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[1] Wang Xiaoping, Zhou Rurong, Wang Zhiguo, Zhang Liyan, et al. Constructing G1 interpolation curveson surfaces with Coons surface [J]. Journal of Southeast University (English Edition), 2004, 20 (2): 187-190. [doi:10.3969/j.issn.1003-7985.2004.02.012]
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Constructing G1 interpolation curveson surfaces with Coons surface()
利用Coons曲面构造曲面上的G1插值曲线
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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:
20
Issue:
2004 2
Page:
187-190
Research Field:
Computer Science and Engineering
Publishing date:
2004-06-30

Info

Title:
Constructing G1 interpolation curveson surfaces with Coons surface
利用Coons曲面构造曲面上的G1插值曲线
Author(s):
Wang Xiaoping;  Zhou Rurong;  Wang Zhiguo;  Zhang Liyan
Research Center of CAD/CAM Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
王小平;  周儒荣;  王志国;  张丽艳
南京航空航天大学CAD/CAM工程研究中心, 南京 210016
Keywords:
interpolation;  Coons surface;  G1 continuity;  surface-to-surface intersection
插值;  Coons曲面;  G1连续;  曲面求交
PACS:
TP391
DOI:
10.3969/j.issn.1003-7985.2004.02.012
Abstract:
Using a bi-cubic Coons surface, a new method for G1-continuous interpolation of an arbitrary sequence of points on an implicitly or parametrically defined surface with a specified tangent direction at every point was presented. Firstly construct a G1-continuous composite Coons surface patch, then compute the intersection of the surface patch and the given surface. The desired interpolation curve is the intersection curve. Unlike some existing methods, introduced into the method were several free parameters that can be used in subsequent interactive modification so that the last curve’s shape meets our demand. Experiments demonstrate the method is simple, feasible and applicable to computer aided design and computer graphics, etc.
利用双三次Coons曲面, 给出了一种对隐式或参数曲面上任意点序列及切方向给定时的G1连续插值方法.首先构造G1连续的组合Coons曲面, 其次求该组合曲面片与已知曲面的交线. 插值曲线是组合Coons曲面片与给定曲面的交线. 由于引入了若干控制参数, 可对曲线进行交互修改使得其最终的形状更好地满足我们的要求. 实验证明该方法简单可行, 适用于计算机辅助设计、计算机图形学等领域.

References:

[1] Litke N, Levin A, Schröder P. Trimming for subdivision surfaces [J]. Computer Aided Geometric Design, 2001, 18(5): 463-481.
[2] Lo C C. Real-time generation and control of cutter path for 5-axis CNC machining [J]. International Journal of Machine Tool and Manufacture, 1999, 39(3): 471-488.
[3] Abdel-Malek K, Yeh H J. Path trajectory verification for robot manipulators in a manufacture environment [J]. IMechE Journal of Engineering Manufacture, 1997, 211(7): 547-556.
[4] Pobegailo A P. Spherical splines and orientation interpolation [J]. The Visual Computer, 1994, 11(2): 63-68.
[5] Shoemake K. Animation rotation with quaternion curves [J]. Computer Graphics, 1995, 19(3): 245-256.
[6] Dietz R, Hoschek J, Jüttler B. Rational patches on quadric surfaces [J]. Computer Aided Design, 1995, 27(1): 27-40.
[7] Hartmann E. G2 interpolation and blending on surfaces [J]. The Visual Computer, 1996, 12(4): 181-192.
[8] Li J, Hoschek J, Hartmann E. Gn-11 functional splines for interpolation and approximation of curves, surfaces and solids [J].Computer Aided Geometric Design, 1990, 7(2): 209-220.
[9] Zhang H. Algorithm of C1 interpolation restricted on smooth surface[J]. Journal of Computer Aided Design and Computer Graphics, 1997, 9(5): 385-390.(in Chinese)
[10] Lin H W, Wang G J. G1 interpolation curve on smooth surface [A]. In: Zhang C M, ed. Proceeding of CSIAM Geometric Design & Computing ’ 2002[C]. Qingdao, 2002. 50-53.(in Chinese)
[11] Su B Q, Liu D Y. Computational geometry [M]. Shanghai: Shanghai Scientific and Technical Publishers, 1981.(in Chinese)

Memo

Memo:
Biographies: Wang Xiaoping(1966—), male, doctor, harayano@hotmail.com; Zhou Rurong(1936—), male, professor, zhoururong@vip.sina.com.
Last Update: 2004-06-20