Körperbewegung
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N-Nachtigal
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274
mods/modlib/vector.lua
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274
mods/modlib/vector.lua
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-- Localize globals
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local assert, math, pairs, rawget, rawset, setmetatable, unpack, vector = assert, math, pairs, rawget, rawset, setmetatable, unpack, vector
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-- Set environment
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local _ENV = {}
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setfenv(1, _ENV)
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local mt_vector = vector
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index_aliases = {
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x = 1,
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y = 2,
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z = 3,
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w = 4;
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"x", "y", "z", "w";
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}
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metatable = {
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__index = function(table, key)
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local index = index_aliases[key]
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if index ~= nil then
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return rawget(table, index)
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end
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return _ENV[key]
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end,
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__newindex = function(table, key, value)
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-- TODO
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local index = index_aliases[key]
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if index ~= nil then
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return rawset(table, index, value)
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end
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return rawset(table, key, value)
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end
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}
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function new(v)
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return setmetatable(v, metatable)
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end
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function zeros(n)
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local v = {}
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for i = 1, n do
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v[i] = 0
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end
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return new(v)
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end
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function from_xyzw(v)
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return new{v.x, v.y, v.z, v.w}
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end
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function from_minetest(v)
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return new{v.x, v.y, v.z}
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end
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function to_xyzw(v)
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return {x = v[1], y = v[2], z = v[3], w = v[4]}
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end
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--+ not necessarily required, as Minetest respects the metatable
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function to_minetest(v)
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return mt_vector.new(unpack(v))
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end
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function equals(v, w)
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for k, v in pairs(v) do
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if v ~= w[k] then return false end
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end
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return true
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end
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metatable.__eq = equals
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function combine(v, w, f)
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local new_vector = {}
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for key, value in pairs(v) do
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new_vector[key] = f(value, w[key])
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end
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return new(new_vector)
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end
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function apply(v, f, ...)
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local new_vector = {}
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for key, value in pairs(v) do
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new_vector[key] = f(value, ...)
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end
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return new(new_vector)
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end
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function combinator(f)
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return function(v, w)
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return combine(v, w, f)
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end, function(v, ...)
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return apply(v, f, ...)
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end
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end
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function invert(v)
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local res = {}
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for key, value in pairs(v) do
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res[key] = -value
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end
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return new(res)
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end
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add, add_scalar = combinator(function(v, w) return v + w end)
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subtract, subtract_scalar = combinator(function(v, w) return v - w end)
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multiply, multiply_scalar = combinator(function(v, w) return v * w end)
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divide, divide_scalar = combinator(function(v, w) return v / w end)
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pow, pow_scalar = combinator(function(v, w) return v ^ w end)
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metatable.__add = add
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metatable.__unm = invert
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metatable.__sub = subtract
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metatable.__mul = multiply
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metatable.__div = divide
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--+ linear interpolation
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--: ratio number from 0 (all the first vector) to 1 (all the second vector)
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function interpolate(v, w, ratio)
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return add(multiply_scalar(v, 1 - ratio), multiply_scalar(w, ratio))
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end
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function norm(v)
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local sum = 0
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for _, value in pairs(v) do
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sum = sum + value ^ 2
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end
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return sum
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end
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function length(v)
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return math.sqrt(norm(v))
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end
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-- Minor code duplication for the sake of performance
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function distance(v, w)
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local sum = 0
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for key, value in pairs(v) do
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sum = sum + (value - w[key]) ^ 2
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end
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return math.sqrt(sum)
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end
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function normalize(v)
