COMMENT ⊗   VALID 00002 PAGES
C REC  PAGE   DESCRIPTION
C00001 00001
C00002 00002	\magnification=\magstep1
C00013 ENDMK
C⊗;
\magnification=\magstep1
\nopagenumbers
\newdimen\u  \u=1pt
\def\p(#1,#2)#3{\raise#2\u\rlap{\kern#1\u\special{#3}}}
\def\q(#1,#2)#3{\raise#2\u\rlap{\kern#1\u{#3}}}
\hbox{}

This figure demonstrates Imagen's ability to produce segments of ellipses.
It also shows how the various parameters are defined in the TeX program to
produce a desired result.

The example shown is for an alpha-offset of 30 degrees and with an alpha0
of 30 degrees and an alpha1 of 180 degrees.  The values alpha0 and alpha1
actually apply to the angles measured for the equivalent points on the
generating circles.  The location of the points on the ellipse that are
not on the major or minor axes are gotten
by computation as shown by the intersecting construction lines for the
alpha0 point.

\bigskip
\centerline{\hbox {%
	\p(0,43.3){point 1}%
	\p(90,43.3){point 2}%
	\p(90,0){point 3}%
	\p(0,90){point 4}%
	\p(-90,0){point 5}%
	\p(0,-90){point 6}%
	\special{join .482 3 5}% the original x axis
	\special{join .482 4 6}% the original y axis
	\p(86.6,50){point 7}%
	\q(86.6,50){ offset(30)}%
	\p(50,86.6){point 8}%
	\q(50,86.6){ alpha0(30)}%
	\p(-86.6,-50){point 9}%
	\q(-86.6,-50){\llap{alpha1(180) \ }}%
	\p(21.6,37.5){point 10}%
	\p(43.3,75){point 11}%
	\p(58.3,58.4){point 12}%
	\p(55.6,53.2){point 13}%
	\p(0,0){point 0}%
	\special{join .241 0 8}% the sixty degree line
	\special{join .482 7 9}% the shifted axis
	\special{join .241 10 12}% construction line
	\special{join .241 11 13}% construction line
	\special{ellipse 1.45 86.6 43.3 30 30 180}%
 	\special{circle .241 43.3  0 360}%
	\special{circle .241 86.6  -140 210}%
	\hfil}}
\vfil\eject\end

\vfil
\centerline{\hbox {%
	\p(0,86.6){point 1}%
	\p(180,86.6){point 2}%
	\p(180,0){point 3}%
	\p(0,180){point 4}%
	\p(-180,0){point 5}%
	\p(0,-180){point 6}%
	\special{join .482 3 5}% the original x axis
	\special{join .482 4 6}% the original y axis
	\p(173.2,100){point 7}%
	\q(173.2,100){ offset(30)}%
	\p(100,173.2){point 8}%
	\q(100,173.2){ alpha0(30)}%
	\p(-173.2,-100){point 9}%
	\q(-173.2,-100){ \ alpha1(180)}%
	\p(43.3,75){point 10}%
	\p(86.6,150){point 11}%
	\p(116.0,116.7){point 12}%
	\p(55.6,106.5){point 13}%
	\p(0,0){point 0}%
	\special{join .241 0 8}% the sixty degree line
	\special{join .482 7 9}% the shifted axis
	\special{join .241 10 12}% construction line
	\special{join .241 11 13}% construction line
	\special{ellipse 2.41 173.2 86.6 30 30 180}%
 	\special{circle .241 86.6  0 360}%
	\special{circle .241 173.2  0 360}%
	\hfil}}
\vfil\eject\end

