I use the page to test scrolling.
Nice, it's also a great test for my https://github.com/EsportToys/LibreScroll
Readit NewsEsportToys commented on Physically Based Rendering in Filament google.github.io/filament... · Posted by u/indigo945
EsportToys commented on I'm Unsatisfied with Easing Functions davepagurek.com/blog/easi... · Posted by u/ndyg
true! I suppose you'd risk getting some oscillations in the anticipation depending on the scale of the force, but that could be desirable, or might not happen if the scale is small enough, and certainly makes the math a little easier
You can trivially calculate the time-to-peak overshoot using the closed form equation. It’s the first (0-indexed) zero of the velocity response, i.e. happens at t = (pi / scale)
And obviously it would only apply for the underdamped case.
EsportToys commented on I'm Unsatisfied with Easing Functions davepagurek.com/blog/easi... · Posted by u/ndyg
I don't imagine stepping through the ODE with finite differences at the same time step as drawing should be very expensive, essentially it's a handful of sums and products. In fact, using a closed form solution with an exponential is probably more expensive.
A middleground is to use fixed timesteps with the closed form solution. Then the integration factors can be statically precomputed as constants, and every frame becomes just a 2x2 matrix multiplication.
And even if you are to calculate the integration factors based on dynamic frame rates, they only need to be computed just once per frame for all objects that share the same damping configuration.
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EsportToys commented on I'm Unsatisfied with Easing Functions davepagurek.com/blog/easi... · Posted by u/ndyg
Wow, this is excellent!
Is there a name for this kind of motion? I'd love to use it sometime.
It’s the general solution to a damped harmonic oscillator/mass-spring-damper system:
m * x’’ + c * x’ + k * x = f(t)
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EsportToys commented on I'm Unsatisfied with Easing Functions davepagurek.com/blog/easi... · Posted by u/ndyg
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.sin( scale*t)/scale , math.cos( scale*t)
elseif resid>0 then
T1,T0 = math.sinh(scale*t)/scale , math.cosh(scale*t)
end
local dissipation = math.exp(-decay*t)
local evolved_pos = dissipation*( pos*(T0+T1*decay) + vel*( T1 ) )
local evolved_vel = dissipation*( pos*(-T1*omega^2) + vel*(T0-T1*decay) )
return evolved_pos , evolved_vel
end