The Perfect Wiggler

--By Quaternions
--localize
local abs=math.abs
local ceil=math.ceil
local min,max=math.min,math.max
local sqrt=math.sqrt
local tan=math.tan

local bit=bit

local insert,remove=table.insert,table.remove

local tick=SysTime
local Angle=Angle
local IsBtn=input.IsMouseDown

local Degree=math.pi/180

local IN_FORWARD=8
local IN_BACK=16
local IN_MOVELEFT=512
local IN_MOVERIGHT=1024
local IN_SPEED=131072
local MOUSE_LEFT=107

local P=LocalPlayer()
local Aspect=ScrH()/ScrW()/tan(P:GetFOV()*Degree/2)

--Settings
local Calibrating=true

local MaxAngleSeconds=0.07
local AveragingDuration=0.1
local MinAveragingFrames=8

local DirectionBarWidth=30
local DirectionBarHeight=300

local DirectionBarColour=Color(75,191,50,128)

--Ongoing collected data
local Data={}
local DataOverwrite=0
local ConsecutiveValidFrames=0
local _00,_01,_10,_11,_0,_1=0,0,0,0,0,0--Used to calculate linear least squares fit of equation constants

--Previous frame data
local Wiggling=false
local LastTime=tick()
local LastAngle=P:EyeAngles().y
local LastVelocity=P:GetAbsVelocity():Length2D()
local CurrentAveragingFrames=0

--Previouse motion data
local LastTime2=LastTime
local TotalAngle
local StrafeDirection=1
local RealAngles
local LastViewAngles

--Make GUI
local RealDirection=vgui.Create("DPanel")
RealDirection:SetSize(DirectionBarWidth,DirectionBarHeight)
RealDirection:SetPos(ScrW()/2-DirectionBarWidth/2,0)
RealDirection:SetBackgroundColor(DirectionBarColour)
RealDirection:SetAlpha(0)

hook.Add("PreDrawHUD","UpdateWiggler",function()
    local CurrentTime=tick()
    local FramePeriod=CurrentTime-LastTime
    local DesiredAveragingFrames=max(MinAveragingFrames,ceil(AveragingDuration/FramePeriod))
    local Velocity=P:GetAbsVelocity()
    local CurrentAngle=P:EyeAngles().y
    local CurrentVelocity=Velocity:Length2D()
    local CurrentYawspeed=((CurrentAngle-LastAngle+180)%360-180)/FramePeriod
    local CurrentAcceleration=(CurrentVelocity-LastVelocity)/FramePeriod

    if DesiredAveragingFrames>CurrentAveragingFrames then
        CurrentAveragingFrames=CurrentAveragingFrames+1
        DataOverwrite=DataOverwrite+1
        insert(Data,DataOverwrite,{v=LastVelocity,w=abs(CurrentYawspeed),a=CurrentAcceleration})
    elseif DesiredAveragingFrames<CurrentAveragingFrames then
        remove(Data,DataOverwrite%CurrentAveragingFrames+1)
        CurrentAveragingFrames=CurrentAveragingFrames-1
        if DataOverwrite>=CurrentAveragingFrames then
            DataOverwrite=1
        else
            DataOverwrite=DataOverwrite+1
        end
        Data[DataOverwrite]={v=LastVelocity,w=abs(CurrentYawspeed),a=CurrentAcceleration}
    else
        DataOverwrite=DataOverwrite%CurrentAveragingFrames+1
        Data[DataOverwrite]={v=LastVelocity,w=abs(CurrentYawspeed),a=CurrentAcceleration}
    end

