2 dofile("builtin/common/vector.lua")
4 describe("vector", function()
5 describe("new()", function()
6 it("constructs", function()
7 assert.same({x = 0, y = 0, z = 0}, vector.new())
8 assert.same({x = 1, y = 2, z = 3}, vector.new(1, 2, 3))
9 assert.same({x = 3, y = 2, z = 1}, vector.new({x = 3, y = 2, z = 1}))
11 assert.is_true(vector.check(vector.new()))
12 assert.is_true(vector.check(vector.new(1, 2, 3)))
13 assert.is_true(vector.check(vector.new({x = 3, y = 2, z = 1})))
15 local input = vector.new({ x = 3, y = 2, z = 1 })
16 local output = vector.new(input)
17 assert.same(input, output)
18 assert.equal(input, output)
19 assert.is_false(rawequal(input, output))
20 assert.equal(input, input:new())
23 it("throws on invalid input", function()
24 assert.has.errors(function()
28 assert.has.errors(function()
34 it("zero()", function()
35 assert.same({x = 0, y = 0, z = 0}, vector.zero())
36 assert.same(vector.new(), vector.zero())
37 assert.equal(vector.new(), vector.zero())
38 assert.is_true(vector.check(vector.zero()))
41 it("copy()", function()
42 local v = vector.new(1, 2, 3)
43 assert.same(v, vector.copy(v))
44 assert.same(vector.new(v), vector.copy(v))
45 assert.equal(vector.new(v), vector.copy(v))
46 assert.is_true(vector.check(vector.copy(v)))
49 it("indexes", function()
50 local some_vector = vector.new(24, 42, 13)
51 assert.equal(24, some_vector[1])
52 assert.equal(24, some_vector.x)
53 assert.equal(42, some_vector[2])
54 assert.equal(42, some_vector.y)
55 assert.equal(13, some_vector[3])
56 assert.equal(13, some_vector.z)
59 assert.equal(100, some_vector.x)
61 assert.equal(101, some_vector[1])
64 assert.equal(100, some_vector.y)
66 assert.equal(102, some_vector[2])
69 assert.equal(100, some_vector.z)
71 assert.equal(103, some_vector[3])
74 it("direction()", function()
75 local a = vector.new(1, 0, 0)
76 local b = vector.new(1, 42, 0)
77 assert.equal(vector.new(0, 1, 0), vector.direction(a, b))
78 assert.equal(vector.new(0, 1, 0), a:direction(b))
81 it("distance()", function()
82 local a = vector.new(1, 0, 0)
83 local b = vector.new(3, 42, 9)
84 assert.is_true(math.abs(43 - vector.distance(a, b)) < 1.0e-12)
85 assert.is_true(math.abs(43 - a:distance(b)) < 1.0e-12)
86 assert.equal(0, vector.distance(a, a))
87 assert.equal(0, b:distance(b))
90 it("length()", function()
91 local a = vector.new(0, 0, -23)
92 assert.equal(0, vector.length(vector.new()))
93 assert.equal(23, vector.length(a))
94 assert.equal(23, a:length())
97 it("normalize()", function()
98 local a = vector.new(0, 0, -23)
99 assert.equal(vector.new(0, 0, -1), vector.normalize(a))
100 assert.equal(vector.new(0, 0, -1), a:normalize())
101 assert.equal(vector.new(), vector.normalize(vector.new()))
104 it("floor()", function()
105 local a = vector.new(0.1, 0.9, -0.5)
106 assert.equal(vector.new(0, 0, -1), vector.floor(a))
107 assert.equal(vector.new(0, 0, -1), a:floor())
110 it("round()", function()
111 local a = vector.new(0.1, 0.9, -0.5)
112 assert.equal(vector.new(0, 1, -1), vector.round(a))
113 assert.equal(vector.new(0, 1, -1), a:round())
116 it("apply()", function()
118 local f = function(x)
