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+%% BEGIN pst-3d.tex
+%%
+%% Tilting and other pseudo-3D tricks for PSTricks v0.93a.
+%% This is experimental. See 3d-test.tex for a test file.
+%% There is not yet any documentation.
+%%
+\def\fileversion{0.93a}
+\def\filedate{93/08/26}
+%%
+%% COPYRIGHT 1993, by Timothy Van Zandt, tvz@Princeton.EDU
+%% See pstricks.tex or pstricks.doc for copying restrictions.
+%%
+
+\message{ v\fileversion, \filedate}
+
+\csname PSTthreeDLoaded\endcsname
+\let\PSTthreeDLoaded\endinput
+
+\ifx\PSTricksLoaded\endinput\else
+ \def\next{\input pstricks.tex}
+ \expandafter\next
+\fi
+
+\edef\TheAtCode{\the\catcode`\@}
+\catcode`\@=11
+
+% \begin{macro}{\tx@SetMatrixThreeD,\tx@ProjThreeD,\tx@SetMatrixEmbed}
+% Viewpoint for 3D coordinates is given by three angles: $\alpha$, $\beta$ and
+% $\gamma$. $\alpha$ and $\beta$ determine the direction from which one is
+% looking. $\gamma$ then determines the orientation of the observing.
+%
+% When $\alpha$, $\beta$ and $\gamma$ are all zero, the observer is looking
+% from the negative part of the $y$-axis, and sees the $xz$-plane the way in
+% 2D one sees the $xy$ plan. Hence, to convert the 3D coordinates to their 2D
+% project, $\la x, y, z\ra$ map to $\la x, z\ra$.
+%
+% When the orientation is different, we rotate the coordinates, and then
+% perform the same projection.
+%
+% We move up to latitude $\beta$, over to longitude $\alpha$, and then rotate
+% by $\gamma$. This means that we first rotate around $y$-axis by $\gamma$,
+% then around $x$-axis by $\beta$, and the around $z$-axis by $\alpha$.
+%
+% Here are the matrices:
+% \begin{eqnarray*}
+% R_z(\alpha) & = & \left[
+% \begin{array}{ccc}
+% \cos \alpha & -\sin \alpha & 0 \\
+% \sin \alpha & cos \alpha & 0 \\
+% 0 & 0 & 1
+% \end{array} \right] \\
+% R_x(\beta) & = & \left[
+% \begin{array}{ccc}
+% 1 & 0 & 0 \\
+% 0 & \cos \beta & \sin \beta \\
+% 0 & -\sin \beta & \cos \beta
+% \end{array} \right] \\
+% R_y(\gamma) & = & \left[
+% \begin{array}{ccc}
+% \cos \gamma & 0 & -\sin \gamma \\
+% 0 & 1 & 0 \\
+% \sin \gamma & 0 & \cos \gamma
+% \end{array} \right]
+% \end{eqnarray*}
+%
+% The rotation of a coordinate is then performed by the matrix $R_z(\alpha)
+% R_x(\beta) R_y(\gamma)$. The first and third columns of the matrix are the
+% basis vectors of the plan upon which the 3D coordinates are project (the old
+% basis vectors were $\la 1, 0, 0\ra$ and $\la 0, 0, 1$\ra; rotating these
+% gives the first and third columns of the matrix).
