From 7148834440d10bc211628aa2652e31166bdd58a0 Mon Sep 17 00:00:00 2001 From: NetherEran <55532075+NetherEran@users.noreply.github.com> Date: Tue, 9 Jun 2020 17:38:39 +0000 Subject: 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 --- builtin/common/tests/vector_spec.lua | 142 +++++++++++++++++++++++++++++++++++ 1 file changed, 142 insertions(+) (limited to 'builtin/common/tests/vector_spec.lua') 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) -- cgit v1.2.3