122 local a = vector.new(0.1, 0.9, -0.5)
123 assert.equal(vector.new(1, 1, 0), vector.apply(a, math.ceil))
124 assert.equal(vector.new(1, 1, 0), a:apply(math.ceil))
125 assert.equal(vector.new(0.1, 0.9, 0.5), vector.apply(a, math.abs))
126 assert.equal(vector.new(0.1, 0.9, 0.5), a:apply(math.abs))
127 assert.equal(vector.new(1.1, 2.9, 2.5), vector.apply(a, f))
128 assert.equal(vector.new(4.1, 5.9, 5.5), a:apply(f))
131 it("equals()", function()
132 local function assertE(a, b)
133 assert.is_true(vector.equals(a, b))
135 local function assertNE(a, b)
136 assert.is_false(vector.equals(a, b))
139 assertE({x = 0, y = 0, z = 0}, {x = 0, y = 0, z = 0})
140 assertE({x = -1, y = 0, z = 1}, {x = -1, y = 0, z = 1})
141 assertE({x = -1, y = 0, z = 1}, vector.new(-1, 0, 1))
142 local a = {x = 2, y = 4, z = -10}
144 assertNE({x = -1, y = 0, z = 1}, a)
146 assert.equal(vector.new(1, 2, 3), vector.new(1, 2, 3))
147 assert.is_true(vector.new(1, 2, 3):equals(vector.new(1, 2, 3)))
148 assert.not_equal(vector.new(1, 2, 3), vector.new(1, 2, 4))
149 assert.is_true(vector.new(1, 2, 3) == vector.new(1, 2, 3))
150 assert.is_false(vector.new(1, 2, 3) == vector.new(1, 3, 3))
153 it("metatable is same", function()
154 local a = vector.new()
155 local b = vector.new(1, 2, 3)
157 assert.equal(true, vector.check(a))
158 assert.equal(true, vector.check(b))
160 assert.equal(vector.metatable, getmetatable(a))
161 assert.equal(vector.metatable, getmetatable(b))
162 assert.equal(vector.metatable, a.metatable)
165 it("sort()", function()
166 local a = vector.new(1, 2, 3)
167 local b = vector.new(0.5, 232, -2)
168 local sorted = {vector.new(0.5, 2, -2), vector.new(1, 232, 3)}
169 assert.same(sorted, {vector.sort(a, b)})
170 assert.same(sorted, {a:sort(b)})
173 it("angle()", function()
174 assert.equal(math.pi, vector.angle(vector.new(-1, -2, -3), vector.new(1, 2, 3)))
175 assert.equal(math.pi/2, vector.new(0, 1, 0):angle(vector.new(1, 0, 0)))
178 it("dot()", function()
179 assert.equal(-14, vector.dot(vector.new(-1, -2, -3), vector.new(1, 2, 3)))
180 assert.equal(0, vector.new():dot(vector.new(1, 2, 3)))
183 it("cross()", function()
184 local a = vector.new(-1, -2, 0)
185 local b = vector.new(1, 2, 3)
186 assert.equal(vector.new(-6, 3, 0), vector.cross(a, b))
187 assert.equal(vector.new(-6, 3, 0), a:cross(b))
190 it("offset()", function()
191 assert.same({x = 41, y = 52, z = 63}, vector.offset(vector.new(1, 2, 3), 40, 50, 60))
192 assert.equal(vector.new(41, 52, 63), vector.offset(vector.new(1, 2, 3), 40, 50, 60))
193 assert.equal(vector.new(41, 52, 63), vector.new(1, 2, 3):offset(40, 50, 60))
196 it("is()", function()
197 local some_table1 = {foo = 13, [42] = 1, "bar", 2}
198 local some_table2 = {1, 2, 3}
199 local some_table3 = {x = 1, 2, 3}
200 local some_table4 = {1, 2, z = 3}
201 local old = {x = 1, y = 2, z = 3}
202 local real = vector.new(1, 2, 3)
204 assert.is_false(vector.check(nil))
205 assert.is_false(vector.check(1))
206 assert.is_false(vector.check(true))
207 assert.is_false(vector.check("foo"))
208 assert.is_false(vector.check(some_table1))
209 assert.is_false(vector.check(some_table2))
