Lua 修复了 tile 移动问题

Question

我正在使用 Lua 重新创建吃豆人夫人，最近才了解到一系列瓷砖用于碰撞和移动；我正在尝试重新创建它。这是瓦片地图：

nodemap = {
    {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1},
    {1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,1,1},
    {1,1,0,1,1,1,1,0,1,1,0,1,1,1,1,1,1,1,1,0,1,1,0,1,1,1,1,0,1,1},
    {1,1,0,1,1,1,1,0,1,1,0,1,1,1,1,1,1,1,1,0,1,1,0,1,1,1,1,0,1,1},
    {1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1},
    {1,1,1,1,0,1,1,0,1,1,1,1,1,0,1,1,0,1,1,1,1,1,0,1,1,0,1,1,1,1},
    {1,1,1,1,0,1,1,0,1,1,1,1,1,0,1,1,0,1,1,1,1,1,0,1,1,0,1,1,1,1},
    {1,1,1,1,0,1,1,0,1,1,1,1,1,0,1,1,0,1,1,1,1,1,0,1,1,0,1,1,1,1},
    {1,0,0,0,0,1,1,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,1,1,0,0,0,0,1},
    {1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1},
    {1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1},
    {1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1},
    {1,1,1,1,0,1,1,1,1,1,0,1,1,1,0,0,1,1,1,0,1,1,1,1,1,0,1,1,1,1},
    {1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,1,1,1,1,0,1,1,1,1},
    {1,1,1,1,0,1,1,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,1,1,1,1},
    {1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0,1,1,0,1,1,0,1,1,1,1},
    {1,1,1,1,0,1,1,0,1,1,0,1,1,1,1,1,1,1,1,0,1,1,0,1,1,0,1,1,1,1},
    {1,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,1},
    {1,1,1,1,0,1,1,1,1,1,1,1,1,0,1,1,0,1,1,1,1,1,1,1,1,0,1,1,1,1},
    {1,1,1,1,0,1,1,1,1,1,1,1,1,0,1,1,0,1,1,1,1,1,1,1,1,0,1,1,1,1},
    {1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,1,1,1,1},
    {1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1},
    {1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1},
    {1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1},
    {1,1,0,1,1,1,1,0,1,1,1,1,1,0,1,1,0,1,1,1,1,1,0,1,1,1,1,0,1,1},
    {1,1,0,1,1,1,1,0,1,1,1,1,1,0,1,1,0,1,1,1,1,1,0,1,1,1,1,0,1,1},
    {1,1,0,1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0,0,1,1,0,1,1,1,1,0,1,1},
    {1,1,0,1,1,1,1,0,1,1,0,1,1,1,1,1,1,1,1,0,1,1,0,1,1,1,1,0,1,1},
    {1,1,0,1,1,1,1,0,1,1,0,1,1,1,1,1,1,1,1,0,1,1,0,1,1,1,1,0,1,1},
    {1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1},
    {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
}

这会创建没有错误的迷宫，但我遇到的问题是 Pacman 在瓷砖之间平滑移动，而不会从瓷砖跳到瓷砖，再到瓷砖......所以我有这段代码可以“顺利”移动 Pacman：

-- Make Pacmans position consist of a single decimal (because over time a number of 1.899999994 will occur and that's ugly)
mrspacman.x = math.floor(mrspacman.x*10)/10
mrspacman.y = math.floor(mrspacman.y*10)/10

--If an arrowkey was pressed (Think of this as "A new direction was queued")
if (mrspacman.nextDirection) then

    -- If Pacman is in the center of a tile, then
    if (mrspacman.x == math.floor(mrspacman.x)) and (mrspacman.y == math.floor(mrspacman.y)) then

        -- If the tile in front of Pacman is empty, set direction to that
        if (nodemap[mrspacman.y-math2.sin(mrspacman.dir)][mrspacman.x+math2.cos(mrspacman.dir)]~=1) then
            mrspacman.dz = mrspacman.dir

            -- Disable this queue
            mrspacman.nextDirection = false
        end
    end
end

-- If Pacman is NOT in the center of a tile
if (mrspacman.x ~= math.floor(mrspacman.x)) or (mrspacman.y ~= math.floor(mrspacman.y)) then

    -- Constantly move forwards
    mrspacman.x = mrspacman.x + (math2.cos(mrspacman.dz)*mrspacman.speed)
    mrspacman.y = mrspacman.y - (math2.sin(mrspacman.dz)*mrspacman.speed)
else

    -- If the tile in front of Pacman is empty, move to that tile
    if (nodemap[mrspacman.y-math2.sin(mrspacman.dz)][mrspacman.x+math2.cos(mrspacman.dz)] ~= 1) then
        mrspacman.x = mrspacman.x + (math2.cos(mrspacman.dz)*mrspacman.speed)
        mrspacman.y = mrspacman.y - (math2.sin(mrspacman.dz)*mrspacman.speed)
    end
end

