Some vector functions useful for working with rotations (#9572)

* added vector.rotate

* added vector.forward_from_rotation and vector.up_from_rotation

* added vector.forward_up_to_rotatiton

* fixed some bugs and formatting with vector functions

* shortened name of some new vector functions and added documentation

* made vector.rotate not require a unit vector as axis

* fixed crash with vector.forward_up_to_rot

* renamed new vector functions, made vector.rotate apply a rotation matrix, old vector.rotate is now called vector.rotate_around_axis

* documented vector function changes

* removed some whitespace to appease luacheck

* implemented and fixed optimization of vector.rotate_around_axis by SmallJoker

* added some unit tests for rotation vector functions

* clarified that rotation vectors are in radians and according to the left hand rule

* hopefully appeased luacheck

* renamed rotation_to_horizontal to forward_at_rotation, rotation_to_vertical to up_at_rotation

* handled cases where sin or cos are 0 in rotation vector functions

* added more comments

* clarified documentation of rotation vector functions

* added more unit tests

* changed way in which vector.rotate_around_axis is adjusted for left handed coordinate systems

* made vector.rotate_around_axis actually left handed

* unrolled matrix multiplication

* removed vector.forward_at_rotation and vector.up_at_rotation

* prettified vector.rotate_around_axis, made previous commits not break anything

* removed references to removed vector.forward_at_rotation and vector.up_at_rotation

* removed documentation of removed vector functions

* clarified documentation and fixed styling of rotation vector functions

* restyled comments minorly

* spelling fixes and some hopefully better comments

* allowed 'up' to be missing from vector.directions_to_rotation and removed requirement for unit vectors as arguments

* made vector.rotate_around_axis() right handed again for consistency

* documented previous changes

* made matrix multiplication actually multiply

* renamed vector.directions_to_rotation() to vector.dir_to_rotation()

* optimized a distance comparison

* Fixed potential false positive in unit tests.

