Spatial C2 closed loops of prescribed arc length defined by Pythagorean-hodograph curves

作者：

Highlights：

• C2 closed loops of prescribed arc length are defined by a single polynomial curve.

• Continuity of the Frenet frame and curvature of such loops is considered.

• PH curves of degree 7 are used.

• Geometrical properties of obtained loops are investigated.

• Swept and tubular surfaces are constructed.

摘要

•C2 closed loops of prescribed arc length are defined by a single polynomial curve.•Continuity of the Frenet frame and curvature of such loops is considered.•PH curves of degree 7 are used.•Geometrical properties of obtained loops are investigated.•Swept and tubular surfaces are constructed.

论文关键词：Spatial closed-loop curves,Continuity conditions,Arc length,Pythagorean-hodograph curves,Euler–Rodrigues frame,Tubular surfaces

论文评审过程：Received 8 December 2019, Revised 11 August 2020, Accepted 22 August 2020, Available online 1 October 2020, Version of Record 1 October 2020.

论文官网地址：https://doi.org/10.1016/j.amc.2020.125653