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// 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; | |
} |
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