(texdraw)Geometric construction

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C.3 Geometric construction
==========================

This example shows a geometric construction which places an ellipse
tangent to an enclosing circle.  The size of the ellipse is determined
from geometric considerations.  Macros are used to modularize the code.
The example alters the unit scale factor.  This allows the drawing to be
carried out in units normalized to the radius of the circle.

     \centertexdraw{
     \arrowheadtype t:V \arrowheadsize l:0.08 w:0.04
     \linewd 0.01
     \setunitscale 1.5            % circle will have radius 1.5 inches

     \def\Btext #1{\bsegment
                     \textref h:C v:T \htext (0 -0.04){#1}
                   \esegment}
     \def\Ttext #1{\bsegment
                     \textref h:C v:B \htext (0 +0.04){#1}
                   \esegment}
     \def\Ltext #1{\bsegment
                     \textref h:R v:C \htext (-0.04 0){#1}
                   \esegment}
     \def\bdot {\fcir f:0 r:0.0133 }
     \def\vtick {\bsegment
                   \move (0 -0.05) \lvec (0 +0.05)
                 \esegment}
     \def\htick {\bsegment
                   \move (-0.05 0) \lvec (+0.05 0)
                 \esegment}
     \def\Hlen #1#2{\bsegment
                      \vtick \avec ({#1} 0) \vtick \avec (0 0)
                      \relsegscale 0.5
                      \move ({#1} 0) \Ttext {#2}
                    \esegment}
     \def\Vlen #1#2{\bsegment
                      \htick \avec (0 {#1}) \htick \avec (0 0)
                      \relsegscale 0.5
                      \move (0 {#1}) \Ltext {#2}
                    \esegment}

     \lcir r:1                         % circle
     \move (-1.05 0) \lvec ( 1.05 0)   % axes
     \move (0 -1.05) \lvec (0  1.05)

     \move (0 0) \lvec (0.707 0.707) \bdot
     \rmove (0.02 0.02) \textref h:L v:B \htext {X}
     \move (0.707 -0.707) \bdot
     \textref h:R v:T \htext(-0.02 -0.02){O}

     \move (0.5 0)                     % center of ellipse
     \bsegment
       \lellip rx:0.435 ry:0.804
       \bdot \Btext {$\beta_2$}
       \move (0 0.15) \Hlen {0.435}{$|\beta_1{+}\beta_3|$}
       \move (-0.7 0) \Vlen {0.804}{$|\beta_1{-}\beta_3|$}
     \esegment
     }