Snagged vec2 from @vrld's HUMP library

This was the original basis of vec3, so why not add it in, too?

modules/vec2.lua

@@ -0,0 +1,191 @@
+--[[
+Copyright (c) 2010-2013 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
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in
+all copies or substantial portions of the Software.
+
+Except as contained in this notice, the name(s) of the above copyright holders
+shall not be used in advertising or otherwise to promote the sale, use or
+other dealings in this Software without prior written authorization.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+THE SOFTWARE.
+]]--
+
+local assert = assert
+local sqrt, cos, sin, atan2 = math.sqrt, math.cos, math.sin, math.atan2
+
+local vector = {}
+vector.__index = vector
+
+local function new(x,y)
+	return setmetatable({x = x or 0, y = y or 0}, vector)
+end
+local zero = new(0,0)
+
+local function isvector(v)
+	return type(v) == 'table' and type(v.x) == 'number' and type(v.y) == 'number'
+end
+
+function vector:clone()
+	return new(self.x, self.y)
+end
+
+function vector:unpack()
+	return self.x, self.y
+end
+
+function vector:__tostring()
+	return "("..tonumber(self.x)..","..tonumber(self.y)..")"
+end
+
+function vector.__unm(a)
+	return new(-a.x, -a.y)
+end
+
+function vector.__add(a,b)
+	assert(isvector(a) and isvector(b), "Add: wrong argument types (<vector> expected)")
+	return new(a.x+b.x, a.y+b.y)
+end
+
+function vector.__sub(a,b)
+	assert(isvector(a) and isvector(b), "Sub: wrong argument types (<vector> expected)")
+	return new(a.x-b.x, a.y-b.y)
+end
+
+function vector.__mul(a,b)
+	if type(a) == "number" then
+		return new(a*b.x, a*b.y)
+	elseif type(b) == "number" then
+		return new(b*a.x, b*a.y)
+	else
+		assert(isvector(a) and isvector(b), "Mul: wrong argument types (<vector> or <number> expected)")
+		return a.x*b.x + a.y*b.y
+	end
+end
+
+function vector.__div(a,b)
+	assert(isvector(a) and type(b) == "number", "wrong argument types (expected <vector> / <number>)")
+	return new(a.x / b, a.y / b)
+end
+
+function vector.__eq(a,b)
+	return a.x == b.x and a.y == b.y
+end
+
+function vector.__lt(a,b)
+	return a.x < b.x or (a.x == b.x and a.y < b.y)
+end
+
+function vector.__le(a,b)
+	return a.x <= b.x and a.y <= b.y
+end
+
+function vector.permul(a,b)
+	assert(isvector(a) and isvector(b), "permul: wrong argument types (<vector> expected)")
+	return new(a.x*b.x, a.y*b.y)
+end
+
+function vector:len2()
+	return self.x * self.x + self.y * self.y
+end
+
+function vector:len()
+	return sqrt(self.x * self.x + self.y * self.y)
+end
+
+function vector.dist(a, b)
+	assert(isvector(a) and isvector(b), "dist: wrong argument types (<vector> expected)")
+	local dx = a.x - b.x
+	local dy = a.y - b.y
+	return sqrt(dx * dx + dy * dy)
+end
+
+function vector.dist2(a, b)
+	assert(isvector(a) and isvector(b), "dist: wrong argument types (<vector> expected)")
+	local dx = a.x - b.x
+	local dy = a.y - b.y
+	return (dx * dx + dy * dy)
+end
+
+function vector:normalize_inplace()
+	local l = self:len()
+	if l > 0 then
+		self.x, self.y = self.x / l, self.y / l
+	end
+	return self
+end
+
+function vector:normalized()
+	return self:clone():normalize_inplace()
+end
+
+function vector:rotate_inplace(phi)
+	local c, s = cos(phi), sin(phi)
+	self.x, self.y = c * self.x - s * self.y, s * self.x + c * self.y
+	return self
+end
+
+function vector:rotated(phi)
+	local c, s = cos(phi), sin(phi)
+	return new(c * self.x - s * self.y, s * self.x + c * self.y)
+end
+
+function vector:perpendicular()
+	return new(-self.y, self.x)
+end
+
+function vector:projectOn(v)
+	assert(isvector(v), "invalid argument: cannot project vector on " .. type(v))
+	-- (self * v) * v / v:len2()
+	local s = (self.x * v.x + self.y * v.y) / (v.x * v.x + v.y * v.y)
+	return new(s * v.x, s * v.y)
+end
+
+function vector:mirrorOn(v)
+	assert(isvector(v), "invalid argument: cannot mirror vector on " .. type(v))
+	-- 2 * self:projectOn(v) - self
+	local s = 2 * (self.x * v.x + self.y * v.y) / (v.x * v.x + v.y * v.y)
+	return new(s * v.x - self.x, s * v.y - self.y)
+end
+
+function vector:cross(v)
+	assert(isvector(v), "cross: wrong argument types (<vector> expected)")
+	return self.x * v.y - self.y * v.x
+end
+
+-- ref.: http://blog.signalsondisplay.com/?p=336
+function vector:trim_inplace(maxLen)
+	local s = maxLen * maxLen / self:len2()
+	s = (s > 1 and 1) or math.sqrt(s)
+	self.x, self.y = self.x * s, self.y * s
+	return self
+end
+
+function vector:angleTo(other)
+	if other then
+		return atan2(self.y, self.x) - atan2(other.y, other.x)
+	end
+	return atan2(self.y, self.x)
+end
+
+function vector:trimmed(maxLen)
+	return self:clone():trim_inplace(maxLen)
+end
+
+
+-- the module
+return setmetatable({new = new, isvector = isvector, zero = zero},
+{__call = function(_, ...) return new(...) end})