The Highest Point for bouncing Mac Application Icons

[dakota224]

When Mac application icons are bouncing in the dock, does their velocity = 0 at their highest point?

Here's what it looks like when you open a new application for Mac if you're not familiar.

Another way I'm thinking about it: What if you have a strip of LED lights and its on a chase pattern going back and forth. Would the velocity of the 'whatever' going back and forth drop to 0 when it switched direction? And isn't that essentially what the app icon is? LEDs lighting up/down?

One answer I've gotten in discussion: "So let's say you capture every frame of the icon moving up and down. You flip through them one at a time. You may or may not see two identical frames where the icon stays put. But if you could render at an infinite frame rate, eventually you would find two identical frames where the icon hadn't moved. I think the simplest answer is graph velocity vs time. When moving up you have a positive velocity and when moving down you have a negative velocity. Move your finger along that graph from the positive to the negative and never cross through zero. Good luck with that."

 

[billy_joule]

Another way I'm thinking about it: What if you have a strip of LED lights and its on a chase pattern going back and forth. Would the velocity of the 'whatever' going back and forth drop to 0 when it switched direction? And isn't that essentially what the app icon is? LEDs lighting up/down?

Why overcomplicate things?
Like the answer you've received states, to transition from positive to negative velocity you must pass through zero.
That is,a bouncing ball moving upwards must come to a stop before it can move downward. And of course that is the highest point the ball reaches and it could be shown by integrating v(t) to get d(t), the maxima and minima of d(t) will coincidence with the points where v(t)=0.

 

[A.T.]

When Mac application icons are bouncing in the dock, does their velocity = 0 at their highest point?

Ho do you define velocity for dicrete cases like this? You could argue the velocity is 0 at every frame, for the duration of a frame, and then switches to the next frame.

 

[sophiecentaur]

The sampled motion can (ideally) be reconstructed in your brain (or by computer) using the samples to create the effect of continuous motion again. All that's necessary is for the sampling to be at a high enough rate (see Nyquist criterion). An appropriate low pass filter is the required (interpolating) function to perform on the samples and it can produce a point in the motion that is actually higher than the two points on either side. The same principle applies to all signal sampling and reconstitution - spatial (digital photographs) , temporal (digital music) or both together (digital TV).

 

[sophiecentaur]

But if you could render at an infinite frame rate, eventually you would find two identical frames where the icon hadn't moved.

I just read this again. You don't actually need to sample this fast to be able to get perfect reconstruction. It would be way over the top, to send or store so many samples. (GB/s, when kB/s would do).