Smoother particle display; store particle states. Forward integration remains.

main.lua

@@ -126,7 +126,7 @@ local function OnVictory()
 end
 
 local function OnImpact( impact )
-
+  if not impact then return end
   local score = BeatScore( impact.t )
   --DEBUG
   state.lastBeatScore = score
@@ -150,6 +150,9 @@ local function OnImpact( impact )
   end
 
   love.audio.play( sound )
+  
+  marble.OnImpact( impact )
+  wave.OnImpact( impact )
 end
 
 
@@ -184,7 +187,15 @@ function love.update( dt )
   while dt > step do
     marble.Integrate( step )
     wave.Integrate( step )
-
+    
+    OnImpact(
+      DetectCollision( 
+        marble.Current(), marble.Next(),
+        wave.Current(), wave.Next() ))
+    
+    marble.Update()
+    wave.Update()
+    
     dt = dt - step
   end
   state.timeToSimulate = dt

marble.lua

@@ -3,31 +3,41 @@ local love = love
 --local wave = assert( require "wave" )
 local oldBuffer = love.graphics.newCanvas()
 local newBuffer = love.graphics.newCanvas()
-local state 
+local oldState, curState, newState
+
 local FRICTION = 0.01
 local MAXSPEED = 5.0
+local ddx, ddy = 0.0, 0.0
 
-local t, x, y, dx, dy, ddx, ddy
+local function State( )
+  return { t = 0, x = 0, y = 0, dx = 0, dy = 0 }
+end
+
+local function Current() return curState end
+local function Next() return newState end
+
+local function Integrate( step )
+  newState.t = love.timer.getTime()
+  newState.dx = (1.0 - FRICTION) * curState.dx + FRICTION * ddx
+  newState.dy = (1.0 - FRICTION) * curState.dy + FRICTION * ddy
+  newState.x = curState.x + newState.dx * step * MAXSPEED
+  newState.y = curState.y + newState.dy * step * MAXSPEED
+end
 
 local function OnImpact( impact )
-  
+  --Adjust current trajectory according to collision.
+  return Integrate( impact.tNext - impact.t ) --Hmm! Maybe this should be a fixed step instead for stability's sake.
 end
 
 local function Update()
-  
+  --Roll the log.
+  for k, v in pairs( oldState ) do
+    oldState[k] = curState[k]
+    curState[k] = newState[k]
+  end
 end
 
-local function Integrate( step )
-  t = love.timer.getTime()
 
-  dx = (1.0 - FRICTION) * dx + FRICTION * ddx
-  dy = (1.0 - FRICTION) * dy + FRICTION * ddy
-  local xf = x + dx * step * MAXSPEED
-  local yf = y + dy * step * MAXSPEED
-  
-  x = xf
-  y = yf
-end
 
 local function OnKey()
   ddx = (love.keyboard.isScancodeDown( "d" ) and 1.0 or 0.0) - (love.keyboard.isScancodeDown( "a" ) and 1.0 or 0.0)
@@ -39,17 +49,18 @@ local function OnKey()
 end
 
 local function Draw()
-  local dt = love.timer.getTime() - t
-  local xf, yf = x + dt * dx, y + dt * dy
   
-  local w, h = love.graphics.getDimensions()
+  love.graphics.print( ddx, 0, 100 )
-  local xi, yi = transform:transformPoint( x, y )
+  love.graphics.print( ddy, 0, 110 )
-  xf, yf = transform:transformPoint( xf, yf )
   
-  love.graphics.setColor( 0, 0, 0, 1 )
+  local xp, yp = transform:transformPoint( oldState.x, oldState.y )
-  love.graphics.print( x, 0, 60 )
+  local xc, yc = transform:transformPoint( curState.x, curState.y )
-  love.graphics.print( y, 0, 80 )
+  local xn, yn = transform:transformPoint( newState.x, newState.y )
   
+  local dt = love.timer.getTime() - newState.t --Integrate forward for slightly smoother rendering.
+  local xf, yf = transform:transformPoint(
+    newState.x + dt * newState.dx,
+    newState.y + dt * newState.dy )
 
   love.graphics.setCanvas( newBuffer )
   love.graphics.setColor(  1.0, 1.0, 1.0 , 0.99 ) -- White.
@@ -57,8 +68,13 @@ local function Draw()
   
