Render wave via shader.

conf.lua

@@ -4,7 +4,7 @@ function love.conf( t )
   t.modules.touch = false
   t.modules.video = false
   
-  t.window.title = "By Your Own Beat"
+  t.window.title = "Your Own Drum"
   t.window.width = 600                
   t.window.height = 600
   t.window.resizable = true

main.lua

@@ -29,24 +29,6 @@ state = {
   currentBeat = 1,
   startTime = 0.0,
 
-  wave = {
-    x   = { 1.0, 0.0, -0.5, 0.2, 0.4, 0.8, 0.3, 0.9, -0.4, 0.8, 0.5, 0.1, -0.9 },
-    dx  = { 1.0, 0.0, -0.5, 0.2, 0.4, 0.8, 0.3, 0.9, -0.4, 0.8, 0.5, 0.1, -0.9 },
-    ddx = { 1.0, 0.0, -0.5, 0.2, 0.4, 0.8, 0.3, 0.9, -0.4, 0.8, 0.5, 0.1, -0.9 },
-    X   = function(th) end,
-    DX  = function(th) end,
-    DDX = function(th) end,
-    Draw = function() end,
-    AddImpulse = function( th, size ) end,
-
-    ImpactPoint = function( xi, yi, xf, yf ) 
-      local impact = { r = 0, th = 0, t = 0, x = 0, y = 0, dx = 0, dy = 0 }
-      return impact
-    end,
-
-    Update = function( dt ) end,
-  },
-
   beat = {
     t = nil,
     mu = nil,

wave.lua

@@ -1,6 +1,6 @@
 --Render and simulate 1D wave equation.
 local love = love
-local N = 15
+local N = 33
 local SOUNDSPEED = 0.5
 local IMPULSESIZE = 20
 local DAMPING = 0.01
@@ -16,6 +16,41 @@ local Derivative
 local SecondDerivative
 local DFT
 
+local shader = love.graphics.newShader([[
+  
+  uniform float re[33];
+  uniform float im[33];
+  
+  //Slow IDFT
+  float r( float x )
+{
+  float r = re[0];
+
+  for( int k = 1; k < 17; k++ )
+  {
+    float c = cos( x * float( k ) );
+    float s = sin( x * float( k ) );
+    r += 
+    + c * re[k]
+    - s * im[k]
+    + c * re[33 - k]
+    + s * im[33 - k];
+  }
+  
+  return r;
+}
+  
+  vec4 effect(vec4 color, Image tex, vec2 texture_coords, vec2 screen_coords)
+{
+    vec2 p = (3.0 * screen_coords - 1.5 * love_ScreenSize.xy ) / love_ScreenSize.y;
+    p.y = -p.y;
+
+    float r = r( atan(p.y, p.x) ) - length( p );
+
+    return vec4(color.x, color.y, color.z, (r > -0.01)) ;
+}
+  ]])
+
 
 --Calculate discrete fourier transform of radius function.
 do
@@ -112,7 +147,7 @@ end
 
 --Apply bandlimited impulse to wave.
 local function OnImpact( impact )
-  
+
   local r = cur.radii
   local theta = impact.th
   local magnitude = IMPULSESIZE * impact.speed
@@ -120,7 +155,7 @@ local function OnImpact( impact )
   for i = 0, N - 1 do
     r[ i + 1 ] = r[ i + 1 ] + dt * magnitude * AliasedSinc(  theta, 2.0 * math.pi * i / N )
   end 
-  
+
   --We've updated the positions, now we need to take a DFT
   --in order to get the bandlimited second spatial derivative.
   cur:DFT() 
@@ -161,10 +196,16 @@ local function Draw()
 
   -- Blue circle.
   love.graphics.setColor(  91 / 255, 206 / 255, 250 / 255 )
-  love.graphics.circle("fill", 0, 0, 1)
+  
+  shader:send( "re", unpack( cur.dftre ) )
+  shader:send( "im", unpack( cur.dftim ) )
+  love.graphics.setShader( shader )
+  love.graphics.circle("fill", 0, 0, 1.5)
   local t = love.timer.getTime()
+  love.graphics.setShader( )
 
   -- Debug dots.
+  --[[
   for i = 1, N do
 
     local th = ( i - 1 ) * 2.0 * math.pi / N
@@ -172,9 +213,9 @@ 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
       --Interpolant.
       love.graphics.setColor( 1.0, 0, 0, 0.7 )
@@ -183,9 +224,9 @@ local function Draw()
       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, 0.7 )
+      --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 )
@@ -199,15 +240,16 @@ local function Draw()
       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 )]]
+      love.graphics.circle( "fill", 2.0 * ( i + k ) / N - 1.2, 0, 0.02 )
-      
+
     end
   end
 
   love.graphics.setColor( 1, 1, 1, 0.5 )
   local r = cur:Interpolate( t )
   local x, y = r * math.cos( t ), r * math.sin( t )
-  love.graphics.circle( "fill", x, y, 0.02 )
+  love.graphics.circle( "fill", x, y, 0.02 )]]
+  
 end
 
 
@@ -219,7 +261,7 @@ local function Update()
       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
@@ -229,16 +271,16 @@ local function Update()
 end
 
 Integrate = function( step )
-  
+
   for i = 1, N do
     local rxx = cur:SecondDerivative( math.pi * 2.0 * ( i - 1 ) / N )
     local r = ( 1.0 - DAMPING ) * ( 2.0 * cur.radii[i] - old.radii[i] + step * step * SOUNDSPEED * rxx ) --Verlet
-     + DAMPING --Damping: oscillate toward 1.
+    + DAMPING --Damping: oscillate toward 1.
     if r > 1.5 then r = 1.5 end
     if r < 0.5 then r = 0.5 end
     new.radii[i] = r
   end
-  
+
   new:DFT( )
 
 end