control over BezierCurve:GetNormal

[kumpuu]

Hello! Thanks for making this module. I was able to adapt it for a different game. However, now I'm stuck with a problem - I need to control the rotation of the CFrame around the tangent (dt). I have an existing object (rocket) in the game world that I want to animate along the curve with GetNormal, but there is no way for me to set an initial rotation of the curve.
I tried modifying UpdateLUT() (If I undertand correctly this is where the work is done) so that I can pass an initial frame

bezier/src/Bezier.lua

Line 246 in 3e85c41

local first = {

but it did not work very well and I have trouble with the vector math.

Picture for illustration

[bstummer]

Hi there,
Did you try to change the variable r in line 245?
If it doesn't work, I can try to find a solution in the next few days.

[kumpuu]

I did that, and I also tried to pass in a complete first frame but somehow it didn't work.

Here is where I was at: (I had to adapt to vanilla lua and the game environment)

Code

function BezierCurve:UpdateLUT(steps, calcNormals, first_frame)
  steps = steps or 101
  local points = self.Points
  local lut = {}
  local len = 0

  --[[
    LUT:
    stores lengths
  ]]
  local last
  for i = 0, steps - 1 do
    local t = i / (steps - 1)
    local point = self:DeCasteljau(t)
    if i ~= 0 then
      len = len + (last - point):len()
    end
    lut[i] = len
    last = point
  end

  --[[
    RMFLUT (rotation minimising frames):
    1 = point
    2 = derivative
    3 = normal vector
    4 = cross product of normal and derivative
  ]]
  self.LUT = lut
  self.Length = len

  if calcNormals or self.RMFLUT then
    local first
    if first_frame then
      first = first_frame
      self.RMFLUT_first_frame  = tableRecursiveCopy(first_frame, true)
    else
      local dt = self:GetDerivative(-0.001)
      local r = (dt + self:GetSecondDerivative(-0.001)):cross(dt):unit()
      first = {
        self:DeCasteljau(0),
        dt,
        r,
        r:cross(dt)
      }
      self.RMFLUT_first_frame = nil
    end

    local frames = {[0] = first}
    local steps = 100
    for i = 0, steps - 1 do
      local x0 = frames[i]
      local t = (i + 1) / steps
      local x1 = {
        self:DeCasteljau(t),
        self:GetDerivative(t)
      }
      local v1 = x1[1] - x0[1]
      local c1 = v1:dot(v1)
      local riL = x0[3] - (v1 * 2 / c1 * v1:dot(x0[3]))
      local dtiL = x0[2] - (v1 * 2 / c1 * v1:dot(x0[2]))

      local v2 = x1[2] - dtiL

      x1[3] = riL - (v2 * 2 / v2:dot(v2) * v2:dot(riL))
      x1[4] = x1[3]:cross(x1[2])
      frames[i + 1] = x1
    end
    self.RMFLUT = frames
  end
end

[kumpuu]

I figured it out... In line 270, I had to swap the operands around. The issue was that the result vector was pointing in the opposite direction, all the signs flipped. I think this was due to how I chose the axis, I had the tangent as Z. So it works now, but if you want to still make a clean solution I would be glad to use it :)