Builtin: Add vector.angle(). Returns the angle between 2 vectors (#7738)

builtin/common/vector.lua

@@ -90,6 +90,14 @@ function vector.direction(pos1, pos2)
 	return {x=x_raw, y=y_raw, z=z_raw}
 end
 
+function vector.angle(a, b)
+	local dotp = a.x * b.x + a.y * b.y + a.z * b.z
+	local cpx = a.y * b.z - a.z * b.y
+	local cpy = a.z * b.x - a.x * b.z
+	local cpz = a.x * b.y - a.y * b.x
+	local crossplen = math.sqrt(cpx ^ 2 + cpy ^ 2 + cpz ^ 2)
+	return math.atan2(crossplen, dotp)
+end
 
 function vector.add(a, b)
 	if type(b) == "table" then

doc/lua_api.txt

@@ -2202,16 +2202,30 @@ Spatial Vectors
 ---------------
 * `vector.new(a[, b, c])`: returns a vector:
     * A copy of `a` if `a` is a vector.
-    * `{x = a, y = b, z = c}`, if all `a, b, c` are defined
-* `vector.direction(p1, p2)`: returns a vector
-* `vector.distance(p1, p2)`: returns a number
-* `vector.length(v)`: returns a number
-* `vector.normalize(v)`: returns a vector
-* `vector.floor(v)`: returns a vector, each dimension rounded down
-* `vector.round(v)`: returns a vector, each dimension rounded to nearest int
-* `vector.apply(v, func)`: returns a vector
-* `vector.equals(v1, v2)`: returns a boolean
-* `vector.sort(v1, v2)`: returns minp, maxp vectors of the cuboid defined by v1 and v2
+    * `{x = a, y = b, z = c}`, if all of `a`, `b`, `c` are defined numbers.
+* `vector.direction(p1, p2)`:
+    * Returns a vector of length 1 with direction `p1` to `p2`.
+    * If `p1` and `p2` are identical, returns `{x = 0, y = 0, z = 0}`.
+* `vector.distance(p1, p2)`:
+    * Returns zero or a positive number, the distance between `p1` and `p2`.
+* `vector.length(v)`:
+    * Returns zero or a positive number, the length of vector `v`.
+* `vector.normalize(v)`:
+    * Returns a vector of length 1 with direction of vector `v`.
+    * If `v` has zero length, returns `{x = 0, y = 0, z = 0}`.
+* `vector.floor(v)`:
+    * Returns a vector, each dimension rounded down.
+* `vector.round(v)`:
+    * Returns a vector, each dimension rounded to nearest integer.
+* `vector.apply(v, func)`:
+    * Returns a vector where the function `func` has been applied to each
+      component.
+* `vector.equals(v1, v2)`:
+    * Returns a boolean, `true` if the vectors are identical.
+* `vector.sort(v1, v2)`:
+    * Returns in order minp, maxp vectors of the cuboid defined by `v1`, `v2`.
+* `vector.angle(v1, v2)`:
+    * Returns the angle between `v1` and `v2` in radians.
 
 For the following functions `x` can be either a vector or a number: