https://youtu.be/CTTCf79MgDY?t=7073

So, in order to smoothly zoom irrespective of how far and or close Casey is to the focused object. He, basically writes the camera velocity as a function of current distance from the object * constant.

I understand that the camera velocity should be proportional to the distance from the object; in other words, as the camera gets further away it needs to move more and more to zoom by the same amount. One of my questions is why do we know the relationship is one of

**linear**proportionality as opposed to some other proportionality relationship. Is this due to how perspective projection works? i.e. suppose z is the forward direction, if you slice a plane through any z, the area of the plane increases linearly.

Second, Casey mentioned that instead of taking the distance from the object as (camerapos - objpos) and multiplying by a constant we would want to actually solve the differential equation since our velocity is only instantaneously correct. EG: moving the mouse by 2 pixels, corresponds to a different zoom, than moving it by 1 pixel 2 times. Is this because our velocity should be changing over the 2 movements of the camera, and we need to actually be integrating the differential velocity equation over those 2 movements to get a position that accounts for the changing velocity as we go, as opposed to using the same velocity for both?

Sorry, if the question is confusing, but it has been over a decade since I've done any calculus haha.