%
  \ifx\psk@fillstyle\@none%
  \else%
    \pscustom{%
      \code{\psk@ThreeDplot@linejoin\space setlinejoin}%
  \fi%
  \psline[#1](A)(B)(C)(A)(B)%
  \ifx\psk@fillstyle\@none\else}\fi%
}\ignorespaces}
%
% draws a threeD square as a polygon
%
% [#1] options
% (#2) starting vector ax,ay,az
% (#3) first direction vector ux,uy,uz
% (#4) second direction vector wx,wy,wz
%
\def\pstThreeDSquare{\pst@object{squareIIID}}
\def\squareIIID@i{\squareIIID@ii}
\def\squareIIID@ii(#1)(#2)(#3){%
  \ifPst@drawCoor%
    {%
    \psset{linestyle=dashed,linewidth=0.5pt}%
    \pstThreeDDot(#1)%
    \pst@addThreeDVec(#1)(#2)\pst@tempa\pst@tempb\pst@tempc%
    \pstThreeDDot(\pst@tempa,\pst@tempb,\pst@tempc)%
    \pst@addThreeDVec(#1)(#3)\pst@tempa\pst@tempb\pst@tempc
    \pstThreeDDot(\pst@tempa,\pst@tempb,\pst@tempc)%
    \pst@addThreeDVec(\pst@tempa,\pst@tempb,\pst@tempc)%
      (#2)\pst@tempa\pst@tempb\pst@tempc%
    \pstThreeDDot(\pst@tempa,\pst@tempb,\pst@tempc)%
    }%
  \fi%
  \getThreeDCoor{#1}\pst@tempa%
  \getThreeDCoor{#2}\pst@tempb%
  \getThreeDCoor{#3}\pst@tempc%
  \begin@OpenObj
    \addto@pscode{%
      /P1 { \pst@tempa\space } def % x y z or Radius longitude lattitude
      /P2 { \pst@tempb\space } def %
      /P3 { \pst@tempc\space } def %
      /Alpha \psk@ThreeDplot@Alpha\space def %
      /Beta \psk@ThreeDplot@Beta\space def %
      /SphericalCoor \ifPst@SphericalCoor true \else false \fi def %
      /xUnit { \pst@number\psxunit\space mul } def
      /yUnit { \pst@number\psyunit\space mul } def
      /dxUnit \psk@ThreeDplot@xThreeDunit\space def
      /dyUnit \psk@ThreeDplot@yThreeDunit\space def
      /dzUnit \psk@ThreeDplot@zThreeDunit\space def
      \pst@3ddict
        P1 saveCoor
	SphericalCoor {ConvertToCartesian} if
        ConvertTo2D
        /x0 x2D xUnit def /y0 y2D yUnit def
        P2 saveCoor
        SphericalCoor {ConvertToCartesian} if
        ConvertTo2D
        /x1 x2D xUnit x0 add def /y1 y2D yUnit y0 add def
        P3 saveCoor
        SphericalCoor {ConvertToCartesian} if
        ConvertTo2D
        /x2 x2D xUnit x1 add def /y2 y2D yUnit y1 add def
        P2 saveCoor
        SphericalCoor {ConvertToCartesian} if
        ConvertTo2D
        /x3 x2D xUnit neg x2 add def /y3 y2D yUnit neg y2 add def
        [ x0 y0 x1 y1 x2 y2 x3 y3 x0 y0
        \pst@cp\space \psline@iii\space \tx@Line\space
      end
    }%
  \end@OpenObj%
}

%
% draws a threeD Box
% [#1] options
% (#2) first direction vector ux,uy,uz
% (#3) second direction vector vx,vy,vz
% (#4) third direction vector wx,wy,wz
%
\def\pstThreeDBox{\@ifnextchar[{\doThreeDBox}{\doThreeDBox[]}}
\def\doThreeDBox[#1](#2)(#3)(#4)(#5){{%
  \pst@killglue%
  \psset{linestyle=\psk@ThreeDplot@invisibleLineStyle}%
  \psset{#1}%
%
%	\psset{linestyle=dashed}
%	\psset{linestyle=\psk@ThreeDplot@invisibleLineStyle}
  \addto@par{linestyle=\psk@ThreeDplot@invisibleLineStyle}
  \pstThreeDSquare[#1](#2)(#4)(#5) % 	lower square
  \pstThreeDSquare(#2)(#3)(#4)% 	back square
%
  \psset{linestyle=\psk@ThreeDplot@visibleLineStyle}
  \pst@addThreeDVec(#2)(#4)\pst@tempa\pst@tempb\pst@tempc
  \pstThreeDSquare(\pst@tempa,\pst@tempb,\pst@tempc)(#3)(#5)% left square
  \pst@addThreeDVec(#2)(#3)\pst@tempa\pst@tempb\pst@tempc
  \pstThreeDSquare(\pst@tempa,\pst@tempb,\pst@tempc)(#4)(#5)% top square
  \pst@addThreeDVec(#2)(#5)\pst@tempa\pst@tempb\pst@tempc
  \pstThreeDSquare(\pst@tempa,\pst@tempb,\pst@tempc)(#3)(#4)% front square
%
}\ignorespaces}
%
% Sphere
%
\def\pstThreeDSphere{\@ifnextchar[{\pst@ThreeDSphere}{\pst@ThreeDSphere[]}}
