--[[
Copyright (c) 2010-2013 Matthias Richter

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]]--

-- Modified to include 3D capabilities by Bill Shillito, April 2014
-- Various bug fixes by Colby Klein, October 2014

--- 3 dimensional vectors.
-- @module vec3
-- @alias vector

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

local vector = {}
vector.__index = vector

--- Instance a new vec3.
-- @param x X value, table containing 3 elements, or another vector.
-- @param y Y value
-- @param z Z value
-- @return vec3
local function new(x,y,z)
	-- allow construction via vec3(a, b, c), vec3 { a, b, c } or vec3 { x = a, y = b, z = c }
	if type(x) == "table" then
		return setmetatable({x=x.x or x[1] or 0, y=x.y or x[2] or 0, z=x.z or x[3] or 0}, vector)
	end
	return setmetatable({x = x or 0, y = y or 0, z = z or 0}, vector)
end

local function isvector(v)
	return getmetatable(v) == vector or (type(v) == "table" and type(v.x) == "number" and type(v.y) == "number" and type(v.z) == "number")
end

local zero = new(0,0,0)
local unit_x = new(1,0,0)
local unit_y = new(0,1,0)
local unit_z = new(0,0,1)

--- Create a new vector containing the same data.
-- @return vec3
function vector:clone()
	return new(self.x, self.y, self.z)
end

--- Unpack the vector into its components.
-- @return number
-- @return number
-- @return number
function vector:unpack()
	return self.x, self.y, self.z
end

function vector:__tostring()
	return string.format("(%+0.3f,%+0.3f,%+0.3f)", self.x, self.y, self.z)
end

function vector.__unm(a)
	return new(-a.x, -a.y, -a.z)
end

function vector.__add(a,b)
	if type(a) == "number" then
		return new(a+b.x, a+b.y, a+b.z)
	elseif type(b) == "number" then
		return new(a.x+b, a.y+b, a.z+b)
	else
		assert(isvector(a) and isvector(b), "Add: wrong argument types (<vector> expected)")
		return new(a.x+b.x, a.y+b.y, a.z+b.z)
	end
end

function vector.__sub(a,b)
	if type(a) == "number" then
		return new(a-b.x, a-b.y, a-b.z)
	elseif type(b) == "number" then
		return new(a.x-b, a.y-b, a.z-b)
	else
		assert(isvector(a) and isvector(b), "Sub: wrong argument types (<vector> expected)")
		return new(a.x-b.x, a.y-b.y, a.z-b.z)
	end
end

function vector.__mul(a,b)
	if type(a) == "number" then
		return new(a*b.x, a*b.y, a*b.z)
	elseif type(b) == "number" then
		return new(b*a.x, b*a.y, b*a.z)
	else
		assert(isvector(a) and isvector(b), "Mul: wrong argument types (<vector> or <number> expected)")
		return new(a.x*b.x, a.y*b.y, a.z*b.z)
	end
end

function vector.__div(a,b)
	if type(a) == "number" then
		return new(a / b.x, a / b.y, a / b.z)
	elseif type(b) == "number" then
		return new(a.x / b, a.y / b, a.z / b)
	else
		assert(isvector(a) and isvector(b), "Div: wrong argument types (<vector> or <number> expected)")
		return new(a.x/b.x, a.y/b.y, a.z/b.z)
	end
end

function vector.__eq(a,b)
	return a.x == b.x and a.y == b.y and a.z == b.z
end

function vector.__lt(a,b)
	-- This is a lexicographical order.
	return a.x < b.x or (a.x == b.x and a.y < b.y) or (a.x == b.x and a.y == b.y and a.z < b.z)
end

function vector.__le(a,b)
	-- This is a lexicographical order.
	return a.x <= b.x and a.y <= b.y and a.z <= b.z
end

--- Dot product.
-- @param a first vec3 to dot with
-- @param b second vec3 to dot with
-- @return number
function vector.dot(a,b)
	assert(isvector(a) and isvector(b), "dot: wrong argument types (<vector> expected)")
	return a.x*b.x + a.y*b.y + a.z*b.z
end

function vector:len2()
	return self.x * self.x + self.y * self.y + self.z * self.z
end

--- Vector length/magnitude.
-- @return number
function vector:len()
	return sqrt(self.x * self.x + self.y * self.y + self.z * self.z)
end

--- Distance between two points.
-- @param a first point
-- @param b second point
-- @return number
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
	local dz = a.z - b.z
	return sqrt(dx * dx + dy * dy + dz * dz)
end

