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CLC number: TP391

On-line Access: 2015-03-04

Received: 2014-07-09

Revision Accepted: 2014-10-29

Crosschecked: 2015-02-04

Cited: 1

Clicked: 7720

Citations:  Bibtex RefMan EndNote GB/T7714

 ORCID:

Leonardo Fernández-Jambrina

http://orcid.org/0000-0002-4872-6973

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Frontiers of Information Technology & Electronic Engineering  2015 Vol.16 No.3 P.173-190

http://doi.org/10.1631/FITEE.14a0210


Interpolation of a spline developable surface between a curve and two rulings


Author(s):  Alicia Cantón, Leonardo Fernández-Jambrina

Affiliation(s):  ETSI Navales, Universidad Politécnica de Madrid, Arco de la Victoria 4, Madrid 28040, Spain

Corresponding email(s):   alicia.canton@upm.es, leonardo.fernandez@upm.es

Key Words:  Developable surfaces, Spline surfaces, Blossoms


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Alicia Cantón, Leonardo Fernández-Jambrina. Interpolation of a spline developable surface between a curve and two rulings[J]. Frontiers of Information Technology & Electronic Engineering, 2015, 16(3): 173-190.

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Abstract: 
In this paper we address the problem of interpolating a spline developable patch bounded by a given spline curve and the first and the last rulings of the developable surface. To complete the boundary of the patch, a second spline curve is to be given. Up to now this interpolation problem could be solved, but without the possibility of choosing both endpoints for the rulings. We circumvent such difficulty by resorting to degree elevation of the developable surface. This is useful for solving not only this problem, but also other problems dealing with triangular developable patches.

The work of this manuscript is a good addition to the theoretical part of developable surfaces. Although Section 5 is basically known stuff from the referenced paper Fernanderze 2007, it extended the original work with both analysis and examples.

已知曲线与直母线插值可展样条曲面

目的:对由给定一条样条曲线和可展曲面中第一及最末直母线(ruling)界定的可展样条面片(patch)进行插值。
创新点:给定一条样条曲线和起始直母线构造插值可展样条曲面,需先给出曲面对边边界样条曲线。而用传统方法构造插值可展样条曲面不能限制两条直母线的全部端点。本文通过将可展样条曲面升阶的方法,在增加起始直母线全部端点的限制条件下,解决已知某一样条曲线和起始直母线的可展样条曲面插值问题。
方法:通过将可展样条曲面升阶,解决给定一条样条曲线和起始直母线及其全部端点情形下可展样条曲面插值问题。
结论:给定一条样条曲线和可展曲面的起始直母线及其端点,通过将可展样条曲面升阶,解决可展样条面片插值构造。此方法同样适用于三角可展样条曲面插值(图10)。

关键词:可展曲面;样条曲面;开花(Blossom)运算

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

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