light_world.lua/examples/vendor/hump/vector-light.lua

--[[
Copyright (c) 2012-2013 Matthias Richter

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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]]--

local sqrt, cos, sin, atan2 = math.sqrt, math.cos, math.sin, math.atan2

local function str(x,y)
	return "("..tonumber(x)..","..tonumber(y)..")"
end

local function mul(s, x,y)
	return s*x, s*y
end

local function div(s, x,y)
	return x/s, y/s
end

local function add(x1,y1, x2,y2)
	return x1+x2, y1+y2
end

local function sub(x1,y1, x2,y2)
	return x1-x2, y1-y2
end

local function permul(x1,y1, x2,y2)
	return x1*x2, y1*y2
end

local function dot(x1,y1, x2,y2)
	return x1*x2 + y1*y2
end

local function det(x1,y1, x2,y2)
	return x1*y2 - y1*x2
end

local function eq(x1,y1, x2,y2)
	return x1 == x2 and y1 == y2
end

local function lt(x1,y1, x2,y2)
	return x1 < x2 or (x1 == x2 and y1 < y2)
end

local function le(x1,y1, x2,y2)
	return x1 <= x2 and y1 <= y2
end

local function len2(x,y)
	return x*x + y*y
end

local function len(x,y)
	return sqrt(x*x + y*y)
end

local function dist2(x1,y1, x2,y2)
	return len2(x1-x2, y1-y2)
end

local function dist(x1,y1, x2,y2)
	return len(x1-x2, y1-y2)
end

local function normalize(x,y)
	local l = len(x,y)
	if l > 0 then
		return x/l, y/l
	end
	return x,y
end

local function rotate(phi, x,y)
	local c, s = cos(phi), sin(phi)
	return c*x - s*y, s*x + c*y
end

local function perpendicular(x,y)
	return -y, x
end

local function project(x,y, u,v)
	local s = (x*u + y*v) / (u*u + v*v)
	return s*u, s*v
end

local function mirror(x,y, u,v)
	local s = 2 * (x*u + y*v) / (u*u + v*v)
	return s*u - x, s*v - y
end

-- ref.: http://blog.signalsondisplay.com/?p=336
local function trim(maxLen, x, y)
	local s = maxLen * maxLen / len2(x, y)
	s = s > 1 and 1 or math.sqrt(s)
	return x * s, y * s
end

local function angleTo(x,y, u,v)
	if u and v then
		return atan2(y, x) - atan2(v, u)
	end
	return atan2(y, x)
end

-- the module
return {
	str = str,

	-- arithmetic
	mul    = mul,
	div    = div,
	add    = add,
	sub    = sub,
	permul = permul,
	dot    = dot,
	det    = det,
	cross  = det,

	-- relation
	eq = eq,
	lt = lt,
	le = le,

	-- misc operations
	len2          = len2,
	len           = len,
	dist2         = dist2,
	dist          = dist,
	normalize     = normalize,
	rotate        = rotate,
	perpendicular = perpendicular,
	project       = project,
	mirror        = mirror,
	trim          = trim,
	angleTo       = angleTo,
}