Hey guys, seen a lot of confusion around camera springs as it relates to physics jitter, just want to clear up this issue.
The main problem:
This is an infographic of the roblox render pipeline, most configurations of camera springs use .RenderStepped which updates earlier than physics, creating a jitter effect you can see in this video: unknown_2021.11.21-17.41
The fix:
If you update camera movement on .Stepped instead, it will be in sync with the physics updates.
(don’t worry if you don’t understand the math jargon which I borrowed from several kind and smart robloxians mentioned below)
Hope this helps!
--[[
modified by SaltyPotter to include orientation
borrowed math and ideas from: @fractality, @Validark, @Quenty, @XAXA, @EgoMoose
use cases:
Camera following anything physics-based (without jitter issues):
---- I'm using dictionaries to send CFrame information ----
local position={RightVector=startCF.RightVector, UpVector=startCF.UpVector, Position=startCF.Position}
local velocity={RightVector=Vector3.new(), UpVector=Vector3.new(), Position=Vector3.new()}
local goal={RightVector=goalCF.RightVector, UpVector=goalCF.UpVector, Position=goalCF.Position}
local spring=springModule.new(position, velocity, goal)
---- you can adjust the frequency and dampness to your liking, i found a 2:1 profile is a nice smooth effect ----
spring.frequency=2
spring.dampener=1
runservice.Stepped:Connect(function(t, dt)
---- update the goal every step ----
spring.goal={RightVector=goalCF.RightVector, UpVector=goalCF.UpVector, Position=goalCF.Position}
---- call :update(), it returns a CFrame ----
camera.CFrame=spring:update(dt)
end)
other:
same as above, but you can use .RenderStepped since there's no physics involved
]]
local spring={}
spring.__index=spring
local tau = math.pi * 2
local exp = math.exp
local sin = math.sin
local cos = math.cos
local sqrt = math.sqrt
local EPSILON = 1e-4
function spring.new(position:{},velocity:{},goal:{})
setmetatable({},spring)
spring.position=position
spring.velocity=velocity
spring.goal=goal
spring.frequency=10
spring.dampener=1
return spring
end
function spring:adjust(key:string,dt:number)
local dampingRatio = self.dampener
local angularFrequency = self.frequency * tau
local goal = self.goal[key]
local p0 = self.position[key]
local v0 = self.velocity[key]
local offset = p0 - goal
local decay = exp(-dampingRatio * angularFrequency * dt)
local position
if dampingRatio == 1 then -- Critically damped
position = (offset * (1 + angularFrequency * dt) + v0 * dt) * decay + goal
self.velocity[key] = (v0 * (1 - angularFrequency * dt) - offset * (angularFrequency * angularFrequency * dt)) * decay
elseif dampingRatio < 1 then -- Underdamped
local e = 1 - dampingRatio * dampingRatio
local c = sqrt(e)
local y = angularFrequency * c
local i = cos(y * dt)
local j = sin(y * dt)
-- Damping ratios approaching 1 can cause division by small numbers.
-- To fix that, group terms around z=j/c and find an approximation for z.
-- Start with the definition of z:
-- z = sin(dt*angularFrequency*c)/c
-- Substitute a=dt*angularFrequency:
-- z = sin(a*c)/c
-- Take the Maclaurin expansion of z with respect to c:
-- z = a - (a^3*c^2)/6 + (a^5*c^4)/120 + O(c^6)
-- z ≈ a - (a^3*c^2)/6 + (a^5*c^4)/120
-- Rewrite in Horner form:
-- z ≈ a + ((a*a)*(c*c)*(c*c)/20 - c*c)*(a*a*a)/6
local z
if c > EPSILON then
z = j / c
else
local a = dt * angularFrequency
local a_2 = a * a
z = a * (((e*e * a_2 - 20*e) / 120) * a_2 + 1)
end
-- Frequencies approaching 0 present a similar problem.
-- We want an approximation for y as angularFrequency approaches 0, where:
-- y = sin(dt*angularFrequency*c)/(angularFrequency*c)
-- Substitute b=dt*c:
-- y = sin(b*c)/b
-- Now reapply the process from z.
if y > EPSILON then
y = j / y
else
local b = y * y
local dd = dt * dt
y = dt * (dd * (b*b*dd / 20 - b) / 6 + 1)
end
local ze = z * dampingRatio
position = (offset * (i + ze) + v0 * y) * decay + goal
self.velocity[key] = (v0 * (i - ze) - offset * (z * angularFrequency)) * decay
else -- Overdamped
local x = -angularFrequency * dampingRatio
local y = angularFrequency * sqrt(dampingRatio * dampingRatio - 1)
local r1 = x + y
local r2 = x - y
local co2 = (v0 - offset * r1) / (2 * y)
local co1 = offset - co2
local e1 = co1 * exp(r1 * dt)
local e2 = co2 * exp(r2 * dt)
position = e1 + e2 + goal
self.velocity[key] = e1 * r1 + e2 * r2
end
self.position[key] = position
end
function spring:update(dt:number)
local t={}
for key,_ in self.goal do
spring:adjust(key,dt)
t[key]=self.position[key]
end
return CFrame.fromMatrix(t.Position,t.RightVector,t.UpVector):Orthonormalize()
end
return spring
