My client wants part of the animation I'm working on to be from the point of view of the camera, as if in a vehicle and moving forward. While moving forward, objects go from being far away, to closer and finally are passed. Let's call them mile markers.
Here's the rub. In the real world, if you travel toward and object and then pass it, that object has an evolving apparent size. When it's far, it's small. As you approach, it appears larger. This apparent size change happens slowly (mile markers way down the road don't seem to change much), but increases in "apparent size" growth rate as it gets closer.
In AE, the apparent size growth seems to work in reverse. The far away mile markers grow quickly and this growth slows as they get closer. I've tried a 3D comp with a camera keyframed to move in a straight ahead direction while the "mile markers" are stationary. I've also tried a more simplistic 2D comp with mile markers changing scale. Both methods work opposite to real life.
So, undaunted, I tried to adjust keyframes. I tried placing temporally equidistant keyframes and adjusting their values, as well as equally spaced keyframes spacially while adjusting their place in the timeline. I even tried a little of both. I could get nowhere near a natural look...my client agrees.
I dove into the math, tho it has been years. I think there is a direct relationship between the object's apparent size as a function of time and a parabola. I reviewed a couple semesters' worth of trig and geometry, thinking I had it licked, but it is either not the right method, or is over my aging head.
This situation must have been encountered before me (even tho I found no posts relating). Tell me there is an easy answer, oh gurus of everything AE.
I believe I may have stumbled into the answer. Was too anxious to post this news, so I haven't looked at what I stumbled into more closely, but it must be the way. And it is so much easier than what I was trying before.