AI Chat Paper
Note: Please note that the following content is generated by AMiner AI. SciOpen does not take any responsibility related to this content.
{{lang === 'zh_CN' ? '文章概述' : 'Summary'}}
{{lang === 'en_US' ? '中' : 'Eng'}}
Chat more with AI
Powered by AMiner. Clicking this button will take you away from SciOpen.
Home Journal of Computer Science and Technology Article
Article Link
Cite
EndNote(RIS) BibTeX
Collect
Submit Manuscript
Show Outline
Outline
Show full outline
Hide outline
Outline
Show full outline
Hide outline
Regular Paper

Quasi-Developable B-Spline Surface Design with Control Rulings

School of Computer Science and Technology, Harbin Institute of Technology, Weihai 264209, China
Shandong Co-Innovation Center of Future Intelligent Computing, Yantai 264005, China
Shandong Province Key Laboratory of Digital Media Technology, Shandong University of Finance and Economics Jinan 250061, China
Show Author Information

Abstract

We propose a method for generating a ruled B-spline surface fitting to a sequence of pre-defined ruling lines and the generated surface is required to be as developable as possible. Specifically, the terminal ruling lines are treated as hard constraints. Different from existing methods that compute a quasi-developable surface from two boundary curves and cannot achieve explicit ruling control, our method controls ruling lines in an intuitive way and serves as an effective tool for computing quasi-developable surfaces from freely-designed rulings. We treat this problem from the point of view of numerical optimization and solve for surfaces meeting the distance error tolerance allowed in applications. The performance and the efficacy of the proposed method are demonstrated by the experiments on a variety of models including an application of the method for the path planning in 5-axis computer numerical control (CNC) flank milling.

Keywords

developable surfacesurface modelingB-spline surfacenumerical optimization

Electronic Supplementary Material

Download File(s)
jcst-37-5-1221-Highlights.pdf (113.2 KB)

References

[1]

Pottmann H, Schiftner A, Bo P B et al. Freeform surfaces from single curved panels. ACM Trans. Graph, 2008, 27(3): Article No. 76. DOI: 10.1145/1360612.1360675.
Crossref Google Scholar
[2]

Chalfant J S, Maekawa T. Design for manufacturing using B-spline developable surfaces. Journal of Ship Research, 1998, 42(03): 207-215. DOI: 10.5957/jsr.1998.42.3.207.
Crossref Google Scholar
[3]

Pérez F, Suárez J A. Quasi-developable B-spline surfaces in ship hull design. Computer-Aided Design, 2007, 39(10): 853-862. DOI: 10.1016/j.cad.2007.04.004.
Crossref Google Scholar
[4]

Chu C H, Chen J T. Tool path planning for five-axis flank milling with developable surface approximation. The International Journal of Advanced Manufacturing Technology, 2006, 29(7/8): 707-713. DOI: 10.1007/s00170-005-2564-6.
Crossref Google Scholar
[5]

Calleja A, Bo P B, González H, Bartoň M, de Lacalle L N L. Highly accurate 5-axis flank CNC machining with conical tools. The International Journal of Advanced Manufacturing Technology, 2018, 97(5/6/7/8): 1605-1615. DOI: 10.1007/s00170-018-2033-7.
Crossref Google Scholar
[6]

Tang C C, Bo P B, Wallner J, Pottmann H. Interactive design of developable surfaces. ACM Trans. Graph, 2016, 35(2): Article No. 12. DOI: 10.1145/2832906.
Crossref Google Scholar
[7]

Chen M, Tang K, Joneja A. Design of developable interpolating strips. Computer-Aided Design and Applications, 2011, 8(4): 557-570. DOI: 10.3722/CADAPS.2011.557-570.
Crossref Google Scholar
[8]

Li C, Zhu C. Designing developable C-Bézier surface with shape parameters. Mathematics, 2020, 8(3): Article No. 402. DOI: 10.3390/math8030402.
Crossref Google Scholar
[9]

Cantón A, Fernández-Jambrina L. Interpolation of a spline developable surface between a curve and two rulings. Frontiers of Information Technology & Electronic Engineering, 2015, 16(3): 173-190. DOI: 10.1631/FITEE.14a0210.
Crossref Google Scholar
[10]

Bo P B, Zheng Y J, Jia X H, Zhang C C. Multi-strip smooth developable surfaces from sparse design curves. Computer-Aided Design, 2019, 114: 1-12. DOI: 10.1016/j.cad.2019.05.001.
Crossref Google Scholar
[11]

Bodduluri R M C, Ravani B. Design of developable surfaces using duality between plane and point geometries. Computer-Aided Design, 1993, 25(10): 621-632. DOI: 10.1016/0010-4485(93)90017-I.
Crossref Google Scholar
[12]

English E, Bridson R. Animating developable surfaces using nonconforming elements. ACM Trans. Graph, 2008, 27(3): Article No. 66. DOI: 10.1145/1360612.1360665.
Crossref Google Scholar
[13]

Solomon J, Vouga E, Wardetzky M, Grinspun E. Flexible developable surfaces. Computer Graphics Forum, 2012, 31(5): 1567-1576. DOI: 10.1111/j.1467-8659.2012.03162.x.
Crossref Google Scholar
[14]

Liu Y, Pottmann H, Wallner J, Yang Y L, Wang W. Geometric modeling with conical meshes and developable surfaces. ACM Trans. Graph, 2006, 25(3): 681-689. DOI: 10.1145/1141911.1141941.
Crossref Google Scholar
[15]

Liu Y J, Tang K, Gong W Y, Wu T R. Industrial design using interpolatory discrete developable surfaces. Computer-Aided Design, 2011, 43(9): 1089-1098. DOI: 10.1016/j.cad.2011.06.001.
Crossref Google Scholar
[16]

