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带法向约束的圆平均非线性细分曲线设计
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作者 刘艳 寿华好 季康松 《中国图象图形学报》 CSCD 北大核心 2023年第2期556-569,共14页
目的对采样设备获取的测量数据进行拟合,可实现原模型的重建及功能恢复。但有些情况下,获取的数据点不仅包含位置信息,还包含法向量信息。针对这一问题,本文提出了基于圆平均的双参数4点binary非线性细分法与单参数3点ternary插值非线... 目的对采样设备获取的测量数据进行拟合,可实现原模型的重建及功能恢复。但有些情况下,获取的数据点不仅包含位置信息,还包含法向量信息。针对这一问题,本文提出了基于圆平均的双参数4点binary非线性细分法与单参数3点ternary插值非线性细分法。方法首先将线性细分法改写为点的重复binary线性平均,然后用圆平均代替相应的线性平均,最后用加权测地线平均计算的法向量作为新插入顶点的法向量。基于圆平均的双参数4点binary细分法的每一次细分过程可分为偏移步与张力步。基于圆平均的单参数3点ternary细分法的每一次细分过程可分为左插步、插值步与右插步。结果对于本文方法的收敛性与C1连续性条件给出了理论证明;数值实验表明,与相应的线性细分相比,本文方法生成的曲线更光滑且具有圆的再生力,可以较好地实现3个封闭曲线重建。结论本文方法可以在带法向量的初始控制顶点较少的情况下,较好地实现带法向约束的离散点集的曲线重建问题。 展开更多
关键词 非线性细分 圆平均 加权测地线平均 点—法向量对 法向约束
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基于法向量的非线性逼近型细分格式
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作者 赵欢喜 陈紫薇 许玲玲 《计算机工程》 CAS CSCD 北大核心 2011年第1期215-217,共3页
提出一种二进制的几何非线性逼近型细分格式。在该格式中,新点不全是旧点的线性组合,其中一个新点是通过在法向量方向偏移所产生,且法向量在每次细分中能自适应计算。引入一些参数来控制细分过程,且参数对曲线形状的影响是局部的。实例... 提出一种二进制的几何非线性逼近型细分格式。在该格式中,新点不全是旧点的线性组合,其中一个新点是通过在法向量方向偏移所产生,且法向量在每次细分中能自适应计算。引入一些参数来控制细分过程,且参数对曲线形状的影响是局部的。实例证明,通过选择适当的参数值,产生的细分曲线具有保凸性和G1连续性。 展开更多
关键词 非线性细分 逼近型 法向量 保凸
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一种基于切向量的非线性ternary插值细分法
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作者 宋倩 《纺织高校基础科学学报》 CAS 2014年第1期125-129,共5页
针对光滑曲线的构造,提出了一种基于切向量的非线性ternary插值细分方法.该细分法通过沿相邻两点的切向量方向产生偏移量来计算新点,其中偏移量可由参数进行控制.文中对该细分格式的性质进行了分析.结果表明该细分格式生成的极限曲线具... 针对光滑曲线的构造,提出了一种基于切向量的非线性ternary插值细分方法.该细分法通过沿相邻两点的切向量方向产生偏移量来计算新点,其中偏移量可由参数进行控制.文中对该细分格式的性质进行了分析.结果表明该细分格式生成的极限曲线具有G1连续性和保凸性,且在参数合适的取值范围内,极限曲线可以避免自交. 展开更多
关键词 非线性细分 切向量 保凸性
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内心细分法的一个变式 被引量:2
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作者 李亚娟 邓重阳 《计算机辅助设计与图形学学报》 EI CSCD 北大核心 2012年第12期1542-1548,共7页
内心细分法中,临时切向调整的方法比较复杂,且几何意义不明显,为此给出了内心细分法的一个变式.给定初始点列及其切向,内心细分法的每一个细分步骤分为2个阶段:首先根据老点和切向确定新点及其临时切向,然后调整临时切向用于下一步细分... 内心细分法中,临时切向调整的方法比较复杂,且几何意义不明显,为此给出了内心细分法的一个变式.给定初始点列及其切向,内心细分法的每一个细分步骤分为2个阶段:首先根据老点和切向确定新点及其临时切向,然后调整临时切向用于下一步细分.文中给出了调整切向的新方法,使切向计算更简单、几何意义更明显.最后通过大量的数值实例验证了极限曲线的G2连续性及光顺性与细分参数选择之间的关系. 展开更多
关键词 非线性细分方法 曲线插值 保形 保圆
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Kernelized fourth quantification theory for mineral target prediction
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作者 CHEN Yongliang LI Xuebin LIN Nan 《Global Geology》 2011年第4期265-278,共14页
This paper presents a nonlinear multidimensional scaling model, called kernelized fourth quantifica- tion theory, which is an integration of kernel techniques and the fourth quantification theory. The model can deal w... This paper presents a nonlinear multidimensional scaling model, called kernelized fourth quantifica- tion theory, which is an integration of kernel techniques and the fourth quantification theory. The model can deal with the problem of mineral prediction without defining a training area. In mineral target prediction, the pre-defined statistical cells, such as grid cells, can be implicitly transformed using kernel techniques from input space to a high-dimensional feature space, where the nonlinearly separable clusters in the input space are ex- pected to be linearly separable. Then, the transformed cells in the feature space are mapped by the fourth quan- tifieation theory onto a low-dimensional scaling space, where the sealed cells can be visually clustered according to their spatial locations. At the same time, those cells, which are far away from the cluster center of the majority of the sealed cells, are recognized as anomaly cells. Finally, whether the anomaly cells can serve as mineral potential target cells can be tested by spatially superimposing the known mineral occurrences onto the anomaly ceils. A case study shows that nearly all the known mineral occurrences spatially coincide with the anomaly cells with nearly the smallest scaled coordinates in one-dimensional sealing space. In the case study, the mineral target cells delineated by the new model are similar to those predicted by the well-known WofE model. 展开更多
关键词 kernel function feature space fourth quantification theory nonlinear transformation mineral target prediction
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A reliable analysis of oxygen diffusion in a spherical cell with nonlinear oxygen uptake kinetics 被引量:2
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作者 Randolph Rach Abdul-Majid Wazwaz Jun-Sheng Duan 《International Journal of Biomathematics》 2014年第2期165-176,共12页
