gistfile1.c

// https://en.wikipedia.org/wiki/Damping
double HTSpringOverdamped(double time, double damping, double freq, double offset, double velocity) {
	NSCParameterAssert(0.0 <= damping);
	NSCParameterAssert(damping < 1.0);
	
	if(time <= 0.0)
		return offset;
	
	const double wd = freq * (2.0 * M_PI);
	const double w0 = wd / sqrt(1.0 - damping * damping);
	const double A = offset;
	const double B = (1.0 / wd) * (damping * w0 * offset + velocity);
	const double expPart = pow(M_E, -damping * w0 * time);
	const double sinusoidPart = A * cos(wd * time) + B * sin(wd * time);
	return expPart * sinusoidPart;
}

double HTAnimationTimingSpring(double elapsed, double duration, double easePoint, double damping, double freq) {
	if(elapsed >= duration)
		return 1.0;
	
	static const double HTSpringNormalisedOffset = 1.0;
	// distance = distance from equilibrium position (i.e., 0.0)
	double startDistance = HTSpringOverdamped(0.0, damping, freq, HTSpringNormalisedOffset, 0.0);
	double currentDistance = HTSpringOverdamped(elapsed, damping, freq, HTSpringNormalisedOffset, 0.0);
	
	easePoint = MAX(0.0, MIN(easePoint, 1.0));
	double easeTime = easePoint * duration;
	if(elapsed > easeTime) {
		double easeValue = (elapsed - easeTime) / (duration - easeTime);
		currentDistance *= (1.0 - HTAnimationTimingSineEaseInOut(easeValue, 1.0));
	}
	
	return 1.0 - (currentDistance / startDistance);
}

double HTAnimationTimingSineEaseInOut(double elapsed, double duration) {
	return HTAnimationTimingSineEaseInOutCanonical(elapsed, duration, 0.0, 1.0);
}

// Based on penner equations: http://www.robertpenner.com/easing/
// t: elapsed, d: duration;
// b: base, c: delta;
static double HTAnimationTimingSineEaseInOutCanonical(double t, double d, double b, double c) {
	return -c/2.0 * (cos(M_PI*t/d) - 1.0) + b;
}