Abstract
This paper proposes a simple surface interpolation attaining tangent‐plane continuity. It is a natural extension of the local quadratic C0 interpolator developed by the author (2005) in one of his works, which has already been applied successfully to diverse engineering problems. The methodology presented in this paper inherits most of the advantages possessed by the C0 scheme. That is, (i) The algorithm is efficient and completely local requiring only the position vectors and normals given at the nodes of a patch, and hence it is suitable for parallel processing. (ii) It converges rapidly to the given surface with the increase in the number of nodes. (iii) Singular points (apexes, sharp edges, etc.) and nonmanifolds can be treated quite easily. (iv) Because of the minimization criteria assigned to the surface coefficients, it is rather robust and amenable to computational analyses. Validity and effectiveness of the proposed technique are demonstrated through numerical examples.
Highlights
There is a significant gap between the requirements on geometric models in the CAD and computational science communities
Models for numerical simulation e.g., the finite element method are almost always represented by fine meshes, where the major interests are in fast, stable, and accurate recovery of the surface information lost during the process of discretization
B simulation of elastoplastic mechanics 3, 4, C ray tracing of optical devices 5. All those applications prohibited the usage of traditional sophisticated surface descriptions, due to severe tolerance as well as geometrical and physical complexity of the systems
Summary
There is a significant gap between the requirements on geometric models in the CAD and computational science communities. Models for numerical simulation e.g., the finite element method are almost always represented by fine meshes, where the major interests are in fast, stable, and accurate recovery of the surface information lost during the process of discretization With this as background, the author proposed an interpolation scheme suitable for such analyses 1. Iv It has the minimum degree two of interpolation necessary for representation of the curvature This property is desirable especially for ray tracing, contact problems, and so forth, which involve implicitization and inversion, since closedform solutions may be obtained. The new algorithm involves correction using a simple rational function retaining the boundary of the C0 patch It is no longer quadratic, but it inherits all other desirable features from the C0 patch, such as complete locality and capability of handling multiple normals.
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