• mrspacman.dz = 所面对的角度。

• mrspacman.dir = 记录的按键操作。

• mrspacman.speed = .1（是允许平稳移动的小数）。

执行此代码会导致 Pacman 在按下后退键时冻结，并且在拐角处旋转、穿过墙壁时其位置会变得混乱......这可以看到 here。

如何解决这个问题？

更新

我添加了一个名为 math2 的表，由 cos 和 sin fx 组成（只会返回 4 个基本方向的值）：

math2 = {
    cos = function(angle)
        vectors = {1,0,-1,0}
        return vectors[(angle/90)+1]
    end,

    sin = function(angle)
        vectors = {0,1,0,-1}
        return vectors[(angle/90)+1]
    end
}

Answer 1

所以这个问题相当广泛：

如何解决这个问题？ 答案是：通过调试你的程序。

问题很模糊，视频中的测试用例很大且没有重点。要了解发生了什么，您至少需要详细查看程序的某些步骤。也就是说，如果墙左侧的瓷砖是空的，那么问题是 mrspacman 可以穿过墙。这暗示检查墙壁是否存在的代码可能存在一些错误。

问题中的代码不完整，因此错误可能来自它之外。尽管如此，在过去的一个小时里，我已经建立了一个原始框架来测试来自问题的代码。 （在答案末尾列出）

在玩弄了代码之后，我现在相信整个 pacman 的编写不仅没有一个三角函数，而且根本没有浮点数。

float numbers 的问题是它们不适合精确计算。一些编译器和计算系统甚至会因为你这样做而对你吐口水。

---

在编辑之前，有问题的代码有正弦和余弦表达式：

math.floor(math.sin(mrspacman.dir*pi/180))

我现在已经在我的计算机上对它进行了评估，实际上对于 dir 的值是 0, 90, 180, 270 它评估为 0, 1, 0, -1。但那是在 64 位机器上。我不确定是否可以信任 TI-Nspire 以产生相同的精度。

---

在我的测试中，我遇到了另一个浮动问题：

mrspacman.x = math.floor(mrspacman.x*10)/10

会在十进制数字中引入错误：对于 mrspacman.x 等于 4.3 它将评估为 4.2 导致 pacwoman 冻结。奇怪的是，当直接在提示中求值时，它的行为是正确的。无论如何，该函数的common implementation 在地板之前添加了一些偏差：math.floor(mrspacman.x*10+0.5)/10。

---

除此之外，还有一些轴方向的小问题，这要归功于框架转储的所有调试信息。

仅此而已。该代码有效（尽管我将在此处留下this 而不需要更多参数）。如果代码仍然无法在您的设备上运行，则需要在其他地方查找问题。

调试代码

我已将您的变量保留为全局变量，因为它们可能在您的程序中，这在单文件脚本中可能无关紧要。但一般来说，创建任何变量 local 是一个很好的做法，除非有非常好的理由。

nodemap = {--I've used small field for debugging
  {1,1,1,1,1,1,1},
  {1,0,0,0,0,0,1},
  {1,0,1,0,1,1,1},
  {1,0,0,0,1,1,1},
  {1,1,1,1,1,1,1},
}

mrspacman={dz=0,dir=false,x=2,y=2,speed=0.1,nextDirection=false}

local dlog=function(...)--debug function
  print(string.format(...))
end

math2 = {
    cos = function(angle)
        vectors = {1,0,-1,0}--this would be better of by being a local variable
        return vectors[(angle/90)+1]
    end,

    sin = function(angle)
        vectors = {0,1,0,-1}--this too
        return vectors[(angle/90)+1]
    end
}


local graphic_lines={}
for _,line in ipairs(nodemap) do
  local l=table.concat(line):gsub("0"," ")
  table.insert(graphic_lines,l)
end

local time_step=1
function draw()--quick and dirty output to terminal
  print(string.format("\nStep %i",time_step))
  time_step=time_step+1
  local x,y = mrspacman.x,mrspacman.y
  local px,py=math.floor(x+0.5),math.floor(y+0.5)
  for index,line in ipairs(graphic_lines) do
    if index~= py then 
      print(line) 
    else
      print( line:sub(1,px-1) .. "@" .. line:sub(px+1))
    end
  end
  print(string.format('Real position (x,y): (%f , %f)',x,y))
  print(string.format('Current direction: %i',mrspacman.dz))
  if mrspacman.nextDirection then
    print(string.format("Trying to turn at %i",mrspacman.dir or "error"))
  end
end


local inputs={--i've mixed up directions due to my renderer
  w=90,
  a=180,
  s=270,
  d=0,
}
local skips={['']=true,[' ']=true}

