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)
	 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)
		local x_diff = x1 - x2
		local v_diff = v1 - v2
		return v1 - x_diff * v_diff:dot(x_diff) / x_diff:mag()^2
end

__gfx__
01230000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
45670000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
89ab0700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
cdef7000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
00077000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
00700700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000