Extraction of Feature Points for Non-Uniform Rational B-Splines(NURBS)-Based Modeling of Human Legs

Methods of digital human modeling have been developed and utilized to reflect human shape features.However,most of published works focused on dynamic visualization or fashion design,instead of high-accuracy modeling,which was strongly demanded by medical or rehabilitation scenarios.Prior to a high-accuracy modeling of human legs based on non-uniform rational B-splines(NURBS),the method of extracting the required quasi-grid network of feature points for human legs is presented in this work.Given the 3 D scanned human body,the leg is firstly segmented and put in standardized position.Then re-sampling of the leg is conducted via a set of equidistant cross sections.Through analysis of leg circumferences and circumferential curvature,the characteristic sections of the leg as well as the characteristic points on the sections are then identified according to the human anatomy and shape features.The obtained collection can be arranged to form a grid of data points for knots calculation and high-accuracy shape reconstruction in future work.

Methods of configuration test and deformation analysis for large airship

In recent years, high-altitude aerostats have been increasingly developed in the direction of multi-functionality and large size. Due to the large size and the high flexibility, new challenges for large aerostats have appeared in the configuration test and the deformation analysis. The methods of the configuration test and the deformation analysis for large airship have been researched and discussed. A tested method of the configuration,named internal scanning, is established to quickly obtain the spatial information of all surfaces for the large airship by the three-dimensional(3D) laser scanning technology. By using the surface wrap method, the configuration parameters of the large airship are calculated. According to the test data of the configuration, the structural dimensions such as the distances between the characteristic sections are measured. The method of the deformation analysis for the airship contains the algorithm of nonuniform rational B-splines(NURBS) and the finite element(FE)method. The algorithm of NURBS is used to obtain the reconfiguration model of the large airship. The seams are considered and the seam areas are divided. The FE model of the middle part of the large airship is established. The distributions of the stress and the strain for the large airship are obtained by the FE method. The position of the larger deformation for the airship is found.

结合互相关和B样条插值的激光三角光斑定位

激光三角光斑定位通常受到像点光斑偏态的影响,为提高激光三角位移传感器的测量精度和物面适应性,在分析激光三角光斑的偏态特征的基础上,针对偏态特性提出了一种基于互相关和非均匀有理B样条插值的光斑定位算法。对光斑信号采取时域和空域相结合的滤波处理方法,降低外部噪声干扰。引入邻域标定光斑进行互相关运算,充分利用光斑偏态分布的灰度和位置相似性约束,确定像素级相关系数分布。最后,对相关系数序列进行三次非均匀有理B样条插值细分,实现亚像素级光斑质心定位。在激光三角位移传感器中验证算法,实验结果表明:该算法通过结合互相关和非均匀有理B样条插值细分,将测量重复性误差降低至0.4μm,精度相对于传统定位算法显著提高;同时,在互相关算法中采用的邻域标定光斑模板不仅容易获取,几何相似度更高,而且对不同物面特性的适应性更强。本文方法精度高、适应性强,为有效提升激光三角位移传感器的性能提供了新的技术路径。

考虑齿形误差的RV减速器摆线针轮副传动误差分析

在摆线轮加工过程中,由于受到机床精度、刀具精度、工装夹具精度及轮坯精度等因素的影响,不可避免地会产生齿形误差。为了评估齿形误差对摆线针轮副传动精度的影响,基于实测的摆线轮齿形误差计算出实际齿面坐标点数据。采用非均匀有理B样条(NURBS)曲线对实测齿面数据进行曲线拟合,得到含齿形误差的摆线轮数字化齿廓。依据齿轮啮合原理对摆线轮数字化齿面进行齿面接触分析,获得了考虑齿形误差的摆线针轮副传动误差曲线。仿真结果表明,齿形误差会改变摆线轮传动误差曲线的形状和幅值。

