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vector = {}
function vector.new(a, b, c)
if type(a) == "table" then
assert(a.x and a.y and a.z, "Invalid vector passed to vector.new()")
return {x=a.x, y=a.y, z=a.z}
elseif a then
assert(b and c, "Invalid arguments for vector.new()")
return {x=a, y=b, z=c}
end
return {x=0, y=0, z=0}
end
function vector.equals(a, b)
return a.x == b.x and
a.y == b.y and
a.z == b.z
end
function vector.length(v)
return math.hypot(v.x, math.hypot(v.y, v.z))
end
function vector.normalize(v)
local len = vector.length(v)
if len == 0 then
return {x=0, y=0, z=0}
else
return vector.divide(v, len)
end
end
function vector.floor(v)
return {
x = math.floor(v.x),
y = math.floor(v.y),
z = math.floor(v.z)
}
end
function vector.round(v)
return {
x = math.floor(v.x + 0.5),
y = math.floor(v.y + 0.5),
z = math.floor(v.z + 0.5)
}
end
function vector.apply(v, func)
return {
x = func(v.x),
y = func(v.y),
z = func(v.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.hypot(x, math.hypot(y, z))
end
function vector.direction(pos1, pos2)
return vector.normalize({
x = pos2.x - pos1.x,
y = pos2.y - pos1.y,
z = pos2.z - pos1.z
})
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 {
x = a.y * b.z - a.z * b.y,
y = a.z * b.x - a.x * b.z,
z = a.x * b.y - a.y * b.x
}
end
function vector.add(a, b)
if type(b) == "table" then
return {x = a.x + b.x,
y = a.y + b.y,
z = a.z + b.z}
else
return {x = a.x + b,
y = a.y + b,
z = a.z + b}
end
end
function vector.subtract(a, b)
if type(b) == "table" then
return {x = a.x - b.x,
y = a.y - b.y,
z = a.z - b.z}
else
return {x = a.x - b,
y = a.y - b,
z = a.z - b}
end
end
function vector.multiply(a, b)
if type(b) == "table" then
return {x = a.x * b.x,
y = a.y * b.y,
z = a.z * b.z}
else
return {x = a.x * b,
y = a.y * b,
z = a.z * b}
end
end
function vector.divide(a, b)
if type(b) == "table" then
return {x = a.x / b.x,
y = a.y / b.y,
z = a.z / b.z}
else
return {x = a.x / b,
y = a.y / b,
z = a.z / b}
end
end
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
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