210 assert.is_false(vector.check(some_table3))
211 assert.is_false(vector.check(some_table4))
212 assert.is_false(vector.check(old))
213 assert.is_true(vector.check(real))
214 assert.is_true(real:check())
217 it("global pairs", function()
219 local vec = vector.new(10, 20, 30)
220 for k, v in pairs(vec) do
223 assert.same({x = 10, y = 20, z = 30}, out)
226 it("abusing works", function()
227 local v = vector.new(1, 2, 3)
231 local a_is_there = false
232 for key, value in pairs(v) do
235 assert.equal(value, 1)
239 assert.is_true(a_is_there)
242 it("add()", function()
243 local a = vector.new(1, 2, 3)
244 local b = vector.new(1, 4, 3)
245 local c = vector.new(2, 6, 6)
246 assert.equal(c, vector.add(a, {x = 1, y = 4, z = 3}))
247 assert.equal(c, vector.add(a, b))
248 assert.equal(c, a:add(b))
249 assert.equal(c, a + b)
250 assert.equal(c, b + a)
253 it("subtract()", function()
254 local a = vector.new(1, 2, 3)
255 local b = vector.new(2, 4, 3)
256 local c = vector.new(-1, -2, 0)
257 assert.equal(c, vector.subtract(a, {x = 2, y = 4, z = 3}))
258 assert.equal(c, vector.subtract(a, b))
259 assert.equal(c, a:subtract(b))
260 assert.equal(c, a - b)
261 assert.equal(c, -b + a)
264 it("multiply()", function()
265 local a = vector.new(1, 2, 3)
266 local b = vector.new(2, 4, 3)
267 local c = vector.new(2, 8, 9)
269 local d = vector.new(2, 4, 6)
270 assert.equal(c, vector.multiply(a, {x = 2, y = 4, z = 3}))
271 assert.equal(c, vector.multiply(a, b))
272 assert.equal(d, vector.multiply(a, s))
273 assert.equal(d, a:multiply(s))
274 assert.equal(d, a * s)
275 assert.equal(d, s * a)
276 assert.equal(-a, -1 * a)
279 it("divide()", function()
280 local a = vector.new(1, 2, 3)
281 local b = vector.new(2, 4, 3)
282 local c = vector.new(0.5, 0.5, 1)
284 local d = vector.new(0.5, 1, 1.5)
285 assert.equal(c, vector.divide(a, {x = 2, y = 4, z = 3}))
286 assert.equal(c, vector.divide(a, b))
287 assert.equal(d, vector.divide(a, s))
288 assert.equal(d, a:divide(s))
289 assert.equal(d, a / s)
290 assert.equal(d, 1/s * a)
291 assert.equal(-a, a / -1)
294 it("to_string()", function()
295 local v = vector.new(1, 2, 3.14)
296 assert.same("(1, 2, 3.14)", vector.to_string(v))
297 assert.same("(1, 2, 3.14)", v:to_string())
298 assert.same("(1, 2, 3.14)", tostring(v))
301 it("from_string()", function()
302 local v = vector.new(1, 2, 3.14)
303 assert.is_true(vector.check(vector.from_string("(1, 2, 3.14)")))
304 assert.same({v, 13}, {vector.from_string("(1, 2, 3.14)")})
305 assert.same({v, 12}, {vector.from_string("(1,2 ,3.14)")})
306 assert.same({v, 12}, {vector.from_string("(1,2,3.14,)")})
307 assert.same({v, 11}, {vector.from_string("(1 2 3.14)")})
308 assert.same({v, 15}, {vector.from_string("( 1, 2, 3.14 )")})
309 assert.same({v, 15}, {vector.from_string(" ( 1, 2, 3.14) ")})
310 assert.same({vector.new(), 8}, {vector.from_string("(0,0,0) ( 1, 2, 3.14) ")})
311 assert.same({v, 22}, {vector.from_string("(0,0,0) ( 1, 2, 3.14) ", 8)})
312 assert.same({v, 22}, {vector.from_string("(0,0,0) ( 1, 2, 3.14) ", 9)})
313 assert.same(nil, vector.from_string("nothing"))
316 -- This function is needed because of floating point imprecision.