基于点云和设计模型的仿真模型快速重构方法

随着产品装配质量要求的不断提高,为了在CAD模型仿真试验中快速且准确地表达零件实际加工质量,提出基于点云和设计模型的仿真模型快速重构方法.采用“一面两孔配准”方法,将零件实测点云数据配准到设计模型上;根据设计模型边界提取出曲面重构所需的控制顶点;采用非均匀有理B样条(NURBS)方法对控制顶点进行曲面拟合;根据仿真需求,结合边界表示法(BREP)和构造实体表示法(CSG)实现模型表面的局部和快速替换.在CATIA中开发基于实测点云数据和设计模型的仿真模型快速重构模块,和基于可拓展标记语言(XML)和特征完全匹配的数字预装配模块.以某航空企业典型零件和舱门预装配为例,验证该方法的重构精度和效率及其在预装配仿真中的高效性和准确性.

FREE-FORM SURFACE RECON-STRUCTION BASED ON NURBS TO SERIAL CROSS-SECTIONS

A new method for recovering shape from cross-sectional contours with complexbranching structures is presented. First, each branching problem by providing an intermediatecontour using distance function and image processing technology is solved. Then, all contours aredivided into several groups of simple contours. For each group, a NURBS curve is fitted to contourpoints in each section within a given accuracy on a common knot vector. Finally, the NURBS surfaceskinning of these contours is performed for providing a smooth geometric model. The method issuitable to reproduce the object by NC machining or rapid prototyping. Some results demonstrate itsusefulness and feasibility.

Application of Dual-blade Stator to Low-speed Ratio Performance Improvement of Torque Converters

With application of the lock-up clutch in the torque converter（TC）, fuel economy is not much determined by its high-speed ratio transmission efficiency. As a benefit, more researches are focused on its low-speed ratio performance so as to improve vehicle gradeability and launching acceleration performance. According to the results of computational fluid dynamics（CFD） analysis, hydrodynamic loss inside the stator cascade accounts for 42% of the total energy loss at stalling speed ratio. It is found that upstream flow with large impingement angle results in boundary layer separation at the leading edge, which aggregates hydrodynamic loss and decreases circular flow rate dramatically at low-speed ratio. In this paper, a dual-blade stator is proposed to suppress the boundary layer separation, which is parameterized by using the non-uniform rational B spline（NURBS） method. The mean camber line and blade profile curve are expressed by a three control points quadratic open NURBS and a cubic closed one respectively. The key design parameters included the slot width and suction side shape of the primary blade are analyzed. The most effective slot width is found to be between 4% and 8% chord length, and the boundary layer separation can be suppressed completely by decreasing distribution of momentum moment at the primary blade and adding it to the leading edge of the secondary blade. As a result, circular flow rate and impeller torque capacity is increased by 17.9% and 9.6% respectively at stalling speed ratio, meanwhile, low-speed ratio efficiency is also improved. Maximum efficiency at high-speed ratio decreases by 0.5%, which can be ignored as the work of lock-up clutch. This research focuses on using the dual-blade stator to optimize low-speed ratio performance of the TC, which is benefit to vehicle power performance.

An efficient data structure for calculation of unstructured T-spline surfaces

To overcome the topological constraints of non-uniform rational B-splines,T-splines have been proposed to define the freeform surfaces.The introduction of T-junctions and extraordinary points makes it possible to represent arbitrarily shaped models by a single T-spline surface.Whereas,the complexity and flexibility of topology structure bring difficulty in programming,which have caused a great obstacle for the development and application of T-spline technologies.So far,research literatures concerning T-spline data structures compatible with extraordinary points are very scarce.In this paper,an efficient data structure for calculation of unstructured T-spline surfaces is developed,by which any complex T-spline surface models can be easily and efficiently computed.Several unstructured T-spline surface models are calculated and visualized in our prototype system to verify the validity of the proposed method.

