Use # operator for vector length

ball.lua

@@ -0,0 +1,65 @@
+ball = {
+	__count = 0,
+	id = nil,
+	pos = vec2:new(0,0),
+  last_pos = vec2:new(0,0),
+	vel = vec2:new(0,0),
+	rad = 1,
+	col = 7,
+  
+  mass = function(self)
+    return self.rad
+  end,
+	
+	draw = function(self, shadow)
+    if (shadow == true) then
+      circfill(self.last_pos.x, self.last_pos.y, self.rad, self.col + 8)
+    end
+		circfill(self.pos.x, self.pos.y, self.rad, self.col)
+	end,
+	
+	move = function(self)
+    self.last_pos = self.pos
+		self.pos += self.vel
+	end,
+	
+	edge_bounce = function(self)
+		edge_normal = vec2:new()
+		for axis in all({"x","y"}) do
+			val = self.pos[axis]
+			if (val - self.rad < 0) then
+				self.pos[axis] = self.rad
+				edge_normal[axis] = 1
+			elseif (val + self.rad > 127) then
+				self.pos[axis] = 127 - self.rad
+				edge_normal[axis] = -1
+			end 
+		end
+		if (edge_normal.x != 0 or edge_normal.y != 0) then
+			self.vel = self.vel:bounce(edge_normal)
+		end
+	end,
+	
+	check_collisions = function(self, balls)
+		for b in all(balls) do
+			if (b.id != self.id and (collisions[b] == nil or collisions[b][self] == nil)) then
+				local diff = self.pos - b.pos
+				if (#diff < self.rad + b.rad) then
+				 collisions[self] = collisions[self] or {}
+				 collisions[self][b] = diff
+				end
+			end
+		end
+	end,
+}
+ball.__index = ball
+
+function ball:new(o)
+	ball.__count += 1
+	local o = o or {}
+	o.id = ball.__count
+	o.col = o.col or o.id % 8
+	setmetatable(o, self)
+	o.__index = self
+	return o
+end

main.lua

@@ -1,14 +1,18 @@
+pal()
+cls()
+
 ball_count = 16
-ball_radius = 5
+max_radius = 16
 
 function _init()
+  pal({9,10,11,12,13,2,15,136,137,138,139,140,141,130,143,8},1)
   balls = {}
 	collisions = {}
 	for i=1,ball_count do
 		add(balls, ball:new({
 			pos=vec2:new(rnd(127),rnd(127)),
 			vel=vec2:new(rnd(2)-1,rnd(2)-1):normal(),
-			col=rnd(15)+1
+			rad = i < max_radius and i or max_radius,
     }))
 	end
 end
@@ -26,9 +30,9 @@ function _update60()
 end	
 
 function _draw()
-	cls()
+	-- cls()
 	for b in all(balls) do
-		b:draw()
+		b:draw(true)
 	end
 end
 
@@ -42,129 +46,24 @@ function handle_collisions()
  	 local t_xpoint = target.pos
  	 repeat
  			steps += 1
- 			rewind += 0.1 * steps
+ 			rewind = 0.1 * steps
  			s_xpoint = source.pos - source.vel * rewind
  			t_xpoint = target.pos - target.vel * rewind
- 		until (s_xpoint - t_xpoint):mag() >= source.rad + target.rad					
- 		source.vel = collision_vel(s_xpoint, source.vel, t_xpoint, target.vel)
- 		target.vel = collision_vel(t_xpoint, target.vel, s_xpoint, source.vel)
+ 		until rewind > 1 or #(s_xpoint - t_xpoint) >= source.rad + target.rad
+    local s_newvel = collision_vel(s_xpoint, source.vel, t_xpoint, target.vel, source:mass(), target:mass())
+ 		local t_newvel = collision_vel(t_xpoint, target.vel, s_xpoint, source.vel, target:mass(), source:mass())
  		source.pos = s_xpoint + source.vel * rewind
  		target.pos = t_xpoint + target.vel * rewind
+    source.vel = s_newvel
+    target.vel = t_newvel
 		end
 	end
 end				
 
