X-Git-Url: https://git.donarmstrong.com/?a=blobdiff_plain;f=lily%2Fbezier.cc;h=4752bc67f91d5850fbbe45d04e055513853d275f;hb=2224e6fdc1d94a2557220ffa92476f8e30e0c4f3;hp=a8cda698382d8191d73b0c583ba9ca80699cddb6;hpb=afc519eae4c31fe515371ec68b077d6532a7e5cf;p=lilypond.git diff --git a/lily/bezier.cc b/lily/bezier.cc index a8cda69838..4752bc67f9 100644 --- a/lily/bezier.cc +++ b/lily/bezier.cc @@ -3,17 +3,19 @@ source file of the GNU LilyPond music typesetter - (c) 1998--2004 Jan Nieuwenhuizen + (c) 1998--2006 Jan Nieuwenhuizen */ -#include - #include "bezier.hh" #include "warn.hh" #include "libc-extension.hh" +Real binomial_coefficient_3[] = { + 1, 3, 3, 1 +}; + Real -binomial_coefficient (Real over , int under) +binomial_coefficient (Real over, int under) { Real x = 1.0; @@ -21,24 +23,24 @@ binomial_coefficient (Real over , int under) { x *= over / Real (under); - over -= 1.0; - under --; + over -= 1.0; + under--; } return x; } void -scale (Array* array, Real x , Real y) +scale (Array *array, Real x, Real y) { for (int i = 0; i < array->size (); i++) { - (*array)[i][X_AXIS] = x* (*array)[i][X_AXIS]; - (*array)[i][Y_AXIS] = y* (*array)[i][Y_AXIS]; + (*array)[i][X_AXIS] = x * (*array)[i][X_AXIS]; + (*array)[i][Y_AXIS] = y * (*array)[i][Y_AXIS]; } } void -rotate (Array* array, Real phi) +rotate (Array *array, Real phi) { Offset rot (complex_exp (Offset (0, phi))); for (int i = 0; i < array->size (); i++) @@ -46,150 +48,200 @@ rotate (Array* array, Real phi) } void -translate (Array* array, Offset o) +translate (Array *array, Offset o) { for (int i = 0; i < array->size (); i++) (*array)[i] += o; } /* - Formula of the bezier 3-spline sum_{j = 0}^3 (3 over j) z_j (1-t)^ (3-j) t^j A is the axis of X coordinate. - */ +*/ Real -Bezier::get_other_coordinate (Axis a, Real x) const +Bezier::get_other_coordinate (Axis a, Real x) const { - Axis other = Axis ((a +1)%NO_AXES); + Axis other = Axis ((a +1) % NO_AXES); Array ts = solve_point (a, x); if (ts.size () == 0) { - programming_error ("No solution found for Bezier intersection."); + programming_error ("no solution found for Bezier intersection"); return 0.0; } - - Offset c = curve_point (ts[0]); +#ifdef PARANOID + Offset c = curve_point (ts[0]); if (fabs (c[a] - x) > 1e-8) - programming_error ("Bezier intersection not correct?"); - - return c[other]; + programming_error ("bezier intersection not correct?"); +#endif + + return curve_coordinate (ts[0], other); } +Real +Bezier::curve_coordinate (Real t, Axis a) const +{ + Real tj = 1; + Real one_min_tj[4]; + one_min_tj[0] = 1; + for (int i = 1; i < 4; i++) + one_min_tj[i] = one_min_tj[i - 1] * (1 - t); + + Real r = 0.0; + for (int j = 0; j < 4; j++) + { + r += control_[j][a] * binomial_coefficient_3[j] + * tj * one_min_tj[3 - j]; + + tj *= t; + } + + return r; +} Offset -Bezier::curve_point (Real t)const +Bezier::curve_point (Real t) const { Real tj = 1; - Real one_min_tj = (1-t)* (1-t)* (1-t); + Real one_min_tj[4]; + one_min_tj[0] = 1; + for (int i = 1; i < 4; i++) + one_min_tj[i] = one_min_tj[i - 1] * (1 - t); Offset o; - for (int j = 0 ; j < 4; j++) + for (int j = 0; j < 4; j++) { - o += control_[j] * binomial_coefficient (3, j) - * pow (t,j) * pow (1-t, 3-j); + o += control_[j] * binomial_coefficient_3[j] + * tj * one_min_tj[3 - j]; tj *= t; - if (1-t) - one_min_tj /= (1-t); } #ifdef PARANOID - assert (fabs (o[X_AXIS] - polynomial (X_AXIS).eval (t))< 1e-8); - assert (fabs (o[Y_AXIS] - polynomial (Y_AXIS).eval (t))< 1e-8); + assert (fabs (o[X_AXIS] - polynomial (X_AXIS).eval (t)) < 1e-8); + assert (fabs (o[Y_AXIS] - polynomial (Y_AXIS).eval (t)) < 1e-8); #endif - + return o; } +/* + Cache binom(3,j) t^j (1-t)^{3-j} +*/ +static struct Polynomial bezier_term_cache[4]; +static bool done_cache_init; + +void +init_polynomial_cache () +{ + for (int j = 0; j <= 3; j++) + bezier_term_cache[j] + = binomial_coefficient_3[j] + * Polynomial::power (j, Polynomial (0, 1)) + * Polynomial::power (3 - j, Polynomial (1, -1)); + done_cache_init = true; +} Polynomial -Bezier::polynomial (Axis a)const +Bezier::polynomial (Axis a) const { + if (!done_cache_init) + init_polynomial_cache (); + Polynomial p (0.0); + Polynomial q; for (int j = 0; j <= 3; j++) { - p += - (control_[j][a] * binomial_coefficient (3, j)) - * Polynomial::power (j, Polynomial (0, 1)) - * Polynomial::power (3 - j, Polynomial (1, -1)); + q = bezier_term_cache[j]; + q *= control_[j][a]; + p += q; } return p; } /** - Remove all numbers outside [0,1] from SOL - */ + Remove all numbers outside [0, 1] from SOL +*/ Array filter_solutions (Array sol) { for (int i = sol.size (); i--;) - if (sol[i] < 0 || sol[i] >1) + if (sol[i] < 0 || sol[i] > 1) sol.del (i); return sol; } /** find t such that derivative is proportional to DERIV - */ +*/ Array -Bezier::solve_derivative (Offset deriv)const +Bezier::solve_derivative (Offset deriv) const { Polynomial xp = polynomial (X_AXIS); Polynomial yp = polynomial (Y_AXIS); xp.differentiate (); yp.differentiate (); - + Polynomial combine = xp * deriv[Y_AXIS] - yp * deriv [X_AXIS]; return filter_solutions (combine.solve ()); } - /* Find t such that curve_point (t)[AX] == COORDINATE */ -Array +Array Bezier::solve_point (Axis ax, Real coordinate) const { Polynomial p (polynomial (ax)); p.coefs_[0] -= coordinate; - + Array sol (p.solve ()); return filter_solutions (sol); } /** Compute the bounding box dimensions in direction of A. - */ +*/ Interval -Bezier::extent (Axis a)const +Bezier::extent (Axis a) const { - int o = (a+1)%NO_AXES; + int o = (a + 1)%NO_AXES; Offset d; - d[Axis (o)] =1.0; + d[Axis (o)] = 1.0; Interval iv; Array sols (solve_derivative (d)); sols.push (1.0); - sols.push (0.0); + sols.push (0.0); for (int i = sols.size (); i--;) { Offset o (curve_point (sols[i])); - iv.unite (Interval (o[a],o[a])); + iv.unite (Interval (o[a], o[a])); } return iv; } +Interval +Bezier::control_point_extent (Axis a) const +{ + Interval ext; + for (int i = CONTROL_COUNT; i--;) + ext.add_point (control_[i][a]); + + return ext; +} + + /** Flip around axis A - */ +*/ void Bezier::scale (Real x, Real y) { @@ -228,6 +280,6 @@ Bezier::reverse () { Bezier b2; for (int i = 0; i < CONTROL_COUNT; i++) - b2.control_[CONTROL_COUNT-i-1] = control_[i]; + b2.control_[CONTROL_COUNT - i - 1] = control_[i]; *this = b2; }