iOS: CAShape Layer Path Transformation

Question

I have used CAShape Layer before doing basic transformation on paths - from a smaller circle into a larger circle. Good enough, but then I tried to transform a

Answer 1

By carefully choosing your control points, etc, you can probably cook up a path which draws as a triangle, but which has the same number of segments and control points as the circle you want to draw. Like this (all numeric values assume iPhone screen, but the point is general):

@implementation ViewController
{
    CAShapeLayer* shapeLayer;
}

- (void)viewDidLoad
{
    [super viewDidLoad];
    // Do any additional setup after loading the view, typically from a nib.

    shapeLayer = [[CAShapeLayer alloc] init];

    CGRect bounds = self.view.bounds;
    bounds.origin.x += 0.25 * bounds.size.width;
    bounds.size.width *= 0.5;
    bounds.origin.y += 0.25 * bounds.size.height;
    bounds.size.height *= 0.5;

    shapeLayer.frame = bounds;
    shapeLayer.backgroundColor = [[UIColor redColor] CGColor];

    [self.view.layer addSublayer: shapeLayer];
    [self toCircle: nil];
}

CGPoint AveragePoints(CGPoint a, CGPoint b)
{
    return CGPointMake((a.x + b.x) * 0.5f, (a.y + b.y) * 0.5f);
}

- (IBAction)toCircle:(id)sender
{
    UIBezierPath* p = [[UIBezierPath alloc] init];

    [p moveToPoint: CGPointMake(80, 56)];
    [p addCurveToPoint:CGPointMake(144, 120) controlPoint1:CGPointMake(115.34622, 56) controlPoint2:CGPointMake(144, 84.653778)];
    [p addCurveToPoint:CGPointMake(135.42563, 152) controlPoint1:CGPointMake(144, 131.23434) controlPoint2:CGPointMake(141.0428, 142.27077)];
    [p addCurveToPoint:CGPointMake(48, 175.42563) controlPoint1:CGPointMake(117.75252, 182.61073) controlPoint2:CGPointMake(78.610725, 193.09874)];
    [p addCurveToPoint:CGPointMake(24.574375, 152) controlPoint1:CGPointMake(38.270771, 169.80846) controlPoint2:CGPointMake(30.191547, 161.72923)];
    [p addCurveToPoint:CGPointMake(47.999996, 64.574379) controlPoint1:CGPointMake(6.9012618, 121.38927) controlPoint2:CGPointMake(17.389269, 82.24749)];
    [p addCurveToPoint:CGPointMake(80, 56) controlPoint1:CGPointMake(57.729225, 58.957207) controlPoint2:CGPointMake(68.765656, 56)];
    [p closePath];

    [CATransaction begin];
    CABasicAnimation *pathAnimation = [CABasicAnimation animationWithKeyPath:@"path"];
    pathAnimation.duration = 3.f;
    pathAnimation.fromValue = (id)shapeLayer.path;
    pathAnimation.toValue = (id)p.CGPath;
    [shapeLayer addAnimation:pathAnimation forKey:@"path"];
    [CATransaction setCompletionBlock:^{
        shapeLayer.path = p.CGPath;
    }];
    [CATransaction commit];

    double delayInSeconds = 4.0;
    dispatch_time_t popTime = dispatch_time(DISPATCH_TIME_NOW, (int64_t)(delayInSeconds * NSEC_PER_SEC));
    dispatch_after(popTime, dispatch_get_main_queue(), ^(void){
        [self toTriangle: nil];
    });

}

- (IBAction)toTriangle: (id)sender
{
    UIBezierPath* p = [[UIBezierPath alloc] init];

