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李亚娟, 邓重阳. 基于双圆弧插值的G^2 Hermite数据容许分割[J]. 计算机辅助设计与图形学学报, 2018, 30(11): 2026-2034. DOI: 10.3724/SP.J.1089.2018.17077
引用本文: 李亚娟, 邓重阳. 基于双圆弧插值的G^2 Hermite数据容许分割[J]. 计算机辅助设计与图形学学报, 2018, 30(11): 2026-2034. DOI: 10.3724/SP.J.1089.2018.17077
Li Yajuan, Deng Chongyang. Dividing G^2 Hermite Data into Admissible G^2 Hermite Data by Biarcs[J]. Journal of Computer-Aided Design & Computer Graphics, 2018, 30(11): 2026-2034. DOI: 10.3724/SP.J.1089.2018.17077
Citation: Li Yajuan, Deng Chongyang. Dividing G^2 Hermite Data into Admissible G^2 Hermite Data by Biarcs[J]. Journal of Computer-Aided Design & Computer Graphics, 2018, 30(11): 2026-2034. DOI: 10.3724/SP.J.1089.2018.17077

基于双圆弧插值的G^2 Hermite数据容许分割

Dividing G^2 Hermite Data into Admissible G^2 Hermite Data by Biarcs

  • 摘要: 螺线是一种具有单调曲率的平面曲线,只能插值容许G^2Hermite数据(即可用螺线插值的G^2Hermite数据).在G^2 Hermite数据A,T_A,O_A,B,T_B,O_B的G1双圆弧插值基础之上,插入一个点(或2个点)以及该点处的切向与曲率值,把给定数据分割成2组(或3组)容许G^2Hermite数据,再用G^2连续的分段螺线插值之.根据双圆弧连接弧的不同情形,提供了3种不同的算法.算法几何意义明显,实用性强,能用不超过3条G^2连续的分段螺线插值任意一组非容许G^2 Hermite数据,彻底解决了用最少螺线段插值任意G^2 Hermite数据的问题,对高速公路、高速铁路、机器人行走路线等对几何品质要求较高的曲线设计有潜在的应用价值,最后给出实例表示.

     

    Abstract: A planar spiral is a kind of curve with single-signed,monotone increasing or decreasing curvature.A spiral can only interpolate a group of admissible G^2 Hermite data(G^2 Hermite data which can be interpolated by spiral).In this paper,we present a biarc-based method for interpolating C-shaped inadmissible G^2 Hermite dataA,T A,OA;B,T B,OBby piecewise spirals.Based on the biarc matching the corresponding G1 Hermite data,one or two new points and their tangents,curvatures are inserted,so that the inadmissible data can be divided into at most three groups of admissible data.Depending on the different positions of the biarc matching G1 data,three methods are proposed.Then piecewise spirals are given to match the divided data.We can generate at most three piecewise spirals for arbitrary C-shaped inadmissible data,and thoroughly solved the problem of interpolating arbitrary data with least spiral segments.It has potential application value to highway designs,railway routes and other geometric design curves.Several examples are given to demonstrate the proposed method.

     

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