+%
+% These new basis vectors are:
+% \begin{eqnarray*}
+% \tilde{x} & = & \left[
+% \begin{array}{c}
+% \cos\alpha \cos\gamma - \sin\beta \sin\alpha \sin\gamma \\
+% \sin\alpha \cos\gamma + \sin\beta \cos\alpha \sin\gamma \\
+% \cos\beta \sin\gamma
+% \end{array} \right] \\
+% \tilde{z} & = & \left[
+% \begin{array}{c}
+% -\cos\alpha \sin\gamma - \sin\beta \sin\alpha \cos\gamma \\
+% -\sin\alpha \sin\gamma + \sin\beta \cos\alpha \cos\gamma \\
+% \cos\beta \cos\gamma
+% \end{array} \right]
+% \end{eqnarray*}
+%
+% Rather than specifying the angles $\alpha$ and $\beta$, the user gives a
+% vector indicating where the viewpoint is. This new viewpoint is the rotation
+% o the old viewpoint. The old viewpoint is $\la 0, -1, 0\ra$, and so the new
+% viewpoint is
+% \[
+% R_z(\alpha) R_x(\beta) \left[ \begin{array}{c} 0\\-1\\0 \end{array} \right]
+% \, = \,
+% \left[ \begin{array}{c}
+% \cos\beta \sin\alpha \\
+% -\cos\beta \cos\alpha \\
+% \sin\beta
+% \end{array} \right]
+% \, = \,
+% \left[ \begin{array}{c} v_1 \\ v_2 \\ v_3 \end{array} \right]
+% \]
+% Therefore,
+% \begin{eqnarray*}
+% \alpha & = & \arc\tan (v_1 / -v_2) \\
+% \beta & = & \arc\tan (v_3 \sin\alpha / v_1)
+% \end{eqnarray*}
+% Unless $p_1=p_2=0$, in which case $\alpha=0$ and $\beta=\sign(p_3)90$, or
+% $p_1=p_3=0$, in which case $\beta=0$.
+%
+% The syntax of "SetMatrixThreeD" is
+% \begin{Ex}
+% $v_1$ $v_2$ $v_3$ $\gamma$ "SetMatrixThreeD"
+% \end{Ex}
+% "SetMatrixThreeD" first computes
+% \[
+% \begin{array}{ll}
+% a=\sin\alpha & b=\cos\alpha\\
+% c=\sin\beta & d=\cos\beta\\
+% e=\sin\gamma & f=\cos\gamma
+% \end{array}
+% \]
+% and then sets "Matrix3D" to "["$\tilde{x}$ $\tilde{z}$"]".
+%
+% \begin{macrocode}
+\pst@def{SetMatrixThreeD}<%
+ dup sin /e ED cos /f ED
+ /p3 ED /p2 ED /p1 ED
+ p1 0 eq
+ { /a 0 def /b p2 0 le { 1 } { -1 } ifelse def
+ p3 p2 abs
+ }
+ { p2 0 eq
+ { /a p1 0 lt { -1 } { 1 } ifelse def /b 0 def
+ p3 p1 abs
+ }
+ { p1 dup mul p2 dup mul add sqrt dup
+ p1 exch div /a ED
+ p2 exch div neg /b ED
+ p3 p1 a div
+ }
+ ifelse
+ }
+ ifelse
+ atan dup sin /c ED cos /d ED
+ /Matrix3D
+ [
+ b f mul c a mul e mul sub
+ a f mul c b mul e mul add
+ d e mul
+ b e mul neg c a mul f mul sub
+ a e mul neg c b mul f mul add
+ d f mul
+ ] def>
+% \end{macrocode}
+%
+% The syntax of "ProjThreeD" is
+% \begin{Ex}
+% $x$ $y$ $z$ ProjThreeD $x'$ $y'$
+% \end{Ex}
+% where $x'=\la x, y, z\ra \cdot \tilde{x}$ and $y'=\la x, y, z\ra \cdot
+% \tilde{z}$.
