1 @interface ViewController ()
 2 
 3 @property (nonatomic, weak) IBOutlet UIView *layerView;
 4 
 5 @end
 6 
 7 @implementation ViewController
 8 
 9 - (void)viewDidLoad
10 {
11     [super viewDidLoad];
12     //create timing function
13     CAMediaTimingFunction *function = [CAMediaTimingFunction functionWithName: kCAMediaTimingFunctionEaseOut];
14     //get control points
15     CGPoint controlPoint1, controlPoint2;
16     [function getControlPointAtIndex:1 values:(float *)&controlPoint1];
17     [function getControlPointAtIndex:2 values:(float *)&controlPoint2];
18     //create curve
19     UIBezierPath *path = [[UIBezierPath alloc] init];
20     [path moveToPoint:CGPointZero];
21     [path addCurveToPoint:CGPointMake(1, 1)
22             controlPoint1:controlPoint1 controlPoint2:controlPoint2];
23     //scale the path up to a reasonable size for display
24     [path applyTransform:CGAffineTransformMakeScale(200, 200)];
25     //create shape layer
26     CAShapeLayer *shapeLayer = [CAShapeLayer layer];
27     shapeLayer.strokeColor = [UIColor redColor].CGColor;
28     shapeLayer.fillColor = [UIColor clearColor].CGColor;
29     shapeLayer.lineWidth = 4.0f;
30     shapeLayer.path = path.CGPath;
31     [self.layerView.layer addSublayer:shapeLayer];
32     //flip geometry so that 0,0 is in the bottom-left
33     self.layerView.layer.geometryFlipped = YES;
34 }
35 
36 @end

@interface ViewController ()

@property (nonatomic, weak) IBOutlet UIView *containerView;
@property (nonatomic, strong) UIImageView *ballView;

@end

@implementation ViewController

- (void)viewDidLoad
{
    [super viewDidLoad];
    //add ball image view
    UIImage *ballImage = [UIImage imageNamed:@"Ball.png"];
    self.ballView = [[UIImageView alloc] initWithImage:ballImage];
    [self.containerView addSubview:self.ballView];
    //animate
    [self animate];
}

- (void)touchesBegan:(NSSet *)touches withEvent:(UIEvent *)event
{
    //replay animation on tap
    [self animate];
}

- (void)animate
{
    //reset ball to top of screen
    self.ballView.center = CGPointMake(150, 32);
    //create keyframe animation
    CAKeyframeAnimation *animation = [CAKeyframeAnimation animation];
    animation.keyPath = @"position";
    animation.duration = 1.0;
    animation.delegate = self;
    animation.values = @[
                         [NSValue valueWithCGPoint:CGPointMake(150, 32)],
                         [NSValue valueWithCGPoint:CGPointMake(150, 268)],
                         [NSValue valueWithCGPoint:CGPointMake(150, 140)],
                         [NSValue valueWithCGPoint:CGPointMake(150, 268)],
                         [NSValue valueWithCGPoint:CGPointMake(150, 220)],
                         [NSValue valueWithCGPoint:CGPointMake(150, 268)],
                         [NSValue valueWithCGPoint:CGPointMake(150, 250)],
                         [NSValue valueWithCGPoint:CGPointMake(150, 268)]
                         ];

    animation.timingFunctions = @[
                                  [CAMediaTimingFunction functionWithName: kCAMediaTimingFunctionEaseIn],
                                  [CAMediaTimingFunction functionWithName: kCAMediaTimingFunctionEaseOut],
                                  [CAMediaTimingFunction functionWithName: kCAMediaTimingFunctionEaseIn],
                                  [CAMediaTimingFunction functionWithName: kCAMediaTimingFunctionEaseOut],
                                  [CAMediaTimingFunction functionWithName: kCAMediaTimingFunctionEaseIn],
                                  [CAMediaTimingFunction functionWithName: kCAMediaTimingFunctionEaseOut],
                                  [CAMediaTimingFunction functionWithName: kCAMediaTimingFunctionEaseIn]
                                  ];

    animation.keyTimes = @[@0.0, @0.3, @0.5, @0.7, @0.8, @0.9, @0.95, @1.0];
    //apply animation
    self.ballView.layer.position = CGPointMake(150, 268);
    [self.ballView.layer addAnimation:animation forKey:nil];
}

@end

 1 float interpolate(float from, float to, float time)
 2 {
 3     return (to - from) * time + from;
 4 }
 5 
 6 - (id)interpolateFromValue:(id)fromValue toValue:(id)toValue time:(float)time
 7 {
 8     if ([fromValue isKindOfClass:[NSValue class]]) {
 9         //get type
10         const char *type = [fromValue objCType];
11         if (strcmp(type, @encode(CGPoint)) == 0) {
12             CGPoint from = [fromValue CGPointValue];
13             CGPoint to = [toValue CGPointValue];
14             CGPoint result = CGPointMake(interpolate(from.x, to.x, time), interpolate(from.y, to.y, time));
15             return [NSValue valueWithCGPoint:result];
16         }
17     }
18     //provide safe default implementation
19     return (time < 0.5)? fromValue: toValue;
20 }
21 
22 - (void)animate
23 {
24     //reset ball to top of screen
25     self.ballView.center = CGPointMake(150, 32);
26     //set up animation parameters
27     NSValue *fromValue = [NSValue valueWithCGPoint:CGPointMake(150, 32)];
28     NSValue *toValue = [NSValue valueWithCGPoint:CGPointMake(150, 268)];
29     CFTimeInterval duration = 1.0;
30     //generate keyframes
31     NSInteger numFrames = duration * 60;
32     NSMutableArray *frames = [NSMutableArray array];
33     for (int i = 0; i < numFrames; i++) {
34         float time = 1 / (float)numFrames * i;
35         [frames addObject:[self interpolateFromValue:fromValue toValue:toValue time:time]];
36     }
37     //create keyframe animation
38     CAKeyframeAnimation *animation = [CAKeyframeAnimation animation];
39     animation.keyPath = @"position";
40     animation.duration = 1.0;
41     animation.delegate = self;
42     animation.values = frames;
43     //apply animation
44     [self.ballView.layer addAnimation:animation forKey:nil];
45 }

1 float quadraticEaseInOut(float t) 
2 {
3     return (t < 0.5)? (2 * t * t): (-2 * t * t) + (4 * t) - 1; 
4 }