Fixed second derivative bug! Looks good now; breaking up Update function for better encapsulation during collision detection.

collision.lua

@@ -1,9 +1,6 @@
-local function DetectCollision(
-  xi, yi, vx, vy, xf, yf,
-  GetRadius,
-  GetRadialDerivative)
-  
-
+local function DetectCollision( curMarble, newMarble, curWave, newWave )
+  local t, r, th, normal
+  if t then return { t = t, r = r, th = th, normal = normal } end
 end
 
 return DetectCollision

main.lua

@@ -1,10 +1,10 @@
 local love = love
-step = 1.0 / 120.0
-local step = step
+local step = 1.0 / 120.0
 local sitelenpona
 local text
 local marble
 local wave
+local DetectCollision
 
 local sounds = {
 
@@ -76,6 +76,7 @@ function love.load()
   text = assert( require "text" )
   marble = assert( require "marble" )
   wave = assert( require "wave" )
+  DetectCollision = assert ( require "collision" )
   return state.Reset()
 
 end
@@ -129,22 +130,26 @@ local function OnImpact( impact )
   local score = BeatScore( impact.t )
   --DEBUG
   state.lastBeatScore = score
+
+  local sound
   if score > state.beatScoreThreshold then
+    sound = sounds.goodPing
 
     state.beatScoreThreshold = 1.0
     state.currentBeat = state.currentBeat + 1
     if state.currentBeat >= 120 then
       return OnVictory()
     end
-    love.audio.play(sounds.goodPing)
+
 
   else
 
+    sound = sounds.badPing
     state.beatScoreThreshold = state.beatScoreThreshold - 0.05
-    love.audio.play(sounds.badPing)
+
   end
 
-
+  love.audio.play( sound )
 end
 
 
@@ -165,7 +170,7 @@ function love.draw()
   wave.Draw()
   love.graphics.pop()
 
-   sitelenpona.Draw( text.tok[state.currentBeat] )
+  sitelenpona.Draw( text.tok[state.currentBeat] )
 
   marble.Draw()
 
@@ -177,8 +182,9 @@ end
 function love.update( dt )
   dt = dt + state.timeToSimulate
   while dt > step do
-    marble.Update()
-    wave.Update()
+    marble.Integrate( step )
+    wave.Integrate( step )
+
     dt = dt - step
   end
   state.timeToSimulate = dt

marble.lua

@@ -3,14 +3,21 @@ local love = love
 --local wave = assert( require "wave" )
 local oldBuffer = love.graphics.newCanvas()
 local newBuffer = love.graphics.newCanvas()
-local step = assert( step )
 local state 
 local FRICTION = 0.01
 local MAXSPEED = 5.0
 
 local t, x, y, dx, dy, ddx, ddy
 
+local function OnImpact( impact )
+  
+end
+
 local function Update()
+  
+end
+
+local function Integrate( step )
   t = love.timer.getTime()
 
   dx = (1.0 - FRICTION) * dx + FRICTION * ddx
@@ -95,6 +102,8 @@ end
 Reset()
 
 return {
+  Integrate = Integrate,
+  OnImpact = OnImpact,
   Update = Update,
   OnKey = OnKey,
   Draw = Draw,

wave.lua

@@ -1,8 +1,7 @@
 --Render and simulate 1D wave equation.
 local love = love
-local step = assert( step )
 
