Maharavo Randrianarivony Tetrahedral transfinite interpolation with B-patch faces: construction and regularity
نویسنده
چکیده
We provide a methodology for efficiently checking whether a tetrahedral transfinite interpolation is regular. From given four triangular surfaces in form of B-patches fulfilling some compatibility conditions, we generate a transfinite interpolation defined on the unit 3D simplex. An efficient subdivision scheme is provided for a B-patch in order to obtain criteria which are verifiable in a discrete manner. That yields an adaptive method where only some parts of the simplex need to be subdivided. In order to reduce the computational cost, we make use of degree reductions. That is achieved by utilizing products of scaled Jacobi polynomials. After each subdivision process, one performs degree reductions provided that the induced error is sufficiently small. This work is important for application in refineable functions and for generation of multiscale or multiresolution bases functions from 3D CAD models.
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