EDGE SUBDIVISIONS OF A GIVEN GEODETIC BLOCK PRESERVING ITS PROPERTY TO BEGEODETIC

In this paper authors have obtained a new necessary and sufficient condition for a graph G to be a geodetic graph. Let g : E --> Z(+) be a function from the set of edges of a graph G to the set of nonnegative integers and let g(G) denote the graph obtained from G by replacing each edge e is an element of E by a suspended are (path) P-g(e+2) of length g(e) + 1. and by using this condition, established a criterion for a function g to be a function which can generate a new geodetic block g(G) from a given geodetic block G.

SUBDIVISION建模在室内有机形态的应用研究

通过探索Subdivision建模技术在室内设计中的潜力,提高室内设计有机形态的吸引力和竞争力,并且有效提高设计师在有机形态设计中的效率。通过分析Subdivision建模原理,介绍其在室内运用的可能性、高效性、调节性、仿生性的特点。对其Subdivision建模在室内设计应用中的有机拓扑形态、空间界面软化、泰森多边形应用、渐消面的运用等几点优势展开讨论。结合乐嘉伦敦展厅和BarinSkiResort、Batwings案例,阐述其非线性美学和有机形态,解读其设计特点。进一步分析Subdivision建模的有机形态表达优势与局限性,探讨Subdivision建模在室内设计中的有机结构建模的可行性。探析出Subdivision建模技术能够更好设计具有非线性美学的有机形态,更有助于创造出独特的艺术形式和空间感受。为相关室内空间有机形态的设计提供了创新的设计思路。

A Subdivision-Based Combined Shape and Topology Optimization in Acoustics

We propose a combined shape and topology optimization approach in this research for 3D acoustics by using the isogeometric boundary element method with subdivision surfaces.The existing structural optimization methods mainly contain shape and topology schemes,with the former changing the surface geometric profile of the structure and the latter changing thematerial distribution topology or hole topology of the structure.In the present acoustic performance optimization,the coordinates of the control points in the subdivision surfaces fine mesh are selected as the shape design parameters of the structure,the artificial density of the sound absorbing material covered on the structure surface is set as the topology design parameter,and the combined topology and shape optimization approach is established through the sound field analysis of the subdivision surfaces boundary element method as a bridge.The topology and shape sensitivities of the approach are calculated using the adjoint variable method,which ensures the efficiency of the optimization.The geometric jaggedness and material distribution discontinuities that appear in the optimization process are overcome to a certain degree by the multiresolution method and solid isotropic material with penalization.Numerical examples are given to validate the effectiveness of the presented optimization approach.

The Weighted Basis for PHT-Splines

PHT-splines are defined as polynomial splines over hierarchical T-meshes with very efficient local refinement properties.The original PHT-spline basis functions constructed by the truncation mechanism have a decay phenomenon,resulting in numerical instability.The non-decay basis functions are constructed as the B-splines that are defined on the 2×2 tensor product meshes associated with basis vertices in Kang et al.,but at the cost of losing the partition of unity.In the field of finite element analysis and topology optimization,forming the partition of unity is the default ingredient for constructing basis functions of approximate spaces.In this paper,we will show that the non-decay PHT-spline basis functions proposed by Kang et al.can be appropriately modified to form a partition of unity.Each non-decay basis function is multiplied by a positive weight to form the weighted basis.The weights are solved such that the sum of weighted bases is equal to 1 on the domain.We provide two methods for calculatingweights,based on geometric information of basis functions and the subdivision of PHT-splines.Weights are given in the form of explicit formulas and can be efficiently calculated.We also prove that the weights on the admissible hierarchical T-meshes are positive.

Generalized nth-Order Perturbation Method Based on Loop Subdivision Surface Boundary Element Method for Three-Dimensional Broadband Structural Acoustic Uncertainty Analysis

In this paper,a generalized nth-order perturbation method based on the isogeometric boundary element method is proposed for the uncertainty analysis of broadband structural acoustic scattering problems.The Burton-Miller method is employed to solve the problem of non-unique solutions that may be encountered in the external acoustic field,and the nth-order discretization formulation of the boundary integral equation is derived.In addition,the computation of loop subdivision surfaces and the subdivision rules are introduced.In order to confirm the effectiveness of the algorithm,the computed results are contrasted and analyzed with the results under Monte Carlo simulations(MCs)through several numerical examples.

