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“…Generally, the UAV route generated by meta-heuristic algorithms is composed of the line segments, which is unsuitable for exact flight. To solve this problem, some methods are used to further optimize the route generated, such as the B-spline curve [ 39 ], the Bezier curve [ 40 ], and the simple circular arcs [ 41 ]. The B-spline curve has the unique superiority in many ways, such as locality, geometrical invariability, symmetry, recursion, continuity, convex hull characters, and convexity-preservation.…”

confidence: 99%

“…Generally, the UAV route generated by meta-heuristic algorithms is composed of the line segments, which is unsuitable for exact flight. To solve this problem, some methods are used to further optimize the route generated, such as the B-spline curve [ 39 ], the Bezier curve [ 40 ], and the simple circular arcs [ 41 ]. The B-spline curve has the unique superiority in many ways, such as locality, geometrical invariability, symmetry, recursion, continuity, convex hull characters, and convexity-preservation.…”

confidence: 99%

“…Several types of quartic and quintic Bézier curves were considered in [3], and deeper analysis of some geometric quintic approximants can be found in [8]. Many new cubic and quartic approximants were also proposed in [9,10,11,12,13]. However, in none of the above papers the optimality of the solution has been considered.…”

confidence: 99%

“…After choosing v = v i the quartic approximation b(t) is depend only on one parameter u. Kim and Ahn [10] proposed the G 2 quartic approximation b with η 2 (t) having double-zero at the midpoint, and Liu et al [12]b with η 2 (t) having zero at t = …”

confidence: 99%

“…Hur and Kim [9] proposed the best G 2 quartic and G 1 cubic approximation of circular arc. Liu et al [12] gave circular arc approximation by quartic G 2 spline having smaller error than previous quartic approximation. In this paper we present a quartic G 2 spline approximation of circular arc having smaller error than previous quartic approximation using alternation of error function.…”

confidence: 99%