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>
This commit is contained in:
NetherEran
Nils Dagsson Moskopp
parent
81e7460b30
commit
153557e3f7
GPG Key ID:
A3BC671C35191080
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@ -43,4 +43,146 @@ describe("vector", function()
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it("add()", function()
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assert.same({ x = 2, y = 4, z = 6 }, vector.add(vector.new(1, 2, 3), { x = 1, y = 2, z = 3 }))
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end)
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-- This function is needed because of floating point imprecision.
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local function almost_equal(a, b)
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if type(a) == "number" then
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return math.abs(a - b) < 0.00000000001
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end
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return vector.distance(a, b) < 0.000000000001
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end
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describe("rotate_around_axis()", function()
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it("rotates", function()
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assert.True(almost_equal({x = -1, y = 0, z = 0},
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vector.rotate_around_axis({x = 1, y = 0, z = 0}, {x = 0, y = 1, z = 0}, math.pi)))
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assert.True(almost_equal({x = 0, y = 1, z = 0},
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vector.rotate_around_axis({x = 0, y = 0, z = 1}, {x = 1, y = 0, z = 0}, math.pi / 2)))
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assert.True(almost_equal({x = 4, y = 1, z = 1},
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vector.rotate_around_axis({x = 4, y = 1, z = 1}, {x = 4, y = 1, z = 1}, math.pi / 6)))
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end)
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it("keeps distance to axis", function()
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local rotate1 = {x = 1, y = 3, z = 1}
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local axis1 = {x = 1, y = 3, z = 2}
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local rotated1 = vector.rotate_around_axis(rotate1, axis1, math.pi / 13)
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assert.True(almost_equal(vector.distance(axis1, rotate1), vector.distance(axis1, rotated1)))
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local rotate2 = {x = 1, y = 1, z = 3}
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local axis2 = {x = 2, y = 6, z = 100}
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local rotated2 = vector.rotate_around_axis(rotate2, axis2, math.pi / 23)
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assert.True(almost_equal(vector.distance(axis2, rotate2), vector.distance(axis2, rotated2)))
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local rotate3 = {x = 1, y = -1, z = 3}
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local axis3 = {x = 2, y = 6, z = 100}
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local rotated3 = vector.rotate_around_axis(rotate3, axis3, math.pi / 2)
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assert.True(almost_equal(vector.distance(axis3, rotate3), vector.distance(axis3, rotated3)))
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end)
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it("rotates back", function()
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local rotate1 = {x = 1, y = 3, z = 1}
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local axis1 = {x = 1, y = 3, z = 2}
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local rotated1 = vector.rotate_around_axis(rotate1, axis1, math.pi / 13)
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rotated1 = vector.rotate_around_axis(rotated1, axis1, -math.pi / 13)
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assert.True(almost_equal(rotate1, rotated1))
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local rotate2 = {x = 1, y = 1, z = 3}
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local axis2 = {x = 2, y = 6, z = 100}
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local rotated2 = vector.rotate_around_axis(rotate2, axis2, math.pi / 23)
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rotated2 = vector.rotate_around_axis(rotated2, axis2, -math.pi / 23)
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assert.True(almost_equal(rotate2, rotated2))
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local rotate3 = {x = 1, y = -1, z = 3}
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local axis3 = {x = 2, y = 6, z = 100}
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local rotated3 = vector.rotate_around_axis(rotate3, axis3, math.pi / 2)
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rotated3 = vector.rotate_around_axis(rotated3, axis3, -math.pi / 2)
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assert.True(almost_equal(rotate3, rotated3))
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end)
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it("is right handed", function()
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local v_before1 = {x = 0, y = 1, z = -1}
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local v_after1 = vector.rotate_around_axis(v_before1, {x = 1, y = 0, z = 0}, math.pi / 4)
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assert.True(almost_equal(vector.normalize(vector.cross(v_after1, v_before1)), {x = 1, y = 0, z = 0}))
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local v_before2 = {x = 0, y = 3, z = 4}