A Methodology for Curve and Surface Fitting with Adaptive Fairing for Digitized Points

A new approach for NURBS(Non-uniform rational B-spline) curve and surface fitting for measured points was presented which employs a fairing method applied to digitized point data with discrete curvature. If measured points are used as control points to construct an NURBS curve, then the curvature of each data point corresponding to control point of the constructed curve can be computed. According to the convex hull and local properties of NURBS, based on the curvatures obtained, the measured points can be faired. If faired measured points are used as target points to modify, the constructed curve passing through these faired points can produce a smooth NURBS curve. This paper also presented the justification for utilizing the curvatures of constructed NURBS curve instead of the conventional interpolated curve to fair the measured points. Based on the presented algorithms, some qualities of the constructed curves can be improved.

Patchwise Mapping Method for Solving Elliptic Boundary Value Problems Containing Multiple Singularities

In the paper [1], the geometrical mapping techniques based on Non-Uniform Rational B-Spline (NURBS) were introduced to solve an elliptic boundary value problem containing a singularity. In the mapping techniques, the inverse function of the NURBS geometrical mapping generates singular functions as well as smooth functions by an unconventional choice of control points. It means that the push-forward of the NURBS geometrical mapping that generates singular functions, becomes a piecewise smooth function. However, the mapping method proposed is not able to catch singularities emerging at multiple locations in a domain. Thus, we design the geometrical mapping that generates singular functions for each singular zone in the physical domain. In the design of the geometrical mapping, we should consider the design of control points on the interface between/among patches so that global basis functions are in C0?space. Also, we modify the B-spline functions whose supports include the interface between/among them. We put the idea in practice by solving elliptic boundary value problems containing multiple singularities.

Parametric Selection and Continual Combination of Building Surface

A method to reparametrize G retional curve to obtain a C^1 curve is given. A practical G^1 continual connective between adjacent NURUS patches along common guadratic boundary curve is presented in this paper, and a specific algorithm for control points and weights of NURBS patches is discussed.

NEW DESIGN METHOD FOR HYPOID GEARS

A digital model is presented for the purpose of design, manufacture and measurement of hypoid gear, based on the non-uniform rational B-spline surface （NURBS） method. The digital model and the function-oriented active design technique are combined to form a new design method for hypoid gears. The method is well adaptable to CNC bevel gear cutting machines and CNC-controlled gear inspection machines, and can be used to create the initial machine tool cutting location data or program measurement path. The presented example verifies the method is correct.

The Mathematical Model of Short-Term Forest Fire Spread

In this paper, we establish a mathematical model of the forest fire spread process based on a partial differential equation. We describe the distribution of time field and velocity field in the whole two-dimensional space by vector field theory. And we obtain a continuous algorithm to predict the dynamic behavior of forest fire spread in a short time. We use the algorithm to interpolate the fire boundary by cubic non-uniform rational B-spline closed curve. The fire boundary curve at any time can be simulated by solving the Eikonal equation. The model is tested in theory and in practice. The results show that the model has good accuracy and stability, and it’s compatible with most of the existing models, such as the elliptic model and the cellular automata model.

Exact geometry based quasi-conforming analysis for Euler-Bernoulli beam

The problem of quick analysis using exact geometry data was proposed by Hughes et al. and the isogeometric analysis framework was introduced as a solution. In this letter, the exact geometry concept is combined into the quasi-conforming framework and a novel method, i.e., the exact geometry based quasi-conforming analysis is proposed. In present method the geometry is exactly described by non-uniform rational B-spline bases, while the solution space by traditional polynomial bases. Present method combines the merits of both isogeometric analysis and quasi-conforming finite element method. In this letter Euler-Bernoulli beam problem is solved as an example and the results show that the present method is effective and promising.

