X-Git-Url: https://git.donarmstrong.com/?a=blobdiff_plain;f=lily%2Fbezier.cc;h=18d7836cbfe1d37762ccf8ce4d5134affe8f949e;hb=5b4b0d6e9a197e8f9eb085b7c2ad78b8be3e5cfc;hp=28634b473c683b283e95cd27d465814a62d15ab4;hpb=bb36bac02a64770871780231ecc709cb18b20932;p=lilypond.git diff --git a/lily/bezier.cc b/lily/bezier.cc index 28634b473c..18d7836cbf 100644 --- a/lily/bezier.cc +++ b/lily/bezier.cc @@ -3,156 +3,235 @@ source file of the GNU LilyPond music typesetter - (c) 1998--2000 Jan Nieuwenhuizen + (c) 1998--2008 Jan Nieuwenhuizen */ -#include #include "bezier.hh" -#include "polynomial.hh" +#include "warn.hh" +#include "libc-extension.hh" -/* +Real binomial_coefficient_3[] = { + 1, 3, 3, 1 +}; - Formula of the bezier 3-spline +void +scale (vector *array, Real x, Real y) +{ + for (vsize i = 0; i < array->size (); i++) + { + (*array)[i][X_AXIS] = x * (*array)[i][X_AXIS]; + (*array)[i][Y_AXIS] = y * (*array)[i][Y_AXIS]; + } +} - sum_{j=0}^3 (3 over j) z_j (1-t)^(3-j) t^j - */ +void +rotate (vector *array, Real phi) +{ + Offset rot (complex_exp (Offset (0, phi))); + for (vsize i = 0; i < array->size (); i++) + (*array)[i] = complex_multiply (rot, (*array)[i]); +} -Bezier::Bezier () +void +translate (vector *array, Offset o) { + for (vsize 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); - Array ts = solve_point (a, x); - + Axis other = Axis ((a +1) % NO_AXES); + vector ts = solve_point (a, x); + + if (ts.size () == 0) + { + programming_error ("no solution found for Bezier intersection"); + return 0.0; + } + +#ifdef PARANOID Offset c = curve_point (ts[0]); - assert (fabs (c[a] - x) < 1e-8); - - return c[other]; + if (fabs (c[a] - x) > 1e-8) + programming_error ("bezier intersection not correct?"); +#endif + + return curve_coordinate (ts[0], other); } Real -binomial_coefficient (Real over , int under) +Bezier::curve_coordinate (Real t, Axis a) const { - Real x = 1.0; + 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); - while (under) + Real r = 0.0; + for (int j = 0; j < 4; j++) { - x *= over / Real (under); + r += control_[j][a] * binomial_coefficient_3[j] + * tj * one_min_tj[3 - j]; - over -= 1.0; - under --; + tj *= t; } - return x; + + 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); } - assert (fabs (o[X_AXIS] - polynomial (X_AXIS).eval (t))< 1e-8); - assert (fabs (o[Y_AXIS] - polynomial (Y_AXIS).eval (t))< 1e-8); +#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); +#endif - return o; } +/* + Cache binom (3, j) t^j (1-t)^{3-j} +*/ +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)); + } +}; + +static Polynomial_cache poly_cache; Polynomial -Bezier::polynomial (Axis a)const +Bezier::polynomial (Axis a) const { Polynomial p (0.0); - for (int j=0; j <= 3; j++) + Polynomial q; + for (int j = 0; j <= 3; j++) { - p += control_[j][a] - * Polynomial::power (j , Polynomial (0,1))* - Polynomial::power (3 - j, Polynomial (1,-1))* - binomial_coefficient(3, j); + q = poly_cache.terms_[j]; + q *= control_[j][a]; + p += q; } return p; } /** - 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) - sol.del (i); + Remove all numbers outside [0, 1] from SOL +*/ +vector +filter_solutions (vector sol) +{ + for (vsize i = sol.size (); i--;) + if (sol[i] < 0 || sol[i] > 1) + sol.erase (sol.begin () + i); return sol; } /** find t such that derivative is proportional to DERIV - */ -Array -Bezier::solve_derivative (Offset deriv)const +*/ +vector +Bezier::solve_derivative (Offset deriv) const { - Polynomial xp=polynomial (X_AXIS); - Polynomial yp=polynomial (Y_AXIS); + 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 +vector Bezier::solve_point (Axis ax, Real coordinate) const { - Polynomial p(polynomial (ax)); + Polynomial p (polynomial (ax)); p.coefs_[0] -= coordinate; - - Array sol (p.solve ()); + + vector 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); - for (int i= sols.size (); i--;) + vector sols (solve_derivative (d)); + sols.push_back (1.0); + sols.push_back (0.0); + for (vsize 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::flip (Axis a) +Bezier::scale (Real x, Real y) { for (int i = CONTROL_COUNT; i--;) - control_[i][a] = - control_[i][a]; + { + control_[i][X_AXIS] = x * control_[i][X_AXIS]; + control_[i][Y_AXIS] = y * control_[i][Y_AXIS]; + } } void @@ -171,9 +250,9 @@ Bezier::translate (Offset o) } void -Bezier::check_sanity () const +Bezier::assert_sanity () const { - for (int i=0; i < CONTROL_COUNT; i++) + for (int i = 0; i < CONTROL_COUNT; i++) assert (!isnan (control_[i].length ()) && !isinf (control_[i].length ())); } @@ -182,7 +261,7 @@ void Bezier::reverse () { Bezier b2; - for (int i =0; i < CONTROL_COUNT; i++) - b2.control_[CONTROL_COUNT-i-1] = control_[i]; + for (int i = 0; i < CONTROL_COUNT; i++) + b2.control_[CONTROL_COUNT - i - 1] = control_[i]; *this = b2; }