EsportToys
Joined 4 years ago
Karma
176
Submissions
79
Member since
Jul 23
Recent submissions
Comment · 8 months ago
Comment · 1 year ago
I wrote https://github.com/EsportToys/TPMouse a while back with the “grid mode” that moves the mouse cursor by bisecting the screen coordinate incrementally.
Comment · 1 year ago
Nice, it's also a great test for my https://github.com/EsportToys/LibreScroll
Comment · 1 year ago
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.
Comment · 1 year ago
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.
Comment · 1 year ago
It’s the general solution to a damped harmonic oscillator/mass-spring-damper system:
m * x’’ + c * x’ + k * x = f(t)
Comment · 1 year ago
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
Comment · 2 years ago
Seconded for Love2D, here's a sample of how simple it is to quickly whip up something in it:
Comment · 3 years ago
Speaking of 2nd-order linear ODEs w/ const factor (a.k.a. mass-spring-damper systems), I wrote a blog post[0] deriving all possible general solutions in a concise matrix that makes it easily implementable in code.
The following is the complete solution in Lua:
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
https://github.com/esporttoys/librescroll