Improved time-optimal B-spline feedrate scheduling for NURBS tool paths in CNC machining

Feedrate scheduling in computer numerical control(CNC)machining is of great importance to fully develop the capabilities of machine tools while maintaining the motion stability of each actuator.Smooth and time-optimal feedrate scheduling plays a critical role in improving the machining efficiency and precision of complex surfaces considering the irregular curvature characteristics of tool paths and the limited drive capacities of machine tools.This study develops a general feedrate scheduling method for non-uniform rational B-splines(NURBS)tool paths in CNC machining aiming at minimizing the total machining time without sacrificing the smoothness of feed motion.The feedrate profile is represented by a B-spline curve to flexibly adapt to the frequent acceleration and deceleration requirements of machining along complex tool paths.The time-optimal B-spline feedrate is produced by continuously increasing the control points sequentially from zero positions in the bidirectional scanning and sampling processes.The required number of knots for the time-optimal B-spline feedrate can be determined using a progressive knot insertion method.To improve the computational efficiency,the B-spline feedrate profile is divided into a series of independent segments and the computation in each segment can be performed concurrently.The proposed feedrate scheduling method is capable of dealing with not only the geometry constraints but also high-order drive constraints for any complex tool path with little computational overhead.Simulations and machining experiments are conducted to verify the effectiveness and superiorities of the proposed method.

A THREE-DIMENSIONAL DESINGULARIZED HIGH ORDER PANEL METHOD BASED ON NURBS

A desingularized high order panel method based on Non-Uniform Rational B-Spline （NURBS） was developed to deal with three-dimensional potential flow problems. A NURBS surface was used to precisely represent the body geometry. Velocity potential on the body surface was described by the B-spline after the source density distribution on the body surface had been solved. The collocation approach was employed to satisfy the Neurnann boundary condition and Gaussian quadrature points were chosen as both the collocation points and the source points. The singularity was removed by a combined method, so the process of the numerical computation was non-singular. In order to verify the method proposed, the unbounded flow problems of sphere and ellipsoid, the wave-making problem of a submerged ellipsoid were chosen as computational examples. It is shown that the numerical results are in good agreement with analytical solutions and other numerical results in all cases, and sufficient accuracy of numerical solution can be reached with a small number of panels.

Prediction of Hydrodynamic Forces on a Moored Ship Induced by a Passing Ship in Shallow Water Using a High-Order Panel Method

A three-dimensional high-order panel method based on non-uniform rational B-spline(NURBS) is developed for predicting the hydrodynamic interaction forces on a moored ship induced by a passing ship in shallow water. An NURBS surface is used to precisely represent the hull geometry. Velocity potential on the hull surface is described by B-spline after the source density distribution on the boundary surface is determined. A collocation approach is applied to the boundary integral equation discretization. Under the assumption of low passing speed, the effect of free surface elevation is neglected in the numerical calculation, and infinite image method is used to deal with the finite water depth effect. The time stepping method is used to solve the velocity potential at each time step. Detailed convergence study with respect to time step, panel size and Green function is undertaken. The present results of hydrodynamic forces are compared with those obtained by slender-body theory to show the validity of the proposed numerical method. Calculations are conducted for different water depths and lateral distances between ships, and the detail results are presented to demonstrate the effects of these factors.

A novel surface mesh deformation method for handling wing-fuselage intersections

This paper describes a method for mesh adaptation in the presence of intersections, such as wing-fuselage. Automatic optimization tools, using Computational Fluid Dynamics（CFD） simulations, face the problem to adapt the computational grid upon deformations of the boundary surface. When mesh regeneration is not feasible, due to the high cost to build up the computational grid, mesh deformation techniques are considered a cheap approach to adapt the mesh to changes on the geometry. Mesh adaptation is a well-known subject in the literature; however, there is very little work which deals with moving intersections. Without a proper treatment of the intersections,the use of automatic optimization methods for aircraft design is limited to individual components.The proposed method takes advantage of the CAD description, which usually comes in the form of Non-Uniform Rational B-Splines（NURBS） patches. This paper describes an algorithm to recalculate the intersection line between two parametric surfaces. Then, the surface mesh is adapted to the moving intersection in parametric coordinates. Finally, the deformation is propagated through the volumetric mesh. The proposed method is tested with the DLR F6 wing-body configuration.