Add metatables to lua vectors (#11039)

Add backwards-compatible metatable functions for vectors.

5 files changed, 420 insertions, 86 deletions

diff --git a/builtin/common/misc_helpers.lua b/builtin/common/misc_helpers.lua
index d5f25f2fe..64c8c9a67 100644
--- a/builtin/common/misc_helpers.lua
+++ b/builtin/common/misc_helpers.lua
@@ -432,21 +432,19 @@ function core.string_to_pos(value)
 		return nil
 	end
 
-	local p = {}
-	p.x, p.y, p.z = string.match(value, "^([%d.-]+)[, ] *([%d.-]+)[, ] *([%d.-]+)$")
-	if p.x and p.y and p.z then
-		p.x = tonumber(p.x)
-		p.y = tonumber(p.y)
-		p.z = tonumber(p.z)
-		return p
-	end
-	p = {}
-	p.x, p.y, p.z = string.match(value, "^%( *([%d.-]+)[, ] *([%d.-]+)[, ] *([%d.-]+) *%)$")
-	if p.x and p.y and p.z then
-		p.x = tonumber(p.x)
-		p.y = tonumber(p.y)
-		p.z = tonumber(p.z)
-		return p
+	local x, y, z = string.match(value, "^([%d.-]+)[, ] *([%d.-]+)[, ] *([%d.-]+)$")
+	if x and y and z then
+		x = tonumber(x)
+		y = tonumber(y)
+		z = tonumber(z)
+		return vector.new(x, y, z)
+	end
+	x, y, z = string.match(value, "^%( *([%d.-]+)[, ] *([%d.-]+)[, ] *([%d.-]+) *%)$")
+	if x and y and z then
+		x = tonumber(x)
+		y = tonumber(y)
+		z = tonumber(z)
+		return vector.new(x, y, z)
 	end
 	return nil
 end
diff --git a/builtin/common/tests/misc_helpers_spec.lua b/builtin/common/tests/misc_helpers_spec.lua
index bb9d13e7f..b16987f0b 100644
--- a/builtin/common/tests/misc_helpers_spec.lua
+++ b/builtin/common/tests/misc_helpers_spec.lua
@@ -1,4 +1,5 @@
 _G.core = {}
+dofile("builtin/common/vector.lua")
 dofile("builtin/common/misc_helpers.lua")
 
 describe("string", function()
@@ -55,8 +56,8 @@ end)
 
 describe("pos", function()
 	it("from string", function()
-		assert.same({ x = 10, y = 5.1, z = -2}, core.string_to_pos("10.0, 5.1, -2"))
-		assert.same({ x = 10, y = 5.1, z = -2}, core.string_to_pos("( 10.0, 5.1, -2)"))
+		assert.equal(vector.new(10, 5.1, -2), core.string_to_pos("10.0, 5.1, -2"))
+		assert.equal(vector.new(10, 5.1, -2), core.string_to_pos("( 10.0, 5.1, -2)"))
 		assert.is_nil(core.string_to_pos("asd, 5, -2)"))
 	end)
 
diff --git a/builtin/common/tests/serialize_spec.lua b/builtin/common/tests/serialize_spec.lua
index 17c6a60f7..e46b7dcc5 100644
--- a/builtin/common/tests/serialize_spec.lua
+++ b/builtin/common/tests/serialize_spec.lua
@@ -3,6 +3,7 @@ _G.core = {}
 _G.setfenv = require 'busted.compatibility'.setfenv
 
 dofile("builtin/common/serialize.lua")
+dofile("builtin/common/vector.lua")
 