317 local function almost_equal(a, b)
318 if type(a) == "number" then
319 return math.abs(a - b) < 0.00000000001
321 return vector.distance(a, b) < 0.000000000001
324 describe("rotate_around_axis()", function()
325 it("rotates", function()
326 assert.True(almost_equal({x = -1, y = 0, z = 0},
327 vector.rotate_around_axis({x = 1, y = 0, z = 0}, {x = 0, y = 1, z = 0}, math.pi)))
328 assert.True(almost_equal({x = 0, y = 1, z = 0},
329 vector.rotate_around_axis({x = 0, y = 0, z = 1}, {x = 1, y = 0, z = 0}, math.pi / 2)))
330 assert.True(almost_equal({x = 4, y = 1, z = 1},
331 vector.rotate_around_axis({x = 4, y = 1, z = 1}, {x = 4, y = 1, z = 1}, math.pi / 6)))
333 it("keeps distance to axis", function()
334 local rotate1 = {x = 1, y = 3, z = 1}
335 local axis1 = {x = 1, y = 3, z = 2}
336 local rotated1 = vector.rotate_around_axis(rotate1, axis1, math.pi / 13)
337 assert.True(almost_equal(vector.distance(axis1, rotate1), vector.distance(axis1, rotated1)))
338 local rotate2 = {x = 1, y = 1, z = 3}
339 local axis2 = {x = 2, y = 6, z = 100}
340 local rotated2 = vector.rotate_around_axis(rotate2, axis2, math.pi / 23)
341 assert.True(almost_equal(vector.distance(axis2, rotate2), vector.distance(axis2, rotated2)))
342 local rotate3 = {x = 1, y = -1, z = 3}
343 local axis3 = {x = 2, y = 6, z = 100}
344 local rotated3 = vector.rotate_around_axis(rotate3, axis3, math.pi / 2)
345 assert.True(almost_equal(vector.distance(axis3, rotate3), vector.distance(axis3, rotated3)))
347 it("rotates back", function()
348 local rotate1 = {x = 1, y = 3, z = 1}
349 local axis1 = {x = 1, y = 3, z = 2}
350 local rotated1 = vector.rotate_around_axis(rotate1, axis1, math.pi / 13)
351 rotated1 = vector.rotate_around_axis(rotated1, axis1, -math.pi / 13)
352 assert.True(almost_equal(rotate1, rotated1))
353 local rotate2 = {x = 1, y = 1, z = 3}
354 local axis2 = {x = 2, y = 6, z = 100}
355 local rotated2 = vector.rotate_around_axis(rotate2, axis2, math.pi / 23)
356 rotated2 = vector.rotate_around_axis(rotated2, axis2, -math.pi / 23)
357 assert.True(almost_equal(rotate2, rotated2))
358 local rotate3 = {x = 1, y = -1, z = 3}
359 local axis3 = {x = 2, y = 6, z = 100}
360 local rotated3 = vector.rotate_around_axis(rotate3, axis3, math.pi / 2)
361 rotated3 = vector.rotate_around_axis(rotated3, axis3, -math.pi / 2)
362 assert.True(almost_equal(rotate3, rotated3))
364 it("is right handed", function()
365 local v_before1 = {x = 0, y = 1, z = -1}
366 local v_after1 = vector.rotate_around_axis(v_before1, {x = 1, y = 0, z = 0}, math.pi / 4)
367 assert.True(almost_equal(vector.normalize(vector.cross(v_after1, v_before1)), {x = 1, y = 0, z = 0}))
369 local v_before2 = {x = 0, y = 3, z = 4}
370 local v_after2 = vector.rotate_around_axis(v_before2, {x = 1, y = 0, z = 0}, 2 * math.pi / 5)
371 assert.True(almost_equal(vector.normalize(vector.cross(v_after2, v_before2)), {x = 1, y = 0, z = 0}))
373 local v_before3 = {x = 1, y = 0, z = -1}
374 local v_after3 = vector.rotate_around_axis(v_before3, {x = 0, y = 1, z = 0}, math.pi / 4)
375 assert.True(almost_equal(vector.normalize(vector.cross(v_after3, v_before3)), {x = 0, y = 1, z = 0}))
377 local v_before4 = {x = 3, y = 0, z = 4}
378 local v_after4 = vector.rotate_around_axis(v_before4, {x = 0, y = 1, z = 0}, 2 * math.pi / 5)
379 assert.True(almost_equal(vector.normalize(vector.cross(v_after4, v_before4)), {x = 0, y = 1, z = 0}))
381 local v_before5 = {x = 1, y = -1, z = 0}
382 local v_after5 = vector.rotate_around_axis(v_before5, {x = 0, y = 0, z = 1}, math.pi / 4)