\def\pst@ThreeDSphere[#1](#2,#3,#4)#5{{%
  \psset{THETA=\psk@ThreeDplot@Beta,PHI=\psk@ThreeDplot@Beta,Dobs=10,Decran=10}%
  \psset{#1}%
  \pstThreeDNode(#2,#3,#4){SphereCenter}%
  \rput(SphereCenter){\SphereThreeD(0,0,0){#5}}%
}\ignorespaces}
%
% set a 3d ellipse/circle
%
% #1 options
% #2 center cx,cy,cz
% #3 radius ax,ay,az
% #4 radius bx,by,bz
%
\def\pstThreeDEllipse{\@ifnextchar[{\doThreeDEllipse}{\doThreeDEllipse[]}}
\def\doThreeDEllipse[#1](#2)(#3)(#4){{%
  \psset{plotstyle=curve,xPlotpoints=\psk@plotpoints}%
  \psset{#1}%
  \getThreeDCoor{#2}\pst@tempc%	 center
  \getThreeDCoor{#3}\pst@tempa%	 a
  \getThreeDCoor{#4}\pst@tempb%	 b
  \parametricplotThreeD(\psk@ThreeDplot@beginAngle,\psk@ThreeDplot@endAngle){%
    \pst@3ddict
      /dxUnit \psk@ThreeDplot@xThreeDunit\space def
      /dyUnit \psk@ThreeDplot@yThreeDunit\space def
      /dzUnit \psk@ThreeDplot@zThreeDunit\space def
      \pst@tempc\space 
      \ifPst@SphericalCoor ConvertToCartesian \else saveCoor \fi
      x y z
      \pst@tempa\space
      \ifPst@SphericalCoor ConvertToCartesian \else saveCoor \fi
      x y z
      \pst@tempb\space
      \ifPst@SphericalCoor ConvertToCartesian \else saveCoor \fi
      x y z
      9 -1 roll t cos 8 -1 roll neg mul add t sin 5 -1 roll mul add
      7 -1 roll t cos 7 -1 roll neg mul add t sin 5 -1 roll mul add
      5 -1 roll t cos 6 -1 roll neg mul add t sin 5 -1 roll mul add
    end
  }%
}\ignorespaces}
%
\def\pstThreeDCircle{\pstThreeDEllipse}
\def\pstThreeDPlotFunc{\psplotThreeD}%	only for compatibility
%
\def\pstRotPoint{\@ifnextchar[{\pstRotPointi}{\pstRotPointi[]}}
\def\pstRotPointi[#1](#2,#3,#4)(#5,#6,#7)#8{{%
  \psset{#1}%
  \def\pst@ThreeDplot@ThetaX{#5}%    rotating angle
  \def\pst@ThreeDplot@ThetaY{#6}%    rotating angle
  \def\pst@ThreeDplot@ThetaZ{#7}%    rotating angle
  \pnode(!%
    \pst@3ddict
      /Alpha \psk@ThreeDplot@Alpha\space def
      /Beta \psk@ThreeDplot@Beta\space def
      \ifPst@SphericalCoor
        #2\space #3\space #4\space
        ConvertToCartesian
      \else
        /x #2\space\psk@ThreeDplot@xThreeDunit\space mul def 
        /y #3\space\psk@ThreeDplot@yThreeDunit\space mul def 
        /z #4\space\psk@ThreeDplot@zThreeDunit\space mul def
      \fi
% rotating on the z-Axes
      /Theta \pst@ThreeDplot@ThetaZ\space def
      /x0 x Theta cos mul y Theta sin mul sub def
      /y x Theta sin mul y Theta cos mul add def
      /x x0 def
% rotating on the y-Axes
      /Theta \pst@ThreeDplot@ThetaY\space def
      /x0 x Theta cos mul z Theta sin mul add def
      /z x neg Theta sin mul z Theta cos mul add def
      /x x0 def
% rotating on the x-Axes
      /Theta \pst@ThreeDplot@ThetaX\space def
      /y0 y Theta cos mul z Theta sin mul sub def
      /z y Theta sin mul z Theta cos mul add def
      /y y0 def
%
      ConvertTo2D x2D y2D 
    end ){#8}%
}\ignorespaces}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\def\psplotinit#1{\xdef\psplot@init{#1 }}
\def\psplot@init{}
%
%\def\psplotThreeD{\@ifnextchar[{\ps@plotThreeD}{\ps@plotThreeD[]}}
\def\psplotThreeD{\def\pst@par{}\pst@object{psplotThreeD}}
\def\psplotThreeD@i(#1,#2)(#3,#4)#5{{%
  \use@par%
  \ifcase\psk@ThreeDplot@drawStyle%
    \psplotThreeD@xLines(#1,#2)(#3,#4){#5}\or%
    \psplotThreeD@yLines(#1,#2)(#3,#4){#5}\or    
    \psplotThreeD@xLines(#1,#2)(#3,#4){#5}%
    \psplotThreeD@yLines(#1,#2)(#3,#4){#5}\or%
    \psplotThreeD@yLines(#1,#2)(#3,#4){#5}%
    \psplotThreeD@xLines(#1,#2)(#3,#4){#5}%
  \fi%
}\ignorespaces}
%
%\def\doPlotThreeD@xLines{\pst@object{psplotThreeD@xLines}}
