APPROXIMATION OF INTERVAL BEZIER SURFACES

Based on the conception of perturbation, an approach to the interval Bezier surfaces approximating ra- tional surfaces is presented using the energy minimization method. The method places more restrictions on the perturbation surfaces than the original surfaces. The applications of the approach are also presented. Experimen- tal result is combined with the subdivision method to obtain a piecewise interval polynomial approximation for a rational surface.

Approximate error correction scheme for three-dimensional surface codes based reinforcement learning

Quantum error correction technology is an important method to eliminate errors during the operation of quantum computers.In order to solve the problem of influence of errors on physical qubits,we propose an approximate error correction scheme that performs dimension mapping operations on surface codes.This error correction scheme utilizes the topological properties of error correction codes to map the surface code dimension to three dimensions.Compared to previous error correction schemes,the present three-dimensional surface code exhibits good scalability due to its higher redundancy and more efficient error correction capabilities.By reducing the number of ancilla qubits required for error correction,this approach achieves savings in measurement space and reduces resource consumption costs.In order to improve the decoding efficiency and solve the problem of the correlation between the surface code stabilizer and the 3D space after dimension mapping,we employ a reinforcement learning(RL)decoder based on deep Q-learning,which enables faster identification of the optimal syndrome and achieves better thresholds through conditional optimization.Compared to the minimum weight perfect matching decoding,the threshold of the RL trained model reaches 0.78%,which is 56%higher and enables large-scale fault-tolerant quantum computation.

Refinement of an Analytical Approximation of the Surface Potential in MOSFETs

A refinement of an analytical approximation of the surface potential in MOSFETs is proposed by introducing a high-order term. As compared to the conventional treatment with accuracy between 1nV and 0. 03mV in the cases with an oxide thickness tox = 1 ～ 10nm and substrate doping concentration Na = 1015 ～ 1018 cm-3 , this method yields an accuracy within about 1pV in all cases. This is comparable to numerical simulations, but does not require trading off much computation efficiency. More importantly, the spikes in the error curve associated with the traditional treatment are eliminated.

ON CURVED SURFACE APPROXIMATION AND HIDDEN SURFACE ELIMINATION IN 3-D COMPUTER AIDED GARMENT DESIGN

An approximation method for curved surface mannequin and hidden surface eliminationin 3-D computer aided garment design system is described. The mannequin is the basis of the3-D modeling for clothes. In terms of the requirements of computer aided garment design,the authors put forward a method for curved surface approximation in the meaning of leastsquares. Using. this method the computation of geometric modeling is simple andefficient. It is also convenient for curved surface modification and shading.

Doppler spectral analysis for time-evolving sea surfaces using second-order small slope approximation

The second-order small slope approximation （SSA2） method is introduced to study the Doppler characteristics from time-evolving sea surfaces. Simulation results show better agreement between the SSA2 model and the numerical method for both vertical and horizontal polarizations, meaning that SSA2 gives a satisfactory prediction of the spectral difference between two po- larizations; while such discrepancy cannot be captured using the lowest-order SSA （SSA1） model. In particular, the Doppler shifts and spectral widths for different incident angles, wind directions and polarizations are analyzed, demonstrating correct variations with respect to such parameters. Those observations prove that the SSA2 provides an efficient and relatively fast tool for sea surface Doppler spectral analysis.

Study of scattering from time-varying Gerstners sea surface using second-order small slope approximation

Backscattered fields from one-dimensional time-varying Gerstners sea surface are calculated utilising the secondorder small slope approximation. It is well known that spectral properties of the backscattered echoes relate to the velocity of the small elementary scatterers on sea surface profiles. Therefore, modeling Doppler spectra from the ocean requires an accurate description of the sea surface motion. The profile of nonlinear Gerstners sea surface shows verticalskewness of sea waves, it is sharper at the crest and flatter at the trough than linear waves, and its maximum slope position is closer to the crest than to the trough. Furthermore, the horizontal component of the small elementary scatterers orbit velocity on the sea surface, which yields noticeable influence on Doppler spectra, can be obtained conveniently by Gerstners sea surface model. In this study the characteristics of Doppler spectra of backscattered fields from time-varying Gerstners sea surface are investigated and the dependences of the Doppler frequency and the Doppler bandwidth on the parameters, such as the wind speed, the radar frequency, the incident angle, etc. are discussed. It is shown that the Doppler bandwidth of microwave scattered fields from Gerstners sea surface is considerably broadened. For the case of high frequency backscattered fields, the values of the higher-order spectrum peaks are larger than those obtained by linear sea surface.