   --Render latest segment in trail.
   love.graphics.setColor( 245 / 255, 169 / 255, 184 / 255, 1.0 ) --Trans pink.
-  love.graphics.circle( "fill", xf, yf, 4.0 ) --TODO: replace with segments.
   --love.graphics.line( xi, yi, xf, yf )
+  --Segment stuff:
+  love.graphics.setLineJoin( "bevel" )
+  love.graphics.setLineStyle( "smooth" )
+  love.graphics.setLineWidth( 8.0 )
+  love.graphics.line( xp, yp, xc, yc, xn, yn, xf, yf )
+  love.graphics.circle( "fill", xf, yf, 4.0 )
   
   love.graphics.setCanvas( oldBuffer )
   love.graphics.clear( 1.0, 1.0, 1.0, 0.0 )
@@ -66,9 +82,9 @@ local function Draw()
   --Render circle directly to screen.
   love.graphics.setCanvas()
   love.graphics.draw( newBuffer )
-  love.graphics.circle( "fill", xf, yf, 5.0 )
+  --love.graphics.circle( "fill", xf, yf, 5.0 )
   love.graphics.setColor( 1, 1, 1, 1.0 ) --White.
-  love.graphics.circle( "line", xf, yf, 5.0 )
+  --love.graphics.circle( "line", xf, yf, 5.0 )
   
   oldBuffer, newBuffer = newBuffer, oldBuffer
 
@@ -87,14 +103,9 @@ local function Resize()
 
 end
 
-local function Reset()
+local function Reset()  
-  t = love.timer.getTime()
+  oldState, curState, newState = State(), State(), State()
-  x = 0
+  Resize()
-  y = 0
-  dx = 0
-  dy = 0
-  ddx = 0
-  ddy = 0
 end
 
 
@@ -110,4 +121,6 @@ return {
   Impact = Impact,
   Reset = Reset,
   Resize = Resize,
+  Current = Current,
+  Next = Next,
 }

wave.lua

@@ -1,7 +1,11 @@
 --Render and simulate 1D wave equation.
 local love = love
+local old, cur, new --States add beginning of last tick, current tick, and next tick respectively.
 
-local N = 11
+local N = 13
+
+local function Current() return cur end
+local function Next() return new end
 
 --Calculate discrete fourier transform of radius function.
 local DFT
@@ -137,11 +141,6 @@ local function Wave( )
   return setmetatable(t, mt)
 end
 
-
-local old = Wave() --State at beginning of tick.
-local cur = Wave() --State at end of tick.
-
-
 local function Draw()
 
   -- Blue circle.
@@ -157,6 +156,7 @@ local function Draw()
     love.graphics.setCanvas()
     love.graphics.setColor( 0, 0, 0, 0.5 )
     love.graphics.circle( "fill", cx, cy, 0.02 )
+    
 
     
     for k = 0.1, 1.0, 0.1 do
@@ -182,6 +182,9 @@ local function Draw()
       --love.graphics.circle( "fill", x, y, 0.01 )
       love.graphics.circle( "fill", th / math.pi - 1.0, r, 0.01)
       
+      love.graphics.setColor( 1.0, 1.0, 1.0, 0.2 )
+      love.graphics.circle( "fill", 2.0 * ( i + k ) / N - 1.2, 0, 0.02 )
+      
     end
   end
 
@@ -196,23 +199,29 @@ local function OnImpact( impact )
 end
 
 local function Update()
-  
-end
 
-local function Integrate( step )
-  local t = love.timer.getTime()
-  for i = 1, N do
-    cur.radii[i] = old.radii[i]
-  end
-  
-  cur:DFT( )
-  
   --Deep copy of current state to old state.
   for name, t in pairs( cur ) do
     for i = 1, N do
       old[name][i] = t[i]
     end
   end
+  
+  --Deep copy of new state to current state.
+  for name, t in pairs( new ) do
+    for i = 1, N do
+      cur[name][i] = t[i]
+    end
+  end
+end
+
+local function Integrate( step )
+  local t = love.timer.getTime()
+  for i = 1, N do
+    new.radii[i] = 0.05 * math.cos( math.sin( t * 0.05 + i ) )
+  end
+  
+  cur:DFT( )
 
 end
 
@@ -223,6 +232,7 @@ end
 local function Reset()
   old = Wave()
   cur = Wave()
+  new = Wave()
 end
 
 Reset()
@@ -234,4 +244,6 @@ return {
   OnImpact = OnImpact,
   DetectCollision = DetectCollision,
   Draw = Draw,
+  Current = Current,
+  Next = Next,
 }