%\def\doPlotThreeD@yLines{\pst@object{psplotThreeD@yLines}}
%
\def\psplotThreeD@xLines(#1,#2)(#3,#4)#5{%
  \pst@killglue%
  \begingroup%
%    \use@par%
    \@pstfalse%
    \@nameuse{beginplot@\psplotstyle}%
    \gdef\psplot@init{}%
    \@nameuse{testqp@\psplotstyle}%
    \if@pst%	lines and dots
      \addto@pscode{%
        /Alpha \psk@ThreeDplot@Alpha\space def
        /Beta \psk@ThreeDplot@Beta\space def
        /xMin #1 def
        /x xMin def
        /x1 #2 def
        /y #3 def
        /y1 #4 def
        /dx x1 x sub \psk@ThreeDplot@xPlotpoints\space dup 0 gt {div}{pop} ifelse def
        /dy y1 y sub \psk@ThreeDplot@yPlotpoints\space dup 0 gt {div}{pop} ifelse def
        /func {#5} def
        /xyz {
          x neg Alpha cos mul y Alpha sin mul add \pst@number\psxunit mul
          x Alpha sin mul y Alpha cos mul add neg Beta sin mul
          func Beta cos mul add \pst@number\psyunit mul} def
        }%
        \psplotThreeD@xLines@ii
    \else%	curves
  \endgroup
  \multido{\n@Y=0+1}{\psk@ThreeDplot@yPlotpoints}{%
    \ifPst@hiddenLine\pscustom[style=hiddenStyle]{\fi
    \@nameuse{beginplot@\psplotstyle}%
    \addto@pscode{%
      /Alpha \psk@ThreeDplot@Alpha\space def
      /Beta \psk@ThreeDplot@Beta\space def
      /xMin #1 def
      /x xMin def
      /x1 #2 def
      /dx x1 x sub \psk@ThreeDplot@xPlotpoints\space dup 0 gt {div}{pop} ifelse def
      /dy #4\space #3\space sub \psk@ThreeDplot@yPlotpoints\space dup 0 gt {div}{pop} ifelse def
      /y #3\space \n@Y\space dy mul add def
      /func {#5} def
      /xyz {
        x neg Alpha cos mul y Alpha sin mul add \pst@number\psxunit mul
        x Alpha sin mul y Alpha cos mul add neg Beta sin mul
        func Beta cos mul add \pst@number\psyunit mul} def
    }%
    \psplotThreeD@xLines@iii%
    \ifPst@hiddenLine }\fi%
  }%
  \fi
  \endgroup
  \ignorespaces%
}
%
\def\psplotThreeD@xLines@ii{%
  \addto@pscode{%
    xyz \@nameuse{beginqp@\psplotstyle}
   \psk@ThreeDplot@yPlotpoints\space 1 add {
     /x xMin def
%     xyz moveto
     \psk@ThreeDplot@xPlotpoints\space 1 add {
       xyz \@nameuse{doqp@\psplotstyle}
       /x x dx add def
     } repeat
     /y y dy add def
   } repeat
   /x x1 def
   /y y1 def
   xyz \@nameuse{doqp@\psplotstyle}
  }%
  \@nameuse{endqp@\psplotstyle}%
}
\def\psplotThreeD@xLines@iii{%    curves
  \addto@pscode{%
    /x xMin def
    mark
    /n 2 def
    \psk@ThreeDplot@xPlotpoints {
      xyz
      n 2 roll
      /n n 2 add def
      /x x dx add def
    } repeat
    /x x1 def
    xyz
    n 2 roll
  }%
  \@nameuse{endplot@\psplotstyle}%
}
%
\def\psplotThreeD@yLines(#1,#2)(#3,#4)#5{%
  \pst@killglue
  \begingroup
%  \use@par%
  \@pstfalse
  \@nameuse{beginplot@\psplotstyle}%
  \gdef\psplot@init{}%
  \@nameuse{testqp@\psplotstyle}%
  \if@pst%	lines and dots
    \addto@pscode{%
      /Alpha \psk@ThreeDplot@Alpha\space def
      /Beta \psk@ThreeDplot@Beta\space def
      /x #1 def
      /x1 #2 def
      /yMin #3 def
      /y yMin def
      /y1 #4 def
      /dx x1 x sub \psk@ThreeDplot@xPlotpoints\space dup 0 gt {div}{pop} ifelse def
      /dy y1 y sub \psk@ThreeDplot@yPlotpoints\space dup 0 gt {div}{pop} ifelse def
      /func {#5} def
      /xyz {
        x neg Alpha cos mul y Alpha sin mul add \pst@number\psxunit mul
        x Alpha sin mul y Alpha cos mul add neg Beta sin mul
        func Beta cos mul add \pst@number\psyunit mul} def
    }%
    \psplotThreeD@yLines@ii
  \else%	curves
    \endgroup
    \multido{\n@X=0+1}{\psk@ThreeDplot@xPlotpoints}{%
