/*
This file is part of LilyPond, the GNU music typesetter.
- Copyright (C) 1997--2011 Han-Wen Nienhuys <hanwen@xs4all.nl>
+ Copyright (C) 1997--2015 Han-Wen Nienhuys <hanwen@xs4all.nl>
LilyPond is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
return z;
}
-Offset
-complex_conjugate (Offset o)
-{
- o[Y_AXIS] = -o[Y_AXIS];
- return o;
-}
-
-Offset
-complex_divide (Offset z1, Offset z2)
+static inline Real
+atan2d (Real y, Real x)
{
- 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]);
+ return atan2 (y, x) * (180.0 / M_PI);
}
Real
Offset::angle_degrees () const
{
- return arg () * 180 / M_PI;
+ Real x = coordinate_a_ [X_AXIS];
+ Real y = coordinate_a_ [Y_AXIS];
+
+ // We keep in the vicinity of multiples of 45 degrees here: this is
+ // where straightforward angles for straightforward angular
+ // relations are most expected. The factors of 2 employed in the
+ // comparison are not really perfect for that: sqrt(2)+1 would be
+ // the factor giving exact windows of 45 degrees rather than what we
+ // have here. It's just that 2 is likely to generate nicer code
+ // than 2.4 and the exact handover does not really matter.
+ //
+ // Comparisons here are chosen appropriately to let infinities end
+ // up in their "exact" branch. As opposed to the normal atan2
+ // function behavior, this makes "competing" infinities result in
+ // NAN angles.
+ if (y < 0.0)
+ {
+ if (2*x < -y)
+ if (-x > -2*y) // x < 0, y < 0, |x| > |2y|
+ return -180 + atan2d (-y, -x);
+ else if (-2*x >= -y) // x < 0, y < 0, |y| < |2x| <= |4y|
+ return -135 + atan2d (x - y, -y - x);
+ else // y < 0, |y| >= |2x|
+ return -90 + atan2d (x, -y);
+ else if (x <= -2*y) // x > 0, y < 0, |y| <= |2x| < |4y|
+ return -45 + atan2d (x + y, x - y);
+ // Drop through for y < 0, x > |2y|
+ }
+ else if (y > 0.0)
+ {
+ if (2*x < y)
+ if (-x > 2*y) // x < 0, y >= 0, |x| > |2y|
+ return 180 - atan2d (y, -x);
+ else if (-2*x >= y) // x < 0, y >= 0, |y| < |2x| <= |4y|
+ return 135 - atan2d (x + y, y - x);
+ else // y >= 0, |y| >= |2x|
+ return 90 - atan2d (x, y);
+ else if (x <= 2*y) // x >= 0, y >= 0, |y| < |2x| < |4y|
+ return 45 - atan2d (x - y, x + y);
+ // Drop through for y > 0, x > |2y|
+ }
+ else
+ // we return 0 for (0,0). NAN would be an option but is a
+ // nuisance for getting back to rectangular coordinates. Strictly
+ // speaking, this argument would be just as valid for (+inf.0,
+ // +inf.0), but then infinities are already an indication of a
+ // problem in LilyPond.
+ return (x < 0.0) ? 180 : 0;
+ return atan2d (y, x);
}
+
+
/**
euclidian vector length / complex modulus
*/
Real
Offset::length () const
{
- return sqrt (sqr (coordinate_a_[X_AXIS])
- + sqr (coordinate_a_[Y_AXIS]));
+ return hypot (coordinate_a_[X_AXIS], coordinate_a_[Y_AXIS]);
}
bool
Offset::direction () const
{
Offset d = *this;
+ if (isinf (d[X_AXIS]))
+ {
+ if (!isinf (d[Y_AXIS]))
+ return Offset ((d[X_AXIS] > 0.0 ? 1.0 : -1.0), 0.0);
+ }
+ else if (isinf (d[Y_AXIS]))
+ return Offset (0.0, (d[Y_AXIS] > 0.0 ? 1.0 : -1.0));
+ else if (d[X_AXIS] == 0.0 && d[Y_AXIS] == 0.0)
+ return d;
+ // The other cases propagate or produce NaN as appropriate.
+
d /= length ();
return d;
}
{
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));
+}
projects / lilypond.git / blobdiff