 describe("serialize", function()
 	it("works", function()
@@ -53,4 +54,16 @@ describe("serialize", function()
 		assert.is_nil(test_out.func)
 		assert.equals(test_out.foo, "bar")
 	end)
+
+	it("vectors work", function()
+		local v = vector.new(1, 2, 3)
+		assert.same({{x = 1, y = 2, z = 3}}, core.deserialize(core.serialize({v})))
+		assert.same({x = 1, y = 2, z = 3}, core.deserialize(core.serialize(v)))
+
+		-- abuse
+		v = vector.new(1, 2, 3)
+		v.a = "bla"
+		assert.same({x = 1, y = 2, z = 3, a = "bla"},
+				core.deserialize(core.serialize(v)))
+	end)
 end)
diff --git a/builtin/common/tests/vector_spec.lua b/builtin/common/tests/vector_spec.lua
index 104c656e9..9ebe69056 100644
--- a/builtin/common/tests/vector_spec.lua
+++ b/builtin/common/tests/vector_spec.lua
@@ -4,14 +4,20 @@ dofile("builtin/common/vector.lua")
 describe("vector", function()
 	describe("new()", function()
 		it("constructs", function()
-			assert.same({ x = 0, y = 0, z = 0 }, vector.new())
-			assert.same({ x = 1, y = 2, z = 3 }, vector.new(1, 2, 3))
-			assert.same({ x = 3, y = 2, z = 1 }, vector.new({ x = 3, y = 2, z = 1 }))
+			assert.same({x = 0, y = 0, z = 0}, vector.new())
+			assert.same({x = 1, y = 2, z = 3}, vector.new(1, 2, 3))
+			assert.same({x = 3, y = 2, z = 1}, vector.new({x = 3, y = 2, z = 1}))
+
+			assert.is_true(vector.check(vector.new()))
+			assert.is_true(vector.check(vector.new(1, 2, 3)))
+			assert.is_true(vector.check(vector.new({x = 3, y = 2, z = 1})))
 
 			local input = vector.new({ x = 3, y = 2, z = 1 })
 			local output = vector.new(input)
 			assert.same(input, output)
-			assert.are_not.equal(input, output)
+			assert.equal(input, output)
+			assert.is_false(rawequal(input, output))
+			assert.equal(input, input:new())
 		end)
 
 		it("throws on invalid input", function()
@@ -25,7 +31,89 @@ describe("vector", function()
 		end)
 	end)
 
-	it("equal()", function()
+	it("indexes", function()
+		local some_vector = vector.new(24, 42, 13)
+		assert.equal(24, some_vector[1])
+		assert.equal(24, some_vector.x)
+		assert.equal(42, some_vector[2])
+		assert.equal(42, some_vector.y)
+		assert.equal(13, some_vector[3])
+		assert.equal(13, some_vector.z)
+
+		some_vector[1] = 100
+		assert.equal(100, some_vector.x)
+		some_vector.x = 101
+		assert.equal(101, some_vector[1])
+
+		some_vector[2] = 100
+		assert.equal(100, some_vector.y)
+		some_vector.y = 102
+		assert.equal(102, some_vector[2])
+
+		some_vector[3] = 100
+		assert.equal(100, some_vector.z)
+		some_vector.z = 103
+		assert.equal(103, some_vector[3])
+	end)
+
+	it("direction()", function()
+		local a = vector.new(1, 0, 0)
+		local b = vector.new(1, 42, 0)
+		assert.equal(vector.new(0, 1, 0), vector.direction(a, b))
+		assert.equal(vector.new(0, 1, 0), a:direction(b))
+	end)
+
+	it("distance()", function()
+		local a = vector.new(1, 0, 0)
+		local b = vector.new(3, 42, 9)
+		assert.is_true(math.abs(43 - vector.distance(a, b)) < 1.0e-12)
+		assert.is_true(math.abs(43 - a:distance(b)) < 1.0e-12)
+		assert.equal(0, vector.distance(a, a))
+		assert.equal(0, b:distance(b))
+	end)
+
+	it("length()", function()
+		local a = vector.new(0, 0, -23)
+		assert.equal(0, vector.length(vector.new()))
+		assert.equal(23, vector.length(a))
+		assert.equal(23, a:length())
+	end)
+
+	it("normalize()", function()
+		local a = vector.new(0, 0, -23)
+		assert.equal(vector.new(0, 0, -1), vector.normalize(a))
+		assert.equal(vector.new(0, 0, -1), a:normalize())
+		assert.equal(vector.new(), vector.normalize(vector.new()))
+	end)
+
+	it("floor()", function()
+		local a = vector.new(0.1, 0.9, -0.5)
+		assert.equal(vector.new(0, 0, -1), vector.floor(a))
+		assert.equal(vector.new(0, 0, -1), a:floor())
+	end)
+
+	it("round()", function()
+		local a = vector.new(0.1, 0.9, -0.5)
+		assert.equal(vector.new(0, 1, -1), vector.round(a))
+		assert.equal(vector.new(0, 1, -1), a:round())
+	end)
+
+	it("apply()", function()
+		local i = 0
+		local f = function(x)
+			i = i + 1
+			return x + i
+		end
+		local a = vector.new(0.1, 0.9, -0.5)
+		assert.equal(vector.new(1, 1, 0), vector.apply(a, math.ceil))
+		assert.equal(vector.new(1, 1, 0), a:apply(math.ceil))
+		assert.equal(vector.new(0.1, 0.9, 0.5), vector.apply(a, math.abs))
+		assert.equal(vector.new(0.1, 0.9, 0.5), a:apply(math.abs))
+		assert.equal(vector.new(1.1, 2.9, 2.5), vector.apply(a, f))
+		assert.equal(vector.new(4.1, 5.9, 5.5), a:apply(f))
+	end)
+
+	it("equals()", function()
 			local function assertE(a, b)
 				assert.is_true(vector.equals(a, b))
 			end
@@ -35,22 +123,164 @@ describe("vector", function()
 
