local bezier = {};

function length(n, func, ...)
    local sum, ranges, sums = 0, {}, {};
    for i = 0, n-1 do
        local p1, p2 = func(i/n, ...), func((i+1)/n, ...)
        local dist = (p2 - p1).magnitude;
        ranges[sum] = {dist, p1, p2};
        table.insert(sums, sum);
        sum = sum + dist;
    end;
    return sum, ranges, sums;
end;

function bezier.new(func, n, ...)
    local self = setmetatable({}, {__index = bezier});
    local sum, ranges, sums = length(n, func, ...);
    self.func = func;
    self.n = n;
    self.points = {...};
    self.length = sum;
    self.ranges = ranges;
    self.sums = sums;
    return self;
end;

function bezier:setPoints(...)
    -- only update the length when the control points are changed
    local sum, ranges, sums = length(self.n, self.func, ...);
    self.points = {...};
    self.length = sum;
    self.ranges = ranges;
    self.sums = sums;
end;

function bezier:calc(t)
    -- if you don't need t to be a percentage of distance
    return self.func(t, unpack(self.points));
end;

function bezier:calcFixed(t)
    local T, near = t * self.length, 0;
    for _, n in next, self.sums do
        if (T - n) < 0 then break; end;
        near = n;
    end;
    local set = self.ranges[near];
    local percent = (T - near)/set[1];
    return set[2], set[3], percent;
end;

return bezier;