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It is time to drop the “R” from NURBS

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Abstract

NURBS were introduced into CAD/CAM systems predominantly for the representation of conventional objects, such as conics and quadrics. Among these, the circle played a critical role in representing a myriad of parts used in the every-day practice. Being the most universally used object, the circle has enjoyed the most popularity in science and engineering. It is an essential entity in both design as well as manufacturing and hence, its representation within CAD/CAM systems requires careful attention. Although the circle enjoys both smoothness as well as a uniform parametrization, its de facto mathematical form, the NURBS form, does not provide either sufficient smoothness or uniform parametrization. On top of all this, NURBS are rational forms requiring homogeneous coordinates in the four-dimensional space, whereas the engineering entity is only Euclidean in 3D. This multiple representational glitch, 3D presence and 4D storage, has given rise to enough headache to warrant reconsideration of the validity of the rational form in engineering design. This paper argues that it is time to drop the “R” from NURBS and to switch to integral splines with approximations where necessary. We also argue that it is time to bury dumb algorithms and consider human-based computing, i.e. our algorithms should be biologically inspired and not based on pure number crunching.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, University of South Florida, Tampa, USA

    Les A. Piegl

  2. 3035 Great Oak Circle, Tyler, TX, USA

    Wayne Tiller

  3. College of Computer Science and Engineering, Najran University, Najran, Saudi Arabia

    Khairan Rajab

Authors
  1. Les A. Piegl
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  2. Wayne Tiller
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  3. Khairan Rajab
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Correspondence to Les A. Piegl.

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Piegl, L.A., Tiller, W. & Rajab, K. It is time to drop the “R” from NURBS. Engineering with Computers 30, 703–714 (2014). https://doi.org/10.1007/s00366-013-0318-x

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  • DOI: https://doi.org/10.1007/s00366-013-0318-x

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