Modern computer graphics applications usually require high resolution object models for realistic rendering. However, it is expensive and difficult to deform such models in real time. In order to reduce the computatio...Modern computer graphics applications usually require high resolution object models for realistic rendering. However, it is expensive and difficult to deform such models in real time. In order to reduce the computational cost during deformations, a dense model is often manipulated through a simplified structure, called cage, which envelops the model. However, cages are usually built interactively by users, which is tedious and time-consuming. In this paper, we introduce a novel method that can build cages automatically for both 2D polygons and 3D triangular meshes. The method consists of two steps： 1） simplifying the input model with quadric error metrics and quadratic programming to build a coarse cage; 2） removing the self-intersections of the coarse cage with Delaunay partitions. With this new method, a user can build a cage to envelop an input model either entirely or partially with the approximate vertex number the user specifies. Experimental results show that, compared to other cage building methods with the same number of vertex, cages built by our method are more similar to the input models. Thus, the dense models can be manipulated with higher accuracy through our cages.展开更多
Motivated by the effort to understand the mathematical structure underlying the Teukolsky equations in a Kerr metric background, a homogeneous integral equation related to the prolate spheroidal function is studied. F...Motivated by the effort to understand the mathematical structure underlying the Teukolsky equations in a Kerr metric background, a homogeneous integral equation related to the prolate spheroidal function is studied. From the consideration of the Fredholm determinant of the integral equation, a family of generalized error function is defined, with which the Fredholm determinant of the sinc kernel is also evaluated. An analytic solution of a special ease of the fifth Painlev~ transcendent is then worked out explicitly.展开更多
Throughout this paper,let(Ω,ι,μ)be a probability space,D the collection of allleft-continuous distribution functions,and D^+={F(0)=0|F∈D},and L(Ω)the collec-tion of all random variables which is a.s.finite on Ω,...Throughout this paper,let(Ω,ι,μ)be a probability space,D the collection of allleft-continuous distribution functions,and D^+={F(0)=0|F∈D},and L(Ω)the collec-tion of all random variables which is a.s.finite on Ω,and L^+={ξ≥0 a.s.|ξ∈L(Ω)}.For random metric (normed) spaces,see [1]or[2].Theorem 1 Let(M,d)be a complete metric space f:M→M,a contract mappingwith contract coefficient α∈[0,1),L(Ω,m)the collection of all M-valued random vari-展开更多
Profile monitoring is used to check the stability of the quality of a product over time when the product quality is best represented by a function at each time point.However,most previous monitoring approaches have no...Profile monitoring is used to check the stability of the quality of a product over time when the product quality is best represented by a function at each time point.However,most previous monitoring approaches have not considered that the argument values may vary from profile to profile,which is common in practice.A novel nonparametric control scheme based on profile error is proposed for monitoring nonlinear profiles with varied argument values.The proposed scheme uses the metrics of profile error as the statistics to construct the control charts.More details about the design of this nonparametric scheme are also discussed.The monitoring performance of the combined control scheme is compared with that of alternative nonparametric methods via simulation.Simulation studies show that the combined scheme is effective in detecting parameter error and is sensitive to small shifts in the process.In addition,due to the properties of the charting statistics,the out-of-control signal can provide diagnostic information for the users.Finally,the implementation steps of the proposed monitoring scheme are given and applied for monitoring the blade manufacturing process.With the application in blade manufacturing of aircraft engines,the proposed nonparametric control scheme is effective,interpretable,and easy to apply.展开更多