Co-authored-by: NetherEran <nethereran@hotmail.com>

1 files changed, 142 insertions, 0 deletions

diff --git a/builtin/common/tests/vector_spec.lua b/builtin/common/tests/vector_spec.lua
index 79f032f28..6f308a4a8 100644
--- a/builtin/common/tests/vector_spec.lua
+++ b/builtin/common/tests/vector_spec.lua
@@ -43,4 +43,146 @@ describe("vector", function()
 	it("add()", function()
 		assert.same({ x = 2, y = 4, z = 6 }, vector.add(vector.new(1, 2, 3), { x = 1, y = 2, z = 3 }))
 	end)
+
+	-- This function is needed because of floating point imprecision.
+	local function almost_equal(a, b)
+		if type(a) == "number" then
+			return math.abs(a - b) < 0.00000000001
+		end
+		return vector.distance(a, b) < 0.000000000001
+	end
+
+	describe("rotate_around_axis()", function()
+		it("rotates", function()
+			assert.True(almost_equal({x = -1, y = 0, z = 0},
+				vector.rotate_around_axis({x = 1, y = 0, z = 0}, {x = 0, y = 1, z = 0}, math.pi)))
+			assert.True(almost_equal({x = 0, y = 1, z = 0},
+				vector.rotate_around_axis({x = 0, y = 0, z = 1}, {x = 1, y = 0, z = 0}, math.pi / 2)))
+			assert.True(almost_equal({x = 4, y = 1, z = 1},
+				vector.rotate_around_axis({x = 4, y = 1, z = 1}, {x = 4, y = 1, z = 1}, math.pi / 6)))
+		end)
+		it("keeps distance to axis", function()
+			local rotate1 = {x = 1, y = 3, z = 1}
+			local axis1 = {x = 1, y = 3, z = 2}
+			local rotated1 = vector.rotate_around_axis(rotate1, axis1, math.pi / 13)
+			assert.True(almost_equal(vector.distance(axis1, rotate1), vector.distance(axis1, rotated1)))
+			local rotate2 = {x = 1, y = 1, z = 3}
+			local axis2 = {x = 2, y = 6, z = 100}
+			local rotated2 = vector.rotate_around_axis(rotate2, axis2, math.pi / 23)
+			assert.True(almost_equal(vector.distance(axis2, rotate2), vector.distance(axis2, rotated2)))
+			local rotate3 = {x = 1, y = -1, z = 3}
+			local axis3 = {x = 2, y = 6, z = 100}
+			local rotated3 = vector.rotate_around_axis(rotate3, axis3, math.pi / 2)
+			assert.True(almost_equal(vector.distance(axis3, rotate3), vector.distance(axis3, rotated3)))
+		end)
+		it("rotates back", function()
+			local rotate1 = {x = 1, y = 3, z = 1}
+			local axis1 = {x = 1, y = 3, z = 2}
+			local rotated1 = vector.rotate_around_axis(rotate1, axis1, math.pi / 13)
+			rotated1 = vector.rotate_around_axis(rotated1, axis1, -math.pi / 13)
+			assert.True(almost_equal(rotate1, rotated1))
+			local rotate2 = {x = 1, y = 1, z = 3}
+			local axis2 = {x = 2, y = 6, z = 100}
+			local rotated2 = vector.rotate_around_axis(rotate2, axis2, math.pi / 23)
+			rotated2 = vector.rotate_around_axis(rotated2, axis2, -math.pi / 23)
+			assert.True(almost_equal(rotate2, rotated2))
+			local rotate3 = {x = 1, y = -1, z = 3}
+			local axis3 = {x = 2, y = 6, z = 100}
+			local rotated3 = vector.rotate_around_axis(rotate3, axis3, math.pi / 2)
+			rotated3 = vector.rotate_around_axis(rotated3, axis3, -math.pi / 2)
+			assert.True(almost_equal(rotate3, rotated3))
+		end)
+		it("is right handed", function()
+			local v_before1 = {x = 0, y = 1, z = -1}
+			local v_after1 = vector.rotate_around_axis(v_before1, {x = 1, y = 0, z = 0}, math.pi / 4)
+			assert.True(almost_equal(vector.normalize(vector.cross(v_after1, v_before1)), {x = 1, y = 0, z = 0}))
+
+			local v_before2 = {x = 0, y = 3, z = 4}
+			local v_after2 = vector.rotate_around_axis(v_before2, {x = 1, y = 0, z = 0},  2 * math.pi / 5)
+			assert.True(almost_equal(vector.normalize(vector.cross(v_after2, v_before2)), {x = 1, y = 0, z = 0}))
+
+			local v_before3 = {x = 1, y = 0, z = -1}
+			local v_after3 = vector.rotate_around_axis(v_before3, {x = 0, y = 1, z = 0}, math.pi / 4)
+			assert.True(almost_equal(vector.normalize(vector.cross(v_after3, v_before3)), {x = 0, y = 1, z = 0}))
+
+			local v_before4 = {x = 3, y = 0, z = 4}
+			local v_after4 = vector.rotate_around_axis(v_before4, {x = 0, y = 1, z = 0}, 2 * math.pi / 5)