--- Squared distance between two points.
-- @param a first point
-- @param b second point
-- @return number
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
	local dz = a.z - b.z
	return (dx * dx + dy * dy + dz * dz)
end

--- Normalize vector.
-- Scales the vector in place such that its length is 1.
-- @return vec3
function vector:normalize_inplace()
	local l = self:len()
	if l > 0 then
		self.x, self.y, self.z = self.x / l, self.y / l, self.z / l
	end
	return self
end

--- Normalize vector.
-- Returns a copy of the vector scaled such that its length is 1.
-- @return vec3
function vector:normalize()
	return self:clone():normalize_inplace()
end

--- Rotate vector about an axis.
-- @param phi Amount to rotate, in radians
-- @param axis Axis to rotate by
-- @return vec3
function vector:rotate(phi, axis)
	if axis == nil then return self end

	local u = axis:normalize() or Vector(0,0,1) -- default is to rotate in the xy plane
	local c, s = cos(phi), sin(phi)

	-- Calculate generalized rotation matrix
	local m1 = new((c + u.x * u.x * (1-c)),       (u.x * u.y * (1-c) - u.z * s), (u.x * u.z * (1-c) + u.y * s))
	local m2 = new((u.y * u.x * (1-c) + u.z * s), (c + u.y * u.y * (1-c)),       (u.y * u.z * (1-c) - u.x * s))
	local m3 = new((u.z * u.x * (1-c) - u.y * s), (u.z * u.y * (1-c) + u.x * s), (c + u.z * u.z * (1-c))      )

	-- Return rotated vector
	return new( m1:dot(self), m2:dot(self), m3:dot(self) )
end

function vector:rotate_inplace(phi, axis)
	self = self:rotated(phi, axis)
end

function vector:perpendicular()
	return new(-self.y, self.x, 0)
end

function vector:project_on(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 + self.z * v.z) / (v.x * v.x + v.y * v.y + v.z * v.z)
	return new(s * v.x, s * v.y, s * v.z)
end

function vector:project_from(v)
	assert(isvector(v), "invalid argument: cannot project vector on " .. type(v))
	-- Does the reverse of projectOn.
	local s = (v.x * v.x + v.y * v.y + v.z * v.z) / (self.x * v.x + self.y * v.y + self.z * v.z)
	return new(s * v.x, s * v.y, s * v.z)
end

function vector:mirror_on(v)
	assert(isvector(v), "invalid argument: cannot mirror vector on " .. type(v))
	local s = 2 * (self.x * v.x + self.y * v.y + self.z * v.z) / (v.x * v.x + v.y * v.y + v.z * v.z)
	return new(s * v.x - self.x, s * v.y - self.y, s * v.z - self.z)
end

--- Cross product.
-- @param v vec3 to cross with
-- @return vec3
function vector:cross(v)
	assert(isvector(v), "cross: wrong argument types (<vector> expected)")
	return new(self.y*v.z - self.z*v.y, self.z*v.x - self.x*v.z, self.x*v.y - self.y*v.x)
end

-- @return vec3
function vector:trim_inplace(maxLen)
	-- ref.: http://blog.signalsondisplay.com/?p=336
	local s = maxLen * maxLen / self:len2()
	s = (s > 1 and 1) or math.sqrt(s)
	self.x, self.y, self.z = self.x * s, self.y * s, self.z * s
	return self
end

-- @return vec3
function vector:trim(maxLen)
	return self:clone():trim_inplace(maxLen)
end

-- @return number
function vector:angle_to(other)
	-- Only makes sense in 2D.
	if other then
		return atan2(self.y-other.y, self.x-other.x)
	end
	return atan2(self.y, self.x)
end

-- @return number
function vector:angle_between(other)
	if other then
		return acos(self:dot(other) / (self:len() * other:len()))
	end
	return 0
end

-- @return vec3
function vector:orientation_to_direction(orientation)
	orientation = orientation or new(0, 1, 0)
	return orientation
		:rotated(self.z, unit_z)
		:rotated(self.y, unit_y)
		:rotated(self.x, unit_x)
end

-- http://keithmaggio.wordpress.com/2011/02/15/math-magician-lerp-slerp-and-nlerp/
function vector.lerp(a, b, s)
	return a + s * (b - a)
end

-- the module
return setmetatable(
	{
		new      = new,
		lerp     = lerp,
		isvector = isvector,
		zero     = zero,
		unit_x   = unit_x,
		unit_y   = unit_y,
		unit_z   = unit_z
	}, {
		__call = function(_, ...) return new(...) end
	}
)