X-Git-Url: https://git.donarmstrong.com/?a=blobdiff_plain;f=lily%2Fbezier.cc;h=0a0f4cfc6ff3f18962548c44bf391e9ba99762ad;hb=a4d6cf4907b5ec9a897f2d8f142b0452222433d0;hp=b341d73754b35ccf5828c9f2372ea65847e5878c;hpb=f7836bbd7dc03e7173590a76e419a5e826b1d689;p=lilypond.git diff --git a/lily/bezier.cc b/lily/bezier.cc index b341d73754..0a0f4cfc6f 100644 --- a/lily/bezier.cc +++ b/lily/bezier.cc @@ -1,16 +1,28 @@ /* - bezier.cc -- implement Bezier and Bezier_bow + This file is part of LilyPond, the GNU music typesetter. - source file of the GNU LilyPond music typesetter + Copyright (C) 1998--2011 Jan Nieuwenhuizen - (c) 1998--2009 Jan Nieuwenhuizen + 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 "bezier.hh" #include "warn.hh" #include "libc-extension.hh" -Real binomial_coefficient_3[] = { +Real binomial_coefficient_3[] = +{ 1, 3, 3, 1 }; @@ -51,7 +63,7 @@ translate (vector *array, Offset o) Real Bezier::get_other_coordinate (Axis a, Real x) const { - Axis other = Axis ((a +1) % NO_AXES); + Axis other = Axis ((a + 1) % NO_AXES); vector ts = solve_point (a, x); if (ts.size () == 0) @@ -69,6 +81,17 @@ Bezier::get_other_coordinate (Axis a, Real x) const return curve_coordinate (ts[0], other); } +vector +Bezier::get_other_coordinates (Axis a, Real x) const +{ + Axis other = other_axis (a); + vector ts = solve_point (a, x); + vector sols; + for (vsize i = 0; i < ts.size (); i++) + sols.push_back (curve_coordinate (ts[i], other)); + return sols; +} + Real Bezier::curve_coordinate (Real t, Axis a) const { @@ -82,7 +105,7 @@ Bezier::curve_coordinate (Real t, Axis a) const for (int j = 0; j < 4; j++) { r += control_[j][a] * binomial_coefficient_3[j] - * tj * one_min_tj[3 - j]; + * tj * one_min_tj[3 - j]; tj *= t; } @@ -103,7 +126,7 @@ Bezier::curve_point (Real t) const for (int j = 0; j < 4; j++) { o += control_[j] * binomial_coefficient_3[j] - * tj * one_min_tj[3 - j]; + * tj * one_min_tj[3 - j]; tj *= t; } @@ -119,15 +142,16 @@ Bezier::curve_point (Real t) const /* Cache binom (3, j) t^j (1-t)^{3-j} */ -struct Polynomial_cache { +struct Polynomial_cache +{ Polynomial terms_[4]; Polynomial_cache () { for (int j = 0; j <= 3; j++) terms_[j] - = binomial_coefficient_3[j] - * Polynomial::power (j, Polynomial (0, 1)) - * Polynomial::power (3 - j, Polynomial (1, -1)); + = binomial_coefficient_3[j] + * Polynomial::power (j, Polynomial (0, 1)) + * Polynomial::power (3 - j, Polynomial (1, -1)); } }; @@ -189,13 +213,68 @@ Bezier::solve_point (Axis ax, Real coordinate) const return filter_solutions (sol); } +/** + Assuming AX is X_AXIS, and D is UP, finds the + maximum value of curve_coordinate(t, Y_AXIS) subject to + l <= curve_coordinate(t, X_AXIS) <= r. +*/ +Real +Bezier::minmax (Axis ax, Real l, Real r, Direction d) const +{ + Axis other = other_axis (ax); + Interval lr (l, r); + vector solutions; + + // Possible solutions are: + // t = 0 or 1, or... + solutions.push_back (0); + solutions.push_back (1); + + // t is a critical point for the other-axis polynomial, or... + Polynomial p_prime (polynomial (other)); + p_prime.differentiate (); + vector criticals = p_prime.solve (); + solutions.insert (solutions.end (), criticals.begin (), criticals.end ()); + + // t solves curve_coordinate(t, X_AXIS) = l or r. + Direction dir = LEFT; + do + { + Polynomial p (polynomial (ax)); + p.coefs_[0] -= lr[dir]; + + vector sol = p.solve (); + solutions.insert (solutions.end (), sol.begin (), sol.end ()); + } + while (flip (&dir) != LEFT); + + Polynomial p (polynomial (ax)); + Polynomial other_p (polynomial (other)); + vector values; + for (vsize i = solutions.size (); i--;) + { + Real t = solutions[i]; + if (t >= 0 && t <= 1 && p.eval (t) >= l && p.eval (t) <= r) + values.push_back (other_p.eval (t)); + } + + if (values.empty ()) + { + programming_error ("no solution found for Bezier intersection"); + return 0.0; + } + + vector_sort (values, less ()); + return (d == DOWN) ? values[0] : values.back (); +} + /** Compute the bounding box dimensions in direction of A. */ Interval Bezier::extent (Axis a) const { - int o = (a + 1)%NO_AXES; + int o = (a + 1) % NO_AXES; Offset d; d[Axis (o)] = 1.0; Interval iv; @@ -217,10 +296,9 @@ Bezier::control_point_extent (Axis a) const for (int i = CONTROL_COUNT; i--;) ext.add_point (control_[i][a]); - return ext; + return ext; } - /** Flip around axis A */ @@ -254,7 +332,7 @@ Bezier::assert_sanity () const { for (int i = 0; i < CONTROL_COUNT; i++) assert (!isnan (control_[i].length ()) - && !isinf (control_[i].length ())); + && !isinf (control_[i].length ())); } void @@ -266,7 +344,6 @@ Bezier::reverse () *this = b2; } - /* Subdivide a bezier at T into LEFT_PART and RIGHT_PART using deCasteljau's algorithm. @@ -276,15 +353,15 @@ Bezier::subdivide (Real t, Bezier *left_part, Bezier *right_part) const { Offset p[CONTROL_COUNT][CONTROL_COUNT]; - for (int i = 0; i < CONTROL_COUNT ; i++) + for (int i = 0; i < CONTROL_COUNT; i++) p[i][CONTROL_COUNT - 1 ] = control_[i]; - for (int j = CONTROL_COUNT - 2; j >= 0 ; j--) - for (int i = 0; i < CONTROL_COUNT -1; i++) - p[i][j] = p[i][j+1] + t * (p[i+1][j+1] - p[i][j+1]); + for (int j = CONTROL_COUNT - 2; j >= 0; j--) + for (int i = 0; i < CONTROL_COUNT - 1; i++) + p[i][j] = p[i][j + 1] + t * (p[i + 1][j + 1] - p[i][j + 1]); for (int i = 0; i < CONTROL_COUNT; i++) { - left_part->control_[i]=p[0][CONTROL_COUNT - 1 - i]; - right_part->control_[i]=p[i][i]; + left_part->control_[i] = p[0][CONTROL_COUNT - 1 - i]; + right_part->control_[i] = p[i][i]; } } @@ -297,20 +374,20 @@ Bezier::extract (Real t_min, Real t_max) const { if ((t_min < 0) || (t_max) > 1) programming_error - ("bezier extract arguments outside of limits: curve may have bad shape"); + ("bezier extract arguments outside of limits: curve may have bad shape"); if (t_min >= t_max) - programming_error - ("lower bezier extract value not less than upper value: curve may have bad shape"); + programming_error + ("lower bezier extract value not less than upper value: curve may have bad shape"); Bezier bez1, bez2, bez3, bez4; if (t_min == 0.0) bez2 = *this; else - subdivide (t_min, &bez1, &bez2); + subdivide (t_min, &bez1, &bez2); if (t_max == 1.0) - return bez2; + return bez2; else - { - bez2.subdivide ((t_max-t_min)/(1-t_min), &bez3, &bez4); - return bez3; - } + { + bez2.subdivide ((t_max - t_min) / (1 - t_min), &bez3, &bez4); + return bez3; + } }