    if Calibrating then
        local EyeAngle=Angle(0,CurrentAngle,0)
        local ControlDirection=EyeAngle:Forward()*((P:KeyDown(IN_FORWARD)and 1 or 0)-(P:KeyDown(IN_BACK)and 1 or 0))+EyeAngle:Right()*((P:KeyDown(IN_MOVERIGHT)and 1 or 0)-(P:KeyDown(IN_MOVELEFT)and 1 or 0))
        local ValidFrame=false
        if CurrentYawspeed~=0 and CurrentAcceleration>0 and not P:OnGround() and CurrentVelocity>0 then
            local cx,cy=ControlDirection.x,ControlDirection.y
            local c2=cx*cx+cy*cy
            if c2>0 then
                local vc=Velocity.x*cx+Velocity.y*cy
                if vc*vc/(c2*CurrentVelocity*CurrentVelocity)<0.0025 then --If the control direction is (approximately) perpendicular to the velocity
                    ValidFrame=true
                end
            end
        end
        if ValidFrame then
            ConsecutiveValidFrames=ConsecutiveValidFrames+1
            if ConsecutiveValidFrames>=CurrentAveragingFrames then
                local v,w,a=0,0,0
                for i=1,CurrentAveragingFrames do
                    local d=Data[i]
                    v,w,a=v+d.v,w+d.w,a+d.a
                end
                v,w,a=v/CurrentAveragingFrames,w/CurrentAveragingFrames,a/CurrentAveragingFrames
                local w2=w*w
                _0=_0-a*w
                _00=_00+w2
                _01=_01-v*w*w2
                _1=_1+a*v*w2
                _10=_10-v*w*w2
                _11=_11+v*v*w2*w2
            end
        elseif ConsecutiveValidFrames>0 then
            ConsecutiveValidFrames=0
        end
    end

    if TotalAngle and RealAngles then
        local RelativeAngle=(RealAngles.y-TotalAngle+180)%360-180
        RealDirection:SetAlpha(255)
        RealDirection:SetPos((ScrW()-DirectionBarWidth)*(0.5-Aspect*tan(RelativeAngle*Degree)/2),0)
    else
        RealDirection:SetAlpha(0)
    end
    LastTime,LastAngle,LastVelocity=CurrentTime,CurrentAngle,CurrentVelocity
end)

hook.Add("CreateMove","Wiggle",function(cmd)
    local CurrentTime=tick()
    local FramePeriod=CurrentTime-LastTime2

    --Autohop
    if not P:OnGround() then
        cmd:SetButtons(bit.band(cmd:GetButtons(),bit.bnot(IN_JUMP)))
    end

    if cmd:KeyDown(IN_SPEED) and (Wiggling or not P:OnGround()) then
        if Wiggling then
            local InputAngles=cmd:GetViewAngles()
            RealAngles=RealAngles+InputAngles-LastViewAngles
        else
            RealAngles=cmd:GetViewAngles()
            TotalAngle=RealAngles.y
            LastViewAngles=RealAngles
            Wiggling=true
        end
        local p=(_0*_11-_1*_01)/(_1*_00-_0*_10)
        local v=P:GetAbsVelocity():Length2D()
        if p==p and v>0 then
            local w=p/(2*v)
            local RelativeAngle=(RealAngles.y-TotalAngle+180)%360-180
            StrafeDirection=RelativeAngle>w*MaxAngleSeconds and 1 or RelativeAngle<-w*MaxAngleSeconds and -1 or StrafeDirection
            local AngleIncrement=StrafeDirection*abs(w*FramePeriod)
            TotalAngle=TotalAngle+AngleIncrement
            local NewAngle=Angle(RealAngles.p,TotalAngle,RealAngles.r)
            cmd:SetViewAngles(NewAngle)
            if StrafeDirection>0 then
                cmd:SetButtons(bit.bor(bit.band(cmd:GetButtons(),bit.bnot(IN_MOVELEFT)),IN_MOVERIGHT))
            else
                cmd:SetButtons(bit.bor(bit.band(cmd:GetButtons(),bit.bnot(IN_MOVERIGHT)),IN_MOVELEFT))
            end
            cmd:SetSideMove((StrafeDirection>0 and 1 or StrafeDirection<0 and -1 or 0)*-10000)
            LastViewAngles=NewAngle
        end
    elseif Wiggling then
        Wiggling=false
        RealAngles=nil
        TotalAngle=nil
    end
    LastTime2=CurrentTime
end)