Rewrite

math/v3.lua

@@ -0,0 +1,114 @@
+--- 3D vector
+local v3
+
+local sqrt = math.sqrt
+
+-- v3 methods
+-- Unless specified otherwise, all operations are done in place and do not create a new vector.
+local v3_mt = {
+	-- Clone the vector. Returns a new vector.
+	clone = function(self)
+		return v3(self[1], self[2], self[3])
+	end,
+
+	-- Set vector
+	set = function(self, other)
+		self[1], self[2], self[3] = other[1], other[2], other[3]
+		return self
+	end,
+
+	-- Retrieve coordinates
+	unpack = function(self)
+		return self[1], self[2], self[3]
+	end,
+
+	-- Normalize
+	normalize = function(self)
+		local x, y, z = self[1], self[2], self[3]
+		local l = sqrt(x*x + y*y + z*z)
+		self[1], self[2], self[3] = x/l, y/l, z/l
+		return self
+	end,
+
+	-- Vector product. Returns a new vector.
+	cross = function(self, other)
+		local x1, y1, z1 = self[1], self[2], self[3]
+		local x2, y2, z2 = other[1], other[2], other[3]
+		return v3(
+			y1*z2 - z1*y2,
+			z1*x2 - x1*z2,
+			x1*y2 - y1*x2
+		)
+	end,
+	dot = function(self, other)
+		return self[1] * other[1] + self[2] * other[2] + self[3] * other[3]
+	end,
+
+	-- Transform by a mat4
+	transform = function(self, matrix)
+		local x, y, z = self[1], self[2], self[3]
+		-- Transform matrix * Homogeneous coordinates
+		local mx = matrix[1]  * x + matrix[2]  * y + matrix[3]  * z + matrix[4]
+		local my = matrix[5]  * x + matrix[6]  * y + matrix[7]  * z + matrix[8]
+		local mz = matrix[9]  * x + matrix[10] * y + matrix[11] * z + matrix[12]
+		local mw = matrix[13] * x + matrix[14] * y + matrix[15] * z + matrix[16]
+		-- Go back to euclidian coordinates
+		self[1], self[2], self[3] = mx/mw, my/mw, mz/mw
+		return self
+	end,
+
+	-- Length
+	len2 = function(self)
+		local x, y, z = self[1], self[2], self[3]
+		return x*x + y*y + z*z
+	end,
+	len = function(self)
+		local x, y, z = self[1], self[2], self[3]
+		return sqrt(x*x + y*y + z*z)
+	end,
+
+	-- Distance
+	distance = function(self, other)
+		return (self - other):len()
+	end,
+	distance2 = function(self, other)
+		return (self - other):len2()
+	end,
+
+	-- Common operations. Returns a new vector.
+	__sub = function(self, other)
+		return v3(self[1] - other[1], self[2] - other[2], self[3] - other[3])
+	end,
+	__add = function(self, other)
+		return v3(self[1] + other[1], self[2] + other[2], self[3] + other[3])
+	end,
+	__unm = function(self)
+		return v3(-self[1], -self[2], -self[3])
+	end,
+	__div = function(self, other)
+		return v3(self[1] / other, self[2] / other, self[3] / other)
+	end,
+	__mul = function(self, other)
+		return v3(self[1] * other, self[2] * other, self[3] * other)
+	end,
+
+	__eq = function(self, other)
+		return self[1] == other[1] and self[2] == other[2] and self[3] == other[3]
+	end,
+
+	__tostring = function(self)
+		return ("v3(%s,%s,%s)"):format(self[1], self[2], self[3])
+	end
+}
+v3_mt.__index = v3_mt
+
+-- If x is a table, will reuse it without copying.
+v3 = function(x, y, z)
+	if type(x) == "number" then
+		return setmetatable({ x, y, z }, v3_mt)
+	else
+		return setmetatable(x, v3_mt)
+	end
+end
+
+return v3