Oetter R, Barry C D, Duffty B, Welter J. Block construction of small ships and boats through use of developable panels. Journal of Ship Production, 2002, 18(02): 65-72. DOI: 10.5957/jsp.2002.18.2.65.
Crossref Google Scholar
[17]
Subag J, Elber G. Piecewise developable surface approximation of general NURBS surfaces with global error bounds. In Proc. the 4th International Conference on Geometric Modeling and Processing, July 2006, pp. 143-156. DOI: 10.1007/11802914_11.
Crossref
[18]

Gavriil K, Schiftner A, Pottmann H. Optimizing B-spline surfaces for developability and paneling architectural freeform surfaces. Computer-Aided Design, 2019, 111: 29-43. DOI: 10.1016/j.cad.2019.01.006.
Crossref Google Scholar
[19]

Tang K, Wang C L. Modeling developable folds on a strip. Journal of Computing and Information Science in Engineering, 2005, 5(1): 35-47. DOI: 10.1115/1.1804206.
Crossref Google Scholar
[20]

Wang C L, Tang K. Optimal boundary triangulations of an interpolating ruled surface. Journal of Computing and Information Science in Engineering, 2005, 5(4): 291-301. DOI: 10.1115/1.2052850.
Crossref Google Scholar
[21]

Tang K, Chen M. Quasi-developable mesh surface interpolation via mesh deformation. IEEE Trans. Visual Comput. Graphics, 2009, 15(3): 518-528. DOI: 10.1109/TVCG.2008.192.
Crossref Google Scholar
[22]

Pottmann H, Farin G. Developable rational Bézier and B-spline surfaces. Computer Aided Geometric Design, 1995, 12(5): 513-531. DOI: 10.1016/0167-8396(94)00031-M.
Crossref Google Scholar
[23]

Chen H Y, Lee I K, Leopoldseder S, Pottmann H, Randrup T, Wallner J. On surface approximation using developable surfaces. Graphical Models and Image Processing, 1999, 61(2): 110-124. DOI: 10.1006/gmip.1999.0487.
Crossref Google Scholar
[24]

Aumann G. A simple algorithm for designing developable Bézier surfaces. Computer Aided Geometric Design, 2003, 20(8/9): 601-619. DOI: 10.1016/j.cagd.2003.07.001.
Crossref Google Scholar
[25]

Aumann G. Degree elevation and developable Bézier surfaces. Computer Aided Geometric Design, 2004, 21(7): 661-670. DOI: 10.1016/j.cagd.2004.04.007.
Crossref Google Scholar
[26]

Hu G, Wu J. Generalized quartic H-Bézier curves: Construction and application to developable surfaces. Advances in Engineering Software, 2019, 138: Article No. 102723. DOI: 10.1016/j.advengsoft.2019.102723.
Crossref Google Scholar
[27]

Chu C H. Geometric design of uniform developable B-spline surfaces: Constraints and degrees of freedom. Journal of Industrial and Production Engineering, 2013, 30(5): 291-295. DOI: 10.1080/21681015.2013.828788.
Crossref Google Scholar
[28]

Chen M, Tang K. Quasi-developable surface modeling of contours with curved triangular patches. Computers & Graphics, 2013, 37(7): 851-861. DOI: 10.1016/j.cag.2013.05.002.
Crossref Google Scholar
[29]

Chen M, Tang K. G2 quasi-developable Bezier surface interpolation of two space curves. Computer-Aided Design, 2013, 45(11): 1365-1377. DOI: 10.1016/j.cad.2013.06.009.
Crossref Google Scholar
[30]

Bo P B, Zheng Y J, Chu D H, Zhang C C. As-developable-as-possible B-spline surface interpolation to B-spline curves. Computer Aided Geometric Design, 2020, 79: Article No. 101863. DOI: 10.1016/j.cagd.2020.101863.
Crossref Google Scholar
[31]

Park F C, Yu J, Chun C, Ravani B. Design of developable surfaces using optimal control. Journal of Mechanical Design, 2002, 124(4): 602-608. DOI: 10.1115/1.1515795.
Crossref Google Scholar
[32]

Fernández-Jambrina L. B-spline control nets for developable surfaces. Computer Aided Geometric Design, 2007, 24(4): 189-199. DOI: 10.1016/j.cagd.2007.03.001.
Crossref Google Scholar
[33]

Zheng W N, Bo P B, Liu Y, Wang W W. Fast B-spline curve fitting by L-BFGS. Computer Aided Geometric Design, 2012, 29(7): 448-462. DOI: 10.1016/j.cagd.2012.03.004.
Crossref Google Scholar
[34]
Hoschek J, Lasser D. Fundamentals of Computer Aided Geometric Design. Peters, 1993.
[35]

Lim C G. A universal parametrization in B-spline curve and surface interpolation. Computer Aided Geometric Design, 1999, 16(5): 407-422. DOI: 10.1016/S0167-8396(99)00010-2.
Crossref Google Scholar
Journal of Computer Science and Technology
Volume 37 Issue 5,
September 2022
Pages 1221-1238
DOI: 10.1007/s11390-022-0680-5
Cite this article:
Hu Z-X, Bo P-B, Zhang C-M. Quasi-Developable B-Spline Surface Design with Control Rulings. Journal of Computer Science and Technology, 2022, 37(5): 1221-1238. https://doi.org/10.1007/s11390-022-0680-5

370

Views

1

Crossref

0

Web of Science

0

Scopus

0

CSCD

Altmetrics
Received: 04 June 2020
Accepted: 10 February 2022
Published: 30 September 2022
©Institute of Computing Technology, Chinese Academy of Sciences 2022
Return