      \ifPst@hiddenLine\pscustom[style=hiddenStyle]{\fi
      \@nameuse{beginplot@\psplotstyle}%
      \addto@pscode{%
        /Alpha \psk@ThreeDplot@Alpha\space def
        /Beta \psk@ThreeDplot@Beta\space def
        /yMin #3 def
        /y yMin def
        /y1 #4 def
        /dy y1 y sub \psk@ThreeDplot@yPlotpoints\space dup 0 gt {div}{pop} ifelse def
        /dx #2\space #1\space sub \psk@ThreeDplot@xPlotpoints\space dup 0 gt {div}{pop} ifelse def
        /x #1\space \n@X\space dx mul add def
        /func {#5} def
        /xyz {
        x neg Alpha cos mul y Alpha sin mul add \pst@number\psxunit mul
        x Alpha sin mul y Alpha cos mul add neg Beta sin mul
        func Beta cos mul add \pst@number\psyunit mul} def
      }%
      \psplotThreeD@yLines@iii%
      \ifPst@hiddenLine }\fi%
    }%
  \fi
  \endgroup
  \ignorespaces%
}
\def\psplotThreeD@yLines@ii{%
  \addto@pscode{%
    xyz \@nameuse{beginqp@\psplotstyle}
    \psk@ThreeDplot@xPlotpoints\space 1 add {
      /y yMin def
%      xyz moveto
      \psk@ThreeDplot@yPlotpoints\space 1 add {
        xyz \@nameuse{doqp@\psplotstyle}
        /y y dy add def
      } repeat
      /x x dx add def
    } repeat
    /x x1 def
    /y y1 def
    xyz \@nameuse{doqp@\psplotstyle}
  }%
  \@nameuse{endqp@\psplotstyle}%
}
\def\psplotThreeD@yLines@iii{%    curves
  \addto@pscode{%
    /y yMin def
    mark
    /n 2 def
    \psk@ThreeDplot@yPlotpoints {
      xyz
      n 2 roll
      /n n 2 add def
      /y y dy add def
    } repeat
    /y y1 def
    xyz
    n 2 roll
  }%
    \@nameuse{endplot@\psplotstyle}%
}
%
% parametricplot ----------------------------------------------------------------
%
\def\parametricplotThreeD{\def\pst@par{}\pst@object{parametricPlotThreeD}}
\def\parametricPlotThreeD@i(#1){%
  \@ifnextchar({\parametricPlotThreeD@ii(#1)}{\parametricPlotThreeD@ii(#1)(0,0)}%
}
\def\parametricPlotThreeD@ii(#1,#2)(#3,#4)#5{{%
  \pst@killglue%
  \use@par%
  \@pstfalse%
  \@nameuse{beginplot@\psplotstyle}%
  \@nameuse{testqp@\psplotstyle}% quick plot or something special
  \pstVerb{%
      /Alpha \psk@ThreeDplot@Alpha\space def
      /Beta \psk@ThreeDplot@Beta\space def
      /3D2DConv {
        3 -1 roll               % y z x
        \psk@ThreeDplot@xThreeDunit\space mul
        dup                     % y z x x
        neg Alpha cos mul       % y z x (x)
        4 -1 roll               % z x (x) y
       \psk@ThreeDplot@yThreeDunit\space mul
       dup                     % z x (x) y y
       5 1 roll                % y z x (x) y
       Alpha sin mul add \pst@number\psxunit mul       % y z x (x2)
       4 1 roll                % (x2) y z x
       Alpha sin mul           % (x2) y z (x)
       3 -1 roll               % (x2) z (x) y
       Alpha cos mul add neg Beta sin mul % (x2) z (x)
       exch                    % (x2) (x) z
       \psk@ThreeDplot@zThreeDunit\space mul
       Beta cos mul add \pst@number\psyunit mul        % (x2) (y2)
      } def
  }%
  \if@pst%
    \def\pslinetype{0}%
    \addto@pscode{%
      /tMin #1 def
      /t tMin def
      /t1 #2 def
      /u #3 def
      /u1 #4 def
      /dt t1 t sub \psk@ThreeDplot@xPlotpoints\space dup 1 gt %
        { 1 sub div }{ pop pop 0 } ifelse def % step for t
      /du u1 u sub \psk@ThreeDplot@yPlotpoints\space dup 1 gt %
        { 1 sub div }{ pop pop 0 } ifelse def % step for u
      /xyz { #5 3D2DConv } def
   }%
   \parametricPlotThreeD@iii%
  \else%
    \def\pslinetype{-3}%
    \endgroup%
    \pst@dima=#3pt\pst@dimb=#4pt
    \ifdim\pst@dima=\pst@dimb\psset{yPlotpoints=1}\fi% #3=#4 ??