Novel method for exactly evaluating the energy of Catmull-Clark subdivision surfaces

A novel method is produced to evaluate the energy of the Catmull-Clark subdivision surface including extraordinary points in the control mesh. A closed-form analytic formula for thin plate energy of the Catmull-Clark subdivision surface of arbitrary topology is derived through translating the Catmull-Clark subdivision surface into bi-cubic B-spline surface pieces. Using this method, both the membrane energy and the thin plate energy can be evaluated without requiring recursive subdivision. Therefore, it is more efficient and more accurate than the existing methods for calculating the energy of the Catmull-Clark subdivision surface with arbitrary topology. The example of surface fairing demonstrates that this method is efficient and successful for evaluating the energy of subdivision surfaces.

基于Cortex-M4的环面蜗杆检测仪的全闭环控制系统（英文）

针对环面蜗杆检测仪系统控制及定位精度的需要,采用Cortex-M4作为主控制器,控制步进电机驱动载物台运动,步进电机采用闭环控制。光栅尺实时检测XYZ导轨的位置信息,并把光栅信号作为反馈信号,构成闭环运动控制系统,实现坐标系中XYZ轴的运动和时栅转台旋转的高精度定位。步进电机的驱动采用软硬件细分方法,克服了步进电机爬行和丢步现象。实验表明:该系统采用全闭环控制、步进电机软硬件细分方法,实现了三坐标轴±2μm的精密定位,保证了环面蜗杆检测仪的准确测量。

Computer aided stitching approach for dental restoration models

According to the bio-characteristics of the lower and upper cavity surfaces of dental restoration, a stitching approach is proposed based on a virtual zipper working mechanism and a minimization of the surface total curvature energy, which is used to resolve the stitching problems existing during computer-aided design for dental restorations. First, the two boundaries corresponding to the lower and upper surfaces are triangulated based on the zipper working mechanism to generate the initial stitching surface patch, of which the edges are distributed uniformly between the boundaries. Secondly, the initial stitching surface patch is subdivided and deformed to reconstruct an optimized surface patch according to the bio-characteristics of the teeth. The optimized surface patch is minimally distinguishable from the surrounding mesh in smoothness and density, and it can stitch the upper and lower cavity surfaces naturally. The experimental results show that the dental restorations obtained by the proposed method can satisfy both the shape aesthetic and the fitting accuracy, and meet the requirements of clinical oral medicine.

Accurate Evaluation of Free-form Surface Profile Error Based on Quasi Particle Swarm Optimization Algorithm and Surface Subdivision

Although significant progress has been made in precision machining of free-form surfaces recently, inspection of such surfaces remains a difficult problem. In order to solve the problem that no specific standards for the verification of free-form surface profile are available, the profile parameters of free-form surface are proposed by referring to ISO standards regarding form tolerances and considering its complexity and non-rotational symmetry. Non-uniform rational basis spline（NURBS） for describing free-form surface is formulated. Crucial issues in surface inspection and profile error verification are localization between the design coordinate system（DCS） and measurement coordinate system（MCS） for searching the closest points on the design model corresponding to measured points. A quasi particle swarm optimization（QPSO） is proposed to search the transformation parameters to implement localization between DCS and MCS. Surface subdivide method which does the searching in a recursively reduced range of the parameters u and v of the NURBS design model is developed to find the closest points. In order to verify the effectiveness of the proposed methods, the design model is generated by NURBS and the measurement data of simulation example are generated by transforming the design model to arbitrary position and orientation, and the parts are machined based on the design model and are measured on CMM. The profile errors of simulation example and actual parts are calculated by the proposed method. The results verify that the evaluation precision of freeform surface profile error by the proposed method is higher 10%-22% than that by CMM software. The proposed method deals with the hard problem that it has a lower precision in profile error evaluation of free-form surface.