-local N = 25
+local N = 11
 
 --Calculate discrete fourier transform of radius function.
 local DFT
@@ -80,11 +79,11 @@ local SecondDerivative = function( wave, x )
   local y = 0
 
   for k = 1, N / 2 do
-    local c, s = k * k * math.cos( x * k ), k * k * math.sin( x * k )
+    local c, s = -k * k * math.cos( x * k ), -k * k * math.sin( x * k )
     y = y
-    - c * re[k + 1]
+    + c * re[k + 1]
     - s * im[k + 1]
-    - c * re[N - k + 1]
+    + c * re[N - k + 1]
     + s * im[N - k + 1]
 
   end
@@ -119,7 +118,7 @@ local mt = { __index = {
 
 local function Wave( )
   local t = {
-    --radii[k] = radius of point on curve at angle (k - 1) / 13
+    --radii[k] = radius of point on curve at angle (k - 1) / N
     radii = {},
     --TIME derivative of radius
     vrad = {},
@@ -130,7 +129,7 @@ local function Wave( )
   }
 
   for i = 1, N do
-    t.radii[i] = 1.0
+    t.radii[i] = 0.3 * math.sin( i * 2.0 * math.pi / N  )
     t.vrad[i] = 0.0
   end
   DFT( t )
@@ -162,23 +161,27 @@ local function Draw()
     
     for k = 0.1, 1.0, 0.1 do
       --Interpolant.
-      love.graphics.setColor( 1.0, 0, 0, 0.5 )
+      love.graphics.setColor( 1.0, 0, 0, 0.7 )
       th = ( i - 1 + k ) * 2.0 * math.pi / N
-      r = cur:Interpolate( th )
-      x, y = r * math.cos( th ), r * math.sin( th )
-      love.graphics.circle( "fill", x, y, 0.01 )
+      local r = cur:Interpolate( th )
+      local x, y = r * math.cos( th ), r * math.sin( th )
+      --love.graphics.circle( "fill", x, y, 0.01 )
+      love.graphics.circle( "fill", th / math.pi - 1.0 , r, 0.01)
       
       --First derivative.
-      love.graphics.setColor( 0, 1.0, 0, 0.5 )
-      r = 1.0 + cur:Derivative( th )
+      love.graphics.setColor( 0, 1.0, 0, 0.7 )
+      r = cur:Derivative( th )
       x, y = r * math.cos( th ), r * math.sin( th )
-      love.graphics.circle( "fill", x, y, 0.01 )
+      --love.graphics.circle( "fill", x, y, 0.01 )
+      love.graphics.circle( "fill", th / math.pi - 1.0, r, 0.01)
       
       --Second derivative.
-      love.graphics.setColor( 0, 0, 1.0, 0.5 )
-      r = 1.0 + cur:SecondDerivative( th )
+      love.graphics.setColor( 0, 0, 1.0, 0.7 )
+      r = cur:SecondDerivative( th )
       x, y = r * math.cos( th ), r * math.sin( th )
-      love.graphics.circle( "fill", x, y, 0.01 )
+      --love.graphics.circle( "fill", x, y, 0.01 )
+      love.graphics.circle( "fill", th / math.pi - 1.0, r, 0.01)
+      
     end
   end
 
@@ -188,23 +191,25 @@ local function Draw()
   love.graphics.circle( "fill", x, y, 0.02 )
 end
 
+local function OnImpact( impact )
+  
+end
+
 local function Update()
+  
+end
+
+local function Integrate( step )
   local t = love.timer.getTime()
   for i = 1, N do
-    local rxx = old:SecondDerivative( 2.0 * math.pi * (i - 1) / N )
-    cur.vrad[i] = 0.7 * old.vrad[i] + 0.5 * step * rxx
-    cur.radii[i] = old.radii[i] + step * cur.vrad[i]
+    cur.radii[i] = old.radii[i]
   end
   
   cur:DFT( )
   
-  if love.math.random( 120 ) < 3 then
-    cur:Impulse( 0, 0.2 )
-  end
-  
   --Deep copy of current state to old state.
   for name, t in pairs( cur ) do
-    for i = 1, 13 do
+    for i = 1, N do
       old[name][i] = t[i]
     end
   end
@@ -225,6 +230,8 @@ Reset()
 return {
   Reset = Reset,
   Update = Update,
+  Integrate = Integrate,
+  OnImpact = OnImpact,
   DetectCollision = DetectCollision,
   Draw = Draw,
 }