A non-linear circle-preserving subdivision scheme
نویسندگان
چکیده
منابع مشابه
A non-linear circle-preserving subdivision scheme
We describe a new method for constructing a sequence of refined polygons, which starts with a sequence of points and associated normals. The newly generated points are sampled from circles which approximate adjacent points and the corresponding normals. By iterating the refinement procedure, we get a limit curve interpolating the data. We show that the limit curve is G, and that it reproduces c...
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The four-point curve subdivision scheme is one of the classic reference points of subdivision theory. It has effective C2 continuity, although the curvature at the data points actually diverges slowly to infinity as very large numbers of subdivision steps are taken. However, it has rather large longitudinal artifacts, so that points interpolated around a curve of almost constant curvature are f...
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We present a tension-controlled 2-point Hermite interpolatory subdivision scheme that is capable of reproducing circles starting from a sequence of sample points with any arbitrary spacing and appropriately chosen first and second derivatives. Whenever the tension parameter is set equal to 1, the limit curve coincides with the rational quintic Hermite interpolant to the given data and has guara...
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Subdivision schemes are commonly used to obtain dense or smooth data representations from sparse discrete data. E. g., B-splines are smooth curves or surfaces that can be constructed by infinite subdivision of a polyline or polygon mesh of control points. New vertices are computed by linear combinations of the initial control points. We present a new non-linear subdivision scheme for the refine...
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The regularity of the limit function of a linear subdivision scheme is essentially irrelevant to the initial data. How data dependent, then, is the regularity of the limit of a nonlinear subdivision scheme? The answer is the most obvious it depends. In this paper, we prove that the nonlinear convexity preserving subdivision scheme developed independently by Floater/Micchelli [12] and Kuijt/van ...
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ژورنال
عنوان ژورنال: Advances in Computational Mathematics
سال: 2006
ISSN: 1019-7168,1572-9044
DOI: 10.1007/s10444-005-9011-y