#include <math.h>
-#include "config.hh"
+#include "bezier.hh"
#include "warn.hh"
#include "libc-extension.hh"
-#include "bezier.hh"
-#include "polynomial.hh"
Real
binomial_coefficient (Real over , int under)
Formula of the bezier 3-spline
- sum_{j=0}^3 (3 over j) z_j (1-t)^ (3-j) t^j
+ sum_{j = 0}^3 (3 over j) z_j (1-t)^ (3-j) t^j
A is the axis of X coordinate.
Real one_min_tj = (1-t)* (1-t)* (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);
Bezier::polynomial (Axis a)const
{
Polynomial p (0.0);
- for (int j=0; j <= 3; j++)
+ 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));
+ p +=
+ (control_[j][a] * binomial_coefficient (3, j))
+ * Polynomial::power (j, Polynomial (0, 1))
+ * Polynomial::power (3 - j, Polynomial (1, -1));
}
return p;
Array<Real>
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 ();
Array<Real> sols (solve_derivative (d));
sols.push (1.0);
sols.push (0.0);
- for (int i= sols.size (); i--;)
+ for (int i = sols.size (); i--;)
{
Offset o (curve_point (sols[i]));
iv.unite (Interval (o[a],o[a]));
/**
Flip around axis A
*/
-
void
Bezier::scale (Real x, Real y)
{
void
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 ()));
}
Bezier::reverse ()
{
Bezier b2;
- for (int i =0; i < CONTROL_COUNT; i++)
+ for (int i = 0; i < CONTROL_COUNT; i++)
b2.control_[CONTROL_COUNT-i-1] = control_[i];
*this = b2;
}