已知曲线与直母线插值可展样条曲面

Cantón Alicia; Fernández-Jambrina Leonardo

doi:10.1631/FITEE.14a0210

Your Location：

Home >

Browse articles >

已知曲线与直母线插值可展样条曲面

计算机与自动化 | Updated：2022-06-06

- 已知曲线与直母线插值可展样条曲面
- Interpolation of a spline developable surface between a curve and two rulings*
- 信息与电子工程前沿（英文） 2015年16卷第3期页码：173-190
- 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：
  
  *Project partially supported by the Spanish Ministerio deEconomíay Competividad (No. TRA2014-56792-P)
- DOI：10.1631/FITEE.14a0210
  中图分类号：
- 收稿：2014-07-09，
  
  修回：2015-02-04，
  
  录用：2014-10-29，
  
  纸质出版：2015-03
- Accepted：
Scan QR Code
已知曲线与直母线插值可展样条曲面[J]. 信息与电子工程前沿（英文）, 2015,16(3):173-190.

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.
已知曲线与直母线插值可展样条曲面[J]. 信息与电子工程前沿（英文）, 2015,16(3):173-190. DOI： 10.1631/FITEE.14a0210.

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

G Aumann . A simple algorithm for designing developable Bézier surfaces . 2003 . Comput. Aided Geom. Des .( 8-9 ): 601 - 619 . DOI: 10.1016/j.cagd.2003.07.001 http://doi.org/10.1016/j.cagd.2003.07.001 .

G Aumann . Degree elevation and developable Bézier surfaces . 2004 . Comput. Aided Geom. Des .( 7 ): 661 - 670 . DOI: 10.1016/j.cagd.2004.04.007 http://doi.org/10.1016/j.cagd.2004.04.007 .

RMC Bodduluri , B Ravani . Design of developable surfaces using duality between plane and point geometries . 1993 . Comput.-Aided Des .( 10 ): 621 - 632 . DOI: 10.1016/0010-4485(93)90017-I http://doi.org/10.1016/0010-4485(93)90017-I .

JS Chalfant , T Maekawa . Design for manufacturing using B-spline developable surfaces . 1998 . J. Ship Res .( 3 ): 207 - 215 .

CH Chu , CH Séquin . Developable Bézier patches: properties and design . 2002 . Comput.-Aided Des .( 7 ): 511 - 527 . DOI: 10.1016/S0010-4485(01)00122-1 http://doi.org/10.1016/S0010-4485(01)00122-1 .

CH Chu , CCL Wang , CR Tsai . Computer aided geometric design of strip using developable Bézier patches . 2008 . Comput. Ind .( 6 ): 601 - 611 . DOI: 10.1016/j.compind.2008.03.001 http://doi.org/10.1016/j.compind.2008.03.001 .

G Farin . Triangular Bernstein-Bézier patches . 1986 . Comput. Aided Geom. Des .( 2 ): 83 - 127 . DOI: 10.1016/0167-8396(86)90016-6 http://doi.org/10.1016/0167-8396(86)90016-6 .

G Farin . Curves and Surfaces for CAGD: a Practical Guide , 2002 . Morgan Kaufmann Publishers Inc., San Francisco, CA, USA .

L Fernández-Jambrina . B-spline control nets for developable surfaces . 2007 . Comput. Aided Geom. Des .( 4 ): 189 - 199 . DOI: 10.1016/j.cagd.2007.03.001 http://doi.org/10.1016/j.cagd.2007.03.001 .

WH Frey , D Bindschadler . Computer aided design of a class of developable Bézier surfaces . 1993 .

G Hu , X Ji , X Qin . Geometric design and shape adjustment for developable B-spline surfaces with multiple shape parameters . 2012 . J. Appl. Sci.-Electron. Inform. Eng .( 3 ): 324 - 330 .

I Juhász , Á Róth . Bézier surfaces with linear isoparametric lines . 2008 . Comput. Aided Geom. Des .( 6 ): 385 - 396 . DOI: 10.1016/j.cagd.2007.09.003 http://doi.org/10.1016/j.cagd.2007.09.003 .

U Kilgore . Developable hull surfaces . 1967 . Fishing Boats of the World, Surrey . 425 - 431 .

J Lang , O Röschel . Developable (1; n)-Bézier surfaces . 1992 . Comput. Aided Geom. Des .( 4 ): 291 - 298 . DOI: 10.1016/0167-8396(92)90036-O http://doi.org/10.1016/0167-8396(92)90036-O .

S Leopoldseder . Algorithms on cone spline surfaces and spatial osculating arc splines . 2001 . Comput. Aided Geom. Des .( 6 ): 505 - 530 . DOI: 10.1016/S0167-8396(01)00047-4 http://doi.org/10.1016/S0167-8396(01)00047-4 .

YJ Liu , K Tang , WY Gong , 等 . Industrial design using interpolatory discrete developable surfaces . 2011 . Comput.-Aided Des .( 9 ): 1089 - 1098 . DOI: 10.1016/j.cad.2011.06.001 http://doi.org/10.1016/j.cad.2011.06.001 .

MJ Mancewicz , WH Frey . Developable surfaces: properties, representations and methods of design . 1992 .

F Pérez , JA Suárez . Quasi-developable B-spline surfaces in ship hull design . 2007 . Comput.-Aided Des .( 10 ): 853 - 862 . DOI: 10.1016/j.cad.2007.04.004 http://doi.org/10.1016/j.cad.2007.04.004 .

F Pérez-Arribas , JA Suárez-Suárez , L Fernández-Jambrina . Automatic surface modelling of a ship hull . 2006 . Comput.-Aided Des .( 6 ): 584 - 594 . DOI: 10.1016/j.cad.2006.01.013 http://doi.org/10.1016/j.cad.2006.01.013 .

M Peternell . Developable surface fitting to point clouds . 2004 . Comput. Aided Geom. Des .( 8 ): 785 - 803 . DOI: 10.1016/j.cagd.2004.07.008 http://doi.org/10.1016/j.cagd.2004.07.008 .

MM Postnikov . Lectures in Geometry: Linear Algebra and Differential Geometry . 1979 . “Nauka”, Moscow .

H Pottmann , G Farin . Developable rational Bézier and B-spline surfaces . 1995 . Comput. Aided Geom. Des .( 5 ): 513 - 531 . DOI: 10.1016/0167-8396(94)00031-M http://doi.org/10.1016/0167-8396(94)00031-M .

H Pottmann , J Wallner . Approximation algorithms for developable surfaces . 1999 . Comput. Aided Geom. Des .( 6 ): 539 - 556 . DOI: 10.1016/S0167-8396(99)00012-6 http://doi.org/10.1016/S0167-8396(99)00012-6 .

H Pottmann , J Wallner . Computational Line Geometry , 2001 . Springer-Verlag, Berlin, p.x+563 .

DJ Struik . Lectures on Classical Differential Geometry . 1988 . Dover Publications Inc., New York, p.x+232 .

L Zeng , YJ Liu , M Chen , 等 . Least square quasi-developable mesh approximation . 2012 . Comput. Aided Geom. Des .( 7 ): 565 - 578 . DOI: 10.1016/j.cagd.2012.03.009 http://doi.org/10.1016/j.cagd.2012.03.009 .

浏览量

Downloads

CSCD

文章被引用时，请邮件提醒。

Submit

工具集

关联资源

Pseudo-evolute curves and caustic surfaces