Maps, essential tools for portraying the Earth’s surface, inherently introduce distortions to geographical features. While various quantification methods exist for assessing these distortions, they often fall short w...Maps, essential tools for portraying the Earth’s surface, inherently introduce distortions to geographical features. While various quantification methods exist for assessing these distortions, they often fall short when evaluating actual geographic features. In our study, we took a novel approach by analyzing map projection distortion from a geometric perspective. We computed the fractal dimensions of different stretches of coastline before and after projection using the divide-and-conquer algorithm and image processing. Our findings revealed that map projections, even when preserving basic shapes, inevitably stretch and compress coastlines in diverse directions. This analysis method provides a more realistic and practical way to measure map-induced distortions, with significant implications for cartography, geographic information systems (GIS), and geomorphology. By bridging the gap between theoretical analysis and real-world features, this method greatly enhances accuracy and practicality when evaluating map projections.展开更多
Demonstrating the approach to protract the figure of three-dimensional graphs with geometrical forms in two-dimensional planes, graphics is a basic technical discipline of examining protracting engineering drawings us...Demonstrating the approach to protract the figure of three-dimensional graphs with geometrical forms in two-dimensional planes, graphics is a basic technical discipline of examining protracting engineering drawings using the method of projection and addressing issues on space geometry as well as its theory and approach. Graphics is also a kind of semiotic system of writing. China boasts of rich tradition of graphics with amazing architectural drawings in Pre-Qin period, booming theories of graphics in Wei and Jin Dynasties, refined protracted drawings in Song and Yuan Dynasties, and graphics being regarded as important instruments in Ming and Qing Dynasties when thorough apprehension were pursued in order to seek the practice of administration. It not only forms the basis for modem and contemporary graphics in China, but also shapes the future development of graphics.展开更多
Rendering technology in computer graphics （CG） is now capable of producing highly photorealistic images, giving rise to the problem of how to identify CG images from natural images. Some methods were proposed to sol...Rendering technology in computer graphics （CG） is now capable of producing highly photorealistic images, giving rise to the problem of how to identify CG images from natural images. Some methods were proposed to solve this problem. In this paper, we give a novel method from a new point of view of image perception. Although the photorealistic CG images are very similar to natural images, they are surrealistic and smoother than natural images, thus leading to the difference in perception. A pert of features are derived from fractal dimension to capture the difference in color perception between CG images and natural images, and several generalized dimensions are used as the rest features to capture difference in coarseness. The effect of these features is verified by experiments. The average accuracy is over 91.2%.展开更多
This paper discuss the stereographic method of martensitic transformation (MT)in the view of computer graphics (CG) and programs are programmed to realize this method. Habit plane resulting from the programs agrees wi...This paper discuss the stereographic method of martensitic transformation (MT)in the view of computer graphics (CG) and programs are programmed to realize this method. Habit plane resulting from the programs agrees with that of numerical analysis in terms of the lattice parameters of austenite and martensite and shear mechanism supposed in Fe-22%Ni-0.8%C alloy, so does orientation relationships.展开更多
Locality preserving projection （LPP） is a typical and popular dimensionality reduction （DR） method,and it can potentially find discriminative projection directions by preserving the local geometric structure in da...Locality preserving projection （LPP） is a typical and popular dimensionality reduction （DR） method,and it can potentially find discriminative projection directions by preserving the local geometric structure in data. However,LPP is based on the neighborhood graph artificially constructed from the original data,and the performance of LPP relies on how well the nearest neighbor criterion work in the original space. To address this issue,a novel DR algorithm,called the self-dependent LPP （sdLPP） is proposed. And it is based on the fact that the nearest neighbor criterion usually achieves better performance in LPP transformed space than that in the original space. Firstly,LPP is performed based on the typical neighborhood graph; then,a new neighborhood graph is constructed in LPP transformed space and repeats LPP. Furthermore,a new criterion,called the improved Laplacian score,is developed as an empirical reference for the discriminative power and the iterative termination. Finally,the feasibility and the effectiveness of the method are verified by several publicly available UCI and face data sets with promising results.展开更多
This article proposes a new approach based on linear programming optimization to solve the problem of determining the color of a complex fractal carpet pattern.The principle is aimed at finding suitable dyes for mixin...This article proposes a new approach based on linear programming optimization to solve the problem of determining the color of a complex fractal carpet pattern.The principle is aimed at finding suitable dyes for mixing and their exact concentrations,which,when applied correctly,gives the desired color.The objective function and all constraints of the model are expressed linearly according to the solution variables.Carpet design has become an emerging technological field known for its creativity,science and technology.Many carpet design concepts have been analyzed in terms of color,contrast,brightness,as well as other mathematical concepts such as geometric changes and formulas.These concepts represent a common process in the carpet industry.This article discusses the use of complex fractal images in carpet design and simplex optimization in color selection.展开更多
