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Abstract: This paper presents an interpolating ternary butterfly subdivision scheme for triangular meshes based on a 1–9 splitting operator. The regular rules are derived from a interpolating subdivision curve, and the irregular rules are established through the Fourier analysis of the regular case. By analyzing the eigenstructures and characteristic maps, we show that the subdivision surfaces generated by this scheme is continuous up to valence 100. In addition, the curvature of regular region is bounded. Finally we demonstrate the visual quality of our subdivision scheme with several examples. [Copyright &y& Elsevier]

A 4-point interpolatory subdivision scheme with a tension parameter is analyzed, and the local property of 4-point interpolatory subdivision scheme and a kind of G1-continuity sufficient condition between surfaces as well as between curves are discussed. An efficient method of generating natural boundary points of 4-point interpolatory curve is presented, as well as a surface modeling method with the entire fairing property by combining energy optimization with subdivision scheme. The method has been applied in modeling 3D virtual garment surface. [Copyright &y& Elsevier]

An introduction is presented in which the editors discuss various reports within the issue on topics including a rigid body motion, interpolating subdivision scheme for curve and surface design based on cubic Bezier curves, and absorbing Markov chain in feature space.

Abstract: In this paper a combined approximating and interpolating subdivision scheme is presented. The relationship between approximating subdivision and interpolating subdivision is derived by directly performing operations on geometric rules. The behavior of the limit curve produced by our combined subdivision scheme is analyzed by the Laurent polynomial and attains degree of smoothness. Furthermore, a non-uniform combined subdivision with shape control parameters is introduced, which allows a different tension value for every edge of the original control polygon. [Copyright &y& Elsevier]

In general the rectangular windows are used by many super-resolution reconstruction approaches, however, they are not suitable for the arc regions of images. In view of this, a novel reconstruction algorithm is proposed in this paper, which is based on the Newton–Thiele׳s rational interpolation by continued fractions in the polar coordinates. In order to get better reconstructed results, we also present a novel model where the Newton–Thiele׳s rational interpolation scheme used to magnify images/videos is combined with the sparse representation scheme used to refine the reconstructed results. Plenty of experiments in image and video sequences demonstrate that the new method can produce high-quality resolution enhancement, as compared with the state-of-the-art methods. Experimental results show that the proposed method achieves much better results than other methods in terms of both visual effect and PSNR. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we present a novel fast mesh parameterization algorithm based on subdivision scheme. First, an algorithm of approximating a given triangular mesh by the 4-point interpolatory subdivision is proposed, then a mesh parameterization method is developed based on the subdivision surface approximation algorithm. The novel mesh parameterization method is a generalization of the chordal parameterization to surface case, and it is more computationally efficient than previous methods because it obviates any computation of linear system of equations. Some numerical experiments show the efficiency of the novel algorithm. [Copyright &y& Elsevier]