Interval Bézier Surfaces Approximation of Rational Surfaces

On the basis of the perturbation, we present an approach to approximating rational surfaces by the interval Btzier surfaces using energy minimization method. The approach makes the perturbation surfaces have more restrictions than the original surfaces. It could be combined with subdivision method to obtain a piecewise interval polynomial approximation for a rational surface. The applications of this approach are illustrated too.

B-Spline Approximation of Ship Waves on the Free Surface

We consider the problem of a ship advancing in waves. In this method, the zone of free surface in the vicinity of body is discretized. On the discretized surface, the first-order and second-order derivatives of ship waves are represented by the B-Spline formulae. Different ship waves are approximated by cubic B-spline and the first and second order derivates of incident waves are calculated and compared with analytical value. It approves that this numerical method has sufficient accuracy and can be also applied to approximate the velocity potential on the free surface.

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.

An automatic grid generation approach over free-form surface for architectural design

An essential step for the realization of free-form surface structures is to create an efficient structural gird that satisfies not only the architectural aesthetics,but also the structural performance.Employing the main stress trajectories as the representation of force flows on a free-form surface,an automatic grid generation approach is proposed for the architectural design.The algorithm automatically plots the main stress trajectories on a 3D free-form surface,and adopts a modified advancing front meshing technique to generate the structural grid.Based on the proposed algorithm,an automatic grid generator named "St-Surmesh" is developed for the practical architectural design of free-form surface structure.The surface geometry of one of the Sun Valleys in Expo Axis for the Expo Shanghai 2010 is selected as a numerical example for validating the proposed approach.Comparative studies are performed to demonstrate how different structural grids affect the design of a free-form surface structure.

Parametric design of a part with free-form surfaces

3D solid models for parts with regular-form surfaces (PRFSs) are effectively generated using traditional parametric design techniques. A new model is obtained by changing some parameters defining the model. The parts with free-form surfaces (PFFSs), however, cannot be defined by several parameters. Usually they are defined by some geometric elements like profile curves. The traditional parametric design approaches have not easily dealt with the PFFSs. A method for generating a solid model and an engineering drawing for PFFSs is proposed in this paper: First, the new profiles are generated from input point data. Second, the profile information is extracted from the existing model. Last, the old profiles are replaced with the new profiles. This method can preserve the associative information of the existing model and automatically generate the drawing including views, dimen- sions, and annotations. The proposed method has been implemented using a commercial CAD/CAM system, Unigraphics, and API functions written in C-language, and were applied to the blades of a turbine generator. Some illustrative examples are pro- vided in order to show the effectiveness of the proposed method.

Approximate merging of B-spline curves and surfaces

Applying the distance function between two B-spline curves with respect to the L2 norm as the approximate error, we investigate the problem of approximate merging of two adjacent B-spline curves into one B-spline curve. Then this method can be easily extended to the approximate merging problem of multiple B-spline curves and of two adjacent surfaces. After minimizing the approximate error between curves or surfaces, the approximate merging problem can be transformed into equations solving. We express both the new control points and the precise error of approximation explicitly in matrix form. Based on homogeneous coordinates and quadratic programming, we also introduce a new framework for approximate merging of two adjacent NURBS curves. Finally, several numerical examples demonstrate the effectiveness and validity of the algorithm.

Study of the Contact Force in Free-form Surfaces Compliant EDM Polishing by Robot

With an elastic negative pole being driven by ultra so nic vibration and being moved along the surface of work-piece compliantly by ro bot, a new kind of effective EDM, the compliant EDM, cuts the electrically condu ctive materials away and polishes work-piece of free-form surface. The study o f the contact force between the end of polishing tool and the surface of work-p iece is the key for the compliant EDM to study its cutting mechanism and to make better use of it. This paper makes a model for the contact force and verifies i t by experiments and simulation based on the theory of elastic body kinetics and dynamic stress concentration. The research work shows that this contact force i s caused by both the electrical impulsion of EDM and the mechanical force of ult rasonic vibration, the discharge frequency of compliant EDM has a much more clos er connection with the vibration frequency of polishing tool rather than the fre quency of ultrasonic vibration.

