0
Research Papers

Evaluation of NURBS Surfaces for Regular Structured Parameter Values

[+] Author and Article Information
Per Bergström

Department of Engineering
Sciences and Mathematics,
Luleå University of Technology,
SE-971 87 Luleå, Sweden
e-mail: per.bergstrom@ltu.se

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING. Manuscript received September 30, 2013; final manuscript received October 22, 2014; published online January 12, 2015. Assoc. Editor: Charlie C. L. Wang.

J. Comput. Inf. Sci. Eng 15(1), 011005 (Mar 01, 2015) (6 pages) Paper No: JCISE-13-1197; doi: 10.1115/1.4028956 History: Received September 30, 2013; Revised October 22, 2014; Online January 12, 2015

The evaluation of surface points and derivatives of NURBS surfaces for parameter values that are regularly distributed in a rectangular structure is considered. Because of the regularity, parts of the computations can be done on just a small portion of all parameter values and computed data is stored and reused for many other parameter values. Hence, the evaluation of NURBS surfaces can be performed faster when the regularity is used. We are making a complexity analysis of the number of floating point operations, which is required for the evaluations. To get knowledge about how the evaluations perform in practice, we are doing a numerical experiment where we are measuring the runtime to obtain the output both by using ordinary evaluation of the NURBS surface and by making use of the regular structure. Making use of the regularity gives significantly faster output.

FIGURES IN THIS ARTICLE
<>
Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.

References

Dimas, E., and Briassoulis, D., 1999, “3D Geometric Modelling Based on NURBS: A Review,” Adv. Eng. Software, 30(9–11), pp. 741–751. [CrossRef]
Farin, G., 1992, “From Conics to NURBS: A Tutorial and Survey,” IEEE Comput. Graphics Appl., 12(5), pp. 78–86. [CrossRef]
Piegl, L., 1991, “On NURBS: A Survey,” IEEE Comput. Graphics Appl., 11(1), pp. 55–71. [CrossRef]
Hoschek, J., and Lasser, D., 1993, Fundamentals of Computer Aided Geometric Design, A. K. Peters, Ltd., Natick, MA.
Coons, S. A., 1967, “Surfaces for Computer Aided Design of Space Forms,” MIT, Cambridge, MA, Technical Report No. MAC-TR-41.
Versprille, K. J., 1975, “Computer-Aided Design Applications of the Rational B-Spline Approximation Form,” Ph.D. thesis, Syracuse University, Syracuse, NY.
Piegl, L., and Tiller, W., 1987, “Curve and Surface Constructions Using Rational B-Splines,” Comput. Aided Des., 19(9), pp. 485–498. [CrossRef]
Tiller, W., 1983, “Rational B-Splines for Curve and Surface Representation,” IEEE Comput. Graphics Appl., 3(6), pp. 6–69. [CrossRef]
Cox, M. G., 1972, “The Numerical Evaluation of B-Splines,” IMA J. Appl. Math., 10(2), pp. 134–149. [CrossRef]
de Boor, C., 1972, “On Calculating With B-Splines,” J. Approximation Theory, 6(1), pp. 50–62. [CrossRef]
Boo, M., Bruguera, J. D., and Lopez-Zapata, E., 2000, “Parallel Architecture for the Computation of NURBS Surfaces,” Proc. SPIE.3970, pp. 37–48. [CrossRef]
Gopi, M. S., and Manohar, S., 1995, “A VLSI Architecture for the Computation of NURBS Patches,” Proceedings of the 8th International Conference on VLSI Design, VLSID'95, IEEE Computer Society, New Delhi, India, Jan. 4–7, pp. 326–331 [CrossRef].
Krishnamurthy, A., Khardekar, R., McMains, S., Haller, K., and Elber, G., 2009, “Performing Efficient NURBS Modeling Operations on the GPU,” IEEE Trans. Visualization Comput. Graphics, 15(4), pp. 530–543. [CrossRef]
Luken, W. L., and Cheng, F., 1996, “Comparison of Surface and Derivative Evaluation Methods for the Rendering of NURB Surfaces,” ACM Trans. Graphics, 15(2), pp. 153–178. [CrossRef]
Balázs, Á., Guthe, M., and Klein, R., 2004, “Efficient Trimmed NURBS Tessellation,” J. WSCG, 12(1), pp. 27–33.
Espino, F. J., Bóo, M., Amor, M., and Bruguera, J., 2003, “Adaptive Tessellation of NURBS Surfaces,” J. WSCG, 11(1), pp. 133–140.
Luken, W. L., 1996, “Tessellation of Trimmed NURB Surfaces,” Comput. Aided Geom. Des., 13(2), pp. 163–177. [CrossRef]
Piegl, L. A., and Richard, A. M., 1995, “Tessellating Trimmed NURBS Surfaces,” Comput. Aided Des., 27(1), pp. 16–26. [CrossRef]
Piegl, L., and Tiller, W., 1997, The NURBS Book, 2nd ed., Springer-Verlag, New York [CrossRef].
de Boor, C., 2001, A Practical Guide to Splines, Rev. ed., Springer-Verlag, New York.

Figures

Grahic Jump Location
Fig. 3

Different alternatives to go through the parameter values. (a) “u-inner” loop order, (b) “v-inner” loop order.

Grahic Jump Location
Fig. 2

Flops efficiency quotients. (a) ϱ∧, (b) ϱ∧', and (c) ϱ∧''.

Grahic Jump Location
Fig. 1

Parameter values, shown as points, are regularly distributed in a rectangular structure

Grahic Jump Location
Fig. 4

NURBS surfaces with bidirectional control net. (a) Torus, (b) Coons, (c) revolved, (d) sine, (e) helicoidal, and (f) swung.

Tables

Errata

Discussions

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