TY - GEN

T1 - Generation of spline approximations to tessellations

AU - Dannenhoffer, John F.

AU - Haimes, Robert

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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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U2 - 10.1007/978-3-540-87921-3_15

DO - 10.1007/978-3-540-87921-3_15

M3 - Conference contribution

AN - SCOPUS:84879521953

SN - 9783540879206

T3 - Proceedings of the 17th International Meshing Roundtable, IMR 2008

SP - 249

EP - 266

BT - Proceedings of the 17th International Meshing Roundtable, IMR 2008

PB - Kluwer Academic Publishers

T2 - 17th International Meshing Roundtable, IMR 2008

Y2 - 12 October 2008 through 15 October 2008

ER -