+%
+% \begin{macrocode}
+\pst@def{ProjThreeD}<%
+ /z ED /y ED /x ED
+ Matrix3D aload pop
+ z mul exch y mul add exch x mul add
+ 4 1 roll
+ z mul exch y mul add exch x mul add
+ exch>
+% \end{macrocode}
+%
+% To embed 2D $\la x, y\ra$ coordinates in 3D, the user specifies the normal
+% vector and an angle. If we decompose this normal vector into an angle, as
+% when converting 3D coordinates to 2D coordinates, and let $\hat\alpha$,
+% $\hat\beta$ and $\hat\gamma$ be the three angles, then when these angles are
+% all zero the coordinate $\la x, y\ra$ gets mapped to $\la x, 0, y\ra$, and
+% otherwise $\la x, y\ra$ gets mapped to
+% \[
+% R_z(\hat\alpha) R_x(\hat\beta) R_y(\hat\gamma)
+% \left[ \begin{array}{c} x \\ 0 \\ y \end{array} \right]
+% \, = \,
+% \left[ \begin{array}{c}
+% \hat{x}_1 x + \hat{z}_1 y\\
+% \hat{x}_2 x + \hat{z}_2 y\\
+% \hat{x}_3 x + \hat{z}_3 y
+% \end{array} \right]
+% \]
+% where $\hat{x}$ and $\hat{z}$ are the first and third columns of
+% $R_z(\hat\alpha) R_x(\hat\beta) R_y(\hat\gamma)$.
+%
+% Now add on a 3D-origin:
+% \[
+% \left[ \begin{array}{c}
+% \hat{x}_1 x + \hat{z}_1 y + x_0\\
+% \hat{x}_2 x + \hat{z}_2 y + y_0\\
+% \hat{x}_3 x + \hat{z}_3 y + z_0
+% \end{array} \right]
+% \]
+%
+% Now when we project back onto 2D coordinates, we get
+% \begin{eqnarray*}
+% x' & = & \tilde{x}_1(\hat{x}_1 x + \hat{z}_1 y + x_0) +
+% \tilde{x}_2(\hat{x}_2 x + \hat{z}_2 y + y_0) +
+% \tilde{x}_3(\hat{x}_3 x + \hat{z}_3 y + z_0)\\
+% & = &
+% (\tilde{x}_1\hat{x}_1 + \tilde{x}_2\hat{x}_2 + \tilde{x}_3\hat{x}_3) x\\
+% + (\tilde{x}_1\hat{z}_1 + \tilde{x}_2\hat{z}_2 + \tilde{x}_3\hat{z}_3) y\\
+% + \tilde{x}_1 x_0 + \tilde{x}_2 y_0 + \tilde{z}_3 z_0
+% y' & = & \tilde{z}_1(\hat{x}_1 x + \hat{z}_1 y + x_0) +
+% \tilde{z}_2(\hat{x}_2 x + \hat{z}_2 y + y_0) +
+% \tilde{z}_3(\hat{x}_3 x + \hat{z}_3 y + z_0)\\
+% & = &
+% (\tilde{z}_1\hat{x}_1 + \tilde{z}_2\hat{x}_2 + \tilde{z}_3\hat{x}_3) x\\
+% + (\tilde{z}_1\hat{z}_1 + \tilde{z}_2\hat{z}_2 + \tilde{z}_3\hat{z}_3) y\\
+% + \tilde{z}_1 x_0 + \tilde{z}_2 y_0 + \tilde{z}_3 z_0
+% \end{eqnarray*}
+% Hence, the transformation matrix is:
+% \[
+% \left[ \begin{array}{c}
+% \tilde{x}_1\hat{x}_1 + \tilde{x}_2\hat{x}_2 + \tilde{x}_3\hat{x}_3) \\
+% \tilde{z}_1\hat{x}_1 + \tilde{z}_2\hat{x}_2 + \tilde{z}_3\hat{x}_3) \\
+% \tilde{x}_1\hat{z}_1 + \tilde{x}_2\hat{z}_2 + \tilde{x}_3\hat{z}_3) \\
+% \tilde{z}_1\hat{z}_1 + \tilde{z}_2\hat{z}_2 + \tilde{z}_3\hat{z}_3) \\
+% \tilde{x}_1 x_0 + \tilde{x}_2 y_0 + \tilde{z}_3 z_0 \\
+% \tilde{z}_1 x_0 + \tilde{z}_2 y_0 + \tilde{z}_3 z_0
+% \end{array} \right]
+% \]
+%
+% The syntax of "SetMatrixEmbed" is
+% \begin{Ex}
+% $x_0$ $y_0$ $z_0$ $\hat{v_1}$ $\hat{v_2}$ $\hat{v_3} $\hat{\gamma}$
+% $v_1$ $v_2$ $v_3$ $\gamma$ "SetMatrixEmbed"
+% \end{Ex}
+% "SetMatrixEmbed" first sets "<x1 x2 x3 y1 y2 y3>" to the basis vectors for
+% the viewpoint projection (the tilde stuff above). Then it sets "Matrix3D" to
+% the basis vectors for the embedded plane. Finally, it sets the
+% transformation matrix to the matrix given above.
