/spacey

--[[

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 = math.sqrt, math.cos, math.sin

local vector = {}

vector.__index = vector

local function new(x,y)

	return setmetatable({x = x or 0, y = y or 0}, vector)

end

local function isvector(v)

	return getmetatable(v) == vector

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: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:trimmed(maxLen)

	return self:clone():trim_inplace(maxLen)

end

-- the module

return setmetatable({new = new, isvector = isvector},

{__call = function(_, ...) return new(...) end})