 			assertE({x = 0, y = 0, z = 0}, {x = 0, y = 0, z = 0})
 			assertE({x = -1, y = 0, z = 1}, {x = -1, y = 0, z = 1})
-			local a = { x = 2, y = 4, z = -10 }
+			assertE({x = -1, y = 0, z = 1}, vector.new(-1, 0, 1))
+			local a = {x = 2, y = 4, z = -10}
 			assertE(a, a)
 			assertNE({x = -1, y = 0, z = 1}, a)
+
+			assert.equal(vector.new(1, 2, 3), vector.new(1, 2, 3))
+			assert.is_true(vector.new(1, 2, 3):equals(vector.new(1, 2, 3)))
+			assert.not_equal(vector.new(1, 2, 3), vector.new(1, 2, 4))
+			assert.is_true(vector.new(1, 2, 3) == vector.new(1, 2, 3))
+			assert.is_false(vector.new(1, 2, 3) == vector.new(1, 3, 3))
 	end)
 
-	it("add()", function()
-		assert.same({ x = 2, y = 4, z = 6 }, vector.add(vector.new(1, 2, 3), { x = 1, y = 2, z = 3 }))
+	it("metatable is same", function()
+		local a = vector.new()
+		local b = vector.new(1, 2, 3)
+
+		assert.equal(true, vector.check(a))
+		assert.equal(true, vector.check(b))
+
+		assert.equal(vector.metatable, getmetatable(a))
+		assert.equal(vector.metatable, getmetatable(b))
+		assert.equal(vector.metatable, a.metatable)
+	end)
+
+	it("sort()", function()
+		local a = vector.new(1, 2, 3)
+		local b = vector.new(0.5, 232, -2)
+		local sorted = {vector.new(0.5, 2, -2), vector.new(1, 232, 3)}
+		assert.same(sorted, {vector.sort(a, b)})
+		assert.same(sorted, {a:sort(b)})
+	end)
+
+	it("angle()", function()
+		assert.equal(math.pi, vector.angle(vector.new(-1, -2, -3), vector.new(1, 2, 3)))
+		assert.equal(math.pi/2, vector.new(0, 1, 0):angle(vector.new(1, 0, 0)))
+	end)
+
+	it("dot()", function()
+		assert.equal(-14, vector.dot(vector.new(-1, -2, -3), vector.new(1, 2, 3)))
+		assert.equal(0, vector.new():dot(vector.new(1, 2, 3)))
+	end)
+
+	it("cross()", function()
+		local a = vector.new(-1, -2, 0)
+		local b = vector.new(1, 2, 3)
+		assert.equal(vector.new(-6, 3, 0), vector.cross(a, b))
+		assert.equal(vector.new(-6, 3, 0), a:cross(b))
 	end)
 
