11–20 of 88 posts
Apple's easing function (like others) is parameterized by physical characteristics (e.g. spring force, damping) that are easier to model from first principles, but there are other parameters (overshoot distance, anticipation size, animation time) that are more useful for animation. A closed-form parametrization with the latter might be tricky to derive, but some kind of iterative solver (plug in desired animation par…
Oscullation/"anticipation" in transitions is so gimmicky and cartoonish. Living things don't move like that, and mechanical things don't unless they are broken, chintzy, or poorly designed (underdamped).
I took your PD controller concept and added anticipation using two targets: the original mouse target, and an "anticipation" target set proportionally based on the distance from the point to the main target[1].
This also made me think of Jelly Car and the amazing simulations they did using rigid frames for soft bodies, called Shape Matching[2]. Instead of simulating the soft body physics directly, they used a frame, springs, and "gas" to constrain points, which moved towards targets fixed to the frame.
[1]: https://editor.p5js.org/Thomascountz/sketches/YXWm_VV6s
[2]: https://www.gamedeveloper.com/programming/deep-dive-the-soft...
Closed-form (non-iterative) PID solution: https://www.desmos.com/calculator/mu80ttc9aa function sprung_response(t,pos,vel,k,c,m) local decay = c/2/m local omega = math.sqrt(k/m) local resid = decay*decay-omega*omega local scale = math.sqrt(math.abs(resid)) local T1,T0 = t , 1 if resid 0 then T1,T0 = math.sinh(scale*t)/scale , math.cosh(scale*t) end local dissipation = math.exp(-decay*t) local evolved_pos = dissipatio…
Oscullation/"anticipation" in transitions is so gimmicky and cartoonish. Living things don't move like that, and mechanical things don't unless they are broken, chintzy, or poorly designed (underdamped).
We see this, not only in mammals and muscles, but in organic systems which evolved to trade speed for power by storing mechanical, electrical, or chemical potential energy over time.
Overshoot and damping is the same in reverse: dissipating kinetic energy when you, for example, bend your knees when you land from a jump (hopefully).
Closed-form (non-iterative) PID solution: https://www.desmos.com/calculator/mu80ttc9aa function sprung_response(t,pos,vel,k,c,m) local decay = c/2/m local omega = math.sqrt(k/m) local resid = decay*decay-omega*omega local scale = math.sqrt(math.abs(resid)) local T1,T0 = t , 1 if resid 0 then T1,T0 = math.sinh(scale*t)/scale , math.cosh(scale*t) end local dissipation = math.exp(-decay*t) local evolved_pos = dissipatio…
Is there a name for this kind of motion? I'd love to use it sometime.
Closed-form (non-iterative) PID solution: https://www.desmos.com/calculator/mu80ttc9aa function sprung_response(t,pos,vel,k,c,m) local decay = c/2/m local omega = math.sqrt(k/m) local resid = decay*decay-omega*omega local scale = math.sqrt(math.abs(resid)) local T1,T0 = t , 1 if resid 0 then T1,T0 = math.sinh(scale*t)/scale , math.cosh(scale*t) end local dissipation = math.exp(-decay*t) local evolved_pos = dissipatio…
Wow, this is excellent! Is there a name for this kind of motion? I'd love to use it sometime.
m * x’’ + c * x’ + k * x = f(t)
I've posted this before for other reasons but https://www.luduxia.com/showdown/ - in this case everything is easing functions, except for, bizarrely, the giant text that announces win/draw and the text inside the counter, which is done with actual physics because that proves better, especially with constantly moving targets.
https://github.com/franciscop/ola
Note: ola means (sea) wave in Spanish