parallel transport frames wtf

mesh.coffee

totalLength = Math.ceil(@model.spline.getLength())

up = LW.UP.clone()
rolledUp = up.clone()
binormal = new THREE.Vector3
bank = lastBank = 0

for i in [0..totalLength]
  u = i / totalLength

  # the center point of the spline at this u, where the center of the rails should be
  position = @model.spline.getPointAt(u)
  
  # forward direction the spline is moving
  tangent = @model.spline.getTangentAt(u).normalize()

  # side, perpindicular to forward and up
  # we calculate it based on the current tangent and the last up vector
  binormal.crossVectors(tangent, up).normalize()
  
  # up, perpindicular to forward and binormal
  # recalculate a new up based on this tangent
  up.crossVectors(binormal, tangent).normalize()

  # world absolute amount this particular up vector should be rolled along the tangent, radians
  bank = THREE.Math.degToRad(@model.getBankAt(u))

  # now we make another up vector, but this time rolled over tangent
  rolledUp.copy(up).applyAxisAngle(tangent, bank - lastBank).normalize()
  
  # and now we need to make a new binormal based on the new up
  binormal.crossVectors(tangent, rolledUp).normalize()

  # store the bank so we can use just the delta next time
  lastBank = bank

  # finally, we convert everything to a matrix we can multiply to any vector3 to apply this frame to that point
  Rframe = new THREE.Matrix4(binormal.x, rolledUp.x, -tangent.x, 0,
                             binormal.y, rolledUp.y, -tangent.y, 0,
                             binormal.z, rolledUp.z, -tangent.z, 0
                             0, 0, 0, 1)