By an improved projective equation approach and a linear variable separation approach, a new family of exact solutions of the （2＋1）-dimensional Broek-Kaup system is derived. Based on the derived solitary wave solut...By an improved projective equation approach and a linear variable separation approach, a new family of exact solutions of the （2＋1）-dimensional Broek-Kaup system is derived. Based on the derived solitary wave solution and by selecting appropriate functions, some novel localized excitations such as instantaneous solitons and fractal solitons are investigated.展开更多
Gravity and magnetic exploration areas are usually irregular,and there is some data defi ciency.Missing data must be interpolated before the vertical derivative conversion in the wavenumber domain.Meanwhile,for improv...Gravity and magnetic exploration areas are usually irregular,and there is some data defi ciency.Missing data must be interpolated before the vertical derivative conversion in the wavenumber domain.Meanwhile,for improved processing precision,the data need to be edge-padded to the length required by the fast Fourier transform algorithm.For conventional vertical derivative conversion of potential fi eld data(PFD),only vertical derivative conversion is considered,or interpolation,border padding,and vertical derivative conversion are executed independently.In this paper,these three steps are considered uniformly,and a vertical derivative conversion method for irregular-range PFD based on an improved projection onto convex sets method is proposed.The cutoff wavenumber of the filter used in the proposed method is determined by fractal model fi tting of the radial average power spectrum(RAPS)of the potential fi eld.Theoretical gravity models and real aeromagnetic data show the following:(1)The fitting of the RAPS with a fractal model can separate useful signals and noise reasonably.(2)The proposed iterative method has a clear physical sense,and its interpolation,border padding error,and running time are much smaller than those of the conventional kriging and minimum curvature methods.展开更多
The relationship between arts and mathematics is very close, computer graphic design is based on digital methodology. The paper reveals the mathematical backgrounds behind graphic design by the example of computer-aid...The relationship between arts and mathematics is very close, computer graphic design is based on digital methodology. The paper reveals the mathematical backgrounds behind graphic design by the example of computer-aided cubic modeling and mathematical exchange methodology. Furthermore, one can get incredible artistic effects if computer graphic designers pay more attention to the probability and use probable numbers and fractal operation in their design activities.Finally, the author also discusses the bidirections between arts and mathematics.展开更多
With a new projective equation, a series of solutions of the （2-J-1）-dimensional dispersive long-water wave system （LWW） is derived. Based on the derived solitary wave solution, we obtain some special fractal loca...With a new projective equation, a series of solutions of the （2-J-1）-dimensional dispersive long-water wave system （LWW） is derived. Based on the derived solitary wave solution, we obtain some special fractal localized structures and chaotic patterns.展开更多
文摘Maps, essential tools for portraying the Earth’s surface, inherently introduce distortions to geographical features. While various quantification methods exist for assessing these distortions, they often fall short when evaluating actual geographic features. In our study, we took a novel approach by analyzing map projection distortion from a geometric perspective. We computed the fractal dimensions of different stretches of coastline before and after projection using the divide-and-conquer algorithm and image processing. Our findings revealed that map projections, even when preserving basic shapes, inevitably stretch and compress coastlines in diverse directions. This analysis method provides a more realistic and practical way to measure map-induced distortions, with significant implications for cartography, geographic information systems (GIS), and geomorphology. By bridging the gap between theoretical analysis and real-world features, this method greatly enhances accuracy and practicality when evaluating map projections.
文摘Demonstrating the approach to protract the figure of three-dimensional graphs with geometrical forms in two-dimensional planes, graphics is a basic technical discipline of examining protracting engineering drawings using the method of projection and addressing issues on space geometry as well as its theory and approach. Graphics is also a kind of semiotic system of writing. China boasts of rich tradition of graphics with amazing architectural drawings in Pre-Qin period, booming theories of graphics in Wei and Jin Dynasties, refined protracted drawings in Song and Yuan Dynasties, and graphics being regarded as important instruments in Ming and Qing Dynasties when thorough apprehension were pursued in order to seek the practice of administration. It not only forms the basis for modem and contemporary graphics in China, but also shapes the future development of graphics.
基金Supported by the National Natural Science Foundation of China (Grant Nos.60633030 and 90604008)National Basic Rearch Program of China (Grant No.2006CB303104)
文摘Rendering technology in computer graphics （CG） is now capable of producing highly photorealistic images, giving rise to the problem of how to identify CG images from natural images. Some methods were proposed to solve this problem. In this paper, we give a novel method from a new point of view of image perception. Although the photorealistic CG images are very similar to natural images, they are surrealistic and smoother than natural images, thus leading to the difference in perception. A pert of features are derived from fractal dimension to capture the difference in color perception between CG images and natural images, and several generalized dimensions are used as the rest features to capture difference in coarseness. The effect of these features is verified by experiments. The average accuracy is over 91.2%.
