X-Git-Url: https://git.donarmstrong.com/?a=blobdiff_plain;f=lily%2Fbezier.cc;h=b341d73754b35ccf5828c9f2372ea65847e5878c;hb=cfc4cbf34569db6a6c8968694f86e36b206a9d05;hp=26ad982419ac2f344db62fd40b61a63e2e572a75;hpb=2c22efe5a46a37065b10c3f51c5d7db00d07d318;p=lilypond.git diff --git a/lily/bezier.cc b/lily/bezier.cc index 26ad982419..b341d73754 100644 --- a/lily/bezier.cc +++ b/lily/bezier.cc @@ -3,36 +3,21 @@ source file of the GNU LilyPond music typesetter - (c) 1998--2005 Jan Nieuwenhuizen + (c) 1998--2009 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) -{ - Real x = 1.0; - - while (under) - { - x *= over / Real (under); - - over -= 1.0; - under--; - } - return x; -} +Real binomial_coefficient_3[] = { + 1, 3, 3, 1 +}; void -scale (Array *array, Real x, Real y) +scale (vector *array, Real x, Real y) { - for (int i = 0; i < array->size (); i++) + 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]; @@ -40,17 +25,17 @@ scale (Array *array, Real x, Real y) } void -rotate (Array *array, Real phi) +rotate (vector *array, Real phi) { Offset rot (complex_exp (Offset (0, phi))); - for (int i = 0; i < array->size (); i++) + for (vsize i = 0; i < array->size (); i++) (*array)[i] = complex_multiply (rot, (*array)[i]); } void -translate (Array *array, Offset o) +translate (vector *array, Offset o) { - for (int i = 0; i < array->size (); i++) + for (vsize i = 0; i < array->size (); i++) (*array)[i] += o; } @@ -66,8 +51,8 @@ translate (Array *array, Offset o) Real 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) { @@ -91,9 +76,7 @@ Bezier::curve_coordinate (Real t, Axis a) const 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); - } + one_min_tj[i] = one_min_tj[i - 1] * (1 - t); Real r = 0.0; for (int j = 0; j < 4; j++) @@ -114,9 +97,7 @@ Bezier::curve_point (Real t) const 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); - } + one_min_tj[i] = one_min_tj[i - 1] * (1 - t); Offset o; for (int j = 0; j < 4; j++) @@ -136,33 +117,30 @@ Bezier::curve_point (Real t) const } /* - Cache binom(3,j) t^j (1-t)^{3-j} + 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; -} +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 { - if (!done_cache_init) - init_polynomial_cache (); - Polynomial p (0.0); Polynomial q; for (int j = 0; j <= 3; j++) { - q = bezier_term_cache[j]; + q = poly_cache.terms_[j]; q *= control_[j][a]; p += q; } @@ -173,19 +151,19 @@ Bezier::polynomial (Axis a) const /** Remove all numbers outside [0, 1] from SOL */ -Array -filter_solutions (Array sol) +vector +filter_solutions (vector sol) { - for (int i = sol.size (); i--;) + for (vsize i = sol.size (); i--;) if (sol[i] < 0 || sol[i] > 1) - sol.del (i); + sol.erase (sol.begin () + i); return sol; } /** find t such that derivative is proportional to DERIV */ -Array +vector Bezier::solve_derivative (Offset deriv) const { Polynomial xp = polynomial (X_AXIS); @@ -201,13 +179,13 @@ Bezier::solve_derivative (Offset deriv) const /* Find t such that curve_point (t)[AX] == COORDINATE */ -Array +vector Bezier::solve_point (Axis ax, Real coordinate) const { Polynomial p (polynomial (ax)); p.coefs_[0] -= coordinate; - Array sol (p.solve ()); + vector sol (p.solve ()); return filter_solutions (sol); } @@ -221,10 +199,10 @@ Bezier::extent (Axis a) const Offset d; 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])); @@ -232,6 +210,17 @@ Bezier::extent (Axis a) const 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 */ @@ -276,3 +265,52 @@ Bezier::reverse () b2.control_[CONTROL_COUNT - i - 1] = control_[i]; *this = b2; } + + +/* + Subdivide a bezier at T into LEFT_PART and RIGHT_PART + using deCasteljau's algorithm. +*/ +void +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++) + 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 i = 0; i < CONTROL_COUNT; i++) + { + left_part->control_[i]=p[0][CONTROL_COUNT - 1 - i]; + right_part->control_[i]=p[i][i]; + } +} + +/* + Extract a portion of a bezier from T_MIN to T_MAX +*/ + +Bezier +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"); + if (t_min >= t_max) + 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); + if (t_max == 1.0) + return bez2; + else + { + bez2.subdivide ((t_max-t_min)/(1-t_min), &bez3, &bez4); + return bez3; + } +}