return z;
}
-Offset
-complex_conjugate (Offset o)
-{
- o[Y_AXIS] = -o[Y_AXIS];
- return o;
-}
-
-Offset
-complex_divide (Offset z1, Offset z2)
-{
- z2 = complex_conjugate (z2);
- Offset z = complex_multiply (z1, z2);
- z *= 1 / z2.length ();
- return z;
-}
-
-Offset
-complex_exp (Offset o)
-{
- Real s = sin (o[Y_AXIS]);
- Real c = cos (o[Y_AXIS]);
-
- Real r = exp (o[X_AXIS]);
-
- return Offset (r * c, r * s);
-}
-
-Real
-Offset::arg () const
-{
- return atan2 (coordinate_a_[Y_AXIS], coordinate_a_[X_AXIS]);
-}
-
static inline Real
atan2d (Real y, Real x)
{
{
return Offset (coordinate_a_[Y_AXIS], coordinate_a_[X_AXIS]);
}
+
+Offset
+offset_directed (Real angle)
+{
+ if (angle <= -360.0 || angle >= 360.0)
+ angle = fmod (angle, 360.0);
+ // Now |angle| < 360.0, and the absolute size is not larger than
+ // before, so we haven't lost precision.
+ if (angle <= -180.0)
+ angle += 360.0;
+ else if (angle > 180.0)
+ angle -= 360.0;
+ // Now -180.0 < angle <= 180.0 and we still haven't lost precision.
+ // We don't work with angles greater than 45 degrees absolute in
+ // order to minimize how rounding errors of M_PI/180 affect the
+ // result. That way, at least angles that are a multiple of 90
+ // degree deliver the expected results.
+ //
+ // Sign of the sine is chosen to avoid -0.0 in results. This
+ // version delivers exactly equal magnitude on x/y for odd multiples
+ // of 45 degrees at the cost of losing some less obvious invariants.
+
+ if (angle > 0)
+ if (angle > 90)
+ return Offset (sin ((90 - angle) * M_PI/180.0),
+ sin ((180 - angle) * M_PI/180.0));
+ else
+ return Offset (sin ((90 - angle) * M_PI/180.0),
+ sin (angle * M_PI/180.0));
+ else if (angle < -90)
+ return Offset (sin ((90 + angle) * M_PI/180.0),
+ sin ((-180 - angle) * M_PI/180.0));
+ else
+ return Offset (sin ((90 + angle) * M_PI/180.0),
+ sin (angle * M_PI/180.0));
+}