-vec2 = {
-	x = 0,
-	y = 0,
-	
-	mag = function(self)
-	 return sqrt(self.x^2+self.y^2)
-	end,
-	
-	dot = function(self,v)
-		return self.x * v.x + self.y * v.y
-	end,
-	
-	normal	= function(self)
-		local mag = self:mag()
-		return vec2:new(self.x/mag, self.y/mag)
-	end,
-	
-	bounce = function(self, n, b)
-		local b = b or 1
-		local n = n:normal()
-		return (n * -2 * self:dot(n) + self) * b
-	end
-}
-
-vec2.__eq = function(v1,v2) return v1.x == v2.x and v1.y == v2.y end
-vec2.__add = function(v1,v2) return vec2:new(v1.x+v2.x,v1.y+v2.y) end
-vec2.__sub = function(v1,v2) return vec2:new(v1.x-v2.x,v1.y-v2.y) end
-vec2.__mul = function(v,s) return vec2:new(v.x*s,v.y*s) end
-vec2.__div = function(v,s) return vec2:new(v.x/s,v.y/s) end
-vec2.__unm = function(v) return vec2:new(-v.x,-v.y) end
-vec2.__tostring = function(v) return "{x: "..v.x..",y: "..v.y.."}" end
-vec2.__index = vec2
-
-function vec2:new(x,y)
-	local x = x or 0
-	local y = y or 0
-	local o = {x=x,y=y}
-	setmetatable(o, self)
-	o.__index = self
-	return o
-end
-
-function vec2:print_debug(v)
-	local v = v or vec2:new(0,1)
-	print("vec: "..vec2.__tostring(self))
-	print("mag: "..self:mag())
-	print("dot: "..self:dot(v))
-	print("normal: "..vec2.__tostring(self:normal()))
-	print("bounce: "..vec2.__tostring(self:bounce(v)))
-	print("inv: "..vec2.__tostring(-self))
-end
-
-ball = {
-	__count = 0,
-	id = nil,
-	pos = vec2:new(0,0),
-	vel = vec2:new(0,0),
-	rad = ball_radius,
-	col = 7,
-	
-	draw = function(self)
-		circfill(self.pos.x, self.pos.y, self.rad, self.col)
-	end,
-	
-	move = function(self)
-		self.pos += self.vel
-	end,
-	
-	edge_bounce = function(self)
-		edge_normal = vec2:new()
-		for axis in all({"x","y"}) do
-			val = self.pos[axis]
-			if (val - self.rad < 0) then
-				self.pos[axis] = self.rad
-				edge_normal[axis] = 1
-			elseif (val + self.rad > 127) then
-				self.pos[axis] = 127 - self.rad
-				edge_normal[axis] = -1
-			end 
-		end
-		if (edge_normal.x != 0 or edge_normal.y != 0) then
-			self.vel = self.vel:bounce(edge_normal)
-		end
-	end,
-	
-	check_collisions = function(self, balls)
-		for b in all(balls) do
-			if (b.id != self.id and (collisions[b] == nil or collisions[b][self] == nil)) then
-				local diff = self.pos - b.pos
-				if ((diff):mag() < self.rad + b.rad) then
-				 collisions[self] = collisions[self] or {}
-				 collisions[self][b] = diff
-				end
-			end
-		end
-	end,
-}
-ball.__index = ball
-
-function ball:new(o)
-	ball.__count += 1
-	local o = o or {}
-	o.id = ball.__count
-	o.col = o.id % 16
-	setmetatable(o, self)
-	o.__index = self
-	return o
-end
-
-function collision_vel(x1,v1,x2,v2)
+function collision_vel(x1,v1,x2,v2,m1,m2)
+    m1 = m1 or 1
+    m2 = m2 or 1
 		local x_diff = x1 - x2
 		local v_diff = v1 - v2
-		return v1 - x_diff * v_diff:dot(x_diff) / x_diff:mag()^2
+		return v1 - x_diff * (2 * m2 / (m1 + m2))  * v_diff:dot(x_diff) / (#x_diff)^2
 end

picosync.json

@@ -1,7 +1,8 @@
 {
   "picoFile":"qphys.p8",
-    
   "sources":[
+    "vec2.lua",
+    "ball.lua",
     "main.lua"
   ]
 }

qphys.p8

@@ -1,67 +1,15 @@
 pico-8 cartridge // http://www.pico-8.com
 version 34
 __lua__
-ball_count = 16
-ball_radius = 5
-
-function _init()
-	balls = {}
-	collisions = {}
-	for i=1,ball_count do
-		add(balls, ball:new({
-			pos=vec2:new(rnd(127),rnd(127)),
-			vel=vec2:new(rnd(2)-1,rnd(2)-1):normal(),
-			col=rnd(15)+1
-		}))
-	end
-end
-
-function _update60()
-	for b in all(balls) do
-		b:move()
-		b:edge_bounce()
-	end
-	for b in all(balls) do
-	 b:check_collisions(balls)
-	end 
-	handle_collisions(balls)
-	collisions = {}
-end	
-
-function _draw()
-	cls()
-	for b in all(balls) do
-		b:draw()
-	end
-end
-
-function handle_collisions()
-	for source,colls in pairs(collisions) do
-		for target,diff in pairs(colls) do
-  	local n = diff:normal()
- 	 local steps = 0
- 	 local rewind = 0
- 	 local s_xpoint = source.pos
- 	 local t_xpoint = target.pos
- 	 repeat
- 			steps += 1
- 			rewind += 0.1 * steps
- 			s_xpoint = source.pos - source.vel * rewind
- 			t_xpoint = target.pos - target.vel * rewind
- 		until (s_xpoint - t_xpoint):mag() >= source.rad + target.rad					
- 		source.vel = collision_vel(s_xpoint, source.vel, t_xpoint, target.vel)
- 		target.vel = collision_vel(t_xpoint, target.vel, s_xpoint, source.vel)
- 		source.pos = s_xpoint + source.vel * rewind
- 		target.pos = t_xpoint + target.vel * rewind 
-		end
-	end
-end				
-
 vec2 = {
 	x = 0,
 	y = 0,
 	