+%
+% \begin{macrocode}
+\pst@def{SetMatrixEmbed}<%
+ \tx@SetMatrixThreeD
+ Matrix3D aload pop
+ /z3 ED /z2 ED /z1 ED /x3 ED /x2 ED /x1 ED
+ \tx@SetMatrixThreeD
+ [
+ Matrix3D aload pop
+ z3 mul exch z2 mul add exch z1 mul add 4 1 roll
+ z3 mul exch z2 mul add exch z1 mul add
+ Matrix3D aload pop
+ x3 mul exch x2 mul add exch x1 mul add 4 1 roll
+ x3 mul exch x2 mul add exch x1 mul add
+ 3 -1 roll 3 -1 roll 4 -1 roll 8 -3 roll 3 copy
+ x3 mul exch x2 mul add exch x1 mul add 4 1 roll
+ z3 mul exch z2 mul add exch z1 mul add
+ ]
+ concat>
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\psset@viewpoint,\psk@viewpoint}
+% \begin{macrocode}
+\let\pssetzlength\pssetylength
+\def\psset@viewpoint#1{%
+ \pst@expandafter\psset@@viewpoint#1 {} {} {} \@nil
+ \let\psk@viewpoint\pst@tempg}
+\def\psset@@viewpoint#1 #2 #3 #4\@nil{%
+ \begingroup
+ \pssetxlength\pst@dima{#1}%
+ \pssetylength\pst@dimb{#2}%
+ \pssetzlength\pst@dimc{#3}%
+ \xdef\pst@tempg{%
+ \pst@number\pst@dima \pst@number\pst@dimb \pst@number\pst@dimc}%
+ \endgroup}
+\psset@viewpoint{1 -1 1}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\psset@viewangle,\psk@viewangle}
+% \begin{macrocode}
+\def\psset@viewangle#1{\pst@getangle{#1}\psk@viewangle}
+\psset@viewangle{0}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\psset@normal,\psk@normal}
+% \begin{macrocode}
+\def\psset@normal#1{%
+ \pst@expandafter\psset@@viewpoint#1 {} {} {} \@nil
+ \let\psk@normal\pst@tempg}
+\psset@normal{0 0 1}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\psset@embedangle,\psk@embedangle}
+% \begin{macrocode}
+\def\psset@embedangle#1{\pst@getangle{#1}\psk@embedangle}
+\psset@embedangle{0}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\tx@TMSave,\tx@TMRestore}
+% \begin{LVerbatim}
+% {<Proc for modifying tm>} TMChange
+% \begin{macrocode}
+\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 % ??? Check this later.
+ CM
+% Set "standard" coor. system , with "pt" units and origin at currentpoint.
+% This let's us rotate, or whatever, around \TeX's current point, without
+% having to worry about strange coordinate systems that the dvi-to-ps
+% driver might be using.
+ CP T \tx@STV
+% Let M = old matrix (on stack), and M' equal current matrix. Then
+% go from M' to M by applying M Inv(M').