function input(macro_input)--read wasd from terminal
  print('your move')
  local key= (macro_input and macro_input()) or io.read();
  if skips[key] then return end
  local dir = inputs[key];
  if not dir then print('wrong key') return end
  mrspacman.dir = dir
  mrspacman.nextDirection=true
end

function sim_step()
dlog('"Smoothing" (%f,%f) through (%f,%f) to (%f,%f)',mrspacman.x,mrspacman.y,mrspacman.x*10,mrspacman.y*10,math.floor(mrspacman.x*10)/10,math.floor(mrspacman.y*10)/10)
dlog('"Fixing smoothing" (%f,%f) through (%f,%f) to (%f,%f)',mrspacman.x,mrspacman.y,(mrspacman.x+0.05)*10,(mrspacman.y+0.05)*10,math.floor((mrspacman.x+0.05)*10)/10,math.floor((mrspacman.y+0.05)*10)/10)

mrspacman.x = math.floor(mrspacman.x*10+.5)/10--these lines are different
mrspacman.y = math.floor(mrspacman.y*10+.5)/10--

--If an arrowkey was pressed (Think of this as "A new direction was queued")
if (mrspacman.nextDirection) then
    dlog("trying to turn")
    -- If Pacman is in the center of a tile, then
    if (mrspacman.x == math.floor(mrspacman.x)) and (mrspacman.y == math.floor(mrspacman.y)) then
        dlog("Pacman is in the center of a tile")
        -- If the tile in front of Pacman is empty, set direction to that
        dlog("lookup dy: %f dx: %f",-math2.sin(mrspacman.dir),math2.cos(mrspacman.dir))
        dlog("lookup y: %f x: %f",mrspacman.y-math2.sin(mrspacman.dir),mrspacman.x+math2.cos(mrspacman.dir))
        dlog(nodemap[mrspacman.y-math2.sin(mrspacman.dir)][mrspacman.x+math2.cos(mrspacman.dir)]==1 and "Its a wall" or "")
        if (nodemap[mrspacman.y-math2.sin(mrspacman.dir)][mrspacman.x+math2.cos(mrspacman.dir)]~=1) then
            dlog("turning")
            mrspacman.dz = mrspacman.dir

            -- Disable this queue
            mrspacman.nextDirection = false
          else
            dlog"not turning"
        end
    end
end

-- If Pacman is NOT in the center of a tile
if (mrspacman.x ~= math.floor(mrspacman.x)) or (mrspacman.y ~= math.floor(mrspacman.y)) then
    dlog("Pacman is NOT in the center of a tile, moving with no collision check")
    -- Constantly move forwards
    dlog("deltaX, deltaY : %f, %f",(math2.cos(mrspacman.dz)*mrspacman.speed),-(math2.sin(mrspacman.dz)*mrspacman.speed))
    dlog("before (%f, %f)",mrspacman.x,mrspacman.y)
    mrspacman.x = mrspacman.x + (math2.cos(mrspacman.dz)*mrspacman.speed)
    mrspacman.y = mrspacman.y - (math2.sin(mrspacman.dz)*mrspacman.speed)
    dlog("after (%f, %f)",mrspacman.x,mrspacman.y)
else
    dlog("moving with collision check")
    -- If the tile in front of Pacman is empty, move to that tile
    if (nodemap[mrspacman.y-math2.sin(mrspacman.dz)][mrspacman.x+math2.cos(mrspacman.dz)] ~= 1) then
        dlog("can move")
        mrspacman.x = mrspacman.x + (math2.cos(mrspacman.dz)*mrspacman.speed)
        mrspacman.y = mrspacman.y - (math2.sin(mrspacman.dz)*mrspacman.speed)
    else
        dlog("hit wall")
    end
end

end


local gen_macro = function(sequence)--function generating predefined set of keypresses
  sequence=sequence or ""
  local step=0
  return function()
    step=step+1
    if (step>sequence:len()) then return end--return to manual control
    return sequence:sub(step,step)
  end
end

local simple_macro= function() return gen_macro("wasd") end--simple sample, "--will do nothing
local horizontal_bend = function()--will bring pacman to bottom left
  local _x10=string.rep(" ",10);
  local sequence=_x10:rep(2).."s".._x10:rep(2).."a".._x10:rep(2)
  return gen_macro(sequence)
end

local angry_monkey=function(length)--gen random sequence of buttons
  length=length or 0
  local keys={"a","s","d","w"," "}
  local seq = {}
  for i=1,length do
    table.insert(seq,keys[math.random(#keys)])
  end
  return gen_macro(table.concat(seq))
end

local macro
--macro=simple_macro()
--macro=horizontal_bend()
--macro = angry_monkey(100)

--dlog=function() end --uncomment this to disable debug

while true do
  draw()
  input(macro)
  sim_step()
--  if time_step>10 then return end
end