Generation of Spline Approximations to Tessellations
Dannenhoffer III, John F. and Robert Haimes
Proceedings, 17th International Meshing Roundtable, Springer-Verlag, pp.249-266, October 12-15 2008
17th International Meshing Roundtable
Pittsburgh, Pennsylvania, U.S.A.
October 12-15, 2008
Syracuse University, Syracuse, NY, USA
Massachusetts Institute of Technology, Cambridge, MA, USA
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.
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