The possibility that quantum mechanics is founded on non-metric space has been previously introduced as an alternative consequence of Bell inequalities violation. This work develops the concept further by an analysis ...The possibility that quantum mechanics is founded on non-metric space has been previously introduced as an alternative consequence of Bell inequalities violation. This work develops the concept further by an analysis of the iconic Heisenberg gedanken experiment. No lower bound is found in the gedanken uncertainly relation for a non-metric spatial background. This result has the fundamental consequence that the quantum particle trajectory is retained in non-metric space and time. Assignment of measurement number-values to unmeasured incompatible variables is found to be mathematically incorrect. The current disagreement between different formulations of the empirically verified error-disturbance relations can be explained as a consequence of the structure of space. Quantum contextuality can likewise be explained geometrically. An alternative analysis of the extendedEPRperfect anti-correlation configuration is given. The consensus that local causality is the sole assumption is found to be incorrect. There is also the additional assumption of orientation independence. Inequalities violation does not therefore mandate rejection of local causality. Violation of the assumption of orientation independence implies rejection of metric, non-contextual variables algebraically representing physical quantities.展开更多
A new conception of generalized set-valued Ф-hemi-contractive mapping in Banach spaces is presented. Some strong convergence theorems of Ishikawa and Mann iterative approximation with errors is proved. The results in...A new conception of generalized set-valued Ф-hemi-contractive mapping in Banach spaces is presented. Some strong convergence theorems of Ishikawa and Mann iterative approximation with errors is proved. The results in this paper improve and extend the earlier results.展开更多
The algorithm of fingerprint constructing for still images based on weighted image structure model is proposed. The error correcting codes that are perfect in weighted Hamming metric are used as a base for fingerprint...The algorithm of fingerprint constructing for still images based on weighted image structure model is proposed. The error correcting codes that are perfect in weighted Hamming metric are used as a base for fingerprint constructing.展开更多
在布料仿真过程中,基于位置的动力学方法(Position Based Dynamics, PBD)在布料模拟的效果及实时性方面展现了其优越的性能,但在布料网格精度提升时,为了加快其收敛速度而增加迭代计算次数,会导致模拟效率大幅降低及约束震荡现象的出现...在布料仿真过程中,基于位置的动力学方法(Position Based Dynamics, PBD)在布料模拟的效果及实时性方面展现了其优越的性能,但在布料网格精度提升时,为了加快其收敛速度而增加迭代计算次数,会导致模拟效率大幅降低及约束震荡现象的出现。为了解决以上问题,文章结合对位置动力学方法的研究,提出一种以多重网格思想为核心的布料模拟方法,采用基于二次误差度量(Quadric Error Metrics, QEM)的网格简化法对布料多重网格进行构建,同时结合空间插值算法进行层与层之间的数据传递及位置矫正,可以构建出质量良好的三角网格结构,避免不规则多边形的出现;在布料层次化模拟的基础上,提出结合逐次超松弛迭代法(Successive Over Relaxation, SOR)与Gauss-Seidel方法(GS)的混合平滑方案并验证了其有效性。经实验分析,布料层次化模拟方法提高了质点数目增加后的收敛速度,具有一定的稳定性。展开更多
基金Supported by the NSFC-Guangdong Joint Fund under Grant Nos. U0735001,U0835004,U0935004the National Basic Research 973 Program of China under Grant No. 2011CB302204
文摘Modern computer graphics applications usually require high resolution object models for realistic rendering. However, it is expensive and difficult to deform such models in real time. In order to reduce the computational cost during deformations, a dense model is often manipulated through a simplified structure, called cage, which envelops the model. However, cages are usually built interactively by users, which is tedious and time-consuming. In this paper, we introduce a novel method that can build cages automatically for both 2D polygons and 3D triangular meshes. The method consists of two steps： 1） simplifying the input model with quadric error metrics and quadratic programming to build a coarse cage; 2） removing the self-intersections of the coarse cage with Delaunay partitions. With this new method, a user can build a cage to envelop an input model either entirely or partially with the approximate vertex number the user specifies. Experimental results show that, compared to other cage building methods with the same number of vertex, cages built by our method are more similar to the input models. Thus, the dense models can be manipulated with higher accuracy through our cages.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11171329,11203003 and 11373013
文摘Motivated by the effort to understand the mathematical structure underlying the Teukolsky equations in a Kerr metric background, a homogeneous integral equation related to the prolate spheroidal function is studied. From the consideration of the Fredholm determinant of the integral equation, a family of generalized error function is defined, with which the Fredholm determinant of the sinc kernel is also evaluated. An analytic solution of a special ease of the fifth Painlev~ transcendent is then worked out explicitly.