+ CM matrix invertmatrix % Inv(M')
+ matrix concatmatrix % M Inv(M')
+% Now modify transformation matrix:
+ exch exec
+% Now apply M Inv(M')
+ concat cp moveto>
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\ThreeDput}
+% \begin{macrocode}
+\def\ThreeDput{\def\pst@par{}\pst@object{ThreeDput}}
+\def\ThreeDput@i{\@ifnextchar({\ThreeDput@ii}{\ThreeDput@ii(\z@,\z@,\z@)}}
+\def\ThreeDput@ii(#1,#2,#3){%
+ \pst@killglue\pst@makebox{\ThreeDput@iii(#1,#2,#3)}}
+\def\ThreeDput@iii(#1,#2,#3){%
+ \begingroup
+ \use@par
+ \if@star\pst@starbox\fi
+ \pst@makesmall\pst@hbox
+ \pssetxlength\pst@dima{#1}%
+ \pssetylength\pst@dimb{#2}%
+ \pssetzlength\pst@dimc{#3}%
+ \leavevmode
+ \hbox{%
+ \pst@Verb{%
+ { \pst@number\pst@dima
+ \pst@number\pst@dimb
+ \pst@number\pst@dimc
+ \psk@normal
+ \psk@embedangle
+ \psk@viewpoint
+ \psk@viewangle
+ \tx@SetMatrixEmbed
+ } \tx@TMChange}%
+ \box\pst@hbox
+ \pst@Verb{\tx@TMRestore}}%
+ \endgroup
+ \ignorespaces}
+% \end{macrocode}
+% \end{macro}
+%
+%
+% \section{Arithmetic\label{Arithmetic}}
+%
+%
+% \begin{macro}{\pst@divide}
+% This is adapted from Donald Arseneau's "shapepar.sty".
+% Syntax:
+% \begin{LVerbatim}
+% \pst@divide{<numerator>}{<denominator>}{<command>}
+% \pst@@divide{<numerator>}{<denominator>}
+% \end{LVerbatim}
+% <numerator> and <denominator> should be dimensions. "\pst@divide" sets
+% <command> to <num>/<den> (in points). "\pst@@divide" sets "\pst@dimg" to
+% <num>/<den>.
+% \begin{macrocode}
+\def\pst@divide#1#2#3{%
+ \pst@@divide{#1}{#2}%
+ \pst@dimtonum\pst@dimg{#3}}
+\def\pst@@divide#1#2{%
+ \pst@dimg=#1\relax
+ \pst@dimh=#2\relax
+ \pst@cntg=\pst@dimh
+ \pst@cnth=67108863
+ \pst@@@divide\pst@@@divide\pst@@@divide\pst@@@divide
+ \divide\pst@dimg\pst@cntg}
+% \end{macrocode}
+% The number 16 is the level of uncertainty. Use a lower power of 2 for more
+% accuracy (2 is most precise). But if you change it, you must change the
+% repetions of "\pst@@@divide" in "\pst@@divide" above:
+% \[
+% \mbox{precision}^\mbox{repetitions} = 65536
+% \]
+% (E.g., $16^4 = 65536$).
+% \begin{macrocode}
+\def\pst@@@divide{%
+ \ifnum
+ \ifnum\pst@dimg<\z@-\fi\pst@dimg<\pst@cnth
+ \multiply\pst@dimg\sixt@@n
+ \else
+ \divide\pst@cntg\sixt@@n
+ \fi}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\pst@pyth}
+% Syntax:
+% \begin{LVerbatim}
+% \pst@pyth{<dim1>}{<dim2>}{<dimen register>}
+% \end{LVerbatim}
+% <dimen register> is set to $((dim1)^2+(dim2)^2)^{1/2}$.
+%
+% The algorithm is copied from \PiCTeX, by Michael Wichura (with permission).
+% Here is his description:
+% \begin{quote}
+% Suppose $x>0$, $y>0$. Put $s = x+y$. Let $z = (x^2+y^2)^{1/2}$. Then $z =
+% s\times f$, where
+% \[
+% f = (t^2 + (1-t)^2)^{1/2} = ((1+\tau^2)/2)^{1/2}
+% \]
+% and $t = x/s$ and $\tau = 2(t-1/2)$.
