modlib/vector.lua

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local mt_vector = vector
local vector = getfenv(1)
index_aliases = {
x = 1,
y = 2,
z = 3,
w = 4
}
modlib.table.add_all(index_aliases, modlib.table.flip(index_aliases))
metatable = {
__index = function(table, key)
local index = index_aliases[key]
if index ~= nil then
return table[index]
end
return vector[key]
end,
__newindex = function(table, key, value)
local index = letters[key]
if index ~= nil then
return rawset(table, index, value)
end
end
}
function new(v)
return setmetatable(v, metatable)
end
function from_xyzw(v)
return new{v.x, v.y, v.z, v.w}
end
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function from_minetest(v)
return new{v.x, v.y, v.z}
end
function to_xyzw(v)
return {x = v[1], y = v[2], z = v[3], w = v[4]}
end
function to_minetest(v)
return mt_vector.new(unpack(v))
end
function equals(v, other_v)
for k, v in pairs(v) do
if v ~= other_v[k] then return false end
end
return true
end
metatable.__eq = equals
function less_than(v, other_v)
for k, v in pairs(v) do
if v >= other_v[k] then return false end
end
return true
end
metatable.__lt = less_than
function less_or_equal(v, other_v)
for k, v in pairs(v) do
if v > other_v[k] then return false end
end
return true
end
metatable.__le = less_or_equal
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function combine(v, other_v, f)
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local new_vector = {}
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for key, value in pairs(v) do
new_vector[key] = f(value, other_v[key])
end
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return new(new_vector)
end
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function apply(v, f, ...)
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local new_vector = {}
for key, value in pairs(v) do
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new_vector[key] = f(value, ...)
end
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return new(new_vector)
end
function combinator(f)
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return function(v, other_v)
return combine(v, other_v, f)
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end, function(v, ...)
return apply(v, f, ...)
end
end
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function invert(v)
for key, value in pairs(v) do
v[key] = -value
end
end
add, add_scalar = combinator(function(a, b) return a + b end)
subtract, subtract_scalar = combinator(function(a, b) return a - b end)
multiply, multiply_scalar = combinator(function(a, b) return a * b end)
divide, divide_scalar = combinator(function(a, b) return a / b end)
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pow, pow_scalar = combinator(function(a, b) return a ^ b end)
metatable.__add = add
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metatable.__unm = invert
metatable.__sub = subtract
metatable.__mul = multiply
metatable.__div = divide
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function norm(v)
local sum = 0
for _, c in pairs(v) do
sum = sum + c*c
end
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return sum
end
function length(v)
return math.sqrt(norm(v))
end
function normalize(v)
return divide_scalar(v, length(v))
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end
function floor(v)
return apply(v, math.floor)
end
function ceil(v)
return apply(v, math.ceil)
end
function clamp(v, min, max)
return apply(apply(v, math.max, min), math.min, max)
end
function cross3(v, other_v)
return new{
v[2] * other_v[3] - v[3] * other_v[2],
v[3] * other_v[1] - v[1] * other_v[3],
v[1] * other_v[2] - v[2] * other_v[1]
}
end
function dot(v, other_v)
local sum = 0
for i, c in pairs(v) do
sum = sum + c * other_v[i]
end
return sum
end
function box_box_collision(diff, box, other_box)
for index, diff in pairs(diff) do
if box[index] + diff > other_box[index + 3] or other_box[index] > box[index + 3] + diff then
return false
end
end
return true
end
--+ Möller-Trumbore
function ray_triangle_intersection(origin, direction, triangle)
local point_1, point_2, point_3 = unpack(triangle)
local edge_1, edge_2 = subtract(point_2, point_1), subtract(point_3, point_1)
local h = cross3(direction, edge_2)
local a = dot(edge_1, h)
if math.abs(a) < 1e-9 then
return
end
local f = 1 / a
local diff = subtract(origin, point_1)
local u = f * dot(diff, h)
if u < 0 or u > 1 then
return
end
local q = cross3(diff, edge_1)
local v = f * dot(direction, q)
if v < 0 or u + v > 1 then
return
end
local pos_on_line = f * dot(edge_2, q)
if pos_on_line >= 0 then
return pos_on_line
end
end
function triangle_normal(triangle)
local point_1, point_2, point_3 = unpack(triangle)
local edge_1, edge_2 = subtract(point_2, point_1), subtract(point_3, point_1)
return normalize(cross3(edge_1, edge_2))
end