Characterization of surface EMG signals using improved approximate entropy

An improved approximate entropy (ApEn) is presented and applied to characterize surface electromyography (sEMG) signals. In most previous experiments using nonlinear dynamic analysis, this certain processing was often confronted with the problem of insufficient data points and noisy circumstances, which led to unsatisfactory results. Compared with fractal dimension as well as the standard ApEn, the improved ApEn can extract information underlying sEMG signals more efficiently and accu- rately. The method introduced here can also be applied to other medium-sized and noisy physiological signals.

ADAPTIVE MEASUREMENT METHOD BASED ON CHANGING-CURVATURE FOR UNKNOWN FREE-FORM SURFACE

Current measurement method for unknown free-form surface has low efficiency.To acquire given precision, a lot of null points are measured. Based on change surface curvature, anew measurement planning is put forward. Sample step is evaluated from the change curvature and thelocally-bounded character of extrapolating curve. Two coefficients, maximum error coefficient andlocal camber coefficient, are used to optimize sampling step. The first coefficient is computed toavoid sampling-point exceeding the measurement range and the second control sampling precision.Compared with the other methods, the proposed planning method can reduce the number of themeasuring-point efficiently for the given precision. Measuring point distributes adaptively by thechange surface curvature. The method can be applied to improve measurement efficiency and accuracy.

NEW VISUAL METHOD FOR FREE-FORM SURFACE RECONSTRUCTION

A new method is put forward combining computer vision with computer aidedgeometric design (CAGD) to resolve the problem of free-form surface reconstruction. The surface isfirst subdivided into N-sided Gregory patches, and a stereo algorithm is used to reconstruct theboundary curves. Then, the cross boundary tangent vectors are computed through reflectance analysis.At last, the whole surface can be reconstructed jointing these patches with G^1 continuity(tangentcontinuity). Examples on synthetic images are given.

Reconstruction of B-spline surface by interpolating boundary curves and approximating inner points

In this paper, we present an algorithm for reconstruction of B-spline surface such that it interpolates the four given bound- ary curves and simultaneously approximates some given inner points. The main idea of our method is： first, we construct an initial surface which interpolates the four given boundary curves; then, while keeping the boundary control points of the initial surface un- changed, we reposition the inner control points of the surface with energy optimization method. Examples show that our algorithm is practicable and effective.

Research on the Fault Monitoring System in Free-form Surface CNC Machining Based on Wavelet Analysis

Carrying out experiments and researches on tool bre ak age and undercut of work-piece of free-form surface by using wavelet analysis, both the fault features can be extracted in a special frequency segment of wave let decompose. According to the feature of transient fault, the author proposes for the first time the automatic determination technology of the threshold by us e of the adaptive filter characteristic of wavelet transform. Based on profound researches on steady fault feature, this dissertation makes an effective token o f steady fault feature by using wavelet energy method, and proposes the new idea to identify cut-in case and cut-out case, thereby successfully gives an uniqu e description quantitatively on the characterization of the variation of fault a nd cutting condition in the monitoring system.

Real-time accurate Free-Form Deformation in terms of triangular Bézier surfaces

We implemented accurate FFD in terms of triangular Bezier surfaces as matrix multiplications in CUDA and rendered them via OpenGL. Experimental results show that the proposed algorithm is more efficient than the previous GPU acceleration algorithm and tessel- lation shader algorithms.

Tool-path planning for free-form surface high-speed high-resolution machining using torus cutter

In CNC machining, two essential components decide the accuracy and machining time for a sculptured surface: one is the step-size interval, the other is the tool-path interval. Due to the limitation of the conventional method for calculating the tool-path interval, it cannot satisfy the machining requirement for high-speed and high-resolution machining. Accordingly, for high-speed and high-resolution machining, the current study proposes a new tool-path interval algorithm, plus a variable step-size algorithm for NURBS. Furthermore, a new type cutter, which can improve the cutting efficiency, is investigated in the paper. The transversal equation of the torus cutter onto the flat plan is given in this paper. The tool-path interval is calculated with the transversal equation and the proposed algorithm. The illustrated example shows that the redundant tool paths can be reduced because an accurate tool-path interval could be calculated.