Divergent/mods/Weapon Parts Overhaul/gamedata/scripts/larp.script

-- LAgrange inteRPolation library
-- algorithm by peete-q
-- Migrated to Anomaly by Asshall
-- Modified and modularized by arti

-- To calculate non linear probability I used a type of interpolation called "Lagrange interpolation". 
-- The basic premise is that you input coordinates for x and y, for the exemple of loot x is the condition of the item to drop and y is the probability to drop such condition
--       For exemple if I input :
--             x  |   y
--             2  |   0
--             25 |   85
-- The probability of getting an item between 2 and 25 % condition is distributed between 0% proba and 85%
-- So in theory there is a 0 percent chance to get a 2% condition drop
-- and a 85% chance to get a 25% condition item with the probalities smoothly distributed between those two
-- This is an overly simplified explication because it's the best I can do, but the gist is that by interpolating n point in a curve you can get an approximation of the y value for all x
-- In this case x represents the condition and y the number to beat to drop.

-- Here is a table exemple
-- [weapon_coords]
-- novice              = 2, 25, 50         :       5,  85, 99
-- trainee             = 2, 25, 50         :       10, 81 ,99 
-- experienced         = 2, 25, 50         :       15, 76 ,98 
-- professional        = 2, 25, 50, 65     :       20 ,71 ,97, 99
-- veteran             = 2, 25, 50, 65     :       20 ,68 ,96, 99
-- expert              = 2, 25, 50, 65     :       20 ,64 ,95, 99
-- master              = 2, 25, 50, 65     :       20 ,62 ,95, 98
-- legend              = 2, 25, 50, 65     :       20 ,57 ,94, 98


-- I did not implement that, peete-q did : https://github.com/peete-q/assets/blob/master/lua-modules/lib/interpolate.lua All credits goes to them 
function lagrange(data, xi)
	local x = data["x"]
	local y = data["y"]
    xi = tonumber(xi)
	local n = #x
	-- Need the same number of points otherwise exit out
	if n ~= #y then return end
	
    -- Brilliant optimisation by peete-q
	local i = 1
    while i <= n and x[i] < xi do
		i = i + 1
	end
	local m = math.min(i + 3, n)
    local k = math.max(i - 4, 1)
	
	local result = 0
    for i=k, m do 
        local term = y[i]
        for j=k, m do
            if j ~= i then
                term = term*(   (xi - x[j]) / (x[i] - x[j])   )
            end
        end
        result = result + term -- term used to be on at the start multiplied by y[i] on this line. Don't know if that makes a difference. It's more lisible for me and I'm a dumb ape
    end
    return clamp(result,math.min(unpack(y)),math.max(unpack(y))) -- Here I clamp the result cause largrange interp can do some weird sutff and go above maxy/bellow miny between two xs
    -- This is suboptimal... Maybe i'm not using the right interp for some data sets or I shouldn't be using interp for those at all. It'll do for now.
end

-- Return min a max of data set of format {x,y} in order minx, maxx, miny, maxy
function get_min_max(coords)
    return math.min(unpack(coords["x"])), math.max(unpack(coords["x"])), math.min(unpack(coords["y"])), math.max(unpack(coords["y"]))
end

-- str_explode but they get parsed into numbers
function str_explode_num(str, sep, plain)
	if not (str and sep) then
		printe("!ERROR str_explode | missing parameter str = %s, sep = %s",str,sep)
		callstack()
	end
	if not (sep ~= "" and str:find(sep,1,plain)) then
		return { tonumber(str) }
	end
	local t = {}
	local size = 0
	for s in str:gsplit(sep,plain) do 
		size = size + 1
		t[size] = tonumber(trim(s))
	end
	return t
end

-- input:
-- coords is a table with x and y, each a list of integers
-- iterations is how many times to run, pass nil to run until we get something
-- returns a weighted value within the x range based on weights in y
function pick(coords, max_iterations)
    if is_empty(coords) then return 0 end
    if #coords["x"] ~= #coords["y"] then
        printe("Input for coord string %s produced inequal output, returning", str)
        return 0
    end
    local minx, maxx, miny, maxy = get_min_max(coords)
    local iter = 0
    while true do
        rnd_x = math.random(minx, maxx)
        local y = lagrange(coords, rnd_x)
        if math.random(miny, maxy) + math.random() > y then
            return round(rnd_x)
        end
        iter = iter + 1
        if max_iterations and iter >= max_iterations then
            return rnd_x
        end
    end
end

-- input: str of format:
-- X1, X2, X3...XN : Y1, Y2, Y3...Yn
function str_to_coords(str)
    coords = {
        ["x"] = {},
        ["y"] = {},
    }
    buffer = str_explode(str, ":")
    
    coords["x"] = str_explode_num(buffer[1], ",")
    coords["y"] = str_explode_num(buffer[2], ",")
    if #coords["x"] ~= #coords["y"] then
        printe("Input for coord string %s produced inequal output, returning", str)
        return nil
    end
    return coords
end