一种基于局部自适应细分的布料模拟的快速方法

为了提高布料模拟的速度和真实感效果 ,文中采用基于矩形域的mass spring模型 ,并结合基于Catmull Clark准则的局部自适应细分 ,设计了一种新算法。通过采用基于局部自适应细分的碰撞检测和响应方法 ,并将SSE(包括Cache控制指令集和SIMD指令 )应用到系统实现中 ,文中的布料模拟系统可以进行高效的实时运动仿真 ,减少超弹性等失真现象 ,在效率和真实感两者间取得较好的折中效果。

CAD Model-Based Intelligent Inspection Planning for Coordinate Measuring Machines

As the market competition among enterprises grows intensively and the demand for high quality products increases rapidly, product quality inspection and control has become one of the most important issues of manufacturing, and improving the efficiency and accuracy of inspection is also one of problems which enterprises must solve. It is particularly important to establish rational inspection planning for parts before inspecting product quality correctly. The traditional inspection methods have been difficult to satisfy the requirements on the speed and accuracy of modern manufacturing, so CAD-based computer-aided inspection planning （CAIP） system with the coordinate measuring machines （CMM） came into being. In this paper, an algorithm for adaptive sampling and collision-free inspection path generation is proposed, aiming at the CAD model-based inspection planning for coordinate measuring machines （CMM）. Firstly, using the method of step adaptive subdivision and iteration , the sampling points for the specified number with even distribution will be generated automatically. Then, it generates the initial path by planning the inspection sequence of measurement points according to the values of each point＇s weight sum of parameters, and detects collision by constructing section lines between the probe swept-volume surfaces and the part surfaces, with axis-aligned bounding box （AABB） filtering to improve the detection efficiency. For collided path segments, it implements collision avoidance firstly aiming at the possible outer-circle features, and then at other collisions, for which the obstacle-avoiding movements are planned with the heuristic rules, and combined with a designed expanded AABB to set the obstacle-avoiding points. The computer experimental results show that the presented algorithm can plan sampling points＇ locations with strong adaptability for different complexity of general surfaces, and generate efficient optimum path in a short time and avoid collision effectively.

A-Spectra and Q-Spectra of Two Classes of Corona Graphs

It is well known that graph spectra store a lot of structural information about a graph,and it is more difficult to compute the spectra of corona graphs. In this paper two classes of new corona graphs,the corona-vertex of the subdivision graph G1◇G2and corona-edge of the subdivision graph G1☆G2were defined. Then,by using the coronal of a graph and some knowledge of linear algebra,the adjacency spectra and the signless Laplacian spectra of the two new graphs were explicitly computed in terms of the corresponding spectra of G1 and G2. As the application,some Aintegral graphs were constructed.

Resources calculation of cobalt-rich crusts with the grid subdivision and integral method

On the basis of three geological models and several orebody boundaries, a method of grid subdivision and integral has been proposed to calculate and evaluate the resources of cobalt-rich crusts on the seamounts in the central Pacific Ocean. The formulas of this method are deduced and the interface of program module is designed. The method is carried out in the software ＂Auto mapping system of submarine topography and geomorphology MBChart＂. This method and program will possibly become a potential tool to calculate the resources of seamounts and determine the target diggings for China＇ s next Five-year Plan.

Reverse Loop subdivision with sharp features

In this paper we introduce a new reverse Loop subdivision method. In contrast to current wavelets based Loop subdivision scheme, our method applies the same rules to both regular and extraordinary vertices and reconstructs the sharp features easily. Furthermore, our method runs faster because it does not need analysis and synthesis procedural. Our main goal is the design of a reverse subdivision method that can reconstruct the coarser mesh from a finer subdivision surface with sharp features for multiresolution representation, The proposed method only needs a little memory storage and brings little error, and it is easy to implement.

