Geometric constraints on quadratic Bézier curves using minimal length and energy

A class of quintic Hermite interpolation curve and the free parameters selection

“…Although the smoothness of a curve is difficult to be expressed in a quantitative way, the strain energy (also called bending energy) minimization or the curvature variation energy minimization is adopted to construct fair curves in most cases (see e.g. Ahn et al, 2014;Žagar, 2011a, 2011b;Li et al, 2012;Li, 2018;Lu, 2015aLu, , 2015bLu et al, 2017;Xu et al, 2011). Here, we determine the values of the free parameters by minimizing curvature variation energy to obtain the fairest αβ-Hermite curve.…”

Cuckoo Search with Lévy Flights for Weighted Bayesian Energy Functional Optimization in Global-Support Curve Data Fitting

“…More recent approaches in this line use error bounds [ 31 ], curvature-based squared distance minimization [ 26 ], or dominant points [ 18 ]. A very interesting approach to this problem consists in exploiting minimization of the energy of the curve [ 32 – 36 ]. This leads to different functionals expressing the conditions of the problem, such as fairness, smoothness, and mixed conditions [ 37 – 40 ].…”

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

“…The general ways to construct fair curves are achieved by minimizing some energy functional representing the fairness (see [4]). The strain energy (bending energy) and curvature variation energy are two widely adopted metrics to describe the fairness of a planar curve, since curvature is the universal shape measure for curves (see [1,[5][6][7][8]). Recently, some works on determining suitable α 0 and α 1 of the planar cubic G 1 Hermite interpolation curve via strain energy minimization or curvature variation energy minimization have been proposed (see [4,[9][10][11][12]).…”