    \multido{\n@Y=0+1}{\psk@ThreeDplot@yPlotpoints}{%
      \@nameuse{beginplot@\psplotstyle}%
      \addto@pscode{%
        /tMin #1 def
        /t tMin def
        /t1 #2 def
	/u1 #2 def
        /dt t1 t sub \psk@ThreeDplot@xPlotpoints\space dup 1 gt %
          { 1 sub div }{ pop pop 0 } ifelse def % step for t
        /du #4\space #3\space sub \psk@ThreeDplot@yPlotpoints\space dup 1 gt %
          { 1 sub div }{ pop pop 0 } ifelse def % step for t
        /u #3\space \n@Y\space du mul add def
        /xyz { #5 3D2DConv } def
     }%
     \parametricPlotThreeD@iv%
    }%
  \fi%
}\ignorespaces}
\def\parametricPlotThreeD@iii{%   without arrows (quickplot)
  \addto@pscode{%
    \psk@ThreeDplot@yPlotpoints\space {
      /t tMin def
      xyz \@nameuse{beginqp@\psplotstyle}
      \psk@ThreeDplot@xPlotpoints {
        xyz \@nameuse{doqp@\psplotstyle}
        /t t dt add def
      } repeat
      /u u du add def
    } repeat
  }%
  \@nameuse{endqp@\psplotstyle}%
}
\def\parametricPlotThreeD@iv{%    with arrows or curve
  \addto@pscode{%
%	    /t tMin def
    mark
    /n 0 def
    \psk@ThreeDplot@xPlotpoints\space {
      xyz
      /n n 2 add def
      n 2 roll
      /t t dt add def
    } repeat
%    /t t1 def
%    /u u1 def
%    xyz
%    n 2 roll
  }%
  \@nameuse{endplot@\psplotstyle}%
}
%
% Plot 3D data
%
\def\fileplotThreeD{\def\pst@par{}\pst@object{fileplotThreeD}}
\def\fileplotThreeD@i#1{%
    \pst@killglue%
    \begingroup%
	\use@par%
	\@pstfalse%
	\@nameuse{testqp@\psplotstyle}%%
	\if@pst
	    \dataplotThreeD@ii{\pst@readfile{#1}}%
	\else
	    \listplotThreeD@ii{\pst@altreadfile{#1}}%
	\fi
    \endgroup%
    \ignorespaces%
}
%
% dataplot
%
\def\dataplotThreeD{\def\pst@par{}\pst@object{dataplotThreeD}}
\def\dataplotThreeD@i#1{%
  \pst@killglue
  \begingroup
    \use@par
    \@pstfalse
    \@nameuse{testqp@\psplotstyle}%
    \if@pst
      \dataplotThreeD@ii{\addto@pscode{#1}}%
    \else
      \listplot@ii{\addto@pscode{#1}}%
    \fi
  \endgroup
  \ignorespaces%
}
\def\dataplotThreeD@ii#1{%
  \@nameuse{beginplot@\psplotstyle}%
    \addto@pscode{%
      /Alpha \psk@ThreeDplot@Alpha\space def
      /Beta \psk@ThreeDplot@Beta\space def
      /Dx { /D { Dy } def } def
      /Dy { /D { Dz } def } def
      /Dz { 			% now we have x y z
	3 -1 roll		% y z x
        \psk@ThreeDplot@xThreeDunit\space div
	dup			% y z x x
	neg Alpha cos mul	% y z x (x)
	4 -1 roll		% z x (x) y
	\psk@ThreeDplot@yThreeDunit\space div
	dup			% z x (x) y y
	5 1 roll		% y z x (x) y
	Alpha sin mul add \pst@number\psxunit mul % y z x (x2)
	4 1 roll		% (x2) y z x
	Alpha sin mul		% (x2) y z (x)
	3 -1 roll		% (x2) z (x) y
	Alpha cos mul add neg Beta sin mul % (x2) z (x)
	exch			% (x2) (x) z
	\psk@ThreeDplot@zThreeDunit\space div
	Beta cos mul add \pst@number\psyunit mul % (x2) (y2)
	Do /D { Dx } def } def
      /D { /D { Dx } def } def
      /Do {
        \@nameuse{beginqp@\psplotstyle}%
        /Do { \@nameuse{doqp@\psplotstyle}} def
      } def}%
    #1%
    \addto@pscode{D}%
  \@nameuse{endqp@\psplotstyle}%
}
%
%
\pst@def{ScalePointsThreeD}<%
	counttomark dup dup cvi eq not { exch pop } if
	/m exch def /n m 3 div cvi def
	n { 				% now we have x y z
		3 -1 roll		% y z x
		\psk@ThreeDplot@xThreeDunit\space div
		dup			% y z x x
		neg Alpha cos mul	% y z x (x)
		4 -1 roll		% z x (x) y
		\psk@ThreeDplot@yThreeDunit\space div
		dup			% z x (x) y y
		5 1 roll		% y z x (x) y
		Alpha sin mul add \pst@number\psxunit mul	% y z x (x2)
		4 1 roll		% (x2) y z x
		Alpha sin mul		% (x2) y z (x)
		3 -1 roll		% (x2) z (x) y
		Alpha cos mul add neg Beta sin mul % (x2) z (x)
		exch			% (x2) (x) z
		\psk@ThreeDplot@zThreeDunit\space div
		Beta cos mul add \pst@number\psyunit mul 	% (x2) (y2)
		m 1 sub 1 roll m 1 sub 1 roll /m m 3 sub def } repeat>
%
% listplotThreeD
%
\def\listplotThreeD{\def\pst@par{}\pst@object{listplotThreeD}}
\def\listplotThreeD@i#1{\listplotThreeD@ii{\addto@pscode{#1}}}
\def\listplotThreeD@ii#1{%
  \@nameuse{beginplot@\psplotstyle}%
  \addto@pscode{%
    /Alpha \psk@ThreeDplot@Alpha\space def
    /Beta \psk@ThreeDplot@Beta\space def
    /D {} def mark %
  }%
  #1%
  \addto@pscode{\tx@ScalePointsThreeD}%
  \@nameuse{endplot@\psplotstyle}%
}
%
% adopted from pst-3d
%
\pst@def{TMSave}<%
  tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
  /TMatrix [ TMatrix CM ] cvx def>
%
\pst@def{TMRestore}<%
  CP /TMatrix [ TMatrix setmatrix ] cvx def moveto>
%
\pst@def{TMChange}<%
  \tx@TMSave
  /cp [ currentpoint ] cvx def
  CM
  CP T \tx@STV
  CM matrix invertmatrix 
  matrix concatmatrix
  exch exec
  concat cp moveto>
%
\def\pstPlanePut{\@ifnextchar[{\pst@PlanePut}{\pst@PlanePut[]}}
