Multi-Quadric函数与Gauss函数的插值比较

径向基函数在散乱数据插值中有着广泛应用.本文对Multi-Quadric函数与常用的Gauss函数列举多个实例,使用Mathematica编程计算,对其参数进行分析与比较,获得效果较好的误差图.

求解频率指派问题的Multi-Quadric算法

为有效解决频率指派问题,提出了一种解决该问题的曲面拟合Multi-Quadric算法,算法将随机指派方案及其对应的干扰值作为多元散乱数据采样点,以此为基础进行多元散乱数据拟合,通过对拟合曲面极小值的寻找从而完成对频率指派问题的优化。优化结果可直接应用于实际工程,也可作为其它优化算法的初始解。算法在电台数量规模较大的应用中体现出良好的性能,算法结果作为蚁群、遗传算法的初始解,后继算法收敛速度明显提高。

SKEWED SYMMETRY DETECTION OF QUADRIC SURFACE SOLIDS UNDER ORTHOGRAPHIC PROJECTION

The skewed symmetry detection plays an improtant role in three-dimensional（3-D） reconstruction. The skewed symmetry depicts a real symmetry viewed from some unknown viewing directions. And the skewed symmetry detection can decrease the geometric constrains and the complexity of 3-D reconstruction. The detection technique for the quadric curve ellipse proposed by Sugimoto is improved to further cover quadric curves including hyperbola and parabola. With the parametric detection, the 3-D quadric curve projection matching is automatical- ly accomplished. Finally, the skewed symmetry surface of the quadric surface solid is obtained. Several examples are used to verify the feasibility of the algorithm and satisfying results can be obtained.

1-quasiconformal mappings on a (2,2)-type quadric

This paper gets the Beltrami equations satisfied by a 1-quasiconformal mapping, which are exactly CR or anti-CR equations on （2,2）-type quadric Q0. This means a 1-quasiconformal mapping on Q0 is CR or anti-CR. This reduces the determination of 1- quasiconformal mappings to a problem on the theory of several complex analysis. The result about the group of CR automorphisms is used to determine the unit component of group of 1-quasiconformal mappings.

GEOMETRIC CONSTRUCTION OF ASSOCIATION SCHEMES FROM DEGENERATE QUADRICS INPROJECTIVE SPACES PG(2ν+δ+ι-1, Fq) FOR q ODD

Let Fq be a finite field with q elements, where q is a power of an odd prime,In this paperl the authors consider a projective space PG(2v + δ + l, Fq) with dimension 2v + δ + l, partitioned into an affine space AG(2v + δ + l, Fq) of dimension 2v + δ + l and a hyperplane H = PG(2v + δ + l - 1, Fq) of dimension 2v + δ + l - 1 at infinity, where l ≠0.The points of the hyperplane H are next partitioned into four subsets. A pair of points a and b of the affine space is defined to belong to class i if the line ab meets the subsct i of H. Finally, a family of four-class association schemes are constructed, and parameters are also computed.

Improved quadric surfaces recognition from scanned mechanical models

This paper presents a novel algorithm for identifying quadric surfaces from scanned mechanical models. We make several important improvements over the existing variational 3D shape segmentation framework, which utilizes Lloyd＇s iteration. First, instead of using randomized initialization （which likely falls into non-optimal minimum）, the RANSAC-based initialization approach is adopted. Given a good initialization, our method converges quickly than previous approaches. Second, in order to enhance the stability and the robustness, we carefully modify the distortion-minimizing flooding algorithm by using seed regions instead of seed triangles. Third, the geometric constraints are introduced into the optimization framework. The segmentation quality is further improved. We validate the efficiency and the robustness of our proposed method on various datasets, and demonstrate that our method outperforms state-of-art approaches.

Subdivision for Generating Quadrics

Quadrics are of basic importance in Computer Graphics and Computer Aided Design. In this paper,we design a subdivision scheme based on the method suggested by G. Morin and J. Warren to generate conics and quadrics conveniently. Given the control polygon(poly-hedron),the corresponding ellipse (ellipsoid)can be generated. The hyperbolas and hyperboloids are generated based on the generation of ellipses and ellipsoids by a simple transformation. The method in this paper is much simpler and easier to apply than those given by Eugenia Montiel et al.

Notes on Association Schemes from Quadrics over Finite Fields of Characteristic Two

By using nondegenerate and degenerate quadrics in projective space over finite fields of characteristic 2, some association schemes were constructed and their parameters were computed by the authors (see Adv. in Math., 3(2000), 120-128 and Acta Math. Appl. Sinica, 1(1999), 96-103). In this note, their polynomial properties, eigenmatrices, imprimitivities, association subschemes and related quotient association schemes are studied.

Combined-Type Continuous Variable Transmission with Quadric Crank Chains and One-Way Clutches

The conventional Continuously Variable Transmission （CVT） has been classified as belt-type or toroidal CVTs. Each CVT is fundamentally composed of several components to transmit the frictional force or torque generated by the driving force. Since the conventional CVTs use friction force, their energy （force or torque） transfer efficiency might be inferior due to slippage and pressure between the transmission components. Consequently, we propose a new type of structural CVT. The CVT we proposed in this paper means a combined-type transmission with quadric crank chains and one-way clutches.

