Generation of spline approximations to tessellations

John F. Dannenhoffer, Robert Haimes

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

In geometrical modeling, one is often provided a description of a surface that is defined in terms of a triangulation, which is supported by a discrete number of nodes in space. These faceted surface representations are defined to be C-0 continuous, and therefore in general have slope and curvature discontinuities at the triangle sides, unless the tessellation is planar. Unfortunately, analytical and computational methods often require a surface description that has well-defined and smoothly-varying gradients and curvatures; in general spline surfaces possess such properties. Described herein is a process for generating a cubic spline surface that approximates, to within a userspecified tolerance, a given tessellated surface that may be non-convex or multiplyconnected. The method combines a local least-squares technique for specifying knot properties as well as an adaptation technique of selecting the necessary knot spacings. This new technique is first described along a curve for illustrative purposes. It is then expanded to the case of the general surface. A reparameterization technique that is required for surfaces with non-smooth parameterizations is described next. Computed results for two configurations are then shown.

Original languageEnglish (US)
Title of host publicationProceedings of the 17th International Meshing Roundtable, IMR 2008
PublisherKluwer Academic Publishers
Pages249-266
Number of pages18
ISBN (Print)9783540879206
DOIs
StatePublished - 2008
Event17th International Meshing Roundtable, IMR 2008 - Pittsburgh, PA, United States
Duration: Oct 12 2008Oct 15 2008

Publication series

NameProceedings of the 17th International Meshing Roundtable, IMR 2008

Other

Other17th International Meshing Roundtable, IMR 2008
CountryUnited States
CityPittsburgh, PA
Period10/12/0810/15/08

ASJC Scopus subject areas

  • Engineering (miscellaneous)

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    Dannenhoffer, J. F., & Haimes, R. (2008). Generation of spline approximations to tessellations. In Proceedings of the 17th International Meshing Roundtable, IMR 2008 (pp. 249-266). (Proceedings of the 17th International Meshing Roundtable, IMR 2008). Kluwer Academic Publishers. https://doi.org/10.1007/978-3-540-87921-3_15