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local v_after2 = vector.rotate_around_axis(v_before2, {x = 1, y = 0, z = 0}, 2 * math.pi / 5)
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assert.True(almost_equal(vector.normalize(vector.cross(v_after2, v_before2)), {x = 1, y = 0, z = 0}))
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local v_before3 = {x = 1, y = 0, z = -1}
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local v_after3 = vector.rotate_around_axis(v_before3, {x = 0, y = 1, z = 0}, math.pi / 4)
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assert.True(almost_equal(vector.normalize(vector.cross(v_after3, v_before3)), {x = 0, y = 1, z = 0}))
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local v_before4 = {x = 3, y = 0, z = 4}
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local v_after4 = vector.rotate_around_axis(v_before4, {x = 0, y = 1, z = 0}, 2 * math.pi / 5)
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assert.True(almost_equal(vector.normalize(vector.cross(v_after4, v_before4)), {x = 0, y = 1, z = 0}))
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local v_before5 = {x = 1, y = -1, z = 0}
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local v_after5 = vector.rotate_around_axis(v_before5, {x = 0, y = 0, z = 1}, math.pi / 4)
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assert.True(almost_equal(vector.normalize(vector.cross(v_after5, v_before5)), {x = 0, y = 0, z = 1}))
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local v_before6 = {x = 3, y = 4, z = 0}
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local v_after6 = vector.rotate_around_axis(v_before6, {x = 0, y = 0, z = 1}, 2 * math.pi / 5)
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assert.True(almost_equal(vector.normalize(vector.cross(v_after6, v_before6)), {x = 0, y = 0, z = 1}))
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end)
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end)
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describe("rotate()", function()
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it("rotates", function()
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assert.True(almost_equal({x = -1, y = 0, z = 0},
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vector.rotate({x = 1, y = 0, z = 0}, {x = 0, y = math.pi, z = 0})))
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assert.True(almost_equal({x = 0, y = -1, z = 0},
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vector.rotate({x = 1, y = 0, z = 0}, {x = 0, y = 0, z = math.pi / 2})))
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assert.True(almost_equal({x = 1, y = 0, z = 0},
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vector.rotate({x = 1, y = 0, z = 0}, {x = math.pi / 123, y = 0, z = 0})))
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end)
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it("is counterclockwise", function()
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local v_before1 = {x = 0, y = 1, z = -1}
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local v_after1 = vector.rotate(v_before1, {x = math.pi / 4, y = 0, z = 0})
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assert.True(almost_equal(vector.normalize(vector.cross(v_after1, v_before1)), {x = 1, y = 0, z = 0}))
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local v_before2 = {x = 0, y = 3, z = 4}
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local v_after2 = vector.rotate(v_before2, {x = 2 * math.pi / 5, y = 0, z = 0})
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assert.True(almost_equal(vector.normalize(vector.cross(v_after2, v_before2)), {x = 1, y = 0, z = 0}))
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local v_before3 = {x = 1, y = 0, z = -1}
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local v_after3 = vector.rotate(v_before3, {x = 0, y = math.pi / 4, z = 0})
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assert.True(almost_equal(vector.normalize(vector.cross(v_after3, v_before3)), {x = 0, y = 1, z = 0}))
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local v_before4 = {x = 3, y = 0, z = 4}
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local v_after4 = vector.rotate(v_before4, {x = 0, y = 2 * math.pi / 5, z = 0})
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assert.True(almost_equal(vector.normalize(vector.cross(v_after4, v_before4)), {x = 0, y = 1, z = 0}))
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local v_before5 = {x = 1, y = -1, z = 0}
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local v_after5 = vector.rotate(v_before5, {x = 0, y = 0, z = math.pi / 4})
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assert.True(almost_equal(vector.normalize(vector.cross(v_after5, v_before5)), {x = 0, y = 0, z = 1}))
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local v_before6 = {x = 3, y = 4, z = 0}
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local v_after6 = vector.rotate(v_before6, {x = 0, y = 0, z = 2 * math.pi / 5})
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assert.True(almost_equal(vector.normalize(vector.cross(v_after6, v_before6)), {x = 0, y = 0, z = 1}))
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end)
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end)
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it("dir_to_rotation()", function()
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-- Comparing rotations (pitch, yaw, roll) is hard because of certain ambiguities,
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-- e.g. (pi, 0, pi) looks exactly the same as (0, pi, 0)
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-- So instead we convert the rotation back to vectors and compare these.
