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/*
This file is part of LilyPond, the GNU music typesetter.
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
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
LilyPond is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with LilyPond. If not, see <http://www.gnu.org/licenses/>.
*/
#include "offset.hh"
#ifndef STANDALONE
string
Offset::to_string () const
{
string s;
s = string (" (") + ::to_string (coordinate_a_[X_AXIS]) + ", "
+ ::to_string (coordinate_a_[Y_AXIS]) + ")";
return s;
}
#endif
/*
free bsd fix by John Galbraith
*/
Offset
complex_multiply (Offset z1, Offset z2)
{
Offset z;
if (!isinf (z2[Y_AXIS]))
{
z[X_AXIS] = z1[X_AXIS] * z2[X_AXIS] - z1[Y_AXIS] * z2[Y_AXIS];
z[Y_AXIS] = z1[X_AXIS] * z2[Y_AXIS] + z1[Y_AXIS] * z2[X_AXIS];
}
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 atan2 (y, x) * (180.0 / M_PI);
}
Real
Offset::angle_degrees () const
{
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 hypot (coordinate_a_[X_AXIS], coordinate_a_[Y_AXIS]);
}
bool
Offset::is_sane () const
{
return !isnan (coordinate_a_[X_AXIS])
&& !isnan (coordinate_a_ [Y_AXIS])
&& !isinf (coordinate_a_[X_AXIS])
&& !isinf (coordinate_a_[Y_AXIS]);
}
Offset
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;
}
Offset
Offset::swapped () const
{
return Offset (coordinate_a_[Y_AXIS], coordinate_a_[X_AXIS]);
}
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