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

Cantón Alicia; Fernández-Jambrina Leonardo

doi:10.1631/FITEE.14a0210

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

Computer & Automation | Updated：2022-06-06

- Interpolation of a spline developable surface between a curve and two rulings*
- 已知曲线与直母线插值可展样条曲面
- Frontiers of Information Technology & Electronic Engineering Vol. 16, Issue 3, Pages: 173-190(2015)
- Affiliations：
  
  ETSI Navales, Universidad Politécnica de Madrid, Arco de la Victoria 4, Madrid 28040, Spain
- Author bio：
  
  E-mail:alicia.canton@upm.esleonardo.fernandez@upm.es
  ‡Corresponding Author
- Funds：
- DOI：10.1631/FITEE.14a0210
  CLC：
- Received：09 July 2014，
  
  Revised：2015-02-04，
  
  Accepted：29 October 2014，
  
  Published：2015-03
- Accepted：
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Cantón Alicia, Fernández-Jambrina Leonardo. Interpolation of a spline developable surface between a curve and two rulings*[J]. Frontiers of Information Technology & Electronic Engineering, 2015, 16(3): 173-190.
DOI：

Cantón Alicia, Fernández-Jambrina Leonardo. Interpolation of a spline developable surface between a curve and two rulings*[J]. Frontiers of Information Technology & Electronic Engineering, 2015, 16(3): 173-190. DOI： 10.1631/FITEE.14a0210.

摘要

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）。

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.

关键词

Keywords

references

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