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—Based on Lagrange polynomials and variation of constants, we devise a novel 2n-1-point interpolatory ternary subdivision scheme that reproduces polynomials of degree 2n-2. We illustrate the technique with a 3-point ternary interpolatory subdivision scheme which can rebuild Hassan and Dodgson's interpolating 3-point ternary subdivision scheme and a new… (More)
—In this paper, we design a ternary even symmetric 2n-point approximating subdivision scheme which generates smooth curves of high order. We illustrate the technique with a new 4-point ternary approximating subdivision scheme which is C 4 and a new 6-point ternary approximating subdivision scheme which can achieve C 7-continuity. The smoothness of the new… (More)
In this paper, we evaluate fractal dimension of the fractal curve generated by the 3-point ternary interpolatory subdivision scheme. A formula between the subdivision parameter and the fractal dimension of the limit fractal curve is obtained. As an application of the obtained results, the generation of fractal curves and surfaces is discussed. The presented… (More)
We study the validity of Zipf's Law in a data set of Chinese city sizes. Previous investigations are restricted to log-log rank-size regression for a fixed sample. In contrast, we use rolling sample regression methods in which the sample is changing with the truncation point. The intuition is that if the distribution is Pareto with a coefficient one (Zipf's… (More)
Subdivision scheme is a discrete modeling method that breaches old model of surface modeling, namely, from discrete data to continuous data and last to discrete data. The method is simple, small computing and fast in modeling. This paper presents a classification standard of subdivision scheme, discusses and compares several subdivision schemes in brief.
A recognition algorithm for a type of coded target widely used in photogrammetry is presented in this paper. An efficient feature vector is first proposed to describe the targets, then mathematical morphological operations are used for clustering to location the the targets in the image. Finally, by ellipse fitting, each coded target in the image is… (More)
Based on the p-ary subdivision rules for B-splines, we show how to design more general subdivision schemes that preserve the B-spline smoothness exactly or almost. We illustrate the technique with new 4-point C5 binary, 4-point C3 ternary and C4 ternary subdivision schemes.
In this paper, we present an efficient 3-DOF registration method to align two overlapping point clouds captured by a range sensor that experiences locally planar motion such as in many robotics applications. The algorithm follows the RANSAC framework and is based on finding a pair of congruent triangles in the source and target clouds. With the assumption… (More)
In this paper, we firstly devise a new and general p-ary subdivision scheme based on normal vectors with multi-parameters to generate fractals. Rich and colorful fractals including some known fractals and a lot of unknown ones can be generated directly and conveniently by using it uniformly. The method is easy to use and effective in generating fractals… (More)