\vfil
\centerline{\hbox {%
	\p(0,86.6){point 1}%
	\p(180,86.6){point 2}%
	\p(180,0){point 3}%
	\p(0,180){point 4}%
	\p(-180,0){point 5}%
	\p(0,-180){point 6}%
	\special{join .482 3 5}% the original x axis
	\special{join .482 4 6}% the original y axis
	\p(173.2,100){point 7}%
	\p(100,173.2){point 8}%
	\p(-173.2,-100){point 9}%
	\p(43.3,75){point 10}%
	\p(86.6,150){point 11}%
	\p(116.0,116.7){point 12}%
	\p(55.6,107.0){point 13}%
	\p(0,0){point 0}%
	\special{join .120 0 8}% the sixty degree line
	\special{join .482 7 9}% the shifted axis
	\special{join .120 10 12}% construction line
	\special{join .120 11 13}% construction line
	\special{ellipse 1.20 173.2 86.6 -30 -30 -180}%
 	\special{circle .241 86.6  0 360}%
	\special{circle .241 173.2  0 360}%
	\hfil}}
\vfil\eject\end

	\p(-1.732,-1){point 1}%
	\p(1.732,-1){point 2}%
	\p(0,2){point 3}%
	\special{join .241 1 2 3 1}%
	\p(0,0){point 0}%
	\special{ellipse 2.41 160 40 -30 30 180}%
	\special{circle 1.20 60 0 30}%
	\special{circle .241 60 0 360}%

	\p(-6.928,-4){point 1}%
	\p(6.928,-4){point 2}%
	\p(0,8){point 3}%
	\special{join .482 1 2 3 1}%
	\p(-15.588,-9){point 1}%
	\p(15.588,-9){point 2}%
	\p(0,18){point 3}%
	\special{join .723 1 2 3 1}%
	\p(-29.112,-16){point 1}%
	\p(29.112,-16){point 2}%
	\p(0,32){point 3}%
	\special{join .964 1 2 3 1}%
	\p(-43.30,-25){point 1}%
	\p(43.30,-25){point 2}%
	\p(0,50){point 3}%
	\special{join 1.206 1 2 3 1}%
	\p(-62.35,-36){point 1}%
	\p(62.35,-36){point 2}%
	\p(0,72){point 3}%
	\special{join 1.446 1 2 3 1}%
	\p(-84.86,-49){point 1}%
	\p(84.86,-49){point 2}%
	\p(0,98){point 3}%
	\special{join 1.69 1 2 3 1}%
	\p(-110.9,-64){point 1}%
	\p(110.9,-64){point 2}%
	\p(0,128){point 3}%
	\special{join 1.98 1 2 3 1}%
	\p(-140.3,-81){point 1}%
	\p(140.3,-81){point 2}%
	\p(0,162){point 3}%
	\special{join 2.17 1 2 3 1}%
	\p(-173.2,-100){point 1}%
	\p(173.2,-100){point 2}%
	\p(0,200){point 3}%
	\special{join 2.41 1 2 3 1}%
	\p(-209.5,-121){point 1}%
	\p(209.5,-121){point 2}%
	\p(0,242){point 3}%
	\special{join 2.65 1 2 3 1}%
	\p(-249.5,-144){point 1}%
	\p(249.5,-144){point 2}%
	\p(0,288){point 3}%
	\special{join 2.89 1 2 3 1}%
	\p(-292.7,-169){point 1}%
	\p(292.7,-169){point 2}%
	\p(0,338){point 3}%
	\special{join 3.13 1 2 3 1}%
	\p(-339.5,-196){point 1}%
	\p(339.5,-196){point 2}%
	\p(0,392){point 3}%
	\special{join 3.37 1 2 3 1}%
	\p(-389.7,-225){point 1}%
 	\p(389.7,-225){point 2}%
	\p(0,450){point 3}%
	\special{join 3.60 1 2 3 1}%
	\p(-389.7,-256){point 1}%
 	\p(389.7,-256){point 2}%
	\special{join 3.86 1 2}%
	\p(-389.7,-289){point 1}%
 	\p(389.7,-289){point 2}%
	\special{join 4.09 1 2}%
	\p(-389.7,-324){point 1}%
 	\p(389.7,-324){point 2}%
	\special{join 4.34 1 2}%
	\p(-389.7,-361){point 1}%
 	\p(389.7,-361){point 2}%
	\special{join 4.57 1 2}%
	\p(-389.7,-400){point 1}%
 	\p(389.7,-400){point 2}%
 	\special{join 4.82 1 2}%
	\hfil}}
\vfil\eject\end