In view of the relative positioning problem between non-regular quadrilateral grids and regular rectangle grid nodes in the wave front construction method, concrete realization problems with four grid positioning meth...In view of the relative positioning problem between non-regular quadrilateral grids and regular rectangle grid nodes in the wave front construction method, concrete realization problems with four grid positioning methods （vector cross product judgment, angle sum, intersection-point, and signs comparison algorithms） in wave front construction which are commonly used in computer graphics are compared and analyzed in this paper. Based on the stability analysis of the location method, the calculation examples show that the vector cross product judgment method is faster and more accurate than other methods in the realization of the relative positioning between non-regular quadrilateral grids and regular rectangle grid nodes in wave front construction. It provides precise grid point attribute values for the next steps of migration and demigration.展开更多
Linear quadtree is a popular image representation method due to its convenient imaging procedure. However, the excessive emphasis on the symmetry of segmentation, i.e. dividing repeatedly a square into four equal sub-...Linear quadtree is a popular image representation method due to its convenient imaging procedure. However, the excessive emphasis on the symmetry of segmentation, i.e. dividing repeatedly a square into four equal sub-squares, makes linear quadtree not an optimal representation. In this paper, a no-loss image representation, referred to as Overlapped Rectangle Image Representation (ORIR), is presented to support fast image operations such as Legendre moments computation. The ORIR doesn’t importune the symmetry of segmentation, and it is capable of representing, by using an identical rectangle, the information of the pixels which are not even adjacent to each other in the sense of 4-neighbor and 8-neighbor. Hence, compared with the linear quadtree, the ORIR significantly reduces the number of rectangles required to represent an image. Based on the ORIR, an algorithm for exact Legendre moments computation is presented. The theoretical analysis and the experimental results show that the ORIR-based algorithm for exact Legendre moments computation is faster than the conventional exact algorithms.展开更多
We report a numerical method to analyze the fractal characteristics of far-field diffraction patterns for two-dimensional Thue-Morse (2-D TM) structures. The far-field diffraction patterns of the 2-D TM structures can...We report a numerical method to analyze the fractal characteristics of far-field diffraction patterns for two-dimensional Thue-Morse (2-D TM) structures. The far-field diffraction patterns of the 2-D TM structures can be obtained by the numerical method, and they have a good agreement with the experimental ones. The analysis shows that the fractal characteristics of far-field diffraction patterns for the 2-D TM structures are determined by the inflation rule, which have potential applications in the design of optical diffraction devices.展开更多
With the aid of symbolic computation Maple, the discrete Ablowitz–Ladik equation is studied via an algebra method, some new rational solutions with four arbitrary parameters are constructed. By analyzing related para...With the aid of symbolic computation Maple, the discrete Ablowitz–Ladik equation is studied via an algebra method, some new rational solutions with four arbitrary parameters are constructed. By analyzing related parameters, the discrete rogue wave solutions with alterable positions and amplitude for the focusing Ablowitz–Ladik equations are derived. Some properties are discussed by graphical analysis, which might be helpful for understanding physical phenomena in optics.展开更多
基金This research work is supported by the Projects of National Science Foundation of China （Grant No, 40574052 and 40437018） and National Basic Research Program of China （973 Program） （Grant No. 2007CB209603）.Acknowledgements We wish to thank Researcher Xu Tao for his advice and comment. We also thank Mrs. Wang Kun for her help in the process of translation.
文摘In view of the relative positioning problem between non-regular quadrilateral grids and regular rectangle grid nodes in the wave front construction method, concrete realization problems with four grid positioning methods （vector cross product judgment, angle sum, intersection-point, and signs comparison algorithms） in wave front construction which are commonly used in computer graphics are compared and analyzed in this paper. Based on the stability analysis of the location method, the calculation examples show that the vector cross product judgment method is faster and more accurate than other methods in the realization of the relative positioning between non-regular quadrilateral grids and regular rectangle grid nodes in wave front construction. It provides precise grid point attribute values for the next steps of migration and demigration.
基金Supported by the National High Technology Research and Development Program of China (No. 2006AA04Z211)
文摘Linear quadtree is a popular image representation method due to its convenient imaging procedure. However, the excessive emphasis on the symmetry of segmentation, i.e. dividing repeatedly a square into four equal sub-squares, makes linear quadtree not an optimal representation. In this paper, a no-loss image representation, referred to as Overlapped Rectangle Image Representation (ORIR), is presented to support fast image operations such as Legendre moments computation. The ORIR doesn’t importune the symmetry of segmentation, and it is capable of representing, by using an identical rectangle, the information of the pixels which are not even adjacent to each other in the sense of 4-neighbor and 8-neighbor. Hence, compared with the linear quadtree, the ORIR significantly reduces the number of rectangles required to represent an image. Based on the ORIR, an algorithm for exact Legendre moments computation is presented. The theoretical analysis and the experimental results show that the ORIR-based algorithm for exact Legendre moments computation is faster than the conventional exact algorithms.
基金supported by the National Natural Science Foundation of China (No.60977048)the International Bilateral Italy-China Joint Projects (CNR/CAS Agreement 2008-2010)+1 种基金the International Collaboration Program of Ningbo (No.2010D10018)the K. C. Wong Magna Fund in Ningbo University, China
文摘We report a numerical method to analyze the fractal characteristics of far-field diffraction patterns for two-dimensional Thue-Morse (2-D TM) structures. The far-field diffraction patterns of the 2-D TM structures can be obtained by the numerical method, and they have a good agreement with the experimental ones. The analysis shows that the fractal characteristics of far-field diffraction patterns for the 2-D TM structures are determined by the inflation rule, which have potential applications in the design of optical diffraction devices.
基金Supported by the Beijing Natural Science Foundation under Grant No.1153004China Postdoctoral Science Foundation under Grant No.2015M570161the Natural Science Foundation of China under Grant No.61471406
文摘With the aid of symbolic computation Maple, the discrete Ablowitz–Ladik equation is studied via an algebra method, some new rational solutions with four arbitrary parameters are constructed. By analyzing related parameters, the discrete rogue wave solutions with alterable positions and amplitude for the focusing Ablowitz–Ladik equations are derived. Some properties are discussed by graphical analysis, which might be helpful for understanding physical phenomena in optics.
