Try using the CAKeyframeAnimation class.

Also see this question: CGPath Animation

However, based on your description, wanting an animation seems like it might not be what you want. IF the user is going to have 'live' control on the left/right slide being the location of the subview on the path, you might want to simply calculate the x/y of the path programatically, and apply the x/y values based only on the user's touches x value.

So, try using the NSBezierPath class to create your paths, then flatten them by calling bezierPathByFlatteningPath, finally, upon a touch that you want to update the view with, walk through the flattened path by looking at each 'elementAtIndex:associatedPoints' until you find the first one greater than your X value. The X/Y of that point will be the point you want to place your object.

Try using the CAKeyframeAnimation class.

Also see this question: CGPath Animation

However, based on your description, wanting an animation seems like it might not be what you want. IF the user is going to have 'live' control on the left/right slide being the location of the subview on the path, you might want to simply calculate the x/y of the path programatically, and apply the x/y values based only on the user's touches x value.

So, try using the NSBezierPath class to create your paths, then flatten them by calling bezierPathByFlatteningPath, finally, upon a touch that you want to update the view with, walk through the flattened path by looking at each 'elementAtIndex:associatedPoints' until you find the first one greater than your X value. The X/Y of that point will be the point you want to place your object.