\def\pst@PlanePut[#1](#2)#3{{%
  \pst@killglue%
  \psset{pOrigin=lB}%
  \psset{#1}%
  \pstThreeDPut[#1](#2){\ps@Plane{#3}}%
}}
%
\def\ps@Plane{\pst@makebox{\psPlane@}}
\def\psPlane@{%
  \begingroup
  \leavevmode%
  \hbox{%
%	    \kern\wd\pst@hbox%
    \pst@Verb{%
      { [ 1 0
        /Alpha \psk@ThreeDplot@Alpha\space def
        /Beta \psk@ThreeDplot@Beta\space def
%
% ###  begin Torsten Suhling
% ------------------------------------------------------------------------
% ===================================================================
% How should 'Alpha' be for planes, if real Alpha and Beta are:
% Alpha	Beta	xy 	    xy (par. y-axis)  yz	  xz
% -------------------------------------------------------------------
% 75	> 0[1]	180 + Alpha 	90 +  Alpha  Alpha	  Alpha + 180 		
% 165	> 0	Alpha 		90 +  Alpha  Alpha	  Alpha 
% 255	> 0	Alpha		270 + Alpha  Alpha + 180  Alpha
% 345	> 0	180 + Alpha 	270 + Alpha  Alpha + 180  Alpha + 180 
% -------------------------------------------------------------------
% 75	< 0	180 - Alpha 	270 - Alpha  Alpha  	  Alpha + 180  
% 165	< 0	-Alpha 		270 - Alpha  Alpha  	  Alpha
%
% 255	< 0	-Alpha 		90 -  Alpha  Alpha + 180  Alpha
%
% 345	< 0	180 -Alpha 	90 -  Alpha  Alpha + 180  Alpha + 180 
% ------------------------------------------------------------------
% How should 'Beta' be for planes, if real Alpha and Beta are:
% Alpha	Beta	xy 	      xy (par. y-axis)	yz		xz
% -------------------------------------------------------------------
% 75 	> 0 	Beta 		Beta 		Beta[2] 	Beta 
% 165	> 0 	Beta 		Beta 		Beta 		Beta 
% 255	> 0 	Beta 		Beta 		Beta 		Beta 
% 345	> 0 	Beta 		Beta 		Beta 		Beta 
% ...................................................................
% 75 	< 0 	-Beta 		-Beta 		Beta 		Beta 
% 165	< 0 	-Beta 		-Beta 		Beta 		Beta 
% 255	< 0 	-Beta 		-Beta 		Beta 		Beta 
% 345	< 0 	-Beta 		-Beta 		Beta 		Beta 
% ================================================================
        \ifx\psk@ThreeDplot@planecorr\ThreeDplot@planecorrOff
		/SignFlag 	1 def
		/AlphaOffset 	0 def
	\else%
          \ifx\psk@ThreeDplot@plane\ThreeDplot@planeXY 			% XY-layer's tag
            \ifx\psk@ThreeDplot@planecorr\ThreeDplot@planecorrXYrot 	% Tag written parallel y-axis
	        Beta  sin 0 lt {/SignFlag  -1}{/SignFlag    1}ifelse def
                Alpha sin 0 gt {/AlphaOffset 180 -90 SignFlag mul add}
		               {/AlphaOffset 180  90 SignFlag mul add} ifelse def 
	    \else% 							% Normal (par. x-axis)
	        Beta  sin 0 gt {/SignFlag      1}{/SignFlag     -1}ifelse def
	        Alpha cos 0 gt {/AlphaOffset 180}{/AlphaOffset   0}ifelse def
	    \fi%
	  \else 							% Vertical layers 
            \ifx\psk@ThreeDplot@plane\ThreeDplot@planeYZ 		% YZ-layer's tag 
		/SignFlag 1 def 
	        Alpha sin 0 gt {/AlphaOffset   0}{/AlphaOffset 180}ifelse def
	    \else% 							% XZ-layer's tag 
		/SignFlag 1 def 
	        Alpha cos 0 gt {/AlphaOffset 180}{/AlphaOffset   0}ifelse def
	    \fi% which vert. layer's tag 
	  \fi% vert. or xy-layer's tag 
	\fi% planecorr or not 
% ------------------------------------------------------------------ Ende
% ------------------------------------------------------------------------
% ###   Aenderung --> es werden die Operatoren SignFlag und AlphaOffset
%	eingefuegt
% ------------------------------------------------------------------------
%       /Delta Beta sin Alpha sin mul Alpha cos atan neg 90 add def 
%       /Gamma Beta sin Alpha cos mul neg Alpha sin atan def 
% ------------------------------------------------------------------------
        /Delta Beta SignFlag mul sin Alpha SignFlag mul AlphaOffset add sin mul Alpha SignFlag mul AlphaOffset add cos atan neg 90 add def 
        /Gamma Beta SignFlag mul sin Alpha SignFlag mul AlphaOffset add cos mul neg Alpha SignFlag mul AlphaOffset add sin atan def 
% ------------------------------------------------------------------- Ende
        \ifx\psk@ThreeDplot@plane\ThreeDplot@planeXY
          270 Delta sub rotate
          /Rho 90 Gamma add Delta add def
        \else%
          \ifx\psk@ThreeDplot@plane\ThreeDplot@planeXZ
            270 Delta sub rotate
            /Rho 180 Delta add def
          \else%
            Gamma rotate
            /Rho 90 Gamma sub def
          \fi%
        \fi%
        Rho cos Rho sin 0 0 ] concat} \tx@TMChange%
    }%
    \box\pst@hbox%
    \pst@Verb{\tx@TMRestore}%
%	    \kern\ht\pst@hbox%
  }%
  \endgroup%
}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Utility stuff
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% posStart=Starting point
% length=  Arrow length.
