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 ...

Both the 4-point and the uniform cubic B-spline subdivisions double the number of vertices of a closed-loop polygon P and produce sequences of vertices fj and bj respectively. We study the J-spline subdivision scheme Js, introduced by Maillot and Stam, which blends these two methods to produce vertices of the form vj=(1–s)fj+sbj. Iterative applications of Js yield a family of limit curves, the ...

This paper proposes to generalize linear subdivision schemes nonlinear for curve and surface modeling by refining vertex positions together with refinement of unit control normals at the vertices. For each round subdivision, new are obtained projections linearly subdivided onto circle or sphere while updating vertices along directions newly normals. Particularly, position is computed weighted a...

In this paper, we propose and analyze a tensor product subdivision scheme which is the extension of three point scheme for curve modeling. The usefulness of the scheme is illustrated by considering different examples along with its application in surface modeling.

A novel 4-point ternary interpolatory subdivision scheme with a tension parameter is analyzed. It is shown that for a certain range of the tension parameter the resulting curve is C2. The role of the tension parameter is demonstrated by a few examples. There is a brief discussion of computational costs.  2001 Elsevier Science B.V. All rights reserved.

The main purpose of this paper consists of demonstrating advantages of using implicit filtering schemes (noncausal IIR filters, in the signal processing language) for some basic image processing and geometric modeling applications. In particular, applications of implicit filtering for curve subdivision, image filtering, estimating image derivatives, and deblurring Gaussian blur are considered.

and Applied Analysis 3 P 1 2i P 1 2i 1 P 1 2i 2 P i 1 P 1 2i 3 P 1 2i 4 P k i 2 P k i a P 1 3i P 1 3i 1 P 1 3i 2 P i 1 P 1 3i 3 P 1 3i 4 P 1 3i 5 P 1 3i 6 P k i 2 P k i b P 1 4i P 1 4i 1 P 1 4i 2 P k i 1 P 1 4i 3 P 1 4i 4 P 1 4i 5 P 1 4i 6 P 1 4i 7 P 1 4i 8 P k i 2 P k i c Figure 1: Solid lines show coarse polygons whereas doted lines are refined polygons. a – c represent binary, ternary, and q...

Keywords: Bé zier curve Curve intersection Bé zier clipping Hybrid clipping a b s t r a c t This paper presents a novel approach, called hybrid clipping, for computing all intersections between two polynomial Bé zier curves within a given parametric domain in the plane. Like Bé zier clipping, we compute a 'fat line' (a region along a line) to bound one of the curves. Then we compute a 'fat curv...

A sequence of rational functions in a variable q is q-holonomic if it satisfies a linear recursion with coefficients polynomials in q and qn. In the paper, we assign a tropical curve to every q-holonomic sequence, which is closely related to the degree of the sequence with respect to q. In particular, we assign a tropical curve to every knot which is determined by the Jones polynomial of the kn...