文摘Throughout this paper,let(Ω,ι,μ)be a probability space,D the collection of allleft-continuous distribution functions,and D^+={F(0)=0|F∈D},and L(Ω)the collec-tion of all random variables which is a.s.finite on Ω,and L^+={ξ≥0 a.s.|ξ∈L(Ω)}.For random metric (normed) spaces,see [1]or[2].Theorem 1 Let(M,d)be a complete metric space f:M→M,a contract mappingwith contract coefficient α∈[0,1),L(Ω,m)the collection of all M-valued random vari-
基金supported by National Natural Science Foundation of China (Grant No. 70931004,Grant No. 70802043)
文摘Profile monitoring is used to check the stability of the quality of a product over time when the product quality is best represented by a function at each time point.However,most previous monitoring approaches have not considered that the argument values may vary from profile to profile,which is common in practice.A novel nonparametric control scheme based on profile error is proposed for monitoring nonlinear profiles with varied argument values.The proposed scheme uses the metrics of profile error as the statistics to construct the control charts.More details about the design of this nonparametric scheme are also discussed.The monitoring performance of the combined control scheme is compared with that of alternative nonparametric methods via simulation.Simulation studies show that the combined scheme is effective in detecting parameter error and is sensitive to small shifts in the process.In addition,due to the properties of the charting statistics,the out-of-control signal can provide diagnostic information for the users.Finally,the implementation steps of the proposed monitoring scheme are given and applied for monitoring the blade manufacturing process.With the application in blade manufacturing of aircraft engines,the proposed nonparametric control scheme is effective,interpretable,and easy to apply.
文摘The possibility that quantum mechanics is founded on non-metric space has been previously introduced as an alternative consequence of Bell inequalities violation. This work develops the concept further by an analysis of the iconic Heisenberg gedanken experiment. No lower bound is found in the gedanken uncertainly relation for a non-metric spatial background. This result has the fundamental consequence that the quantum particle trajectory is retained in non-metric space and time. Assignment of measurement number-values to unmeasured incompatible variables is found to be mathematically incorrect. The current disagreement between different formulations of the empirically verified error-disturbance relations can be explained as a consequence of the structure of space. Quantum contextuality can likewise be explained geometrically. An alternative analysis of the extendedEPRperfect anti-correlation configuration is given. The consensus that local causality is the sole assumption is found to be incorrect. There is also the additional assumption of orientation independence. Inequalities violation does not therefore mandate rejection of local causality. Violation of the assumption of orientation independence implies rejection of metric, non-contextual variables algebraically representing physical quantities.
文摘A new conception of generalized set-valued Ф-hemi-contractive mapping in Banach spaces is presented. Some strong convergence theorems of Ishikawa and Mann iterative approximation with errors is proved. The results in this paper improve and extend the earlier results.
文摘The algorithm of fingerprint constructing for still images based on weighted image structure model is proposed. The error correcting codes that are perfect in weighted Hamming metric are used as a base for fingerprint constructing.
文摘在布料仿真过程中,基于位置的动力学方法(Position Based Dynamics, PBD)在布料模拟的效果及实时性方面展现了其优越的性能,但在布料网格精度提升时,为了加快其收敛速度而增加迭代计算次数,会导致模拟效率大幅降低及约束震荡现象的出现。为了解决以上问题,文章结合对位置动力学方法的研究,提出一种以多重网格思想为核心的布料模拟方法,采用基于二次误差度量(Quadric Error Metrics, QEM)的网格简化法对布料多重网格进行构建,同时结合空间插值算法进行层与层之间的数据传递及位置矫正,可以构建出质量良好的三角网格结构,避免不规则多边形的出现;在布料层次化模拟的基础上,提出结合逐次超松弛迭代法(Successive Over Relaxation, SOR)与Gauss-Seidel方法(GS)的混合平滑方案并验证了其有效性。经实验分析,布料层次化模拟方法提高了质点数目增加后的收敛速度,具有一定的稳定性。
