منابع مشابه
Tricubic polynomial interpolation.
A new triangular "finite element" is described; it involves the 12-parameter family of all quartic polynomial functions that are "tricubic" in that their variation is cubic along any parallel to any side of the triangle. An interpolation scheme is described that approximates quite accurately any smooth function on any triangulated domain by a continuously differentiable function, tricubic on ea...
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Binary-defined 3D objects are common in volume graphics and medical imaging as a result of voxelization algorithms, segmentation methods, and binary operations such as clipping. Traditionally, renderings of binary objects suffer from severe image quality problems, especially when one tries to zoom-in and render the binary data from up close. We present a new rendering technique for discrete bin...
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Consider a family of functions of a single variable x: Φ(x; a0, a1, . . . , an), where a0, . . . , an are the parameters. The problem of interpolation for Φ can be stated as follows: Given n + 1 real or complex pairs of numbers (xi, fi), i = 0, . . . , n, with xi 6= xk for i 6= k, determine a0, . . . , an such that Φ(xi; a0, . . . , an) = fi, i = 0, . . . , n. The above is a linear interpolatio...
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In previous works a polynomial interpolation method for triangular meshes has been introduced. This interpolant can be used to design smooth surfaces of arbitrary topological type. In a design process, it is very useful to be able to locate the deformation made on a geometric model. The previously introduced interpolant has the so-called strict locality property: when a mesh vertex is changed, ...
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The Alexander-Hirschowitz theorem says that a general collection of k double points in P imposes independent conditions on homogeneous polynomials of degree d with a well known list of exceptions. We generalize this theorem to arbitrary zero-dimensional schemes contained in a general union of double points. We work in the polynomial interpolation setting. In this framework our main result says ...
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ژورنال
عنوان ژورنال: Proceedings of the National Academy of Sciences
سال: 1971
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.68.6.1162