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local function Polar( x, y )
local arctan = math.atan2( y, x )
--maybe we don't need this line?
--if arctan < 0.0 then arctan = arctan + 2.0 * math.pi end
return math.sqrt( x * x + y * y ), arctan
end
local function tPolar( t )
return Polar( t.x, t.y )
end
local function LerpWave( cur, new, alpha, x )
local a = cur:Interpolate( x )
local b = new:Interpolate( x )
return alpha * b + ( 1.0 - alpha ) * a
end
--Peak of alpha * cur + (1 - alpha) * new on interval [xi, xf]
local function GetMinimum( cur, new, alpha, xi, xf )
local ri, rf = LerpWave( cur, new, alpha, xi ), LerpWave( cur, new, alpha, xf )
local xm = 0.5 * ( xi + xf )
local rm = LerpWave( cur, new, alpha, 0.5 * ( xi + xf ) )
return math.min( ri, rf )
end
local function GetTimeFromAlpha( alpha, curM, newM )
return alpha * newM.t + ( 1.0 - alpha ) * curM.t
end
local function DetectCollision( curMarble, newMarble, curWave, newWave )
local t, dt, r, th, normal
--Polar coordinates:
local iRadius, iTheta = tPolar( curMarble )
local fRadius, fTheta = tPolar( newMarble )
local iWaveRadius = curWave:Interpolate( iTheta )
local fWaveRadius = curWave:Interpolate( fTheta )
local speed = newMarble.dx * newMarble.dx + newMarble.dy * newMarble.dy
--Case 1: marble is already outside the curve.
if iRadius > iWaveRadius then
return {
speed = speed,
dt = newMarble.t - curMarble.t,
t = curMarble.t,
r = iWaveRadius,
th = iTheta,
normal = iTheta - math.atan( curWave:Derivative( iTheta ) ), }
end
--Case 2: marble is outside the curve by tick end.
if fRadius > fWaveRadius then
--This isn't right, fix later.
return {
speed = speed,
dt = 0,
t = newMarble.t,
r = fWaveRadius,
th = fTheta,
normal = fTheta - math.atan( curWave:Derivative( iTheta ) ) }
end
--Case 3: check whether marble passed through analog peak.
--Case 4: marble must have remained inside curve.
return
end
return DetectCollision