 	it("offset()", function()
-		assert.same({ x = 41, y = 52, z = 63 }, vector.offset(vector.new(1, 2, 3), 40, 50, 60))
+		assert.same({x = 41, y = 52, z = 63}, vector.offset(vector.new(1, 2, 3), 40, 50, 60))
+		assert.equal(vector.new(41, 52, 63), vector.offset(vector.new(1, 2, 3), 40, 50, 60))
+		assert.equal(vector.new(41, 52, 63), vector.new(1, 2, 3):offset(40, 50, 60))
+	end)
+
+	it("is()", function()
+		local some_table1 = {foo = 13, [42] = 1, "bar", 2}
+		local some_table2 = {1, 2, 3}
+		local some_table3 = {x = 1, 2, 3}
+		local some_table4 = {1, 2, z = 3}
+		local old = {x = 1, y = 2, z = 3}
+		local real = vector.new(1, 2, 3)
+
+		assert.is_false(vector.check(nil))
+		assert.is_false(vector.check(1))
+		assert.is_false(vector.check(true))
+		assert.is_false(vector.check("foo"))
+		assert.is_false(vector.check(some_table1))
+		assert.is_false(vector.check(some_table2))
+		assert.is_false(vector.check(some_table3))
+		assert.is_false(vector.check(some_table4))
+		assert.is_false(vector.check(old))
+		assert.is_true(vector.check(real))
+		assert.is_true(real:check())
+	end)
+
+	it("global pairs", function()
+		local out = {}
+		local vec = vector.new(10, 20, 30)
+		for k, v in pairs(vec) do
+			out[k] = v
+		end
+		assert.same({x = 10, y = 20, z = 30}, out)
+	end)
+
+	it("abusing works", function()
+		local v = vector.new(1, 2, 3)
+		v.a = 1
+		assert.equal(1, v.a)
+
+		local a_is_there = false
+		for key, value in pairs(v) do
+			if key == "a" then
+				a_is_there = true
+				assert.equal(value, 1)
+				break
+			end
+		end
+		assert.is_true(a_is_there)
+	end)
+
+	it("add()", function()
+		local a = vector.new(1, 2, 3)
+		local b = vector.new(1, 4, 3)
+		local c = vector.new(2, 6, 6)
+		assert.equal(c, vector.add(a, {x = 1, y = 4, z = 3}))
+		assert.equal(c, vector.add(a, b))
+		assert.equal(c, a:add(b))
+		assert.equal(c, a + b)
+		assert.equal(c, b + a)
+	end)
+
+	it("subtract()", function()
+		local a = vector.new(1, 2, 3)
+		local b = vector.new(2, 4, 3)
+		local c = vector.new(-1, -2, 0)
+		assert.equal(c, vector.subtract(a, {x = 2, y = 4, z = 3}))
+		assert.equal(c, vector.subtract(a, b))
+		assert.equal(c, a:subtract(b))
+		assert.equal(c, a - b)
+		assert.equal(c, -b + a)
+	end)
+
+	it("multiply()", function()
+		local a = vector.new(1, 2, 3)
+		local b = vector.new(2, 4, 3)
+		local c = vector.new(2, 8, 9)
+		local s = 2
+		local d = vector.new(2, 4, 6)
+		assert.equal(c, vector.multiply(a, {x = 2, y = 4, z = 3}))
+		assert.equal(c, vector.multiply(a, b))
+		assert.equal(d, vector.multiply(a, s))
+		assert.equal(d, a:multiply(s))
+		assert.equal(d, a * s)
+		assert.equal(d, s * a)
+		assert.equal(-a, -1 * a)
+	end)
+
+	it("divide()", function()
+		local a = vector.new(1, 2, 3)
+		local b = vector.new(2, 4, 3)
+		local c = vector.new(0.5, 0.5, 1)
+		local s = 2
+		local d = vector.new(0.5, 1, 1.5)
+		assert.equal(c, vector.divide(a, {x = 2, y = 4, z = 3}))
+		assert.equal(c, vector.divide(a, b))
+		assert.equal(d, vector.divide(a, s))
+		assert.equal(d, a:divide(s))
+		assert.equal(d, a / s)
+		assert.equal(d, 1/s * a)
+		assert.equal(-a, a / -1)
 	end)
 
 	it("to_string()", function()
 		local v = vector.new(1, 2, 3.14)
 		assert.same("(1, 2, 3.14)", vector.to_string(v))
+		assert.same("(1, 2, 3.14)", v:to_string())
+		assert.same("(1, 2, 3.14)", tostring(v))
 	end)
 
 	it("from_string()", function()
diff --git a/builtin/common/vector.lua b/builtin/common/vector.lua
index 2ef8fc617..cbaa872dc 100644
--- a/builtin/common/vector.lua
+++ b/builtin/common/vector.lua
@@ -1,15 +1,43 @@
+--[[
+Vector helpers
+Note: The vector.*-functions must be able to accept old vectors that had no metatables
+]]
+
+-- localize functions
+local setmetatable = setmetatable
 
