Construction of G2 planar Hermite interpolants with prescribed arc lengths

作者：

Highlights：

• We presents a Hermite interpolation scheme for G2 boundary data and arc length constraint using Pythagorean hodograph (PH) curves of degree 7.

• The interpolation scheme is completely local. Each spline segment is defined as a PH biarc curve of degree 7.

• In this way the solution of the G2 continuity equations can be derived in a closed form, depending on four free parameters.

• By fixing two of them to zero, it is proven that the length constraint can be satisfied for any data and any chosen ratio between the two boundary tangents.

摘要

•We presents a Hermite interpolation scheme for G2 boundary data and arc length constraint using Pythagorean hodograph (PH) curves of degree 7.•The interpolation scheme is completely local. Each spline segment is defined as a PH biarc curve of degree 7.•In this way the solution of the G2 continuity equations can be derived in a closed form, depending on four free parameters.•By fixing two of them to zero, it is proven that the length constraint can be satisfied for any data and any chosen ratio between the two boundary tangents.

论文关键词：Pythagorean–hodograph curves,Biarc curves,Geometric Hermite interpolation,Arc–length constraint,Spline construction

论文评审过程：Received 25 August 2021, Revised 23 December 2021, Accepted 12 March 2022, Available online 12 April 2022, Version of Record 26 April 2022.

论文官网地址：https://doi.org/10.1016/j.amc.2022.127092