In this paper, we investigate the diffusion of oxygen in a spherical cell including nonlin- ear uptake kinetics. The Lane-Emden boundary value problem with Michaelis-Menten kinetics is used to model the dimensionless ... In this paper, we investigate the diffusion of oxygen in a spherical cell including nonlin- ear uptake kinetics. The Lane-Emden boundary value problem with Michaelis-Menten kinetics is used to model the dimensionless oxygen concentration in our analysis. We first convert the Lane-Emden equation to the equivalent Volterra integral form that incorporates the boundary condition at the cell's center, but which still leaves one unknown constant of integration, as an intermediate step. Next we evaluate the Volterra integral form of the concentration and its flux at the cell membrane and substitute them into the remaining boundary condition to determine the unknown constant of integration by appropriate algebraic manipulations. Upon substitution we have converted the equivalent Volterra integral form to the equivalent Fredholm Volterra integral form, and use the Duan Rach modified recursion scheme to effectively decompose the unknown constant of integration by formula. The Adomian decomposition method is then applied to solve the equivalent nonlinear Fredholm-Volterra integral representation of the LaneEmden model for the concentration of oxygen within the spherical cell. Our approach shows enhancements over existing techniques. 展开更多
关键词 Oxygen diffusion Volterra integral form Michaelis-Menten kinetics Adomian decomposition method Adomian polynomials.
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Oscillatory blood flow through a capillary in presence of thermal radiation 被引量:1
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作者 A. Sinha G. C. Shit 《International Journal of Biomathematics》 2015年第1期181-199,共19页
This paper deals with the theoretical investigation of a fundamental problem of magne- tohydrodynamic (MHD) flow of blood in a capillary in the presence of thermal radiation and chemical reaction. The unsteadiness i... This paper deals with the theoretical investigation of a fundamental problem of magne- tohydrodynamic (MHD) flow of blood in a capillary in the presence of thermal radiation and chemical reaction. The unsteadiness in the flow and temperature fields is caused by the time-dependence of the stretching velocity and the surface temperature. The fluid is considered to be non-Newtonian, whose flow is governed by the equation of a third-order fluid. The problem is first reduced to solving a system of coupled nonlinear differential equations involving several parameters. Considering blood as an electrically conducting fluid and using the present analysis, an attempt is made to compute some parameters of the blood flow by developing a suitable numerical method and by devising an appropri- ate finite difference scheme. The computational results are presented in graphical form, and thereby some theoretical predictions are made with respect to the hemodynamical flow of the blood in a hyperthermal state under the action of a magnetic field. Com- putational results for the variation in velocity, temperature, concentration, skin-friction coefi^icient, Nusselt number and Sherwood number are presented in graphical/tabular form. Since the study takes care of thermal radiation in blood flow, the results reported here are likely to have an important bearing on the therapeutic procedure of hyperthermia, particularly in understanding blood flow and heat transfer in capillaries. 展开更多
关键词 Third-order fluid stretching wall thermal radiation oscillatory motion
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On a non-autonomous reaction-convection diffusion model to study the bacteria distribution in a river 被引量:1
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作者 Imene Meriem Mostefaoui Ali Moussaoui 《International Journal of Biomathematics》 2017年第6期25-49,共25页
In this paper, we propose a non-autonomous convection-reaction diffusion system (CDI) with a nonlinear reaction source function. This model refers to the quantification and the distribution of antibiotic resistant b... In this paper, we propose a non-autonomous convection-reaction diffusion system (CDI) with a nonlinear reaction source function. This model refers to the quantification and the distribution of antibiotic resistant bacteria (ARB) in a river. The main contributions of this paper are: (i) the determination of the limit set of the system by applying the semigroups theory, it is shown that it is reduced to the solutions of the associated elliptic system (CDI)e, (ii) sufficient conditions for the existence of a positive solution of (CDI)e based on the Leray-Schauder's degree theory. Numerical simulations which support our theoretical analysis are also given. 展开更多
关键词 Reaction-diffusion systems steady states problems degree theory semi-groups.
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STABILITY ANALYSIS OF A DISCRETE NONLINEAR DELAY SURVIVAL RED BLOOD CELLS MODEL
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作者 SHUFANG MA YUANGANG ZU 《International Journal of Biomathematics》 2012年第4期147-155,共9页
In this article we consider the kth-order discrete delay survival red blood cells model. The general form of the discrete dynamical system is rewritten as Xn+l = f(Pn,δn,xn,... ,xn+1) where Pn,δn converge to the... In this article we consider the kth-order discrete delay survival red blood cells model. The general form of the discrete dynamical system is rewritten as Xn+l = f(Pn,δn,xn,... ,xn+1) where Pn,δn converge to the parametric values P and 6. We show that when the parameters are replaced by sequences, the stability results of the original system still hold. 展开更多
关键词 Discrete delay survival red blood cells model stability.
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