-	mag = function(self)
+  angle = function(self)
+    return atan2(y, x);
+  end,
+
+	length = function(self)
 	 return sqrt(self.x^2+self.y^2)
 	end,
 	
@@ -70,23 +18,32 @@ vec2 = {
 	end,
 	
 	normal = function(self)
-		local mag = self:mag()
-		return vec2:new(self.x/mag, self.y/mag)
+		return vec2:new(self.x/#self, self.y/#self)
 	end,
 	
-	bounce = function(self, n, b)
-		local b = b or 1
+  bounce = function(self, n)
 		local n = n:normal()
-		return (n * -2 * self:dot(n) + self) * b
-	end
+		return n * -2 * self:dot(n) + self
+	end,
 }
 
 vec2.__eq = function(v1,v2) return v1.x == v2.x and v1.y == v2.y end
 vec2.__add = function(v1,v2) return vec2:new(v1.x+v2.x,v1.y+v2.y) end
 vec2.__sub = function(v1,v2) return vec2:new(v1.x-v2.x,v1.y-v2.y) end
-vec2.__mul = function(v,s) return vec2:new(v.x*s,v.y*s) end
+vec2.__mul = function(o1,o2)
+  local s,v
+  if(tonum(o1)) then
+    s = o1
+    v = o2
+  else
+    s = o2
+    v = o1
+  end
+  return vec2:new(v.x*s,v.y*s)
+end
 vec2.__div = function(v,s) return vec2:new(v.x/s,v.y/s) end
 vec2.__unm = function(v) return vec2:new(-v.x,-v.y) end
+vec2.__len = function(v) return v:length() end 
 vec2.__tostring = function(v) return "{x: "..v.x..",y: "..v.y.."}" end
 vec2.__index = vec2
 
@@ -102,26 +59,36 @@ end
 function vec2:print_debug(v)
 	local v = v or vec2:new(0,1)
 	print("vec: "..vec2.__tostring(self))
-	print("mag: "..self:mag())
+	print("length: "..self:length())
 	print("dot: "..self:dot(v))
 	print("normal: "..vec2.__tostring(self:normal()))
 	print("bounce: "..vec2.__tostring(self:bounce(v)))
 	print("inv: "..vec2.__tostring(-self))
 end
 
+-->8
 ball = {
 	__count = 0,
 	id = nil,
 	pos = vec2:new(0,0),
+  last_pos = vec2:new(0,0),
 	vel = vec2:new(0,0),
-	rad = ball_radius,
+	rad = 1,
 	col = 7,
   
-	draw = function(self)
+  mass = function(self)
+    return self.rad
+  end,
+	
+	draw = function(self, shadow)
+    if (shadow == true) then
+      circfill(self.last_pos.x, self.last_pos.y, self.rad, self.col + 8)
+    end
 		circfill(self.pos.x, self.pos.y, self.rad, self.col)
 	end,
 	
 	move = function(self)
+    self.last_pos = self.pos
 		self.pos += self.vel
 	end,
 	
@@ -146,7 +113,7 @@ ball = {
 		for b in all(balls) do
 			if (b.id != self.id and (collisions[b] == nil or collisions[b][self] == nil)) then
 				local diff = self.pos - b.pos
-				if ((diff):mag() < self.rad + b.rad) then
+				if (#diff < self.rad + b.rad) then
 				 collisions[self] = collisions[self] or {}
 				 collisions[self][b] = diff
 				end
@@ -160,16 +127,81 @@ function ball:new(o)
 	ball.__count += 1
 	local o = o or {}
 	o.id = ball.__count
-	o.col = o.id % 16
+	o.col = o.col or o.id % 8
 	setmetatable(o, self)
 	o.__index = self
 	return o
 end
 
