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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.

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Figures

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Fig. 1

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

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Fig. 2

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

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Fig. 3

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

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Fig. 4

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

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