+% \end{quote}
+% \begin{macrocode}
+\def\pst@pyth#1#2#3{%
+ \begingroup
+ \pst@dima=#1\relax
+ \ifnum\pst@dima<\z@\pst@dima=-\pst@dima\fi % dima=abs(x)
+ \pst@dimb=#2\relax
+ \ifnum\pst@dimb<\z@\pst@dimb=-\pst@dimb\fi % dimb=abs(y)
+ \advance\pst@dimb\pst@dima % dimb=s=abs(x)+abs(y)
+ \ifnum\pst@dimb=\z@
+ \global\pst@dimg=\z@ % dimg=z=sqrt(x^2+y^2)
+ \else
+ \multiply\pst@dima 8\relax % dima= 8abs(x)
+ \pst@@divide\pst@dima\pst@dimb % dimg =8t=8abs(x)/s
+ \advance\pst@dimg -4pt % dimg = 4tau = (8t-4)
+ \multiply\pst@dimg 2
+ \pst@dimtonum\pst@dimg\pst@tempa
+ \pst@dima=\pst@tempa\pst@dimg % dima=(8tau)^2
+ \advance\pst@dima 64pt % dima=u=[64+(8tau)^2]/2
+ \divide\pst@dima 2\relax % =(8f)^2
+ \pst@dimd=7pt % initial guess at sqrt(u)
+ \pst@@pyth\pst@@pyth\pst@@pyth % dimd=sqrt(u)
+ \pst@dimtonum\pst@dimd\pst@tempa
+ \pst@dimg=\pst@tempa\pst@dimb
+ \global\divide\pst@dimg 8 % dimg=z=(8f)*s/8
+ \fi
+ \endgroup
+ #3=\pst@dimg}
+\def\pst@@pyth{% dimd = g <-- (g + u/g)/2
+ \pst@@divide\pst@dima\pst@dimd
+ \advance\pst@dimd\pst@dimg
+ \divide\pst@dimd 2\relax}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\pst@sinandcos}
+% Syntax:
+% \begin{LVerbatim}
+% \pst@sinandcos{<dim>}{<int>}
+% \end{LVerbatim}
+% <dim>, in "sp" units, should equal 100,000 times the angle, in degrees
+% between 0 and 90. <int> should equal the angle's quadrant (0, 1, 2 or 3).
+% "\pst@dimg" is set to $\sin(\theta)$ and "\pst@dimh" is set to
+% $\cos(\theta)$ (in pt's).
+%
+% The algorithms uses the usual McLaurin expansion.
+% \begin{macrocode}
+\def\pst@sinandcos#1{%
+ \begingroup
+ \pst@dima=#1\relax
+ \pst@dima=.366022\pst@dima %Now 1pt=1/32rad
+ \pst@dimb=\pst@dima % dimb->32sin(angle) in pts
+ \pst@dimc=32\p@ % dimc->32cos(angle) in pts
+ \pst@dimtonum\pst@dima\pst@tempa
+ \pst@cntb=\tw@
+ \pst@cntc=-\@ne
+ \pst@cntg=32
+ \loop
+ \ifnum\pst@dima>\@cclvi % 256
+ \pst@dima=\pst@tempa\pst@dima
+ \divide\pst@dima\pst@cntg
+ \divide\pst@dima\pst@cntb
+ \ifodd\pst@cntb
+ \advance\pst@dimb \pst@cntc\pst@dima
+ \pst@cntc=-\pst@cntc
+ \else
+ \advance\pst@dimc by \pst@cntc\pst@dima
+ \fi
+ \advance\pst@cntb\@ne
+ \repeat
+ \divide\pst@dimb\pst@cntg
+ \divide\pst@dimc\pst@cntg
+ \global\pst@dimg\pst@dimb
+ \global\pst@dimh\pst@dimc
+ \endgroup}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\pst@getsinandcos}
+% "\pst@getsinandcos" normalizes the angle to be in the first quadrant, sets
+% "\pst@quadrant" to 0 for the first quadrant, 1 for the second, 2 for the
+% third, and 3 for the fourth, invokes "\pst@sinandcos", and sets "\pst@sin"
+% to the sine and "\pst@cos" to the cosine.
