Generation of interpolation curves with the least energy using dynamic programming

In shape construction, it is often required for a curve to interpolate smoothly among given points and to be compatible with physical phenomena. A curve with the minimum strain energy is known as a smooth curve satisfying those requirements. Some interpolation methods have been developed to approximate the strain energy in a suitable way and to generate a curve for which the approximated strain energy is minimum. Nevertheless, generated curves sometimes contain ‘wiggles’ or ‘bumps’. The purpose of this paper is to solve directly an equation to construct the C(1) piecewise curve with the minimum strain energy and to generate the curve with little ‘wiggles’ or ‘bumps’. For this purpose, the optimality equation for the minimum strain energy is established by applying dynamic programming to the energy minimization problem. Then, the solution to the optimality equation is obtained by a numerical method and the curve with the minimum energy is generated.