+			assert.True(almost_equal(vector.normalize(vector.cross(v_after4, v_before4)), {x = 0, y = 1, z = 0}))
+
+			local v_before5 = {x = 1, y = -1, z = 0}
+			local v_after5 = vector.rotate_around_axis(v_before5, {x = 0, y = 0, z = 1}, math.pi / 4)
+			assert.True(almost_equal(vector.normalize(vector.cross(v_after5, v_before5)), {x = 0, y = 0, z = 1}))
+
+			local v_before6 = {x = 3, y = 4, z = 0}
+			local v_after6 = vector.rotate_around_axis(v_before6, {x = 0, y = 0, z = 1}, 2 * math.pi / 5)
+			assert.True(almost_equal(vector.normalize(vector.cross(v_after6, v_before6)), {x = 0, y = 0, z = 1}))
+		end)
+	end)
+
+	describe("rotate()", function()
+		it("rotates", function()
+			assert.True(almost_equal({x = -1, y = 0, z = 0},
+				vector.rotate({x = 1, y = 0, z = 0}, {x = 0, y = math.pi, z = 0})))
+			assert.True(almost_equal({x = 0, y = -1, z = 0},
+				vector.rotate({x = 1, y = 0, z = 0}, {x = 0, y = 0, z = math.pi / 2})))
+			assert.True(almost_equal({x = 1, y = 0, z = 0},
+				vector.rotate({x = 1, y = 0, z = 0}, {x = math.pi / 123, y = 0, z = 0})))
+		end)
+		it("is counterclockwise", function()
+			local v_before1 = {x = 0, y = 1, z = -1}
+			local v_after1 = vector.rotate(v_before1, {x = math.pi / 4, y = 0, z = 0})
+			assert.True(almost_equal(vector.normalize(vector.cross(v_after1, v_before1)), {x = 1, y = 0, z = 0}))
+
+			local v_before2 = {x = 0, y = 3, z = 4}
+			local v_after2 = vector.rotate(v_before2, {x = 2 * math.pi / 5, y = 0, z = 0})
+			assert.True(almost_equal(vector.normalize(vector.cross(v_after2, v_before2)), {x = 1, y = 0, z = 0}))
+
+			local v_before3 = {x = 1, y = 0, z = -1}
+			local v_after3 = vector.rotate(v_before3, {x = 0, y = math.pi / 4, z = 0})
+			assert.True(almost_equal(vector.normalize(vector.cross(v_after3, v_before3)), {x = 0, y = 1, z = 0}))
+
+			local v_before4 = {x = 3, y = 0, z = 4}
+			local v_after4 = vector.rotate(v_before4, {x = 0, y = 2 * math.pi / 5, z = 0})
+			assert.True(almost_equal(vector.normalize(vector.cross(v_after4, v_before4)), {x = 0, y = 1, z = 0}))
+
+			local v_before5 = {x = 1, y = -1, z = 0}
+			local v_after5 = vector.rotate(v_before5, {x = 0, y = 0, z = math.pi / 4})
+			assert.True(almost_equal(vector.normalize(vector.cross(v_after5, v_before5)), {x = 0, y = 0, z = 1}))
+
+			local v_before6 = {x = 3, y = 4, z = 0}
+			local v_after6 = vector.rotate(v_before6, {x = 0, y = 0, z = 2 * math.pi / 5})
+			assert.True(almost_equal(vector.normalize(vector.cross(v_after6, v_before6)), {x = 0, y = 0, z = 1}))
+		end)
+	end)
+
+	it("dir_to_rotation()", function()
+		-- Comparing rotations (pitch, yaw, roll) is hard because of certain ambiguities,
+		-- e.g. (pi, 0, pi) looks exactly the same as (0, pi, 0)
+		-- So instead we convert the rotation back to vectors and compare these.
+		local function forward_at_rot(rot)
+			return vector.rotate(vector.new(0, 0, 1), rot)
+		end
+		local function up_at_rot(rot)
+			return vector.rotate(vector.new(0, 1, 0), rot)
+		end
+		local rot1 = vector.dir_to_rotation({x = 1, y = 0, z = 0}, {x = 0, y = 1, z = 0})
+		assert.True(almost_equal({x = 1, y = 0, z = 0}, forward_at_rot(rot1)))
+		assert.True(almost_equal({x = 0, y = 1, z = 0}, up_at_rot(rot1)))
+		local rot2 = vector.dir_to_rotation({x = 1, y = 1, z = 0}, {x = 0, y = 0, z = 1})
+		assert.True(almost_equal({x = 1/math.sqrt(2), y = 1/math.sqrt(2), z = 0}, forward_at_rot(rot2)))
+		assert.True(almost_equal({x = 0, y = 0, z = 1}, up_at_rot(rot2)))
+		for i = 1, 1000 do
+			local rand_vec = vector.new(math.random(), math.random(), math.random())
+			if vector.length(rand_vec) ~= 0 then
+				local rot_1 = vector.dir_to_rotation(rand_vec)
+				local rot_2 = {
+					x = math.atan2(rand_vec.y, math.sqrt(rand_vec.z * rand_vec.z + rand_vec.x * rand_vec.x)),
+					y = -math.atan2(rand_vec.x, rand_vec.z),
+					z = 0
+				}
+				assert.True(almost_equal(rot_1, rot_2))
+			end
+		end
+
+	end)
 end)