The Offset Surface of Helicoid

Based on the fairing requirements for the strain energy and jerk energy of a thin elastic beam，an estimation method for the NURBS curve’s weights is presented： first discretize these energy to get a functional，then minimize it to find the weights．Meanwhile，this fairing criterion given here merges a group of existing different fairing criteria in the literature．In order to simplify the computation for derivatives，the matrix representation of NURBS is used． Finally，some numerical examples are given．