 vector = {}
 
+local metatable = {}
+vector.metatable = metatable
+
+local xyz = {"x", "y", "z"}
+
+-- only called when rawget(v, key) returns nil
+function metatable.__index(v, key)
+	return rawget(v, xyz[key]) or vector[key]
+end
+
+-- only called when rawget(v, key) returns nil
+function metatable.__newindex(v, key, value)
+	rawset(v, xyz[key] or key, value)
+end
+
+-- constructors
+
+local function fast_new(x, y, z)
+	return setmetatable({x = x, y = y, z = z}, metatable)
+end
+
 function vector.new(a, b, c)
 	if type(a) == "table" then
 		assert(a.x and a.y and a.z, "Invalid vector passed to vector.new()")
-		return {x=a.x, y=a.y, z=a.z}
+		return fast_new(a.x, a.y, a.z)
 	elseif a then
 		assert(b and c, "Invalid arguments for vector.new()")
-		return {x=a, y=b, z=c}
+		return fast_new(a, b, c)
 	end
-	return {x=0, y=0, z=0}
+	return fast_new(0, 0, 0)
 end
 
 function vector.from_string(s, init)
@@ -27,48 +55,49 @@ end
 function vector.to_string(v)
 	return string.format("(%g, %g, %g)", v.x, v.y, v.z)
 end
+metatable.__tostring = vector.to_string
 
 function vector.equals(a, b)
 	return a.x == b.x and
 	       a.y == b.y and
 	       a.z == b.z
 end
+metatable.__eq = vector.equals
+
+-- unary operations
 
 function vector.length(v)
 	return math.hypot(v.x, math.hypot(v.y, v.z))
 end
+-- Note: we can not use __len because it is already used for primitive table length
 
 function vector.normalize(v)
 	local len = vector.length(v)
 	if len == 0 then
-		return {x=0, y=0, z=0}
+		return fast_new(0, 0, 0)
 	else
 		return vector.divide(v, len)
 	end
 end
 
 function vector.floor(v)
-	return {
-		x = math.floor(v.x),
-		y = math.floor(v.y),
-		z = math.floor(v.z)
-	}
+	return vector.apply(v, math.floor)
 end
 
 function vector.round(v)
-	return {
-		x = math.round(v.x),
-		y = math.round(v.y),
-		z = math.round(v.z)
-	}
+	return fast_new(
+		math.round(v.x),
+		math.round(v.y),
+		math.round(v.z)
+	)
 end
 
 function vector.apply(v, func)
-	return {
-		x = func(v.x),
-		y = func(v.y),
-		z = func(v.z)
-	}
+	return fast_new(
+		func(v.x),
+		func(v.y),
+		func(v.z)
+	)
 end
 
 function vector.distance(a, b)
@@ -79,11 +108,7 @@ function vector.distance(a, b)
 end
 
 function vector.direction(pos1, pos2)
-	return vector.normalize({
-		x = pos2.x - pos1.x,
-		y = pos2.y - pos1.y,
-		z = pos2.z - pos1.z
-	})
+	return vector.subtract(pos2, pos1):normalize()
 end
 
 function vector.angle(a, b)
@@ -98,70 +123,137 @@ function vector.dot(a, b)
 end
 
 function vector.cross(a, b)
-	return {
-		x = a.y * b.z - a.z * b.y,
-		y = a.z * b.x - a.x * b.z,
-		z = a.x * b.y - a.y * b.x
-	}
+	return fast_new(
+		a.y * b.z - a.z * b.y,
+		a.z * b.x - a.x * b.z,
+		a.x * b.y - a.y * b.x
+	)
 end
 
