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Research Papers

Filling N-Sided Holes With Trimmed B-Spline Surfaces Based on Energy-Minimization Method

[+] Author and Article Information
Xiaodong Liu

National Engineering Research Center for
Technological Innovation Method and Tool,
Hebei University of Technology,
Tianjin 300130, China;
School of Mechanical Engineering,
Hebei University of Technology,
Tianjin 300130, China
e-mail: xdg.liu@googlemail.com

http://geom.hebut.edu.cn - VBS kernel is a non-profit research project, and it is freely available to researchers from qualified institutions.

It should be noted that, other items, e.g., some traditional non-linear energy items, could also be included and be solved efficiently, but they are not related to the n-sided method discussed in this paper and are beyond the scope of this paper.

1In CAD systems, numerical tolerances or deviations are inevitable, and all CAD calculations are performed with specified tolerances. The tolerance in CAD is always measured by the relative tolerance, and in this paper, we assume that the generated surface is within a box of 1 × 1 × 1 m. Simply speaking, for B-Spline, the tolerance of 1.0 × 10−6 m is considered to be a good or accurate result to build waterproof models in CAD systems, and 1.0 × 10−6 m is used as the tolerance requirement in this paper.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING. Manuscript received December 23, 2013; final manuscript received September 20, 2014; published online November 7, 2014. Assoc. Editor: Krishnan Suresh.

J. Comput. Inf. Sci. Eng 15(1), 011001 (Mar 01, 2015) (9 pages) Paper No: JCISE-13-1290; doi: 10.1115/1.4028632 History: Received December 23, 2013; Revised September 20, 2014; Online November 07, 2014

Using a trimmed rectangular B-Spline surface to fill an n-sided hole is a much desired operation in computer aided design (CAD), but few papers have addressed this issue. Based on an energy-minimization or variational B-Spline technique, the paper presents the technique of using one single trimmed rectangular B-Spline surface to fill an n-sided hole. The method is efficient and robust, and takes a fraction of a second to fill n-sided holes with high-quality waterproof B-Spline surfaces under complex constraints. As the foundation of filling n-sided holes, the paper also presents the framework and addresses the key issues on variational B-Spline technique. Without any precalculation, the variational B-Spline technique discussed in this paper can solve virtually any B-Spline surface with up to 20,000 control points in real time, which is much more efficient and powerful than previous work in the variational B-Spline field. Moreover, the result is accurate and satisfies CAD systems' high-precision requirements.

FIGURES IN THIS ARTICLE
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Copyright © 2015 by ASME
Topics: B-splines
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References

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VBS Kernel Website, Sept. 2014, http://geom.hebut.edu.cn/Research/demo1.htm
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Figures

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Fig. 1

Filling a six-sided hole: The method discussed in this paper uses one single rectangular B-Spline surface with 12 × 12 = 144 control points to fill the six-sided hole. (The hole is shown as a small picture at the bottom right. To demonstrate the operation of filling an n-sided hole, the entire untrimmed rectangular B-Spline surface is shown.) The tolerance requirement is less than 1.0 × 10−6 m.

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Fig. 2

The model for benchmark testing

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Fig. 3

Comparing surfaces or curves created with different energy functional

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Fig. 4

Gaps or overlaps between curves

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Fig. 5

Filling n-sided holes

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Fig. 6

Solving a hard-constraint system

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