vec3: Rename angle_to -> angle_between

In vec2, angle_to is signed and angle_between is unsigned. We only have
the unsigned version in vec3, so use the corresponding name.

Remove the vec3 implementation from vec2 and use vec2's style
implementation. It doesn't allocate new vectors and works even if you
somehow call vec3.angle_between(vec2(), vec2()).

modules/vec2.lua

@@ -257,18 +257,14 @@ end
 
 --- Unsigned angle between two vectors.
 -- Directionless and thus commutative.
+-- Input vectors must be non-zero.
 -- @tparam vec2 a Vector
 -- @tparam vec2 b Vector
 -- @treturn number angle in [0, pi]
 function vec2.angle_between(a, b)
 	if b then
-		if vec2.is_vec2(a) then
-			return acos(a:dot(b) / (a:len() * b:len()))
-		end
-
-		return acos(vec3.dot(a, b) / (vec3.len(a) * vec3.len(b)))
+		return acos(a:dot(b) / (a:len() * b:len()))
 	end
-
 	return 0
 end
 

modules/vec3.lua

@@ -4,6 +4,7 @@
 local modules = (...):gsub('%.[^%.]+$', '') .. "."
 local precond = require(modules .. "_private_precond")
 local private = require(modules .. "_private_utils")
+local acos    = math.acos
 local sqrt    = math.sqrt
 local cos     = math.cos
 local sin     = math.sin
@@ -330,9 +331,20 @@ function vec3.flip_z(a)
 	return vec3.new(a.x, a.y, -a.z)
 end
 
-function vec3.angle_to(a, b)
-	local v = a:normalize():dot(b:normalize())
-	return math.acos(v)
+-- No angle_to because that requires defining an axis of rotation. Instead you
+-- likely want to convert both into vec2 and use vec2.angle_to.
+
+--- Unsigned angle between two vectors.
+-- Directionless and thus commutative.
+-- Input vectors must be non-zero.
+-- @tparam vec3 a Vector
+-- @tparam vec3 b Vector
+-- @treturn number angle in [0, pi]
+function vec3.angle_between(a, b)
+	if b then
+		return acos(a:dot(b) / (a:len() * b:len()))
+	end
+	return 0
 end
 
 --- Return a boolean showing if a table is or is not a vec3.

spec/vec3_spec.lua

@@ -232,30 +232,33 @@ describe("vec3:", function()
 		assert.is.equal(temp, vec3(-1, -2, -3))
 	end)
 
-	it("get two 3-vectors angle", function()
-		local angle_to = function(a, b)
-			local deg = math.deg(a:angle_to(b))
+	it("gets angle between two 3-vectors", function()
+		local angle_between = function(a, b)
+			local deg = math.deg(a:angle_between(b))
 			return string.format('%.2f', deg)
 		end
 
 		local a = vec3(1,2,3)
-		assert.is.equal(angle_to(a, vec3(3, 2, 1)), '44.42')
-		assert.is.equal(angle_to(a, vec3(0, 10, 0)), '57.69')
-		assert.is.equal(angle_to(a, vec3(0, -12, -10)), '157.51')
+		assert.is.equal(angle_between(a, a), '0.00')
+		assert.is.equal(angle_between(a, vec3(3, 2, 1)), '44.42')
+		assert.is.equal(angle_between(a, vec3(0, 10, 0)), '57.69')
+		assert.is.equal(angle_between(a, vec3(0, -12, -10)), '157.51')
 
 		a = vec3.unit_z
-		assert.is.equal(angle_to(a, vec3(0, 10, 0)), '90.00')
-		assert.is.equal(angle_to(a, vec3(-123, 10, 0)), '90.00')
-		assert.is.equal(angle_to(a, vec3(-10, 0, 10)), '45.00')
-		assert.is.equal(angle_to(a, vec3(-10, 0, -10)), '135.00')
-		assert.is.equal(angle_to(a, vec3(0, -10, -10)), '135.00')
-		assert.is.equal(angle_to(a, vec3(0, 0, -10)), '180.00')
-		assert.is.equal(angle_to(a, vec3(0, 0, 100)), '0.00')
+		assert.is.equal(angle_between(a, a), '0.00')
+		assert.is.equal(angle_between(a, vec3(0, 10, 0)), '90.00')
+		assert.is.equal(angle_between(a, vec3(-123, 10, 0)), '90.00')
+		assert.is.equal(angle_between(a, vec3(-10, 0, 10)), '45.00')
+		assert.is.equal(angle_between(a, vec3(-10, 0, -10)), '135.00')
+		assert.is.equal(angle_between(a, vec3(0, -10, -10)), '135.00')
+		assert.is.equal(angle_between(a, vec3(0, 0, -10)), '180.00')
+		assert.is.equal(angle_between(a, vec3(0, 0, 100)), '0.00')
 
 		a = vec3(100, 100, 0)
-		assert.is.equal(angle_to(a, vec3(0, 0, 100)), '90.00')
-		assert.is.equal(angle_to(a, vec3(0, 0, -100)), '90.00')
-		assert.is.equal(angle_to(a, vec3(-10, -10, 0)), '180.00')
-		assert.is.equal(angle_to(a, vec3.unit_z), '90.00')
+		assert.is.equal(angle_between(a, a), '0.00')
+		assert.is.equal(angle_between(a, vec3(0, 0, 100)), '90.00')
+		assert.is.equal(angle_between(a, vec3(0, 0, -100)), '90.00')
+		assert.is.equal(angle_between(a, vec3(-10, -10, 0)), '180.00')
+		assert.is.equal(angle_between(a, vec3.unit_z), '90.00')
 	end)
 end)