A Boundary-Blending Method for the Parametrization of 2D Surfaces With Highly Irregular Boundaries

[+] Author and Article Information
Jui-Jen Chuang, Daniel C. H. Yang

Mechanical and Aerospace Engineering Department, University of California, Los Angeles, Los Angeles, CA 90095

J. Mech. Des 126(2), 327-335 (May 05, 2004) (9 pages) doi:10.1115/1.1667912 History: Received June 01, 2001; Revised July 01, 2003; Online May 05, 2004
Copyright © 2004 by ASME
Your Session has timed out. Please sign back in to continue.


Mortenson, Michael E., 1985, Geometric Modeling, John Wiley & Sons, Inc.
Yamaguchi, Fujio, 1988, Curves and Surfaces in Computer Aided Geometric Design, Springer-Verlag.
Risler, J. J., 1992, Mathematical Methods for CAD, Cambridge University Press.
Farin, Gerald, 1988, Curves and Surfaces for Computer Aided Geometric Design, A Practical Guide, Academic Press, Inc.
Piegl, Les, and Tiller, Wayne, 1997, The NURBS Book, Second Edition, Springer.
Coons, S. A., 1964, “Surfaces for Computer-Aided Design of Space Figures,” MIT ESL 9442-M-139, January.
Soni,  Bharat, K., 2000, “Grid Generation: Past, present, and future,” Appl. Numer. Math., 32, pp. 361–369.
Gordon, W. J., and Thiel, L. C., 1982, “Transfinite Mappings and Their Applications to Grid Generation,” Numerical Grid Generation, Joe F. Thompson, ed., North-Holland.
Soni,  B. K., 1992, “Grid Generation for Internal Flow Configurations,” Comput. Math. Appl., 24(5/6), pp. 191–201.
Smith, Robert E., 1983, “Three-Dimensional Algebraic Grid Generation,” AIAA 6th Computational Fluid Dynamics Conference, Danvers, Massachusetts.
Eiseman, Peter R., and Smith, Robert, 1980, “Mech Generation Using Algebraic Techniques,” Numerical Grid Generation Techniques, Robert E. Smith, ed., NASA CP-2166, 1980.
Thompson, Joe F., Warsi, Z. U. A., and Mastin, C. Wayne, 1985, Numerical Grid Generation, Foundations and Applications, Elsevier Science Publishing Co, Inc.
Hsu,  K., and Lee,  S. L., 1992, “A Numerical Technique for Two-Dimensional Grid Generation with Grid Control at All of the Boundaries,” J. Comput. Phys., 96(2), October, pp. 451–469.
Sorenson, Reese L., and Steger, Joseph L., 1980, “Numerical Generation of Two-Dimensional Grids by the Use of Poisson Equations With Grid Control at Boundaries,” Proceedings of Workshop on Numerical Grid Generation, NASA CP-2166, pp. 449–461.
Coleman, Roderick M., 1980, “Generation of Orthogonal Boundary-Fitted Coordinate System,” Proceedings of Workshop on Numerical Grid Generation, NASA CP-2166, pp. 213–219.
Lehtimäki,  Reijo, 1990, “Elliptic Grid Generation,” AIAA J., 37(6), pp. 768–770.
Steger,  J. L., and Chausee,  D. S., 1980, “Generation of Body-fitted Coordinates Using Hyperbolic Partial Differential Equations,” SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput., pp. 431.
Chuang, Jui-Jen, 2001, “Boundary Conforming Tool-Path Generation for Trimmed Free-form Surfaces in CAD/CAM Integration,” Doctoral Thesis, Mechanical and Aerospace Engineering Department, UCLA, Dec.
Hoffmann, Klaus A., 1989, Computational Fluid Dynamics for Engineers, Engineering Education System.
Kreyszig, Erwin, 1983, Advanced Engineering Mathematics, 5th edition, John Wiley & Sons.
Weatherill, N. P., 1990, “Grid Generation,” von Karman Institute for Fluid Dynamics, Lecture Series 1990–06, Numerical Grid Generation.
Gerald, Curtis F., and Wheatley, Patrick O., 1994, Applied Numerical Analysis, 5th ed., Addison-Wesley Publishing Co.


Grahic Jump Location
Boundary interpolated plane patches
Grahic Jump Location
2D parametrization with relatively uneven grid distribution via Laplace generation method
Grahic Jump Location
The dual geometric offsetting procedures for a unidirectional 2D surface parametrization
Grahic Jump Location
Geometric definition in the design of nonuniform offset vector
Grahic Jump Location
Two examined examples for the design of offsetting vector
Grahic Jump Location
Direction adjustment factor λj vs. isoparametric value vj
Grahic Jump Location
The effect of different ρ values to the parametrization result
Grahic Jump Location
The plot of function Kj−1(u) vs. κj−1
Grahic Jump Location
The effect of μ values on the speed of curvature averaging
Grahic Jump Location
Plot of combined curvature blending function ωj−1 vs. (j/n)
Grahic Jump Location
Surface composition in bi-directional 2D parametrization using nonuniform offsetting method
Grahic Jump Location
Examples of 2D boundary-fitted parametrization




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In