Rewrite

math/qt.lua

@@ -0,0 +1,90 @@
+--- Quaternion
+local qt
+
+local sin, cos = math.sin, math.cos
+local m4 = require((...):match("^(.*)qt$").."m4")
+
+-- qt methods
+-- Unless specified otherwise, all operations are done in place and do not create a new quaternion.
+local qt_mt = {
+	-- Clone the quaternion. Returns a new quaternion.
+	clone = function(self)
+		return qt(self[1], self[2], self[3], self[4])
+	end,
+
+	-- Set quaternion
+	set = function(self, other)
+		self[1], self[2], self[3], self[4] = other[1], other[2], other[3], other[4]
+		return self
+	end,
+
+	-- Retrieve coordinates
+	unpack = function(self)
+		return self[1], self[2], self[3], self[4]
+	end,
+
+	-- Convert to m4 rotation matrix. Returns a new 4x4 matrix.
+	toM4 = function(self)
+		local x, y, z, w = self[1], self[2], self[3], self[4]
+		local xx, yy, zz = x*x, y*y, z*z
+		local xw, xy, xz = x*w, x*y, x*z
+		local yw, yz = y*w, y*z
+		local zw = z*w
+		return m4{
+			1-2*(yy+zz), 2*(xy-zw),   2*(xz+yw),   0,
+			2*(xy+zw),   1-2*(xx+zz), 2*(yz-xw),   0,
+			2*(xz-yw),   2*(yz+xw),   1-2*(xx+yy), 0,
+			0,           0,           0,           1
+		}
+	end,
+
+	-- Common operations. Returns a new quaternion.
+	__sub = function(self, other)
+		return qt(self[1] - other[1], self[2] - other[2], self[3] - other[3], self[4] - other[4])
+	end,
+	__add = function(self, other)
+		return qt(self[1] + other[1], self[2] + other[2], self[3] + other[3], self[4] - other[4])
+	end,
+	__unm = function(self)
+		return qt(-self[1], -self[2], -self[3], -self[4])
+	end,
+	__mul = function(self, other)
+		local sx, sy, sz, sw = self[1], self[2], self[3], self[4]
+		local ox, oy, oz, ow = other[1], other[2], other[3], other[4]
+		return qt(sw * ow - sx * ox - sy * oy - sz * oz, sx * ow + sw * ox + sy * oz - sz * oy, sy * ow + sw * oy + sz * ox - sx * oz, sz * ow + sw * oz + sx * oy - sy * ox)
+	end,
+
+	__eq = function(self, other)
+		return self[1] == other[1] and self[2] == other[2] and self[3] == other[3] and self[4] == other[4]
+	end,
+
+	__tostring = function(self)
+		return ("qt(%s,%s,%s,%s)"):format(self[1], self[2], self[3], self[4])
+	end
+}
+qt_mt.__index = qt_mt
+
+qt = setmetatable({
+	--- Create a new identity quaternion
+	identity = function()
+		return qt(0, 0, 0, 1)
+	end,
+
+	--- Create a new quaternion from a rotation
+	fromAngleAxis = function(angle, axis)
+		local halfAngle = angle / 2
+		local s = sin(halfAngle)
+		return qt(axis[1] * s, axis[2] * s, axis[3] * s, cos(halfAngle))
+	end,
+}, {
+	-- If x is a table, will reuse it without copying.
+	__call = function(self, x, y, z, w)
+		if type(x) == "number" then
+			return setmetatable({ x, y, z, w }, qt_mt)
+		else
+			return setmetatable(x, qt_mt)
+		end
+	end
+})
+
+return qt