摘要：The energy minimization had been wieldy applied to select two free parameters of the planar cubic geometric Hermite interpolation curve. However, the energy minimization of the spatial cubic geometric Hermite interpolation curve seems to have been neglected. Since the spatial geometric Hermite interpolation curve has both bending and twisting, the bending energy and twisting energy should be simultaneously considered when selecting the two free parameters by energy minimization. This paper introduces the bending energy and the twisting energy of the spatial cubic geometric Hermite interpolation curve, and then presents the bending and twisting energy minimization method for selecting the two free parameters. The proposed minimization is achieved by solving a bi-objective optimization problem, and the unique approximate solution of the bi-objective optimization problem is given. Some numerical examples show that the proposed method makes the spatial cubic geometric Hermite interpolation curve have the minimum bending energy as well as the minimum twisting energy.