+function metatable.__unm(v)
+	return fast_new(-v.x, -v.y, -v.z)
+end
+
+-- add, sub, mul, div operations
+
 function vector.add(a, b)
 	if type(b) == "table" then
-		return {x = a.x + b.x,
-			y = a.y + b.y,
-			z = a.z + b.z}
+		return fast_new(
+			a.x + b.x,
+			a.y + b.y,
+			a.z + b.z
+		)
 	else
-		return {x = a.x + b,
-			y = a.y + b,
-			z = a.z + b}
+		return fast_new(
+			a.x + b,
+			a.y + b,
+			a.z + b
+		)
 	end
 end
+function metatable.__add(a, b)
+	return fast_new(
+		a.x + b.x,
+		a.y + b.y,
+		a.z + b.z
+	)
+end
 
 function vector.subtract(a, b)
 	if type(b) == "table" then
-		return {x = a.x - b.x,
-			y = a.y - b.y,
-			z = a.z - b.z}
+		return fast_new(
+			a.x - b.x,
+			a.y - b.y,
+			a.z - b.z
+		)
 	else
-		return {x = a.x - b,
-			y = a.y - b,
-			z = a.z - b}
+		return fast_new(
+			a.x - b,
+			a.y - b,
+			a.z - b
+		)
 	end
 end
+function metatable.__sub(a, b)
+	return fast_new(
+		a.x - b.x,
+		a.y - b.y,
+		a.z - b.z
+	)
+end
 
 function vector.multiply(a, b)
 	if type(b) == "table" then
-		return {x = a.x * b.x,
-			y = a.y * b.y,
-			z = a.z * b.z}
+		return fast_new(
+			a.x * b.x,
+			a.y * b.y,
+			a.z * b.z
+		)
 	else
-		return {x = a.x * b,
-			y = a.y * b,
-			z = a.z * b}
+		return fast_new(
+			a.x * b,
+			a.y * b,
+			a.z * b
+		)
+	end
+end
+function metatable.__mul(a, b)
+	if type(a) == "table" then
+		return fast_new(
+			a.x * b,
+			a.y * b,
+			a.z * b
+		)
+	else
+		return fast_new(
+			a * b.x,
+			a * b.y,
+			a * b.z
+		)
 	end
 end
 
 function vector.divide(a, b)
 	if type(b) == "table" then
-		return {x = a.x / b.x,
-			y = a.y / b.y,
-			z = a.z / b.z}
+		return fast_new(
+			a.x / b.x,
+			a.y / b.y,
+			a.z / b.z
+		)
 	else
-		return {x = a.x / b,
-			y = a.y / b,
-			z = a.z / b}
+		return fast_new(
+			a.x / b,
+			a.y / b,
+			a.z / b
+		)
 	end
 end
+function metatable.__div(a, b)
+	-- scalar/vector makes no sense
+	return fast_new(
+		a.x / b,
+		a.y / b,
+		a.z / b
+	)
+end
+
+-- misc stuff
 
 function vector.offset(v, x, y, z)
-	return {x = v.x + x,
-		y = v.y + y,
-		z = v.z + z}
+	return fast_new(
+		v.x + x,
+		v.y + y,
+		v.z + z
+	)
 end
 
 function vector.sort(a, b)
-	return {x = math.min(a.x, b.x), y = math.min(a.y, b.y), z = math.min(a.z, b.z)},
-		{x = math.max(a.x, b.x), y = math.max(a.y, b.y), z = math.max(a.z, b.z)}
+	return fast_new(math.min(a.x, b.x), math.min(a.y, b.y), math.min(a.z, b.z)),
+		fast_new(math.max(a.x, b.x), math.max(a.y, b.y), math.max(a.z, b.z))
+end
+
+function vector.check(v)
+	return getmetatable(v) == metatable
 end
 
 local function sin(x)
@@ -229,7 +321,7 @@ end
 
 function vector.dir_to_rotation(forward, up)
 	forward = vector.normalize(forward)
-	local rot = {x = math.asin(forward.y), y = -math.atan2(forward.x, forward.z), z = 0}
+	local rot = vector.new(math.asin(forward.y), -math.atan2(forward.x, forward.z), 0)
 	if not up then
 		return rot
 	end
@@ -237,7 +329,7 @@ function vector.dir_to_rotation(forward, up)
 			"Invalid vectors passed to vector.dir_to_rotation().")
 	up = vector.normalize(up)
 	-- Calculate vector pointing up with roll = 0, just based on forward vector.
-	local forwup = vector.rotate({x = 0, y = 1, z = 0}, rot)
+	local forwup = vector.rotate(vector.new(0, 1, 0), rot)
 	-- 'forwup' and 'up' are now in a plane with 'forward' as normal.
 	-- The angle between them is the absolute of the roll value we're looking for.
 	rot.z = vector.angle(forwup, up)