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_G.vector = {}
dofile("builtin/common/vector.lua")
describe("vector", function()
describe("new()", function()
it("constructs", function()
assert.same({ x = 0, y = 0, z = 0 }, vector.new())
assert.same({ x = 1, y = 2, z = 3 }, vector.new(1, 2, 3))
assert.same({ x = 3, y = 2, z = 1 }, vector.new({ x = 3, y = 2, z = 1 }))
local input = vector.new({ x = 3, y = 2, z = 1 })
local output = vector.new(input)
assert.same(input, output)
assert.are_not.equal(input, output)
end)
it("throws on invalid input", function()
assert.has.errors(function()
vector.new({ x = 3 })
end)
assert.has.errors(function()
vector.new({ d = 3 })
end)
end)
end)
it("equal()", function()
local function assertE(a, b)
assert.is_true(vector.equals(a, b))
end
local function assertNE(a, b)
assert.is_false(vector.equals(a, b))
end
assertE({x = 0, y = 0, z = 0}, {x = 0, y = 0, z = 0})
assertE({x = -1, y = 0, z = 1}, {x = -1, y = 0, z = 1})
local a = { x = 2, y = 4, z = -10 }
assertE(a, a)
assertNE({x = -1, y = 0, z = 1}, a)
end)
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)
it("offset()", function()
assert.same({ x = 41, y = 52, z = 63 }, vector.offset(vector.new(1, 2, 3), 40, 50, 60))
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)
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