Length and curvature variation energy minimizing planar cubic G1 Hermite interpolation curve

Abstract

In this paper, we study how to construct a planar cubic G1 Hermite interpolation curve with minimal length and curvature variation energy. This problem is solved by a bi-objective optimization model. We prove that there is a unique solution to this problem and give the expression of the solution. Some numerical examples show that the proposed method makes the curvature variation energy of the curve as small as possible when the length of the curve as short as possible.

Keywords

• hermite interpolation curve
• length
• curvature variation energy
• minimization
• bi-objective optimization