383 assert.True(almost_equal(vector.normalize(vector.cross(v_after5, v_before5)), {x = 0, y = 0, z = 1}))
385 local v_before6 = {x = 3, y = 4, z = 0}
386 local v_after6 = vector.rotate_around_axis(v_before6, {x = 0, y = 0, z = 1}, 2 * math.pi / 5)
387 assert.True(almost_equal(vector.normalize(vector.cross(v_after6, v_before6)), {x = 0, y = 0, z = 1}))
391 describe("rotate()", function()
392 it("rotates", function()
393 assert.True(almost_equal({x = -1, y = 0, z = 0},
394 vector.rotate({x = 1, y = 0, z = 0}, {x = 0, y = math.pi, z = 0})))
395 assert.True(almost_equal({x = 0, y = -1, z = 0},
396 vector.rotate({x = 1, y = 0, z = 0}, {x = 0, y = 0, z = math.pi / 2})))
397 assert.True(almost_equal({x = 1, y = 0, z = 0},
398 vector.rotate({x = 1, y = 0, z = 0}, {x = math.pi / 123, y = 0, z = 0})))
400 it("is counterclockwise", function()
401 local v_before1 = {x = 0, y = 1, z = -1}
402 local v_after1 = vector.rotate(v_before1, {x = math.pi / 4, y = 0, z = 0})
403 assert.True(almost_equal(vector.normalize(vector.cross(v_after1, v_before1)), {x = 1, y = 0, z = 0}))
405 local v_before2 = {x = 0, y = 3, z = 4}
406 local v_after2 = vector.rotate(v_before2, {x = 2 * math.pi / 5, y = 0, z = 0})
407 assert.True(almost_equal(vector.normalize(vector.cross(v_after2, v_before2)), {x = 1, y = 0, z = 0}))
409 local v_before3 = {x = 1, y = 0, z = -1}
410 local v_after3 = vector.rotate(v_before3, {x = 0, y = math.pi / 4, z = 0})
411 assert.True(almost_equal(vector.normalize(vector.cross(v_after3, v_before3)), {x = 0, y = 1, z = 0}))
413 local v_before4 = {x = 3, y = 0, z = 4}
414 local v_after4 = vector.rotate(v_before4, {x = 0, y = 2 * math.pi / 5, z = 0})
415 assert.True(almost_equal(vector.normalize(vector.cross(v_after4, v_before4)), {x = 0, y = 1, z = 0}))
417 local v_before5 = {x = 1, y = -1, z = 0}
418 local v_after5 = vector.rotate(v_before5, {x = 0, y = 0, z = math.pi / 4})
419 assert.True(almost_equal(vector.normalize(vector.cross(v_after5, v_before5)), {x = 0, y = 0, z = 1}))
421 local v_before6 = {x = 3, y = 4, z = 0}
422 local v_after6 = vector.rotate(v_before6, {x = 0, y = 0, z = 2 * math.pi / 5})
423 assert.True(almost_equal(vector.normalize(vector.cross(v_after6, v_before6)), {x = 0, y = 0, z = 1}))
427 it("dir_to_rotation()", function()
428 -- Comparing rotations (pitch, yaw, roll) is hard because of certain ambiguities,
429 -- e.g. (pi, 0, pi) looks exactly the same as (0, pi, 0)
430 -- So instead we convert the rotation back to vectors and compare these.
431 local function forward_at_rot(rot)
432 return vector.rotate(vector.new(0, 0, 1), rot)
434 local function up_at_rot(rot)
435 return vector.rotate(vector.new(0, 1, 0), rot)
437 local rot1 = vector.dir_to_rotation({x = 1, y = 0, z = 0}, {x = 0, y = 1, z = 0})
438 assert.True(almost_equal({x = 1, y = 0, z = 0}, forward_at_rot(rot1)))
439 assert.True(almost_equal({x = 0, y = 1, z = 0}, up_at_rot(rot1)))
440 local rot2 = vector.dir_to_rotation({x = 1, y = 1, z = 0}, {x = 0, y = 0, z = 1})
441 assert.True(almost_equal({x = 1/math.sqrt(2), y = 1/math.sqrt(2), z = 0}, forward_at_rot(rot2)))
442 assert.True(almost_equal({x = 0, y = 0, z = 1}, up_at_rot(rot2)))
444 local rand_vec = vector.new(math.random(), math.random(), math.random())
445 if vector.length(rand_vec) ~= 0 then
446 local rot_1 = vector.dir_to_rotation(rand_vec)
448 x = math.atan2(rand_vec.y, math.sqrt(rand_vec.z * rand_vec.z + rand_vec.x * rand_vec.x)),
449 y = -math.atan2(rand_vec.x, rand_vec.z),
452 assert.True(almost_equal(rot_1, rot_2))