\def\Arrows{\@ifnextchar[{\pst@Arrows}{\pst@Arrows[]}}
\def\pst@Arrows[#1](#2)(#3){{%
	\psset{#1}%
	\pst@getcoor{#2}\pst@tempa
	\pst@getcoor{#3}\pst@tempb
	\pnode(!%
		/StartArrow \psk@ThreeDplot@posStart\space def
		/LengthArrow \psk@ThreeDplot@length\space def
		\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
		/denominateur XB XA sub def
		/numerateur YB YA sub def
		/angleDirectionAB numerateur denominateur Atan def
		/XD StartArrow angleDirectionAB cos mul XA add def
		/YD StartArrow angleDirectionAB sin mul YA add def
		/XF XD LengthArrow angleDirectionAB cos mul add def
		/YF YD LengthArrow angleDirectionAB sin mul add def
		XD YD ){ArrowStart}
	\pnode(! XF YF){ArrowEnd}
	\psset{arrows=->}
	\psline[#1](ArrowStart)(ArrowEnd)%
}\ignorespaces}
%
% draw a line (===) outside: #2-----#3=======#4
%
\def\psOutLine{\@ifnextchar[{\pst@ToDrawOut}{\pst@ToDrawOut[]}}
\def\pst@ToDrawOut[#1](#2)(#3)#4{{%
	\psset{#1}%
	\pst@getcoor{#2}\pst@tempa
	\pst@getcoor{#3}\pst@tempb
	\pnode(!%
		/LengthArrow \psk@ThreeDplot@length\space def
		\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
		/denominateur XB XA sub def
		/numerateur YB YA sub def
		/angleDirectionAB numerateur denominateur Atan def
		/Xend XB LengthArrow angleDirectionAB cos mul add def
		/Yend YB LengthArrow angleDirectionAB sin mul add def
		Xend Yend){#4}
	\psline[#1](#3)(#4)
}\ignorespaces}
%
% draw a line (===) before: #4========#2-----#3
%
\def\psBeforeLine{\@ifnextchar[{\pst@BeforeLine}{\pst@BeforeLine[]}}
\def\pst@BeforeLine[#1](#2)(#3)#4{{%
	\psset{#1}%
	\pst@getcoor{#2}\pst@tempa
	\pst@getcoor{#3}\pst@tempb
	\pnode(!%
		/LengthArrow \psk@ThreeDplot@length\space def
		\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
		/denominateur XB XA sub def
		/numerateur YB YA sub def
		/angleDirectionAB numerateur denominateur Atan def
		/Xstart XA LengthArrow angleDirectionAB cos mul sub def
		/Ystart YA LengthArrow angleDirectionAB sin mul sub def
		Xstart Ystart){#4}
	\psline[#1](#4)(#2)%
}\ignorespaces}
%
% intersection de deux droites
% 2 juillet 2001/ rewritten 2003-01-27 Herbert
%
\def\ABinterCD(#1)(#2)(#3)(#4)#5{%
    \pst@getcoor{#1}\pst@tempa
    \pst@getcoor{#2}\pst@tempb
    \pst@getcoor{#3}\pst@tempc
    \pst@getcoor{#4}\pst@tempd
\pnode(!%
    /YA \pst@tempa exch pop \pst@number\psyunit div def
    /XA \pst@tempa pop \pst@number\psxunit div def
    /YB \pst@tempb exch pop \pst@number\psyunit div def
    /XB \pst@tempb pop \pst@number\psxunit div def
    /YC \pst@tempc exch pop \pst@number\psyunit div def
    /XC \pst@tempc pop \pst@number\psxunit div def
    /YD \pst@tempd exch pop \pst@number\psyunit div def
    /XD \pst@tempd pop \pst@number\psxunit div def
    /dY1 YB YA sub def
    /dX1 XB XA sub def
    /dY2 YD YC sub def
    /dX2 XD XC sub def
    dX1 abs 0.01 lt {
	/m2 dY2 dX2 div def
	XA dup XC sub m2 mul YC add 
    }{
	dX2 abs 0.01 lt {
	    /m1 dY1 dX1 div def
	    XC dup XA sub m1 mul YA add 
	}{%
	    /m1 dY1 dX1 div def
	    /m2 dY2 dX2 div def
	    m1 XA mul m2 XC mul sub YA sub YC add m1 m2 sub div dup
	    XA sub m1 mul YA add 
	} ifelse
    } ifelse ){#5}
}
%
% draw a parallel line
%     #2---------#3
%         #4----------#5(new)  
\def\Parallel{\@ifnextchar[{\pst@Parallel}{\pst@Parallel[]}}
