Combined internal energy minimizing planar cubic Hermite curve

Abstract

The stretch energy, the strain energy and the curvature variation energy are three well known internal energies of the planar curve, they respectively represent length, curvature and variation of curvature that are the typical geometric characteristics of the curve (see Veltkamp and Wesselink, 1995;Xu et al, 2011a). Although there is no recognized way to describe the smoothness of a planar curve, a curve constructed by minimizing one of the internal energies is generally considered smooth. Some examples are the construction of energy-minimizing Bézier curve (

Smoothing Connected Ball Bézier Curves by Energy Minimization

“…ese objective functionals can be roughly divided into two categories: the internal energy of curves and the external energy of curves. e internal energy of a curve oftentimes includes three forms: the stretch energy, the strain energy, and the curvature variation energy (see [12][13][14][15][16][17]). e external energy of a curve usually includes two forms: the point attractor and the curve attractor (see [17]).…”