minetest/builtin/common/vector.lua

351 lines
7.1 KiB
Lua

--[[
Vector helpers
Note: The vector.*-functions must be able to accept old vectors that had no metatables
]]
-- localize functions
local setmetatable = setmetatable
vector = {}
local metatable = {}
vector.metatable = 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 type(a) == "table" then
assert(a.x and a.y and a.z, "Invalid vector passed to vector.new()")
return fast_new(a.x, a.y, a.z)
elseif a then
assert(b and c, "Invalid arguments for vector.new()")
return fast_new(a, b, c)
end
return fast_new(0, 0, 0)
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 {x = x, y = y, z = 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.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