\def\pst@Parallel[#1](#2)(#3)(#4)#5{{%
	\psset{#1}%
	\pst@getcoor{#2}\pst@tempa
	\pst@getcoor{#3}\pst@tempb
	\pst@getcoor{#4}\pst@tempc
	\pnode(!%
		/LengthArrow \psk@ThreeDplot@length\space def
		\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
		\pst@tempc /YC exch \pst@number\psyunit div def
		/XC exch \pst@number\psxunit div def
		/denominateur XB XA sub def
		/numerateur YB YA sub def
		/angleDirectionAB numerateur denominateur Atan def
		/XstartParallel XC LengthArrow angleDirectionAB cos mul add def
		/YstartParallel YC LengthArrow angleDirectionAB sin mul add def
		XstartParallel YstartParallel){#5}
	\psline[#1](#4)(#5)
}\ignorespaces}
%
% arrowLine[options](A)(B){n}
% #2---->---->---->---->----#3  #4-arrows inside
\def\arrowLine{\@ifnextchar[{\pst@arrowLine}{\pst@arrowLine[]}}
\def\pst@arrowLine[#1](#2)(#3)#4{{%
  \psset{arrowsize=4pt,arrows=->}% the defaults
  \psset{#1}%
  \def\pst@ThreeDplot@n{#4}%
  \pst@getcoor{#2}\pst@tempa
  \pst@getcoor{#3}\pst@tempb
  \pnode(!%
    /YA \pst@tempa exch pop \pst@number\psyunit div def
    /XA \pst@tempa pop \pst@number\psxunit div def
    /YB \pst@tempb exch pop \pst@number\psyunit div def
    /XB \pst@tempb pop \pst@number\psxunit div def
    /dY YB YA sub \pst@ThreeDplot@n\space 1 add div def
    /dX XB XA sub \pst@ThreeDplot@n\space 1 add div def
    /Alpha dY dX atan def
    /dYOffset \psk@ThreeDplot@arrowOffset\space Alpha sin mul def
    /dXOffset \psk@ThreeDplot@arrowOffset\space Alpha cos mul def
    XA YA ){tempArrowC}
  \multido{\i=1+1}{#4}{%
    \pnode(!%
      XA dX \i\space mul add dXOffset add
      YA dY \i\space mul add dYOffset add ){tempArrowB}
    \psline(tempArrowC)(tempArrowB)
    \pnode(tempArrowB){tempArrowC}
  }
  \psline[arrows=-](tempArrowB)(#3)
}\ignorespaces}
%
%   #1------#3------#2
\def\nodeBetween(#1)(#2)#3{%    Herbert 2003/01/05
  \pst@getcoor{#1}\pst@tempa
  \pst@getcoor{#2}\pst@tempb
  \pnode(!%
    /XA \pst@tempa pop \pst@number\psxunit div def
    /YA \pst@tempa exch pop \pst@number\psyunit div def
    /XB \pst@tempb pop \pst@number\psxunit div def
    /YB \pst@tempb exch pop \pst@number\psyunit div def
    XB XA add 2 div YB YA add 2 div){#3}
}
%
% rotateNode(A)
% (A) the node
% #2  the angle
% Herbert Voss <voss@perce.de> 2003-01-26
\def\rotateNode{\pst@rotateNode}
\def\pst@rotateNode(#1)#2{{%
    \pst@getcoor{#1}\pst@tempa%
    \def\pst@ThreeDplot@angle{#2}%        the rotating angle
    \pnode(!%
    	/YA \pst@tempa exch pop \pst@number\psyunit div def
	/XA \pst@tempa pop \pst@number\psxunit div def
	YA 0 eq XA 0 eq and {0 0}{
	    /r XA dup mul YA dup mul add sqrt def
	    /AlphaOld YA XA atan def
	    /AlphaNew AlphaOld \pst@ThreeDplot@angle\space add def
	    r AlphaNew cos mul r AlphaNew sin mul
	} ifelse ){temp}%
    \pnode(temp){#1}%
}\ignorespaces}
%
\def\rotateTriangle{\pst@rotateTriangle}
\def\pst@rotateTriangle(#1)(#2)(#3)#4{{%
    \rotateNode(#1){#4}%
    \rotateNode(#2){#4}%
    \rotateNode(#3){#4}%
}\ignorespaces}
%
\def\rotateFrame{\pst@rotateFrame}
\def\pst@rotateFrame(#1)(#2)(#3)(#4)#5{{%
    \rotateNode(#1){#5}%
    \rotateNode(#2){#5}%
    \rotateNode(#3){#5}%
    \rotateNode(#4){#5}%
}\ignorespaces}
\catcode`\@=\PstAtCode\relax
%
%% END: pst-3dplot.tex
\endinput