-function collision_vel(x1,v1,x2,v2)
+-->8
+pal()
+cls()
+
+ball_count = 16
+max_radius = 16
+
+function _init()
+  pal({9,10,11,12,13,2,15,136,137,138,139,140,141,130,143,8},1)
+  balls = {}
+	collisions = {}
+	for i=1,ball_count do
+		add(balls, ball:new({
+			pos=vec2:new(rnd(127),rnd(127)),
+			vel=vec2:new(rnd(2)-1,rnd(2)-1):normal(),
+			rad = i < max_radius and i or max_radius,
+    }))
+	end
+end
+
+function _update60()
+	for b in all(balls) do
+		b:move()
+		b:edge_bounce()
+	end
+	for b in all(balls) do
+	 b:check_collisions(balls)
+	end 
+	handle_collisions(balls)
+	collisions = {}
+end	
+
+function _draw()
+	-- cls()
+	for b in all(balls) do
+		b:draw(true)
+	end
+end
+
+function handle_collisions()
+	for source,colls in pairs(collisions) do
+		for target,diff in pairs(colls) do
+  	local n = diff:normal()
+ 	 local steps = 0
+ 	 local rewind = 0
+ 	 local s_xpoint = source.pos
+ 	 local t_xpoint = target.pos
+ 	 repeat
+ 			steps += 1
+ 			rewind = 0.1 * steps
+ 			s_xpoint = source.pos - source.vel * rewind
+ 			t_xpoint = target.pos - target.vel * rewind
+ 		until rewind > 1 or #(s_xpoint - t_xpoint) >= source.rad + target.rad
+    local s_newvel = collision_vel(s_xpoint, source.vel, t_xpoint, target.vel, source:mass(), target:mass())
+ 		local t_newvel = collision_vel(t_xpoint, target.vel, s_xpoint, source.vel, target:mass(), source:mass())
+ 		source.pos = s_xpoint + source.vel * rewind
+ 		target.pos = t_xpoint + target.vel * rewind
+    source.vel = s_newvel
+    target.vel = t_newvel
+		end
+	end
+end				
+
+function collision_vel(x1,v1,x2,v2,m1,m2)
+    m1 = m1 or 1
+    m2 = m2 or 1
 		local x_diff = x1 - x2
 		local v_diff = v1 - v2
-		return v1 - x_diff * v_diff:dot(x_diff) / x_diff:mag()^2
+		return v1 - x_diff * (2 * m2 / (m1 + m2))  * v_diff:dot(x_diff) / (#x_diff)^2
 end
 
 __gfx__

vec2.lua

@@ -0,0 +1,64 @@
+vec2 = {
+	x = 0,
+	y = 0,
+	
+  angle = function(self)
+    return atan2(y, x);
+  end,
+
+	length = function(self)
+	 return sqrt(self.x^2+self.y^2)
+	end,
+	
+	dot = function(self,v)
+		return self.x * v.x + self.y * v.y
+	end,
+	
+	normal = function(self)
+		return vec2:new(self.x/#self, self.y/#self)
+	end,
+	
+  bounce = function(self, n)
+		local n = n:normal()
+		return n * -2 * self:dot(n) + self
+	end,
+}
+
+vec2.__eq = function(v1,v2) return v1.x == v2.x and v1.y == v2.y end
+vec2.__add = function(v1,v2) return vec2:new(v1.x+v2.x,v1.y+v2.y) end
+vec2.__sub = function(v1,v2) return vec2:new(v1.x-v2.x,v1.y-v2.y) end
+vec2.__mul = function(o1,o2)
+  local s,v
+  if(tonum(o1)) then
+    s = o1
+    v = o2
+  else
+    s = o2
+    v = o1
+  end
+  return vec2:new(v.x*s,v.y*s)
+end
+vec2.__div = function(v,s) return vec2:new(v.x/s,v.y/s) end
+vec2.__unm = function(v) return vec2:new(-v.x,-v.y) end
+vec2.__len = function(v) return v:length() end 
+vec2.__tostring = function(v) return "{x: "..v.x..",y: "..v.y.."}" end
+vec2.__index = vec2
+
+function vec2:new(x,y)
+	local x = x or 0
+	local y = y or 0
+	local o = {x=x,y=y}
+	setmetatable(o, self)
+	o.__index = self
+	return o
+end
+
+function vec2:print_debug(v)
+	local v = v or vec2:new(0,1)
+	print("vec: "..vec2.__tostring(self))
+	print("length: "..self:length())
+	print("dot: "..self:dot(v))
+	print("normal: "..vec2.__tostring(self:normal()))
+	print("bounce: "..vec2.__tostring(self:bounce(v)))
+	print("inv: "..vec2.__tostring(-self))
+end