source file of the GNU LilyPond music typesetter
- (c) 1998--2005 Jan Nieuwenhuizen <janneke@gnu.org>
+ (c) 1998--2009 Jan Nieuwenhuizen <janneke@gnu.org>
*/
-#include <math.h>
-
#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<Offset> *array, Real x, Real y)
+scale (vector<Offset> *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];
}
void
-rotate (Array<Offset> *array, Real phi)
+rotate (vector<Offset> *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<Offset> *array, Offset o)
+translate (vector<Offset> *array, Offset o)
{
- for (int i = 0; i < array->size (); i++)
+ for (vsize i = 0; i < array->size (); i++)
(*array)[i] += o;
}
Real
Bezier::get_other_coordinate (Axis a, Real x) const
{
- Axis other = Axis ((a +1)%NO_AXES);
- Array<Real> ts = solve_point (a, x);
+ Axis other = Axis ((a +1) % NO_AXES);
+ vector<Real> ts = solve_point (a, x);
if (ts.size () == 0)
{
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++)
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++)
}
/*
- 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;
}
/**
Remove all numbers outside [0, 1] from SOL
*/
-Array<Real>
-filter_solutions (Array<Real> sol)
+vector<Real>
+filter_solutions (vector<Real> 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<Real>
+vector<Real>
Bezier::solve_derivative (Offset deriv) const
{
Polynomial xp = polynomial (X_AXIS);
/*
Find t such that curve_point (t)[AX] == COORDINATE
*/
-Array<Real>
+vector<Real>
Bezier::solve_point (Axis ax, Real coordinate) const
{
Polynomial p (polynomial (ax));
p.coefs_[0] -= coordinate;
- Array<Real> sol (p.solve ());
+ vector<Real> sol (p.solve ());
return filter_solutions (sol);
}
Offset d;
d[Axis (o)] = 1.0;
Interval iv;
- Array<Real> sols (solve_derivative (d));
- sols.push (1.0);
- sols.push (0.0);
- for (int i = sols.size (); i--;)
+ vector<Real> 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]));
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
*/
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;
+ }
+}
projects / lilypond.git / blobdiff