4 function vector.new(a, b, c)
5 if type(a) == "table" then
6 assert(a.x and a.y and a.z, "Invalid vector passed to vector.new()")
7 return {x=a.x, y=a.y, z=a.z}
9 assert(b and c, "Invalid arguments for vector.new()")
10 return {x=a, y=b, z=c}
12 return {x=0, y=0, z=0}
15 function vector.equals(a, b)
21 function vector.length(v)
22 return math.hypot(v.x, math.hypot(v.y, v.z))
25 function vector.normalize(v)
26 local len = vector.length(v)
28 return {x=0, y=0, z=0}
30 return vector.divide(v, len)
34 function vector.floor(v)
42 function vector.round(v)
44 x = math.floor(v.x + 0.5),
45 y = math.floor(v.y + 0.5),
46 z = math.floor(v.z + 0.5)
50 function vector.apply(v, func)
58 function vector.distance(a, b)
62 return math.hypot(x, math.hypot(y, z))
65 function vector.direction(pos1, pos2)
66 return vector.normalize({
73 function vector.angle(a, b)
74 local dotp = vector.dot(a, b)
75 local cp = vector.cross(a, b)
76 local crossplen = vector.length(cp)
77 return math.atan2(crossplen, dotp)
80 function vector.dot(a, b)
81 return a.x * b.x + a.y * b.y + a.z * b.z
84 function vector.cross(a, b)
86 x = a.y * b.z - a.z * b.y,
87 y = a.z * b.x - a.x * b.z,
88 z = a.x * b.y - a.y * b.x
92 function vector.add(a, b)
93 if type(b) == "table" then
94 return {x = a.x + b.x,
104 function vector.subtract(a, b)
105 if type(b) == "table" then
106 return {x = a.x - b.x,
116 function vector.multiply(a, b)
117 if type(b) == "table" then
118 return {x = a.x * b.x,
128 function vector.divide(a, b)
129 if type(b) == "table" then
130 return {x = a.x / b.x,
140 function vector.sort(a, b)
141 return {x = math.min(a.x, b.x), y = math.min(a.y, b.y), z = math.min(a.z, b.z)},
142 {x = math.max(a.x, b.x), y = math.max(a.y, b.y), z = math.max(a.z, b.z)}
145 local function sin(x)
146 if x % math.pi == 0 then
153 local function cos(x)
154 if x % math.pi == math.pi / 2 then
161 function vector.rotate_around_axis(v, axis, angle)
162 local cosangle = cos(angle)
163 local sinangle = sin(angle)
164 axis = vector.normalize(axis)
165 -- https://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula
166 local dot_axis = vector.multiply(axis, vector.dot(axis, v))
167 local cross = vector.cross(v, axis)
169 cross.x * sinangle + (v.x - dot_axis.x) * cosangle + dot_axis.x,
170 cross.y * sinangle + (v.y - dot_axis.y) * cosangle + dot_axis.y,
171 cross.z * sinangle + (v.z - dot_axis.z) * cosangle + dot_axis.z
175 function vector.rotate(v, rot)
176 local sinpitch = sin(-rot.x)
177 local sinyaw = sin(-rot.y)
178 local sinroll = sin(-rot.z)
179 local cospitch = cos(rot.x)
180 local cosyaw = cos(rot.y)
181 local cosroll = math.cos(rot.z)
182 -- Rotation matrix that applies yaw, pitch and roll
185 sinyaw * sinpitch * sinroll + cosyaw * cosroll,
186 sinyaw * sinpitch * cosroll - cosyaw * sinroll,
195 cosyaw * sinpitch * sinroll - sinyaw * cosroll,
196 cosyaw * sinpitch * cosroll + sinyaw * sinroll,
200 -- Compute matrix multiplication: `matrix` * `v`
202 matrix[1][1] * v.x + matrix[1][2] * v.y + matrix[1][3] * v.z,
203 matrix[2][1] * v.x + matrix[2][2] * v.y + matrix[2][3] * v.z,
204 matrix[3][1] * v.x + matrix[3][2] * v.y + matrix[3][3] * v.z
208 function vector.dir_to_rotation(forward, up)
209 forward = vector.normalize(forward)
210 local rot = {x = math.asin(forward.y), y = -math.atan2(forward.x, forward.z), z = 0}
214 assert(vector.dot(forward, up) < 0.000001,
215 "Invalid vectors passed to vector.dir_to_rotation().")
216 up = vector.normalize(up)
217 -- Calculate vector pointing up with roll = 0, just based on forward vector.
218 local forwup = vector.rotate({x = 0, y = 1, z = 0}, rot)
219 -- 'forwup' and 'up' are now in a plane with 'forward' as normal.
220 -- The angle between them is the absolute of the roll value we're looking for.
221 rot.z = vector.angle(forwup, up)
223 -- Since vector.angle never returns a negative value or a value greater
224 -- than math.pi, rot.z has to be inverted sometimes.
225 -- To determine wether this is the case, we rotate the up vector back around
226 -- the forward vector and check if it worked out.
227 local back = vector.rotate_around_axis(up, forward, -rot.z)
229 -- We don't use vector.equals for this because of floating point imprecision.
230 if (back.x - forwup.x) * (back.x - forwup.x) +
231 (back.y - forwup.y) * (back.y - forwup.y) +
232 (back.z - forwup.z) * (back.z - forwup.z) > 0.0000001 then