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<<ANGLE degrees> <CENTER x y z> <FROM x y z> <TO x y z>
<NORMAL dx dy dz> <RADIUS r> <TITLE "text">>
Default: ARC ABSOLUTE CENTER 0 0 0 FROM 1 0 0 TO 0 1 0 ANGLE 90 -
NORMAL 0 0 1 RADIUS 1 TITLE ''
Draw an optionally-labelled 3-D circular arc. The center of the arc is
given by the CENTER subcommand. The arc lies in a plane containing the
FROM and TO vectors and perpendicular to the NORMAL vector.
Coordinates may be either ABSOLUTE, or RELATIVE to the current point,
as determined by the first subcommand. Relative coordinates are
particularly useful for defining position-independent arcs. In either
case, the current point on successful command completion is at the end
of the arc, where it intersects the TO vector.
The radius may be explicitly specified with the RADIUS subcommand, or
implicitly determined by the distance between the CENTER point and the
FROM point. If the radius is explicitly given, then the FROM
subcommand only specifies the direction of a radial vector intersecting
the arc.
The angle of rotation about the NORMAL vector may be specified by
explicitly by the ANGLE subcommand, or implicitly by the angle between
the vectors connecting the FROM and TO points with the CENTER point.
In either case, a positive angle is counterclockwise about the rotation
axis when looking down the positive axis to the center point. If an
arc angle of 180 degrees or more is required, then the ANGLE subcommand
must be given, since the smaller angle between the FROM and TO radial
vectors will otherwise be chosen.
If the TITLE subcommand defines a string of 1 or more characters, they
will be drawn centered along the arc using the current font and
character height. The height will temporarily be reduced if the string
is longer than 80 percent of the arc length in order to make it fit.
Since the character boxes are centered along this line, if more than
one character is drawn along a small arc, the boxes can overlap at
their bases. This can be avoided by increasing the intercharacter
spacing with the CHARACTER SPACE command.
The three vectors FROM, TO, and NORMAL overdetermine the arc, since
only two are needed to define the arc plane. They are provided for
convenience. If all three are given, two of them are used to determine
the other one, according to the following simple rule. With the vector
definitions
F = FROM - CENTER; T = TO - CENTER; N = NORMAL - CENTER;
the vector cross-product relations are:
N = F x T F = T x N T = N x F
When a FROM, TO, or NORMAL subcommand is processed, the cross-product
rule referencing that point in the first position is used if the second
vector is already defined; otherwise the cross-product rule referencing
the point in the second position is used. For example, suppose the
command contains "ARC FROM 0 1 0 NORMAL 0 0 1 ...". When FROM has been
encountered, neither N nor F can be determined. However, once NORMAL
has been parsed, T can be determined from N x F, and TO can be
automatically set to CENTER + T.