Обычно когда говорят просто дуга подразумевают дугу окружности.
С безье все несколько сложнее. Вот сишный код:
| Код |
const double TOLERANCE = 0.0000001; // Application specific tolerance
extern double sqrt(double);
struct point2d {
double x, y;
};
double q1, q2, q3, q4, q5; // These belong to balf()
//---------------------------------------------------------------------------
double balf(double t) // Bezier Arc Length Function
{
double result = q5 + t*(q4 + t*(q3 + t*(q2 + t*q1)));
result = sqrt(result);
return result;
}
//---------------------------------------------------------------------------
// NOTES: TOLERANCE is a maximum error ratio
// if n_limit isn't a power of 2 it will be act like the next higher
// power of two.
double Simpson (
double (*f)(double),
double a,
double b,
int n_limit,
double TOLERANCE)
{
int n = 1;
double multiplier = (b - a)/6.0;
double endsum = f(a) + f(b);
double interval = (b - a)/2.0;
double asum = 0;
double bsum = f(a + interval);
double est1 = multiplier * (endsum + 2 * asum + 4 * bsum);
double est0 = 2 * est1;
while(n < n_limit
&& (_ABS(est1) > 0 && _ABS((est1 - est0) / est1) > TOLERANCE)) {
n *= 2;
multiplier /= 2;
interval /= 2;
asum += bsum;
bsum = 0;
est0 = est1;
double interval_div_2n = interval / (2.0 * n);
for (int i = 1; i < 2 * n; i += 2) {
double t = a + i * interval_div_2n;
bsum += f(t);
}
est1 = multiplier*(endsum + 2*asum + 4*bsum);
}
return est1;
}
//
//---------------------------------------------------------------------------
//
double BezierArcLength(point2d p1, point2d p2, point2d p3, point2d p4)
{
point2d k1, k2, k3, k4;
k1 = -p1 + 3*(p2 - p3) + p4;
k2 = 3*(p1 + p3) - 6*p2;
k3 = 3*(p2 - p1);
k4 = p1;
q1 = 9.0*(sqr(k1.x) + sqr(k1.y));
q2 = 12.0*(k1.x*k2.x + k1.y*k2.y);
q3 = 3.0*(k1.x*k3.x + k1.y*k3.y) + 4.0*(sqr(k2.x) + sqr(k2.y));
q4 = 4.0*(k2.x*k3.x + k2.y*k3.y);
q5 = sqr(k3.x) + sqr(k3.y);
double result = Simpson(balf, 0, 1, 1024, 0.001);
return result;
}
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