A Curvature Smooth Lofting Scheme for Singular Point Treatments

  • Elaine CohenEmail author
  • Robert Haimes
  • Richard Riesenfeld
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9213)


This paper presents a new end condition scheme for lofting through singular points, one that is easily specified and can generate shapes that are appropriate for lofting to the noses of subsonic/transonic aerodynamic and some hydrodynamic crafts. A degeneracy in the tensor product parameterization is typical in representations of spheres and ellipsoids, or topological equivalents. In that case a grid of data typically sets a whole row to a single value, so it becomes difficult and cumbersome to specify shape characteristics in different directions emanating from that point. Some standardly used end conditions result in shapes that are \(C^0\) at the singular point, an undesirable outcome in nose regions of subsonic aircraft, so the straightforward nose-to-tail lofts are intractable for these vehicles. The proposed method overcomes this problem (See Figs. 1 and 2 for examples).


Tensor product lofting Singular point 



This work is supported in part by NSF IIS-1117997 and in part through NASA Cooperative Agreement NNX11AI66A – Christopher Heath (NASA Glenn Research Center) is the Technical Monitor.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Elaine Cohen
    • 1
    Email author
  • Robert Haimes
    • 2
  • Richard Riesenfeld
    • 1
  1. 1.School of ComputingUniversity of UtahSalt Lake CityUSA
  2. 2.Department of Aeronautics and AstronauticsMassachusetts Institute of TechnologyCambridgeUSA

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