Surface-based geometric modeling has many advantages in terms of visualization and traditional subtractive manufacturing using computer-numerical-control cutting-machine tools.However,it is not an ideal solution for a...Surface-based geometric modeling has many advantages in terms of visualization and traditional subtractive manufacturing using computer-numerical-control cutting-machine tools.However,it is not an ideal solution for additive manufacturing because to digitally print a surface-represented geometric object using a certain additive manufacturing technology,the object has to be converted into a solid representation.However,converting a known surface-based geometric representation into a printable representation is essentially a redesign process,and this is especially the case,when its interior material structure needs to be considered.To specify a 3D geometric object that is ready to be digitally manufactured,its representation has to be in a certain volumetric form.In this research,we show how some of the difficulties experienced in additive manufacturing can be easily solved by using implicitly represented geometric objects.Like surface-based geometric representation is subtractive manufacturing-friendly,implicitly described geometric objects are additive manufacturing-friendly:implicit shapes are 3D printing ready.The implicit geometric representation allows to combine a geometric shape,material colors,an interior material structure,and other required attributes in one single description as a set of implicit functions,and no conversion is needed.In addition,as implicit objects are typically specified procedurally,very little data is used in their specifications,which makes them particularly useful for design and visualization with modern cloud-based mobile devices,which usually do not have very big storage spaces.Finally,implicit modeling is a design procedure that is parallel computing-friendly,as the design of a complex geometric object can be divided into a set of simple shape-designing tasks,owing to the availability of shape-preserving implicit blending operations.展开更多
In this paper, the well known implicit function theorem was applied to study existence and uniqueness of periodic solution of Duffing-type equation. Un-der appropriate conditions around the origin, a unique periodic s...In this paper, the well known implicit function theorem was applied to study existence and uniqueness of periodic solution of Duffing-type equation. Un-der appropriate conditions around the origin, a unique periodic solution was obtained.展开更多
We prove a global version of the implicit function theorem under a special condition and apply this result to the proof of a modified Hyers-Ulam-Rassias stability of exact differential equations of the form, g（x, y）...We prove a global version of the implicit function theorem under a special condition and apply this result to the proof of a modified Hyers-Ulam-Rassias stability of exact differential equations of the form, g（x, y） ＋ h（x, y）y＇ =0.展开更多
In this paper,we present an approach for smooth surface reconstructions interpolating triangular meshes with ar- bitrary topology and geometry.The approach is based on the well-known radial basis functions (RBFs) and ...In this paper,we present an approach for smooth surface reconstructions interpolating triangular meshes with ar- bitrary topology and geometry.The approach is based on the well-known radial basis functions (RBFs) and the constructed surfaces are generalized thin-plate spline surfaces.Our algorithm first defines a pair of offset points for each vertex of a given mesh to en- hance the controUability of local geometry and to assure stability of the construction.A linear system is then solved by LU decomposi- tion and the implicit governing equation of interpolating surface is obtained.The constructed surfaces finally are visualized by a Marching Cubes based polygonizer.The approach provides a robust and efficient solution for smooth surface reconstruction from various 3 D meshes.展开更多
In this article, we study the impacts of nonlinearity and dispersion on signals likely to propagate in the context of the dynamics of four-wave mixing. Thus, we use an indirect resolution technique based on the use of...In this article, we study the impacts of nonlinearity and dispersion on signals likely to propagate in the context of the dynamics of four-wave mixing. Thus, we use an indirect resolution technique based on the use of the iB-function to first decouple the nonlinear partial differential equations that govern the propagation dynamics in this case, and subsequently solve them to propose some prototype solutions. These analytical solutions have been obtained;we check the impact of nonlinearity and dispersion. The interest of this work lies not only in the resolution of the partial differential equations that govern the dynamics of wave propagation in this case since these equations not at all easy to integrate analytically and their analytical solutions are very rare, in other words, we propose analytically the solutions of the nonlinear coupled partial differential equations which govern the dynamics of four-wave mixing in optical fibers. Beyond the physical interest of this work, there is also an appreciable mathematical interest.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.61502402 and 61379080)the Natural Science Foundation of Fujian Province of China(Grant No.2015J05129).
文摘Surface-based geometric modeling has many advantages in terms of visualization and traditional subtractive manufacturing using computer-numerical-control cutting-machine tools.However,it is not an ideal solution for additive manufacturing because to digitally print a surface-represented geometric object using a certain additive manufacturing technology,the object has to be converted into a solid representation.However,converting a known surface-based geometric representation into a printable representation is essentially a redesign process,and this is especially the case,when its interior material structure needs to be considered.To specify a 3D geometric object that is ready to be digitally manufactured,its representation has to be in a certain volumetric form.In this research,we show how some of the difficulties experienced in additive manufacturing can be easily solved by using implicitly represented geometric objects.Like surface-based geometric representation is subtractive manufacturing-friendly,implicitly described geometric objects are additive manufacturing-friendly:implicit shapes are 3D printing ready.The implicit geometric representation allows to combine a geometric shape,material colors,an interior material structure,and other required attributes in one single description as a set of implicit functions,and no conversion is needed.In addition,as implicit objects are typically specified procedurally,very little data is used in their specifications,which makes them particularly useful for design and visualization with modern cloud-based mobile devices,which usually do not have very big storage spaces.Finally,implicit modeling is a design procedure that is parallel computing-friendly,as the design of a complex geometric object can be divided into a set of simple shape-designing tasks,owing to the availability of shape-preserving implicit blending operations.
文摘In this paper, the well known implicit function theorem was applied to study existence and uniqueness of periodic solution of Duffing-type equation. Un-der appropriate conditions around the origin, a unique periodic solution was obtained.
文摘We prove a global version of the implicit function theorem under a special condition and apply this result to the proof of a modified Hyers-Ulam-Rassias stability of exact differential equations of the form, g（x, y） ＋ h（x, y）y＇ =0.
文摘In this paper,we present an approach for smooth surface reconstructions interpolating triangular meshes with ar- bitrary topology and geometry.The approach is based on the well-known radial basis functions (RBFs) and the constructed surfaces are generalized thin-plate spline surfaces.Our algorithm first defines a pair of offset points for each vertex of a given mesh to en- hance the controUability of local geometry and to assure stability of the construction.A linear system is then solved by LU decomposi- tion and the implicit governing equation of interpolating surface is obtained.The constructed surfaces finally are visualized by a Marching Cubes based polygonizer.The approach provides a robust and efficient solution for smooth surface reconstruction from various 3 D meshes.
文摘In this article, we study the impacts of nonlinearity and dispersion on signals likely to propagate in the context of the dynamics of four-wave mixing. Thus, we use an indirect resolution technique based on the use of the iB-function to first decouple the nonlinear partial differential equations that govern the propagation dynamics in this case, and subsequently solve them to propose some prototype solutions. These analytical solutions have been obtained;we check the impact of nonlinearity and dispersion. The interest of this work lies not only in the resolution of the partial differential equations that govern the dynamics of wave propagation in this case since these equations not at all easy to integrate analytically and their analytical solutions are very rare, in other words, we propose analytically the solutions of the nonlinear coupled partial differential equations which govern the dynamics of four-wave mixing in optical fibers. Beyond the physical interest of this work, there is also an appreciable mathematical interest.
