iOS animate/morph shape from circle to square

Based on @Danchoys answer, here it is for Objective-C.

info is a button of 60px and infoVC is the next ViewController being pushed:

    UIBezierPath * maskPath = [UIBezierPath new];
    [maskPath addArcWithCenter:info.center radius:15.0f startAngle:DEGREES_TO_RADIANS(180) endAngle:DEGREES_TO_RADIANS(270) clockwise:true];
    [maskPath addArcWithCenter:info.center radius:15.0f startAngle:DEGREES_TO_RADIANS(270) endAngle:DEGREES_TO_RADIANS(0) clockwise:true];
    [maskPath addArcWithCenter:info.center radius:15.0f startAngle:DEGREES_TO_RADIANS(0) endAngle:DEGREES_TO_RADIANS(90) clockwise:true];
    [maskPath addArcWithCenter:info.center radius:15.0f startAngle:DEGREES_TO_RADIANS(90) endAngle:DEGREES_TO_RADIANS(180) clockwise:true];
    [maskPath closePath];

    UIBezierPath * endPath = [UIBezierPath new];
    [endPath moveToPoint:CGPointMake(0,0)];
    [endPath addLineToPoint:endPath.currentPoint];
    [endPath addLineToPoint:CGPointMake(w, 0)];
    [endPath addLineToPoint:endPath.currentPoint];
    [endPath addLineToPoint:CGPointMake(w, h)];
    [endPath addLineToPoint:endPath.currentPoint];
    [endPath addLineToPoint:CGPointMake(0, h)];
    [endPath addLineToPoint:endPath.currentPoint];
    [endPath closePath];

    CAShapeLayer *maskLayer = [CAShapeLayer layer];
    maskLayer.frame = info.bounds;
    maskLayer.path = maskPath.CGPath;
    _infoVC.view.layer.mask = maskLayer;

    CABasicAnimation * animation = [CABasicAnimation animationWithKeyPath:@"path"];
    animation.fromValue = (id)maskPath.CGPath;
    animation.toValue = (id)endPath.CGPath;
    animation.duration = 0.3f;
    [maskLayer addAnimation:animation forKey:nil];
    [maskLayer setPath:endPath.CGPath];

I know this is an old question but this might help someone.

I think its better to animate corner radius to get this effect.

    let v1 = UIView(frame: CGRect(x: 100, y: 100, width: 50, height: 50))
    v1.backgroundColor = UIColor.green
    view.addSubview(v1)

animation:

    let animation = CABasicAnimation(keyPath: "cornerRadius")
    animation.timingFunction = CAMediaTimingFunction(name: kCAMediaTimingFunctionLinear)
    animation.fillMode = kCAFillModeForwards
    animation.isRemovedOnCompletion = false
    animation.fromValue = v1.layer.cornerRadius
    animation.toValue = v1.bounds.width/2
    animation.duration = 3
    v1.layer.add(animation, forKey: "cornerRadius")

After playing with it for a little while in the playground I noticed that each arc adds two segments to the bezier path, not just one. Moreover, calling closePath adds two more. So to keep the number of segments consistent, I ended up with adding fake segments to my square path. The code is in Swift, but I think it doesn't matter.

func circlePathWithCenter(center: CGPoint, radius: CGFloat) -> UIBezierPath {
    let circlePath = UIBezierPath()
    circlePath.addArcWithCenter(center, radius: radius, startAngle: -CGFloat(M_PI), endAngle: -CGFloat(M_PI/2), clockwise: true)
    circlePath.addArcWithCenter(center, radius: radius, startAngle: -CGFloat(M_PI/2), endAngle: 0, clockwise: true)
    circlePath.addArcWithCenter(center, radius: radius, startAngle: 0, endAngle: CGFloat(M_PI/2), clockwise: true)
    circlePath.addArcWithCenter(center, radius: radius, startAngle: CGFloat(M_PI/2), endAngle: CGFloat(M_PI), clockwise: true)
    circlePath.closePath()
    return circlePath
}

func squarePathWithCenter(center: CGPoint, side: CGFloat) -> UIBezierPath {
    let squarePath = UIBezierPath()
    let startX = center.x - side / 2
    let startY = center.y - side / 2
    squarePath.moveToPoint(CGPoint(x: startX, y: startY))
    squarePath.addLineToPoint(squarePath.currentPoint)
    squarePath.addLineToPoint(CGPoint(x: startX + side, y: startY))
    squarePath.addLineToPoint(squarePath.currentPoint)
    squarePath.addLineToPoint(CGPoint(x: startX + side, y: startY + side))
    squarePath.addLineToPoint(squarePath.currentPoint)
    squarePath.addLineToPoint(CGPoint(x: startX, y: startY + side))
    squarePath.addLineToPoint(squarePath.currentPoint)
    squarePath.closePath()
    return squarePath
}