制作立方体缓入曲线可动态切换其目标位置

Question

使用，Lua，我已经立即生成一个函数（缓和/“加速”，然后缓和/“减速”）从一个数字到另一个数字插值; SimpleSpline取0-1之间的数字（动画进行的时间，最简单的放置），而SimpleSplineBetween也是如此，但是将它保持在两个给定的最小/最大值之间。

function SimpleSpline( v )
    local vSquared = v*v
    return (3 * vSquared - 2 * vSquared * v)
end

function SimpleSplineBetween( mins, maxs, v )
    local fraction = SimpleSpline( v )
    return (maxs * fraction + mins * (1 - fraction))
end

一切正常。但是，我遇到了一些问题。我希望这会更有活力。例如，假设我的“分钟”是0.5，而我的“maxs”是1，那么我有一个变量作为V传递的时间;我们会说它是0.5，所以我们当前的插值是0.75。现在，让我们假设突然，“maxs”被猛拉到0.25，所以现在，我们有一个新目标要达到。

我目前处理上述情况的方法是重置我们的“时间”变量并将“分钟”改为我们当前的值;在上面的情况下0.75等。但是，这会在动画中产生非常明显的“停止”或“冻结”，因为它正在完全重置。

我的问题是，如果没有那个停止，我怎么能让这个动态？我希望它能够从一个目标号码顺利过渡到另一个目标号码。

Answer 1

local Start_New_Spline, Calculate_Point_on_Spline, Recalculate_Old_Spline
do

   local current_spline_params

   local function Start_New_Spline(froms, tos)
      current_spline_params = {d=0, froms=froms, h=tos-froms, last_v=0}
   end

   local function Calculate_Point_on_Spline(v)  --  v = 0...1
      v = v < 0 and 0 or v > 1 and 1 or v
      local d     = current_spline_params.d
      local h     = current_spline_params.h
      local froms = current_spline_params.froms
      current_spline_params.last_v = v
      return (((d-2*h)*v+3*h-2*d)*v+d)*v+froms
   end

   local function Recalculate_Old_Spline(new_tos)
      local d     = current_spline_params.d
      local v     = current_spline_params.last_v
      local h     = current_spline_params.h
      local froms = current_spline_params.froms
      froms = (((d-2*h)*v+3*h-2*d)*v+d)*v+froms
      d = ((3*d-6*h)*v+6*h-4*d)*v+d
      current_spline_params = {d=d, froms=froms, h=new_tos-froms, last_v=0}
   end

end

根据您的值使用示例：

Start_New_Spline(0.5, 1)      -- "mins" is 0.5, "maxs" is 1
local inside_spline = true
while inside_spline do
   local goal_has_changed = false
   for time = 0, 1, 0.015625 do  -- time = 0...1
      -- It's time to draw next frame
      goal_has_changed = set to true when goal is changed
      if goal_has_changed then
         -- time == 0.5 ->  s == 0.75, suddenly "maxs" is jerked up to 0.25
         Recalculate_Old_Spline(0.25)  -- 0.25 is the new goal
         -- after recalculation, "time" must be started again from zero
         break  -- exiting this loop
      end
      local s = Calculate_Point_on_Spline(time)  -- s = mins...maxs
      Draw_something_at_position(s)
      wait()
   end
   if not goal_has_changed then
      inside_spline = false
   end
end