Desmos dot thing idk

math.randomseed(os.time())

local function toCart(r, a)
    return {x = math.cos(a)*r, y = math.sin(a)*r}
end

local function s(text)
    return "_{"..text.."}"
end

local function line(x1,y1,x2,y2)
    local L = "\\left"
    local R = "\\right"

    local out = ""
    local init = "(t("..(x2-x1)..")+"..x1..",t("..(y2-y1)..")+"..y1..")"

    for i = 1, #init do
        local c = init:sub(i,i)
        if c == "(" or c == "{" or c == "[" then
            out = out..L..c
        elseif c == ")" or c == "}" or c == "]" then
            out = out..R..c
        else
            out = out..c
        end
    end

    return out
end

local movers = {}
for i = 1, 5 do
    local b = {}
    b.Vel = toCart(1, math.random(0, 360)*math.pi/180)
    b.Bounds = {xmin = -5, xmax = 5, ymin = -5, ymax = 5}
    b.Pos = {x = 0, y = 0}
    table.insert(movers, b)
end

local out = "I\\left(a,s,l\\right)=a\\left[s,...s+l\\right]\n"
out = out.."p=\\left["
local keyframes = 100
local subframes = 5
local frames = {}

for m, mover in ipairs(movers) do
    local frame = {}
    for f = 1, keyframes do
        for s = 1, subframes do
            local AA = "\\left("..mover.Pos.x..","..mover.Pos.y.."\\right)"
            table.insert(frame, AA)
            mover.Pos.x = mover.Pos.x + mover.Vel.x/subframes
            mover.Pos.y = mover.Pos.y + mover.Vel.y/subframes

            if mover.Pos.x > mover.Bounds.xmax then
                mover.Pos.x = mover.Bounds.xmax
                mover.Vel.x = mover.Vel.x * -1
            end
            if mover.Pos.x < mover.Bounds.xmin then
                mover.Pos.x = mover.Bounds.xmin
                mover.Vel.x = mover.Vel.x * -1
            end
            if mover.Pos.y > mover.Bounds.ymax then
                mover.Pos.y = mover.Bounds.ymax
                mover.Vel.y = mover.Vel.y * -1
            end
            if mover.Pos.y < mover.Bounds.ymin then
                mover.Pos.y = mover.Bounds.ymin
                mover.Vel.y = mover.Vel.y * -1
            end
        end
    end
    table.insert(frames, frame)
end

local i = 1
while i < keyframes*subframes do
  for p, f in ipairs(frames) do
    -- for i, s in ipairs(f) do
        out = out..f[i]

        -- if p ~= #frames then
        --  out = out..","
        -- end
    if i < keyframes*subframes-1 or p ~= #frames then
      out = out..","
    end
    -- end
  end
  i = i+1
end

out = out.."\\right]\n"
out = out.."I\\left(p,T,"..(#movers-1).."\\right)\n"
out = out.."T=0"

print(out)