--//Most formulas used are from https://www.forrestthewoods.com/blog/solving_ballistic_trajectories/

local Polynomial = loadstring(game:HttpGet("https://pastebin.com/raw/cJLiwfs9"))()
local Ballistic = {}

local math = math
Ballistic.Gravity = 196.2

local rad45 = math.rad(45)
local msin = math.sin(rad45)
local mcos = math.cos(rad45)

local up = Vector3.new(0, 1, 0)
local onefourth = .25
local onehalf = .5

local sqrtwo = math.sqrt(2)

function Ballistic.GetMaxTime(speed, height)
	--return (2 * speed * msin + height) / Ballistic.Gravity3
	local holder = {}

	local yspeed = msin * speed
	local yspeedsq = yspeed * yspeed

	local ans = Polynomial.SolveQuadric(Ballistic.Gravity, yspeed, height, holder)
	--local ans2 = (-yspeed + math.sqrt(yspeedsq + 2 * Ballistic.Gravity * -height)) / Ballistic.Gravity
	--local ans3 = (-yspeed - math.sqrt(yspeedsq + 2 * Ballistic.Gravity * -height)) / Ballistic.Gravity

	--print(table.find(holder, ans2))

	if ans > 0 then
		return math.max(unpack(holder)) - math.min(unpack(holder))
	end
end

function Ballistic.GetRange(speed, height)
	return speed * mcos * (speed * msin + math.sqrt(speed * speed * msin * msin + 2 * Ballistic.Gravity * height)) / Ballistic.Gravity
end

function Ballistic.GetRangeAtTime(tim, speed)
	return tim * speed * mcos
end

function Ballistic.IsInRange(origin, speed, target, tvel)
	local diff = origin - target

	if tvel then
		local maxtime = Ballistic.GetRange(speed, diff.Y) / (speed * mcos)
		local newtargetpos = target + tvel * maxtime
		local newthing = origin - newtargetpos
		local range = Ballistic.GetRangeAtTime(maxtime, speed)


		return range >= Vector3.new(newthing.X, 0, newthing.Z).Magnitude
	end

	local range = Ballistic.GetRange(speed, diff.Y)
	return range >= diff.Magnitude
end

function Ballistic.SolveStationary(origin, speed, target, islob)
	local dir = target - origin
	local xdir = Vector3.new(dir.X, 0, dir.Z)

	local xdist = xdir.Magnitude
	local sqspeed = speed * speed
	local quspeed = sqspeed * sqspeed
	local xgrav = Ballistic.Gravity * xdist

	local sol = quspeed - Ballistic.Gravity * (xgrav * xdist + 2 * dir.Y * sqspeed)

	if sol < 0 then
		return
	end

	local ang = math.atan2(sqspeed + (islob and math.sqrt(sol) or -math.sqrt(sol)), xgrav)
	return xdir.Unit * math.cos(ang) + up * math.sin(ang), xdir.Magnitude / (speed * math.cos(ang))
end

--//http://playtechs.blogspot.com/2007/04/aiming-at-moving-target.html
function Ballistic.SolveMoving(origin, speed, target, tvel, islob)
	local roots = {}
	local diff = target - origin

	local H = diff.X
	local J = diff.Z
	local K = diff.Y
	local L = -onehalf * Ballistic.Gravity

	local P = tvel.X
	local Q = tvel.Y
	local R = tvel.Z

	local c0 = L * L
	local c1 = -2 * Q * L
	local c2 = Q * Q - 2 * K * L - speed * speed + P * P + R * R
	local c3 = 2 * (K * Q + H * P + J * R)
	local c4 = K * K + H * H + J * J

	local num = Polynomial.SolveQuartic(c0, c1, c2, c3, c4, roots)

	if num > 0 then
		local bullet, lob = math.huge, math.huge

		for i = 1, num do
			local val = roots[i]

			if val > 0 then
				if val < bullet then
					lob = bullet
					bullet = val
				elseif val < lob then
					lob = val
				end
			end
		end

		if bullet ~= math.huge then
			local smallest = (islob and lob ~= math.huge and lob) or bullet
			return Vector3.new(H / smallest + P, K / smallest + Q - L * smallest, J / smallest + R), islob and lob or bullet;
		end
	end
end

function Ballistic.SolveMoving2(origin, speed, jump, grav, target, tvel, islob)
    local roots = {}

    local g = grav
    local diff = target - origin

    local c0 = g * g * onefourth
    local c1 = -tvel.Y * g
    local c2 = tvel:Dot(tvel) + g * -diff.Y - speed * speed
    local c3 = 2 * (tvel:Dot(diff) - speed * jump)
    local c4 = diff:Dot(diff) - jump * jump

    local num = Polynomial.SolveQuartic(c0, c1, c2, c3, c4, roots)

    if num > 0 then
        local bullet, lob = math.huge, math.huge

        for i = 1, num do
            local val = roots[i]

            if val > 0 then
                if val < bullet then
                    lob = bullet
                    bullet = val
                elseif val < lob then
                    lob = val
                end
            end
        end

        if bullet ~= math.huge then
            local smallest = (islob and lob ~= math.huge and lob) or bullet
            local divisor = speed * smallest + jump

            return (diff + tvel * smallest - Vector3.new(0, onehalf * g * smallest * smallest, 0)) / divisor, islob and lob or bullet
        end
    end
end

return Ballistic