X-Git-Url: https://git.donarmstrong.com/?a=blobdiff_plain;f=flower%2Foffset.cc;h=db1654f2d3d517f0ef29b90a3d8750353f0a89d5;hb=a6a51abfd0195a3cf7d6ea095cf69808852f21ce;hp=b45809e0b9ed82322fb243a18fef7a748540f1c3;hpb=b37e3f652677ae0298423db9fa0e552e5fce0c92;p=lilypond.git diff --git a/flower/offset.cc b/flower/offset.cc index b45809e0b9..db1654f2d3 100644 --- a/flower/offset.cc +++ b/flower/offset.cc @@ -1,31 +1,35 @@ /* - offset.cc -- implement Offset + This file is part of LilyPond, the GNU music typesetter. - source file of the GNU LilyPond music typesetter + Copyright (C) 1997--2015 Han-Wen Nienhuys - (c) 1997--2006 Han-Wen Nienhuys + 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 . */ #include "offset.hh" - #ifndef STANDALONE -std::string +string Offset::to_string () const { - std::string s; - s = std::string (" (") + std::to_string (coordinate_a_[X_AXIS]) + ", " - + std::to_string (coordinate_a_[Y_AXIS]) + ")"; + string s; + s = string (" (") + ::to_string (coordinate_a_[X_AXIS]) + ", " + + ::to_string (coordinate_a_[Y_AXIS]) + ")"; return s; } #endif -bool -isinf_b (Real r) -{ - return (fabs (r) > 1e20); -} - /* free bsd fix by John Galbraith */ @@ -34,7 +38,7 @@ Offset complex_multiply (Offset z1, Offset z2) { Offset z; - if (!isinf_b (z2[Y_AXIS])) + 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]; @@ -42,54 +46,142 @@ complex_multiply (Offset z1, Offset z2) return z; } -Offset -complex_conjugate (Offset o) +static inline Real +atan2d (Real y, Real x) { - 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); + return atan2 (y, x) * (180.0 / M_PI); } Real -Offset::arg () const +Offset::angle_degrees () const { - return atan2 (coordinate_a_[Y_AXIS], coordinate_a_[X_AXIS]); + 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::is_sane () const { return !isnan (coordinate_a_[X_AXIS]) - && !isnan (coordinate_a_ [Y_AXIS]) - && !isinf (coordinate_a_[X_AXIS]) - && !isnan (coordinate_a_[Y_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]); +} + +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)); }