+% \begin{macrocode}
+\def\pst@getsinandcos#1{%
+ \pst@dimg=100000sp
+ \pst@dimg=#1\pst@dimg
+ \pst@dimh=36000000sp
+ \pst@cntg=0
+ \loop
+ \ifnum\pst@dimg<\z@
+ \advance\pst@dimg\pst@dimh
+ \repeat
+ \loop
+ \ifnum\pst@dimg>\pst@dimh
+ \advance\pst@dimg-\pst@dimh
+ \repeat
+ \pst@dimh=9000000sp
+ \def\pst@tempg{%
+ \ifnum\pst@dimg<\pst@dimh\else
+ \advance\pst@dimg-\pst@dimh
+ \advance\pst@cntg\@ne
+ \ifnum\pst@cntg>\thr@@ \advance\pst@cntg-4 \fi
+ \expandafter\pst@tempg
+ \fi}%
+ \pst@tempg
+ \chardef\pst@quadrant\pst@cntg
+ \ifdim\pst@dimg=\z@
+ \def\pst@sin{0}%
+ \def\pst@cos{1}%
+ \else
+ \pst@sinandcos\pst@dimg
+ \pst@dimtonum\pst@dimg\pst@sin
+ \pst@dimtonum\pst@dimh\pst@cos
+ \fi}
+% \end{macrocode}
+% \end{macro}
+%
+% \section{Tilting}
+%
+% \begin{macro}{\pstilt}
+% \begin{macrocode}
+\def\pstilt#1{\pst@makebox{\pstilt@{#1}}}
+\def\pstilt@#1{%
+ \begingroup
+ \leavevmode
+ \pst@getsinandcos{#1}%
+ \hbox{%
+ \ifcase\pst@quadrant
+ \kern\pst@cos\dp\pst@hbox
+ \pst@dima=\pst@cos\ht\pst@hbox
+ \ht\pst@hbox=\pst@sin\ht\pst@hbox
+ \dp\pst@hbox=\pst@sin\dp\pst@hbox
+ \or
+ \kern\pst@sin\ht\pst@hbox
+ \pst@dima=\pst@sin\dp\pst@hbox
+ \ht\pst@hbox=\pst@cos\ht\pst@hbox
+ \dp\pst@hbox=\pst@cos\dp\pst@hbox
+ \or
+ \kern\pst@cos\ht\pst@hbox
+ \pst@dima=\pst@sin\dp\pst@hbox
+ \pst@dimg=\pst@sin\ht\pst@hbox
+ \ht\pst@hbox=\pst@sin\dp\pst@hbox
+ \dp\pst@hbox=\pst@dimg
+ \or
+ \kern\pst@sin\dp\pst@hbox
+ \pst@dima=\pst@sin\ht\pst@hbox
+ \pst@dimg=\pst@cos\ht\pst@hbox
+ \ht\pst@hbox=\pst@cos\dp\pst@hbox
+ \dp\pst@hbox=\pst@dimg
+ \fi
+ \pst@Verb{%
+ { [ 1 0
+ \pst@cos\space \ifnum\pst@quadrant>\@ne neg \fi
+ \pst@sin\space
+ \ifnum\pst@quadrant>\z@\ifnum\pst@quadrant<\thr@@ neg \fi\fi
+ \ifodd\pst@quadrant exch \fi
+ 0 0
+ ] concat
+ } \tx@TMChange}%
+ \box\pst@hbox
+ \pst@Verb{\tx@TMRestore}%
+ \kern\pst@dima}%
+ \endgroup}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\psTilt}
+% \begin{macrocode}
+\def\psTilt#1{\pst@makebox{\psTilt@{#1}}}
+\def\psTilt@#1{%
+ \begingroup
+ \leavevmode
+ \pst@getsinandcos{#1}%
+ \hbox{%
+ \ifodd\pst@quadrant
+ \pst@@divide{\dp\pst@hbox}{\pst@cos\p@}%
+ \ifnum\pst@quadrant=\thr@@\kern\else\pst@dima=\fi\pst@sin\pst@dimg
+ \pst@@divide{\ht\pst@hbox}{\pst@cos\p@}%