    // Triangle using the same number and kind of points...
    [p moveToPoint: CGPointMake(80, 56)];
    [p addCurveToPoint: AveragePoints(CGPointMake(80, 56), CGPointMake(135.42563, 152))  controlPoint1:CGPointMake(80, 56) controlPoint2:AveragePoints(CGPointMake(80, 56), CGPointMake(135.42563, 152))];
    [p addCurveToPoint:CGPointMake(135.42563, 152) controlPoint1:AveragePoints(CGPointMake(80, 56), CGPointMake(135.42563, 152)) controlPoint2:CGPointMake(135.42563, 152)];
    [p addCurveToPoint:AveragePoints(CGPointMake(135.42563, 152), CGPointMake(24.574375, 152)) controlPoint1:CGPointMake(135.42563, 152) controlPoint2:AveragePoints(CGPointMake(135.42563, 152), CGPointMake(24.574375, 152))];
    [p addCurveToPoint:CGPointMake(24.574375, 152) controlPoint1:AveragePoints(CGPointMake(135.42563, 152), CGPointMake(24.574375, 152)) controlPoint2:CGPointMake(24.574375, 152)];
    [p addCurveToPoint: AveragePoints(CGPointMake(24.574375, 152),CGPointMake(80, 56)) controlPoint1:CGPointMake(24.574375, 152) controlPoint2:AveragePoints(CGPointMake(24.574375, 152),CGPointMake(80, 56)) ];
    [p addCurveToPoint:CGPointMake(80, 56) controlPoint1:AveragePoints(CGPointMake(24.574375, 152),CGPointMake(80, 56)) controlPoint2:CGPointMake(80, 56)];
    [p closePath];

    [CATransaction begin];
    CABasicAnimation *pathAnimation = [CABasicAnimation animationWithKeyPath:@"path"];
    pathAnimation.duration = 3.f;
    pathAnimation.fromValue = (id)shapeLayer.path;
    pathAnimation.toValue = (id)p.CGPath;
    [shapeLayer addAnimation:pathAnimation forKey:@"path"];
    [CATransaction setCompletionBlock:^{
        shapeLayer.path = p.CGPath;
    }];
    [CATransaction commit];

    double delayInSeconds = 4.0;
    dispatch_time_t popTime = dispatch_time(DISPATCH_TIME_NOW, (int64_t)(delayInSeconds * NSEC_PER_SEC));
    dispatch_after(popTime, dispatch_get_main_queue(), ^(void){
        [self toCircle: nil];
    });

}

Even with the number of segments and control points being the same, the animation still looks a little wonky and probably isn't what you wanted. The reason for that is that CA seems to be matching up all the segments and control points one-to-one and then linearly interpolating between them for all points. Because the relationship between control points and the resulting path is not linear (cubic in this case), interpolating control point positions linearly isn't going to result in the path moving in a linear fashion. If you run this code, you can see that as it transitions, there are weird humps in the side of the triangle where the circle path had other points in the arc.

More generally, it's just not going to be reasonable to expect CA to magically morph between two arbitrary paths in some specific way that turns out to be desirable in appearance. Even going to the effort to hand construct these paths such that they might have a prayer of morphing, they still failed to look like I thought they should.

It might be more reasonable to achieve the desired effects by working with flattened paths (i.e. paths made up of many small straight lines instead of curved path elements). Even that seems like it would be non-trivial, since you would, again, need both paths to have the same number of segments, and you would have to construct those segments such that the common points were the right number of segments along the whole path.

In sum: This is a fairly complex problem and the naive/free solution that CoreAnimation has provided is unlikely to what you want.

Answer 2

From the documentation of the path property on CAShapeLayer:

If the two paths have a different number of control points or segments the results are undefined.

So yes, I would say that this is expected since a circle and a triangle are different shapes.

This article describe custom path animations in great detail.

Answer 3

I'm guessing here! You can define a circle using 3 points. That way you will have the same number of points as the triangle. To define the circle this will be your best friend

+ (UIBezierPath *)bezierPathWithArcCenter:(CGPoint)center radius:(CGFloat)radius startAngle:(CGFloat)startAngle endAngle:(CGFloat)endAngle clockwise:(BOOL)clockwise;