文摘This paper discuss the stereographic method of martensitic transformation (MT)in the view of computer graphics (CG) and programs are programmed to realize this method. Habit plane resulting from the programs agrees with that of numerical analysis in terms of the lattice parameters of austenite and martensite and shear mechanism supposed in Fe-22%Ni-0.8%C alloy, so does orientation relationships.
基金Supported by the National Natural Science Foundation of China (60973097)the Scientific Research Foundation of Liaocheng University(X0810029)~~
文摘Locality preserving projection （LPP） is a typical and popular dimensionality reduction （DR） method,and it can potentially find discriminative projection directions by preserving the local geometric structure in data. However,LPP is based on the neighborhood graph artificially constructed from the original data,and the performance of LPP relies on how well the nearest neighbor criterion work in the original space. To address this issue,a novel DR algorithm,called the self-dependent LPP （sdLPP） is proposed. And it is based on the fact that the nearest neighbor criterion usually achieves better performance in LPP transformed space than that in the original space. Firstly,LPP is performed based on the typical neighborhood graph; then,a new neighborhood graph is constructed in LPP transformed space and repeats LPP. Furthermore,a new criterion,called the improved Laplacian score,is developed as an empirical reference for the discriminative power and the iterative termination. Finally,the feasibility and the effectiveness of the method are verified by several publicly available UCI and face data sets with promising results.
文摘This article proposes a new approach based on linear programming optimization to solve the problem of determining the color of a complex fractal carpet pattern.The principle is aimed at finding suitable dyes for mixing and their exact concentrations,which,when applied correctly,gives the desired color.The objective function and all constraints of the model are expressed linearly according to the solution variables.Carpet design has become an emerging technological field known for its creativity,science and technology.Many carpet design concepts have been analyzed in terms of color,contrast,brightness,as well as other mathematical concepts such as geometric changes and formulas.These concepts represent a common process in the carpet industry.This article discusses the use of complex fractal images in carpet design and simplex optimization in color selection.
基金Project supported by the Natural Science Foundation of Zhejiang Province of China (Grant Nos. Y606252 and Y604106)the Scientific Research Fund of the Education Department of Zhejiang Province of China (Grant No. 200805981)the Natural Science Foundation of Zhejiang Lishui University (Grant No. KZ09005)
文摘By an improved projective equation approach and a linear variable separation approach, a new family of exact solutions of the （2＋1）-dimensional Broek-Kaup system is derived. Based on the derived solitary wave solution and by selecting appropriate functions, some novel localized excitations such as instantaneous solitons and fractal solitons are investigated.
基金supported by the National Natural Science Foundation of China (Grant Nos. 41804136, 41774156, 61773389)the Young Talent Fund of University Association for Science and Technology in Shaanxi,China (Grant No.20180702)
文摘Gravity and magnetic exploration areas are usually irregular,and there is some data defi ciency.Missing data must be interpolated before the vertical derivative conversion in the wavenumber domain.Meanwhile,for improved processing precision,the data need to be edge-padded to the length required by the fast Fourier transform algorithm.For conventional vertical derivative conversion of potential fi eld data(PFD),only vertical derivative conversion is considered,or interpolation,border padding,and vertical derivative conversion are executed independently.In this paper,these three steps are considered uniformly,and a vertical derivative conversion method for irregular-range PFD based on an improved projection onto convex sets method is proposed.The cutoff wavenumber of the filter used in the proposed method is determined by fractal model fi tting of the radial average power spectrum(RAPS)of the potential fi eld.Theoretical gravity models and real aeromagnetic data show the following:(1)The fitting of the RAPS with a fractal model can separate useful signals and noise reasonably.(2)The proposed iterative method has a clear physical sense,and its interpolation,border padding error,and running time are much smaller than those of the conventional kriging and minimum curvature methods.
文摘The relationship between arts and mathematics is very close, computer graphic design is based on digital methodology. The paper reveals the mathematical backgrounds behind graphic design by the example of computer-aided cubic modeling and mathematical exchange methodology. Furthermore, one can get incredible artistic effects if computer graphic designers pay more attention to the probability and use probable numbers and fractal operation in their design activities.Finally, the author also discusses the bidirections between arts and mathematics.
基金Supported by the Natural Science Foundation of Zhejiang Province under Grant Nos.Y604106, Y606128the Scientific Research Fund of Zhejiang Provincial Education Department of China under Grant No.20070568the Natural Science Foundation of Zhejiang Lishui University under Grant No.KY08003
文摘With a new projective equation, a series of solutions of the （2-J-1）-dimensional dispersive long-water wave system （LWW） is derived. Based on the derived solitary wave solution, we obtain some special fractal localized structures and chaotic patterns.