+ \ifnum\pst@quadrant=\@ne\kern\else\pst@dima=\fi\pst@sin\pst@dimg
+ \else
+ \ifdim\pst@sin\p@=\z@
+ \@pstrickserr{\string\psTilt\space angle cannot be 0 or 180}\@ehpa
+ \def\pst@sin{.7071}%
+ \def\pst@cos{.7071}%
+ \fi
+ \pst@@divide{\dp\pst@hbox}{\pst@sin\p@}%
+ \ifnum\pst@quadrant=\z@\kern\else\pst@dima=\fi\pst@cos\pst@dimg
+ \pst@@divide{\ht\pst@hbox}{\pst@sin\p@}%
+ \ifnum\pst@quadrant=\tw@\kern\else\pst@dima=\fi\pst@cos\pst@dimg
+ \fi
+ \ifnum\pst@quadrant>\@ne
+ \pst@dimg=\ht\pst@hbox
+ \ht\pst@hbox=\dp\pst@hbox
+ \dp\pst@hbox=\pst@dimg
+ \fi
+ \pst@Verb{%
+ { [ 1 0
+ \pst@cos\space \pst@sin\space
+ \ifodd\pst@quadrant exch \fi
+ \tx@Div
+ \ifnum\pst@quadrant>\z@\ifnum\pst@quadrant<\thr@@ neg \fi\fi
+ \ifnum\pst@quadrant>\@ne -1 \else 1 \fi
+ 0 0
+ ] concat
+ } \tx@TMChange}%
+ \box\pst@hbox
+ \pst@Verb{\tx@TMRestore}%
+ \kern\pst@dima}%
+ \endgroup}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\psset@Tshadowsize,\psTshadowsize}
+% \begin{macrocode}
+\def\psset@Tshadowsize#1{\pst@checknum{#1}\psTshadowsize}
+\psset@Tshadowsize{1}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\psset@Tshadowangle,\psk@Tshadowangle}
+% \begin{macrocode}
+\def\psset@Tshadowangle#1{\pst@getangle{#1}\psk@Tshadowangle}
+\psset@Tshadowangle{60}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\psset@Tshadowcolor,\psTshadowcolor}
+% \begin{macrocode}
+\def\psset@Tshadowcolor#1{\pst@getcolor{#1}\psTshadowcolor}
+\psset@Tshadowcolor{lightgray}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\psshadow}
+% \begin{macrocode}
+\def\psshadow{\def\pst@par{}\pst@object{psshadow}}
+\def\psshadow@i{\pst@makebox{\psshadow@ii}}
+\def\psshadow@ii{%
+ \begingroup
+ \use@par
+ \leavevmode
+ \pst@getsinandcos{\psk@Tshadowangle}%
+ \hbox{%
+ \lower\dp\pst@hbox\hbox{%
+ \pst@Verb{%
+ { [ 1 0
+ \pst@cos\space \psTshadowsize mul
+ \ifnum\pst@quadrant>\@ne neg \fi
+ \pst@sin\space \psTshadowsize mul
+ \ifnum\pst@quadrant>\z@\ifnum\pst@quadrant<\thr@@ neg \fi\fi
+ \ifodd\pst@quadrant exch \fi
+ 0 0
+ ] concat
+ } \tx@TMChange}}%
+ \hbox to\z@{{\@nameuse{\psTshadowcolor}\copy\pst@hbox\hss}}%
+ \pst@Verb{\tx@TMRestore}%
+ \box\pst@hbox}%
+ \endgroup}
+% \end{macrocode}
+% \end{macro}
+
+\catcode`\@=\TheAtCode\relax
+
+\endinput
+
+%% END pst-3d.tex