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.

THE RELATIONSHIP BETWEEN PROJECTIVE GEOMETRIC AND RATIONAL QUADRATIC B-SPLINE CURVES

Abstract For two rational quadratic B spline curves with same control vertexes, the cross ratio of four collinear points are represented: which are any one of the vertexes, and the two points that the ray initialing from the vertex intersects with the corresponding segments of the two curves, and the point the ray intersecting with the connecting line between the two neighboring vertexes. Different from rational quadratic Bézier curves, the value is generally related with the location of the ray, and the necessary and sufficient condition of the ratio being independent of the ray's location is showed. Also another cross ratio of the following four collinear points are suggested, i.e. one vertex, the points that the ray from the initial vertex intersects respectively with the curve segment, the line connecting the segments end points, and the line connecting the two neighboring vertexes. This cross ratio is concerned only with the ray's location, but not with the weights of the curve. Furthermore, the cross ratio is projective invariant under the projective transformation between the two segments.

Shape Control and Modification of Rational Cubic B-Spline Curves

This paper considers the construction of a rational cubic B-spline curve that willinterpolate a sequence of data points x'+ith specified tangent directions at those points. It is emphasisedthat the constraints are purely geometrical and that the pararnetric tangent magnitudes are notassigned as in many' curl'e manipulation methods. The knot vector is fixed and the unknowns are thecontrol points and x'eightsf in this respect the technique is fundamentally different from otherswhere knot insertion is allowed.First. the theoretical result3 for the uniform rational cubic B-spline are presented. Then. in theplanar case. the effect of changes to the tangent at a single point and the acceptable bounds for thechange are established so that all the weights and tangent magnitUdes remain positive. Finally, aninteractive procedure for controlling the shape of a planar rational cubic B-spline curve is presented.

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.

Spline-based automatic path generation of welding robot

This paper presents a flexible method for the representation of welded seam based on spline interpolation. In this method, the tool path of welding robot can be generated automatically from a 3D CAD model. This technique has been implemented and demonstrated in the FANUC Arc Welding Robot Workstation. According to the method, a software system is developed using VBA of SolidWorks 2006. It offers an interface between SolidWorks and ROBOGUIDE, the off-line programming software of FANUC robot. It combines the strong modeling function of the former and the simulating function of the latter. It also has the capability of with on-line robot. The result data have shown its high accuracy and strong reliability in experiments. This method will improve the intelligence and the flexibility of the welding robot workstation.

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.

具有公共三次曲线的NURBS曲面片G^2光滑拼接算法(英文)

Non-uniform rational B-spline (NURBS) curves and surfaces are becoming increasingly widespread. The author have explored G^1 continuity condition between adjacent NURBS surface patches along common cubic boundary curve. On the basis of the research performed, this paper presents a G^2 continuity condition between adjacent NURBS patches along common cubic boundary curve and deduces a specific algorithm for contro1 points and weights of NURBS patch. For making another NURBS patch and one given NURBS patch to attain G^2, according to algorithm condition, one can adjust another patch control points and weights. It is much more convenient for engineers to apply.

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.

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.

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.

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.

Constructing iterative non-uniform B-spline curve and surface to fit data points

In this paper, based on the idea of profit and loss modification, we presentthe iterative non-uniform B-spline curve and surface to settle a key problem in computeraided geometric design and reverse engineering, that is, constructing the curve (surface)fitting (interpolating) a given ordered point set without solving a linear system. We startwith a piece of initial non-uniform B-spline curve (surface) which takes the given point setas its control point set. Then by adjusting its control points gradually with iterative formula,we can get a group of non-uniform B-spline curves (surfaces) with gradually higherprecision. In this paper, using modern matrix theory, we strictly prove that the limit curve(surface) of the iteration interpolates the given point set. The non-uniform B-spline curves(surfaces) generated with the iteration have many advantages, such as satisfying theNURBS standard, having explicit expression, gaining locality, and convexity preserving,etc

Offset approximation based on reparameterizing the path of a moving point along the base circle

This paper presents a novel algorithm for planar curve offsetting. The basic idea is to regard the locus relative to initial base circle, which is formed by moving the unit normal vectors of the base curve, as a unit circular arc first, then accurately to represent it as a rational curve, and finally to reparameterize it in a particular way to approximate the offset. Examples illustrated that the algorithm yields fewer curve segments and control points as well as C^1 continuity, and so has much significance in terms of saving computing time, reducing the data storage and smoothing curves entirely.

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.

PRACTICAL G^2 CONTINUITY ALGORITHMS BETWEEN ADJACENT NURBS PATCHES

Non-uniform rationa1 B-spline (NURBS) curves and sdrices are becomingincreasingly widespread. 'The authors have explored G1 continuity condition between adja-cent NURBS surface patches along common boundary curve. This paper presents a G2continuity condition between adjacent NURBS patches along common quadratic boundarycurve and deduces a specific algorithm for control Points and weights of NURBS patch.For making another NURBS patch and one given NURBS patch to attain G2, according toalgorithms condition, one can adjust another patch control ponts and weights. It is muchmore convenient for engineers to apply.

Robust fault diagnosis for non-Gaussian stochastic systems based on the rational square-root approximation model

The task of robust fault detection and diagnosis of stochastic distribution control （SDC） systems with uncertainties is to use the measured input and the system output PDFs to still obtain possible faults information of the system. Using the rational square-root B-spline model to represent the dynamics between the output PDF and the input, in this paper, a robust nonlinear adaptive observer-based fault diagnosis algorithm is presented to diagnose the fault in the dynamic part of such systems with model uncertainties. When certain conditions are satisfied, the weight vector of the rational square-root B-spline model proves to be bounded. Conver- gency analysis is performed for the error dynamic system raised from robust fault detection and fault diagnosis phase. Computer simulations are given to demon- strate the effectiveness of the proposed algorithm.

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.

RESEARCH AND REALIZATION OF MUTUAL TRIMMING OF NURBS

Since regular surface is defined by a mapping from 2-D parameter plane to 3-D space, trimming of NURBS surface is equivalent to changing a valid parameter region ofthe surface with the same mapping. In this paper, by presenting a rigid and comprehensi-ble definition of union, difference and intersection of two intersecting loops in the parame-ter region of NURBS surface, and by working out the corresponding algorithm, a rebui1d-ing algorithm of the valid parameter region of NURBS surface is obtained.