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return divide_scalar(v, length(v))
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end
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function normalize_zero(v)
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local len = length(v)
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if len == 0 then
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-- Return a zeroed vector with the same keys
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local zeroed = {}
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for k in pairs(v) do
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zeroed[k] = 0
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end
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return new(zeroed)
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end
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return divide_scalar(v, len)
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end
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function floor(v)
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return apply(v, math.floor)
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end
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function ceil(v)
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return apply(v, math.ceil)
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end
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function clamp(v, min, max)
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return apply(apply(v, math.max, min), math.min, max)
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end
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function cross3(v, w)
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assert(#v == 3 and #w == 3)
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return new{
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v[2] * w[3] - v[3] * w[2],
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v[3] * w[1] - v[1] * w[3],
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v[1] * w[2] - v[2] * w[1]
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}
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end
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function dot(v, w)
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local sum = 0
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for i, c in pairs(v) do
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sum = sum + c * w[i]
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end
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return sum
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end
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function reflect(v, normal --[[**normalized** plane normal vector]])
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return subtract(v, multiply_scalar(normal, 2 * dot(v, normal))) -- reflection of v at the plane
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end
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--+ Angle between two vectors
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--> Signed angle in radians
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function angle(v, w)
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-- Based on dot(v, w) = |v| * |w| * cos(x)
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return math.acos(dot(v, w) / length(v) / length(w))
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end
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-- See https://www.euclideanspace.com/maths/geometry/rotations/conversions/eulerToAngle/
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function axis_angle3(euler_rotation)
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assert(#euler_rotation == 3)
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euler_rotation = divide_scalar(euler_rotation, 2)
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local cos = apply(euler_rotation, math.cos)
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local sin = apply(euler_rotation, math.sin)
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return normalize_zero{
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sin[1] * sin[2] * cos[3] + cos[1] * cos[2] * sin[3],
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sin[1] * cos[2] * cos[3] + cos[1] * sin[2] * sin[3],
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cos[1] * sin[2] * cos[3] - sin[1] * cos[2] * sin[3],
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}, 2 * math.acos(cos[1] * cos[2] * cos[3] - sin[1] * sin[2] * sin[3])
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end
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-- Uses Rodrigues' rotation formula
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-- axis must be normalized
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function rotate3(v, axis, angle)
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assert(#v == 3 and #axis == 3)
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local cos = math.cos(angle)
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return multiply_scalar(v, cos)
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-- Minetest's coordinate system is *left-handed*, so `v` and `axis` must be swapped here
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+ multiply_scalar(cross3(v, axis), math.sin(angle))
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+ multiply_scalar(axis, dot(axis, v) * (1 - cos))
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end
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function box_box_collision(diff, box, other_box)
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for index, diff in pairs(diff) do
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if box[index] + diff > other_box[index + 3] or other_box[index] > box[index + 3] + diff then
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return false
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end
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end
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return true
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end
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local function moeller_trumbore(origin, direction, triangle, is_tri)
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local point_1, point_2, point_3 = unpack(triangle)
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local edge_1, edge_2 = subtract(point_2, point_1), subtract(point_3, point_1)
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local h = cross3(direction, edge_2)
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local a = dot(edge_1, h)
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if math.abs(a) < 1e-9 then
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return
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end
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local f = 1 / a
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local diff = subtract(origin, point_1)
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local u = f * dot(diff, h)
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if u < 0 or u > 1 then
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return
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end
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local q = cross3(diff, edge_1)
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local v = f * dot(direction, q)
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if v < 0 or (is_tri and u or 0) + v > 1 then
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return
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end
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local pos_on_line = f * dot(edge_2, q)
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if pos_on_line >= 0 then
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return pos_on_line, u, v
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end
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end
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function ray_triangle_intersection(origin, direction, triangle)
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return moeller_trumbore(origin, direction, triangle, true)
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end
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function ray_parallelogram_intersection(origin, direction, parallelogram)
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return moeller_trumbore(origin, direction, parallelogram)
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end
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function triangle_normal(triangle)
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local point_1, point_2, point_3 = unpack(triangle)
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local edge_1, edge_2 = subtract(point_2, point_1), subtract(point_3, point_1)
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return normalize(cross3(edge_1, edge_2))
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end
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-- Export environment
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return _ENV
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