Continuously Variable Transmission Using Quadric Crank Chains and Ratchets

This paper describes the CVT （continuously variable transmission）. Generally, CVTs are classified as belt-type or toroidal CVTs, and each CVT is basically composed of two parts such as the V-belt and pulley, or friction wheels. In the belt-type CVT, the pulley is driven by a belt placed between two （left and right） circle boards, while in the toroidal CVT, two rollers rotate under the condition being pushed by strong compression power. Since these conventional CVTs use friction force, their energy transfer efficiency might be inferior. Furthermore, although these CVTs require precise structures and processing, they make noise, and are not durable. Consequently, we propose a new structural CVT in this paper.

Topologically Correct Intersection Curves of Two Trimmed Quadrics with Tolerance Control

Surface/surface intersection is a fundamental problem in Compute Aided Design and Geometric Modeling since it is essential to solid modeling,numerically controlled machining,feature recognition,computer animation,etc.In practical applications,quadric surfaces,which are the most basic type of surfaces,are typically bounded surfaces trimmed by a sequence of planes.In this paper,a robust algorithm is proposed for computing the intersection curve segments of two trimmed quadrics based on the parametric representation of the intersection curves of two quadrics.The proposed algorithm guarantees correct topology and ensures that the approximation errors of the end points of the intersection curve segments are less than a given tolerance.The error control is based on an effective solution to a set of polynomial inequality system using the root isolation technique.Some examples are presented to validate the robustness and effectiveness of the proposed algorithm.

On the Quantum Cohomology of Blow-ups of Four-dimensional Quadrics

We propose a conjecture relevant to Galkin’s lower bound conjecture,and verify it for the blow-ups of a four-dimensional quadric at a point or along a projective plane.We also show that Conjecture O holds in these two cases.

Clifford Deformations of Koszul Frobenius Algebras and Noncommutative Quadrics

A Clifford deformation of a Koszul Frobenius algebra E is a finite dimensional Z_(2)-graded algebra E(θ),which corresponds to a noncommutative quadric hypersurface E^(!)/(z)for some central regular element z∈E_(2)^(!).It turns out that the bounded derived category D^(b)(gr_(Z_(2))E(θ))is equivalent to the stable category of the maximal Cohen-Macaulay modules over E^(!)/(z)provided that E!is noetherian.As a consequence,E^(!)/(z)is a noncommutative isolated singularity if and only if the corresponding Clifford deformation E(θ)is a semisimple Z_(2)-graded algebra.The preceding equivalence of triangulated categories also indicates that Clifford deformations of trivial extensions of a Koszul Frobenius algebra are related to Knörrer's periodicity theorem for quadric hypersurfaces.As an application,we recover Knörrer's periodicity theorem without using matrix factorizations.

旋转曲面融入课程思政的教学设计

探究融入课程思政的旋转曲面教学设计.通过有思政内涵的生活实例和小实验创设问题情境,归纳旋转曲面的定义,探索旋转曲面的方程.运用旋转曲面方程和图形解释生活中常见的旋转二次曲面模型,自然地融入思政元素,实现知识传授与价值引领的融合统一.

在复二维仿射锥上的完备余齐性一Kahler度量

In this paper,we revisit the Kahler structures on the affine quadrics M1={z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=1}in the paper by Bo Yang and Fang-Yang Zheng.We found that the Kahler structures on the complex surface are more complicated than what they have thought.We shall also give some detail calculations and found that our results fit quite well with earlier papers of the first author,one of them with X.X.Chen.

QUADRICS IN AG(n, F_q)FOR q EVEN

In this letter we assume that F_q is a finite field with q elements, where q is a power of 2. Let N={x^2+x|x∈F_q} and choose a fixed element α of F_q not belonging to N. Theorem 1. Under affine transformations any quadric in AG(n, F_q), where q is even, can be carried into a quadric with one of the following quadratic equations as its equation:

Solution of a hollow thick-wall cylinder subject to quadric function pressures and its limit when l→∞

The problem of a hollow thick-wall cylinder subject to quadric function pressures is solved with a new stress function, thus laying the basis for solving the spatial symmetric deformation of a hollow cylinder subject to arbitrarily distributed pressures.

Automatic Cage Building with Quadric Error Metrics

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.

基于二次误差度量的保持特征的模型简化算法

使用二次误差度量的边折叠简化算法,提供了一种通用的、高效的、高质量的模型简化方案。然而这些方法仍然存在一些不足,如忽略模型的一些几何特征,模型简化均匀,在高简化率下不能很好的保持模型形状特征。因此,提出一种基于二次误差度量的模型简化算法,将顶点曲率,顶点的平展度因子以及顶点的面积属性考虑进顶点二次误差度量中,在简化过程中改变边的折叠顺序。实验表明,在相同的简化率下,算法能进行更高质量的模型简化,并且经过大规模简化后,能保持模型表面的重要几何特征。

Stability of hypersurface sections of quadric threefolds

Let S be a complete intersection of a smooth quadric 3-fold Q and a hypersurface of degree d in P4.We analyze GIT stability of S with respect to the natural G=SO(5,C)-action.We prove that if d 4 and S has at worst semi-log canonical singularities then S is G-stable.Also,we prove that if d 3 and S has at worst semi-log canonical singularities then S is G-semistable.