iOS tweening, adapted from Webkit

JXBezier.c

#include "JXBezier.h"
#include <math.h>

JXUnitBezier JXUnitBezierMake(double p1x, double p1y, double p2x, double p2y) {
    JXUnitBezier bezier;
    bezier.cx = 3.0 * p1x;
    bezier.bx = 3.0 * (p2x - p1x) - bezier.cx;
    bezier.ax = 1.0 - bezier.cx - bezier.bx;
    bezier.cy = 3.0 * p1y;
    bezier.by = 3.0 * (p2y - p1y) - bezier.cy;
    bezier.ay = 1.0 - bezier.cy - bezier.by;
    return bezier;
}

double JXBezierEpsilon(double duration) {
    return 1.0 / (200.0 * duration);
}

double JXUnitBezierSampleCurveDerivativeX(JXUnitBezier b, double t) {
    return (3.0 * b.ax * t + 2.0 * b.bx) * t + b.cx;
}

double JXUnitBezierSampleCurveX(JXUnitBezier b, double t) {
    return ((b.ax * t + b.bx) * t + b.cx) * t;
}

double JXUnitBezierSampleCurveY(JXUnitBezier b, double t) {
    return ((b.ay * t + b.by) * t + b.cy) * t;
}

double JXUnitBezierSolveCurveX(JXUnitBezier b, double x, double epsilon) {
    double t0;
    double t1;
    double t2;
    double x2;
    double d2;
    int i;
    
    for (t2 = x, i = 0; i < 8; i++) {
        x2 = JXUnitBezierSampleCurveX(b, t2) - x;
        if (fabs(x2) < epsilon)
            return t2;
        d2 = JXUnitBezierSampleCurveDerivativeX(b, t2);
        if (fabs(d2) < 1e-6)
            break;
        t2 = t2 - x2 / d2;
    }
    
    t0 = 0.0;
    t1 = 1.0;
    t2 = x;
    
    if (t2 < t0)
        return t0;
    if (t2 > t1)
        return t1;
    
    while (t0 < t1) {
        x2 = JXUnitBezierSampleCurveX(b, t2);
        if (fabs(x2 - x) < epsilon)
            return t2;
        if (x > x2)
            t0 = t2;
        else
            t1 = t2;
        t2 = (t1 - t0) * .5 + t0;
    }
    
    return t2;
}

double JXUnitBezierSolve(JXUnitBezier b, double x, double epsilon) {
    return JXUnitBezierSampleCurveY(b, JXUnitBezierSolveCurveX(b, x, epsilon));
}

double JXCubicBezierSolve(double p1x, double p1y, double p2x, double p2y, double t, double duration) {
    JXUnitBezier bezier = JXUnitBezierMake(p1x, p1y, p2x, p2y);
    return JXUnitBezierSolve(bezier, t, JXBezierEpsilon(duration));
}

JXBezier.h

#ifndef _JXBEZIER_H_
#define _JXBEZIER_H_

typedef struct {
    double ax;
    double bx;
    double cx;
    double ay;
    double by;
    double cy;    
} JXUnitBezier;

JXUnitBezier JXUnitBezierMake(double p1x, double p1y, double p2x, double p2y);
double JXBezierEpsilon(double duration);
double JXUnitBezierSampleCurveDerivativeX(JXUnitBezier b, double t);
double JXUnitBezierSampleCurveX(JXUnitBezier b, double t);
double JXUnitBezierSampleCurveY(JXUnitBezier b, double t);
double JXUnitBezierSolveCurveX(JXUnitBezier b, double x, double epsilon);
double JXUnitBezierSolve(JXUnitBezier b, double x, double epsilon);
double JXCubicBezierSolve(double p1x, double p1y, double p2x, double p2y, double t, double duration);

#endif

JXTween.h

#import <QuartzCore/QuartzCore.h>

@interface JXTween : NSObject

@property (strong, nonatomic) CAMediaTimingFunction *timingFunction;
@property (assign, nonatomic) double startTime;
@property (assign, nonatomic) double duration;
@property (assign, nonatomic) double startValue;
@property (assign, nonatomic) double endValue;

+ (instancetype)tweenWithFunction:(CAMediaTimingFunction *)tf
                        startTime:(double)st
                         duration:(double)du
                       startValue:(double)sv
                         endValue:(double)ev;

- (double)valueAtTime:(double)now;

@end

JXTween.m

#import "JXTween.h"
#import "JXBezier.h"

@interface JXTween ()
@property (assign, nonatomic) double p1x;
@property (assign, nonatomic) double p1y;
@property (assign, nonatomic) double p2x;
@property (assign, nonatomic) double p2y;
@end

@implementation JXTween

+ (instancetype)tweenWithFunction:(CAMediaTimingFunction *)tf
                        startTime:(double)st
                         duration:(double)du
                       startValue:(double)sv
                         endValue:(double)ev
{
    JXTween *t = [[JXTween alloc] init];
    t.timingFunction = tf;
    t.startTime = st;
    t.duration = du;
    t.startValue = sv;
    t.endValue = ev;
    return t;
}

- (void)setTimingFunction:(CAMediaTimingFunction *)function
{
    _timingFunction = function;
    
    float p1[2];
    [_timingFunction getControlPointAtIndex:1 values:p1];
    float p2[2];
    [_timingFunction getControlPointAtIndex:2 values:p2];

    _p1x = (double)p1[0];
    _p1y = (double)p1[1];
    _p2x = (double)p2[0];
    _p2y = (double)p2[1];
}

- (double)valueAtTime:(double)now
{
    double elapsed = now - _startTime;

    if (elapsed >= _duration)
        return _endValue;

    double fractionalTime = elapsed / _duration;
    double solution = JXCubicBezierSolve(_p1x, _p1y, _p2x, _p2y, fractionalTime, _duration);
    double delta = _endValue - _startValue;
    double value = _startValue + (solution * delta);

    return value;
}

@end