Abstract

In this paper, we aim at smoothing two connected ball Bézier curves from Cr−1 to Cr r ≥ 1 by minimizing the energies of the curves. We propose the algorithms based on internal energy minimization and curve attractor minimization. Then, we combine the internal energy and the curve attractor and give the algorithm based on combined energy minimization. All algorithms are established by solving bi-objective minimizations. Some numerical examples show that the proposed algorithms are effective, making them useful for smoothing 3D objects constructed by connected ball Bézier curves.