通信工程、自动化技术 |
|
|
|
|
以已知曲线为渐进线的可展曲面束的设计 |
刘羽, 王国瑾 |
浙江大学 计算机图像图形研究所,浙江 杭州 310027 |
|
Designing developable surface pencil through given curve as its common asymptotic curve |
LIU Yu, WANG Guo-jin |
Institute of Computer Images and Graphics, Zhejiang University, Hangzhou 310027, China |
[1] CONTOPOULOS G. Asymptotic curves and escapes in Hamiltonian systems [J]. Astronomy and Astrophysics, 1990, 231(1): 41-55.
[2] EFTHYMIOPOULOS C, CONTOPOULOS G, VOGLIS N, et al. Islands and asymptotic curves in the stickiness region [J]. Celestial Mechanics and Dynamical Astronomy, 1999, 73(1/2/3/4): 221-230.
[3] FLRY S, POTTMANN H. Ruled surfaces for rationalization and design in architecture [C]∥ Proceedings of the Conference of the Association for Computer Aided Design in Architecture (ACADIA).\ [S.l.\]:ACADIA, 2010.
[4] WANG H J, NI Q. A new method of moving asymptotes for large-scale unconstrained optimization [J]. Applied Mathematics and Computation, 2008, 203(1): 62-71.
[5] BLETZINGER K U. Extended method of moving asymptotes based on second-order information structural optimization [J]. Structural and Multidisciplinary Optimization, 1993, 5(3): 175-183.
[6] WANG G J, TANG T, TAI C L. Parametric representation of a surface pencil with a common spatial geodesic [J].Computer-Aided Design, 2004, 36(5): 447-459.
[7] ZHAO H Y, WANG G J. A new approach for designing rational Bézier surfaces from a given geodesic [J]. Journal of Information and Computational Science, 2007, 4(2): 879-887.
[8] ZHAO H Y, WANG G J. A new method for designing a developable surface utilizing the surface pencil through a given curve [J]. Progress in Natural Science, 2008, 18(1): 105-110.
[9] ZHAO H Y, WANG G J. Design of optimized surface passing through a given geodesic [J]. Journal of computer research and development, 2009, 46(2): 289-294.
[10] KASAP E, AKYILDIZ F T, ORBAY K. A generalization of surfaces family with common spatial geodesic [J]. Applied Mathematics and Computation, 2008, 201(1/2): 781-789.
[11] LI C Y, WANG R H, ZHU C G. Parametric representation of a surface pencil with a common line of curvature [J].Computer-Aided Design, 2011, 43(9): 1110-1117.
[12] BAYRAM E, GLER F, KASAP E. Parametric representation of a surface pencil with a common asymptotic curve [J]. Computer-Aided Design, 2012,44(7):637-643.
[13] HARTMAN P, WINTNER A. On the asymptotic curves of a surface [J]. American Journal of Mathematics, 1951, 73(1): 149-172.
[14] KITAGAWA Y. Periodicity of the asymptotic curves on flat tori in S3 [J]. Journal of the Mathematical Society of Japan, 1988, 40(3): 457-496.
[15] GARCIA R, GUTIERREZ C, SOTOMAYOR J. Structural stability of asymptotic lines on surfaces immersed in R3 [J]. Bulletin des Sciences Mathématiques, 1999, 123(8): 599-622.
[16] AUMMANN G. A simple algorithm for designing developable Bézier surfaces [J]. Computer Aided Geometric Design, 2003, 20(8/9): 601-619.
[17] AUMANN G. Degree elevation and developable Bézier surfaces [J]. Computer Aided Geometric Design, 2004, 21(7): 661-670.
[18] CRENSHAW H C, EDELSTEIN-KESHET L. Orientation by helical motion II. changing the direction of the axis of motion [J]. Bulletin of Mathematical Biology, 1993, 55 (1): 213-230.
[19] FAROUKI R T, SZAFRANA N, BIARDA L. Existence conditions for coons patches interpolating geodesic boundary curves [J]. Computer Aided Geometric Design, 2009, 26(5): 599-614.
[20] 沈一兵. 整体微分几何初步[M]. 3版. 北京: 高等教育出版社, 2009.
[21] AUMANN G. Interpolation with developable patches [J]. Computer Aided Geometric Design, 1991, 8(5): 409-420.
[22] CHALFANT J S, MAEKAWA T. Design for manufacturing using B-spline developable surfaces [J]. Journal of Ship Production, 1998, 42(3): 207-215.
[23] MAEKAWA T, CHALFANT J S. Design and tessellation of B-spline developable surfaces [J]. ASME Transaction: Journal of Mechanical Design, 1998, 120(3): 453-461.
[24] 王国瑾, 汪国昭, 郑建民. 计算机辅助几何设计[M]. 北京: 高等教育出版社, 2001. |
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
|
Shared |
|
|
|
|
|
Discussed |
|
|
|
|