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-rw-r--r--builtin/common/tests/vector_spec.lua142
-rw-r--r--builtin/common/vector.lua93
2 files changed, 235 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)
diff --git a/builtin/common/vector.lua b/builtin/common/vector.lua
index ca6541eb4..1fd784ce2 100644
--- a/builtin/common/vector.lua
+++ b/builtin/common/vector.lua
@@ -141,3 +141,96 @@ function vector.sort(a, b)
return {x = math.min(a.x, b.x), y = math.min(a.y, b.y), z = math.min(a.z, b.z)},
{x = math.max(a.x, b.x), y = math.max(a.y, b.y), z = math.max(a.z, b.z)}
end
+
+local function sin(x)
+ if x % math.pi == 0 then
+ return 0
+ else
+ return math.sin(x)
+ end
+end
+
+local function cos(x)
+ if x % math.pi == math.pi / 2 then
+ return 0
+ else
+ return math.cos(x)
+ end
+end
+
+function vector.rotate_around_axis(v, axis, angle)
+ local cosangle = cos(angle)
+ local sinangle = sin(angle)
+ axis = vector.normalize(axis)
+ -- https://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula
+ local dot_axis = vector.multiply(axis, vector.dot(axis, v))
+ local cross = vector.cross(v, axis)
+ return vector.new(
+ cross.x * sinangle + (v.x - dot_axis.x) * cosangle + dot_axis.x,
+ cross.y * sinangle + (v.y - dot_axis.y) * cosangle + dot_axis.y,
+ cross.z * sinangle + (v.z - dot_axis.z) * cosangle + dot_axis.z
+ )
+end
+
+function vector.rotate(v, rot)
+ local sinpitch = sin(-rot.x)
+ local sinyaw = sin(-rot.y)
+ local sinroll = sin(-rot.z)
+ local cospitch = cos(rot.x)
+ local cosyaw = cos(rot.y)
+ local cosroll = math.cos(rot.z)
+ -- Rotation matrix that applies yaw, pitch and roll
+ local matrix = {
+ {
+ sinyaw * sinpitch * sinroll + cosyaw * cosroll,
+ sinyaw * sinpitch * cosroll - cosyaw * sinroll,
+ sinyaw * cospitch,
+ },
+ {
+ cospitch * sinroll,
+ cospitch * cosroll,
+ -sinpitch,
+ },
+ {
+ cosyaw * sinpitch * sinroll - sinyaw * cosroll,
+ cosyaw * sinpitch * cosroll + sinyaw * sinroll,
+ cosyaw * cospitch,
+ },
+ }
+ -- Compute matrix multiplication: `matrix` * `v`
+ return vector.new(
+ matrix[1][1] * v.x + matrix[1][2] * v.y + matrix[1][3] * v.z,
+ matrix[2][1] * v.x + matrix[2][2] * v.y + matrix[2][3] * v.z,
+ matrix[3][1] * v.x + matrix[3][2] * v.y + matrix[3][3] * v.z
+ )
+end
+
+function vector.dir_to_rotation(forward, up)
+ forward = vector.normalize(forward)
+ local rot = {x = math.asin(forward.y), y = -math.atan2(forward.x, forward.z), z = 0}
+ if not up then
+ return rot
+ end
+ assert(vector.dot(forward, up) < 0.000001,
+ "Invalid vectors passed to vector.dir_to_rotation().")
+ up = vector.normalize(up)
+ -- Calculate vector pointing up with roll = 0, just based on forward vector.
+ local forwup = vector.rotate({x = 0, y = 1, z = 0}, rot)
+ -- 'forwup' and 'up' are now in a plane with 'forward' as normal.
+ -- The angle between them is the absolute of the roll value we're looking for.
+ rot.z = vector.angle(forwup, up)
+
+ -- Since vector.angle never returns a negative value or a value greater
+ -- than math.pi, rot.z has to be inverted sometimes.
+ -- To determine wether this is the case, we rotate the up vector back around
+ -- the forward vector and check if it worked out.
+ local back = vector.rotate_around_axis(up, forward, -rot.z)
+
+ -- We don't use vector.equals for this because of floating point imprecision.
+ if (back.x - forwup.x) * (back.x - forwup.x) +
+ (back.y - forwup.y) * (back.y - forwup.y) +
+ (back.z - forwup.z) * (back.z - forwup.z) > 0.0000001 then
+ rot.z = -rot.z
+ end
+ return rot
+end