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local function forward_at_rot(rot)
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return vector.rotate(vector.new(0, 0, 1), rot)
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end
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local function up_at_rot(rot)
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return vector.rotate(vector.new(0, 1, 0), rot)
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end
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local rot1 = vector.dir_to_rotation({x = 1, y = 0, z = 0}, {x = 0, y = 1, z = 0})
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assert.True(almost_equal({x = 1, y = 0, z = 0}, forward_at_rot(rot1)))
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assert.True(almost_equal({x = 0, y = 1, z = 0}, up_at_rot(rot1)))
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local rot2 = vector.dir_to_rotation({x = 1, y = 1, z = 0}, {x = 0, y = 0, z = 1})
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assert.True(almost_equal({x = 1/math.sqrt(2), y = 1/math.sqrt(2), z = 0}, forward_at_rot(rot2)))
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assert.True(almost_equal({x = 0, y = 0, z = 1}, up_at_rot(rot2)))
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for i = 1, 1000 do
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local rand_vec = vector.new(math.random(), math.random(), math.random())
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if vector.length(rand_vec) ~= 0 then
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local rot_1 = vector.dir_to_rotation(rand_vec)
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local rot_2 = {
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x = math.atan2(rand_vec.y, math.sqrt(rand_vec.z * rand_vec.z + rand_vec.x * rand_vec.x)),
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y = -math.atan2(rand_vec.x, rand_vec.z),
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z = 0
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}
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assert.True(almost_equal(rot_1, rot_2))
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end
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end
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end)
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end)
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@ -141,3 +141,96 @@ function vector.sort(a, b)
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return {x = math.min(a.x, b.x), y = math.min(a.y, b.y), z = math.min(a.z, b.z)},
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{x = math.max(a.x, b.x), y = math.max(a.y, b.y), z = math.max(a.z, b.z)}
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end
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local function sin(x)
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if x % math.pi == 0 then
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return 0
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else
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return math.sin(x)
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end
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end
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local function cos(x)
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if x % math.pi == math.pi / 2 then
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return 0
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else
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return math.cos(x)
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end
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end
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function vector.rotate_around_axis(v, axis, angle)
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local cosangle = cos(angle)
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local sinangle = sin(angle)
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axis = vector.normalize(axis)
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-- https://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula
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local dot_axis = vector.multiply(axis, vector.dot(axis, v))
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local cross = vector.cross(v, axis)
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return vector.new(
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cross.x * sinangle + (v.x - dot_axis.x) * cosangle + dot_axis.x,
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cross.y * sinangle + (v.y - dot_axis.y) * cosangle + dot_axis.y,
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cross.z * sinangle + (v.z - dot_axis.z) * cosangle + dot_axis.z
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)
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end
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function vector.rotate(v, rot)
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local sinpitch = sin(-rot.x)
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local sinyaw = sin(-rot.y)
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local sinroll = sin(-rot.z)
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local cospitch = cos(rot.x)
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local cosyaw = cos(rot.y)
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local cosroll = math.cos(rot.z)
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-- Rotation matrix that applies yaw, pitch and roll
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local matrix = {
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{
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sinyaw * sinpitch * sinroll + cosyaw * cosroll,
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sinyaw * sinpitch * cosroll - cosyaw * sinroll,
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sinyaw * cospitch,
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},
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{
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cospitch * sinroll,
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cospitch * cosroll,
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-sinpitch,
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},
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{
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cosyaw * sinpitch * sinroll - sinyaw * cosroll,
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cosyaw * sinpitch * cosroll + sinyaw * sinroll,
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cosyaw * cospitch,
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},
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}
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-- Compute matrix multiplication: `matrix` * `v`
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return vector.new(
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matrix[1][1] * v.x + matrix[1][2] * v.y + matrix[1][3] * v.z,
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matrix[2][1] * v.x + matrix[2][2] * v.y + matrix[2][3] * v.z,
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matrix[3][1] * v.x + matrix[3][2] * v.y + matrix[3][3] * v.z
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)
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end
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function vector.dir_to_rotation(forward, up)
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forward = vector.normalize(forward)
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local rot = {x = math.asin(forward.y), y = -math.atan2(forward.x, forward.z), z = 0}
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if not up then
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return rot
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end
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assert(vector.dot(forward, up) < 0.000001,
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"Invalid vectors passed to vector.dir_to_rotation().")
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up = vector.normalize(up)
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-- Calculate vector pointing up with roll = 0, just based on forward vector.
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local forwup = vector.rotate({x = 0, y = 1, z = 0}, rot)
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-- 'forwup' and 'up' are now in a plane with 'forward' as normal.
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-- The angle between them is the absolute of the roll value we're looking for.
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rot.z = vector.angle(forwup, up)
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-- Since vector.angle never returns a negative value or a value greater
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-- than math.pi, rot.z has to be inverted sometimes.
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-- To determine wether this is the case, we rotate the up vector back around
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-- the forward vector and check if it worked out.
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local back = vector.rotate_around_axis(up, forward, -rot.z)
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-- We don't use vector.equals for this because of floating point imprecision.
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if (back.x - forwup.x) * (back.x - forwup.x) +
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(back.y - forwup.y) * (back.y - forwup.y) +
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(back.z - forwup.z) * (back.z - forwup.z) > 0.0000001 then
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rot.z = -rot.z
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end
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return rot
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end
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