Improvement of the termination criterion for subdivision of the rational Bézier curves

By using some elementary inequalities, authors in this paper makes further improvement for estimating the heights of Bézier curve and rational Bézier curve. And the termination criterion for subdivision of the rational Bézier curve is also improved. The conclusion of the extreme value problem is thus further confirmed.

SUBDIVIDING VERBS TO IMPROVE SYNTACTIC PARSING

This paper proposes a new way to improve the performance of dependency parser: subdividing verbs according to their grammatical functions and integrating the information of verb subclasses into lexicalized parsing model. Firstly,the scheme of verb subdivision is described. Secondly,a maximum entropy model is presented to distinguish verb subclasses. Finally,a statistical parser is developed to evaluate the verb subdivision. Experimental results indicate that the use of verb subclasses has a good influence on parsing performance.

Subdivision Surface-Based Isogeometric Boundary Element Method for Steady Heat Conduction Problems with Variable Coefficient

The present work couples isogeometric analysis(IGA)and boundary element methods(BEM)for three dimensional steady heat conduction problems with variable coefficients.The Computer-Aided Design(CAD)geometries are built by subdivision surfaces,and meantime the basis functions of subdivision surfaces are employed to discretize the boundary integral equations for heat conduction analysis.Moreover,the radial integration method is adopted to transform the additional domain integrals caused by variable coefficients to the boundary integrals.Several numerical examples are provided to demonstrate the correctness and advantages of the proposed algorithm in the integration of CAD and numerical analysis.

Noise Pollution Reduction through a Novel Optimization Procedure in Passive Control Methods

This paper proposes a novel optimization framework in passive control techniques to reduce noise pollution.The geometries of the structures are represented by Catmull-Clark subdivision surfaces,which are able to build gap-free Computer-Aided Design models and meanwhile tackle the extraordinary points that are commonly encountered in geometricmodelling.The acoustic fields are simulated using the isogeometric boundary elementmethod,and a density-based topology optimization is conducted to optimize distribution of sound-absorbing materials adhered to structural surfaces.The approach enables one to perform acoustic optimization from Computer-Aided Design models directly without needingmeshing and volume parameterization,thereby avoiding the geometric errors and time-consuming preprocessing steps in conventional simulation and optimization methods.The effectiveness of the present method is demonstrated by three dimensional numerical examples.

The Odd-Point Ternary Approximating Schemes

We present a general formula to generate the family of odd-point ternary approximating subdivision schemes with a shape parameter for describing curves. The influence of parameter to the limit curves and the sufficient conditions of the continuities from C0 to C5 of 3- and 5-point schemes are discussed. Our family of 3-point and 5-point ternary schemes has higher order of derivative continuity than the family of 3-point and 5-point schemes presented by [Jian-ao Lian, On a-ary subdivision for curve design: II. 3-point and 5-point interpolatory schemes, Applications and Applied Mathematics: An International Journal, 3(2), 2008, 176-187]. Moreover, a 3-point ternary cubic B-spline is special case of our family of 3-point ternary scheme. The visual quality of schemes with examples is also demonstrated.

DCEFM Model for Emergency Risk Assessment of Ship Inflow

This paper proposes a risk assessment model considering danger zone,capsizing time,and evaluation time factors(DCEFM)to quantify the emergency risk of ship inflow and calculate the degree of different factors to the emergency risk of water inflow.The DCEFM model divides the water inflow risk factors into danger zone,capsizing time,and evacuation time factors.The danger zone,capsizing time,and evacuation factors are calculated on the basis of damage stability probability,the numerical simulation of water inflow,and personnel evacuation simulation,respectively.The risk of a capsizing scenario is quantified by risk loss.The functional relationship between the location of the danger zone and the probability of damage,the information of breach and the water inflow time,the inclination angle and the evacuation time,and the contribution of different factors to the risk model of ship water inflow are obtained.Results of the DCEFM show that the longitudinal position of the damaged zone and the area of the breach have the greatest impact on the risk.A simple local watertight plate adjustment in the high-risk area can improve the safety of the ship.