void CachingOrbit::sample(double start, double t, int nSamples,
OrbitSampleProc& proc) const
{
double dt = t / (double) nSamples;
for (int i = 0; i < nSamples; i++)
proc.sample(positionAtTime(start + dt * i));
}
void EllipticalOrbit::sample(double, double t, int nSamples,
OrbitSampleProc& proc) const
{
if (eccentricity >= 1.0)
{
double dE = 1 * PI / (double) nSamples;
for (int i = 0; i < nSamples; i++)
proc.sample(t, positionAtE(dE * i), velocityAtE(dE * i));
}
else
{
// Adaptive sampling of the orbit; more samples in regions of high curvature.
// nSamples is the number of samples that will be used for a perfectly circular
// orbit. Elliptical orbits will have regions of higher curvature thar require
// additional sample points.
double E = 0.0;
double dE = 2 * PI / (double) nSamples;
double w = (1 - square(eccentricity));
double M0 = E - eccentricity * sin(E);
while (E < 2 * PI)
{
// Compute the time tag for this sample
double M = E - eccentricity * sin(E); // Mean anomaly from ecc anomaly
double tsamp = t + (M - M0) * period / (2 * PI); // Time from mean anomaly
proc.sample(tsamp, positionAtE(E), velocityAtE(E));
// Compute the curvature
double k = w * pow(square(sin(E)) + w * w * square(cos(E)), -1.5);
// Step amount based on curvature--constrain it so that we don't end up
// taking too many samples anywhere. Clamping the curvature to 20 effectively
// limits the numbers of samples to 3*nSamples
E += dE / max(min(k, 20.0), 1.0);
}
}
}
void EllipticalOrbit::sample(double, double, int nSamples, OrbitSampleProc& proc) const
{
double dE = 2. * M_PI / (double) nSamples;
for (int i = 0; i < nSamples; i++)
proc.sample(positionAtE(dE * i));
}
