summaryrefslogtreecommitdiff
path: root/builtin/common/vector.lua
blob: a08472e322c7b42513f084e9f94560791e778e20 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
--[[
Vector helpers
Note: The vector.*-functions must be able to accept old vectors that had no metatables
]]

-- localize functions
local setmetatable = setmetatable

-- vector.metatable is set by C++.
local metatable = vector.metatable

local xyz = {"x", "y", "z"}

-- only called when rawget(v, key) returns nil
function metatable.__index(v, key)
	return rawget(v, xyz[key]) or vector[key]
end

-- only called when rawget(v, key) returns nil
function metatable.__newindex(v, key, value)
	rawset(v, xyz[key] or key, value)
end

-- constructors

local function fast_new(x, y, z)
	return setmetatable({x = x, y = y, z = z}, metatable)
end

function vector.new(a, b, c)
	if a and b and c then
		return fast_new(a, b, c)
	end

	-- deprecated, use vector.copy and vector.zero directly
	if type(a) == "table" then
		return vector.copy(a)
	else
		assert(not a, "Invalid arguments for vector.new()")
		return vector.zero()
	end
end

function vector.zero()
	return fast_new(0, 0, 0)
end

function vector.copy(v)
	assert(v.x and v.y and v.z, "Invalid vector passed to vector.copy()")
	return fast_new(v.x, v.y, v.z)
end

function vector.from_string(s, init)
	local x, y, z, np = string.match(s, "^%s*%(%s*([^%s,]+)%s*[,%s]%s*([^%s,]+)%s*[,%s]" ..
			"%s*([^%s,]+)%s*[,%s]?%s*%)()", init)
	x = tonumber(x)
	y = tonumber(y)
	z = tonumber(z)
	if not (x and y and z) then
		return nil
	end
	return fast_new(x, y, z), np
end

function vector.to_string(v)
	return string.format("(%g, %g, %g)", v.x, v.y, v.z)
end
metatable.__tostring = vector.to_string

function vector.equals(a, b)
	return a.x == b.x and
	       a.y == b.y and
	       a.z == b.z
end
metatable.__eq = vector.equals

-- unary operations

function vector.length(v)
	return math.sqrt(v.x * v.x + v.y * v.y + v.z * v.z)
end
-- Note: we can not use __len because it is already used for primitive table length

function vector.normalize(v)
	local len = vector.length(v)
	if len == 0 then
		return fast_new(0, 0, 0)
	else
		return vector.divide(v, len)
	end
end

function vector.floor(v)
	return vector.apply(v, math.floor)
end

function vector.round(v)
	return fast_new(
		math.round(v.x),
		math.round(v.y),
		math.round(v.z)
	)
end

function vector.apply(v, func)
	return fast_new(
		func(v.x),
		func(v.y),
		func(v.z)
	)
end

function vector.combine(a, b, func)
	return fast_new(
		func(a.x, b.x),
		func(a.y, b.y),
		func(a.z, b.z)
	)
end

function vector.distance(a, b)
	local x = a.x - b.x
	local y = a.y - b.y
	local z = a.z - b.z
	return math.sqrt(x * x + y * y + z * z)
end

function vector.direction(pos1, pos2)
	return vector.subtract(pos2, pos1):normalize()
end

function vector.angle(a, b)
	local dotp = vector.dot(a, b)
	local cp = vector.cross(a, b)
	local crossplen = vector.length(cp)
	return math.atan2(crossplen, dotp)
end

function vector.dot(a, b)
	return a.x * b.x + a.y * b.y + a.z * b.z
end

function vector.cross(a, b)
	return fast_new(
		a.y * b.z - a.z * b.y,
		a.z * b.x - a.x * b.z,
		a.x * b.y - a.y * b.x
	)
end

function metatable.__unm(v)
	return fast_new(-v.x, -v.y, -v.z)
end

-- add, sub, mul, div operations

function vector.add(a, b)
	if type(b) == "table" then
		return fast_new(
			a.x + b.x,
			a.y + b.y,
			a.z + b.z
		)
	else
		return fast_new(
			a.x + b,
			a.y + b,
			a.z + b
		)
	end
end
function metatable.__add(a, b)
	return fast_new(
		a.x + b.x,
		a.y + b.y,
		a.z + b.z
	)
end

function vector.subtract(a, b)
	if type(b) == "table" then
		return fast_new(
			a.x - b.x,
			a.y - b.y,
			a.z - b.z
		)
	else
		return fast_new(
			a.x - b,
			a.y - b,
			a.z - b
		)
	end
end
function metatable.__sub(a, b)
	return fast_new(
		a.x - b.x,
		a.y - b.y,
		a.z - b.z
	)
end

function vector.multiply(a, b)
	if type(b) == "table" then
		return fast_new(
			a.x * b.x,
			a.y * b.y,
			a.z * b.z
		)
	else
		return fast_new(
			a.x * b,
			a.y * b,
			a.z * b
		)
	end
end
function metatable.__mul(a, b)
	if type(a) == "table" then
		return fast_new(
			a.x * b,
			a.y * b,
			a.z * b
		)
	else
		return fast_new(
			a * b.x,
			a * b.y,
			a * b.z
		)
	end
end

function vector.divide(a, b)
	if type(b) == "table" then
		return fast_new(
			a.x / b.x,
			a.y / b.y,
			a.z / b.z
		)
	else
		return fast_new(
			a.x / b,
			a.y / b,
			a.z / b
		)
	end
end
function metatable.__div(a, b)
	-- scalar/vector makes no sense
	return fast_new(
		a.x / b,
		a.y / b,
		a.z / b
	)
end

-- misc stuff

function vector.offset(v, x, y, z)
	return fast_new(
		v.x + x,
		v.y + y,
		v.z + z
	)
end

function vector.sort(a, b)
	return fast_new(math.min(a.x, b.x), math.min(a.y, b.y), math.min(a.z, b.z)),
		fast_new(math.max(a.x, b.x), math.max(a.y, b.y), math.max(a.z, b.z))
end

function vector.check(v)
	return getmetatable(v) == metatable
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 = vector.new(math.asin(forward.y), -math.atan2(forward.x, forward.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(vector.new(0, 1, 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