Evolution of Surface Cold Patches in the North Yellow Sea Based on Satellite SST Data

Ten years （from 2005 to 2014） of satellite sea surface temperature （SST） data from the Advanced Very High Resolution Radiometer （AVHRR） are analyzed to reveal the monthly changes in surface cold patches （SCPs） in the main areas of the Northern Yellow Sea （NYS）. The Canny edge detection algorithm is used to identify the edges of the patches. The monthly changes are de- scribed in terms of location, temperature and area. The inter-annual variations, including changes in the location and area of the SCPs from 2010 to 2014, are briefly discussed. The formation mechanisms of the SCPs in different periods are systematically analyzed using both in situ data and numerical simulation. The results show that from May to October, the location and area of the SCPs re- main stable, with a north-south orientation. The SCPs altogether cover about I° of longitude （124°E-125°E） in width and 2° of lati- tude （37.5°N-39.5°N） in length. In November, the SCP separates from the Jangsan Cape and forms a closed, isolated, and approxi- mately circular cold patch in the central NYS. From May to October, the upweUing that leads to the formation of the SCP is mainly triggered by the headland residual current, wind field, climbing movement of the current and secondary circulation at the tide front. In November, cyclonic circulation in the NYS is primarily responsible for generating the upwelling that leads to the formation of the closed and isolated SCE

SUPPORT SYSTEM FOR FREE SURFACE GRINDING BASED ON PATCH DIVISION

To obtain accurate forms and surfaces in free surface grinding, it is important to provide grinding conditions suitable for a curved surface. A grinding support system for the free surface （GSX-F） is proposed to help the operator grind a free surface with the high accuracy and the high productivity. To succeed in free surface grinding, the property of a ball type wheel must be known. Therefore, a basic study of free surface grinding with a ball type wheel is carried out based on the grinding center （GC）. Some working points for achieving sufficient accuracy in free surface grinding are discussed. GSX-F is constructed using the patch division method and is used to test grinding. Reasonable results are obtained.

Ship hull plate processing surface fairing with constraints based on B-spline

The problem of ship hull plate processing surface fairing with constraints based on B-spline is solved in this paper. The algorithm for B-spline curve fairing with constraints is one of the most common methods in plane curve fairing. The algorithm can be applied to global and local curve fairing. It can constrain the perturbation range of the control points and the shape variation of the curve, and get a better fairing result in plane curves. In this paper, a new fairing algorithm with constraints for curves and surfaces in space is presented. Then this method is applied to the experiments of ship hull plate processing surface. Finally numerical results are obtained to show the efficiency of this 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.

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.

Symmetric alteration of four knots of B-spline and NURBS surfaces

Modifying the knots of a B-spline curve, the shape of the curve will be changed. In this paper, we present the effect of the symmetric alteration of four knots of the B-spline and the NURBS surfaces, i.e., symmetrical alteration of the knots of surface, the extended paths of points of the surface will converge to a point which should be expressed with several control points. This theory can be used in the constrained shape modification of B-spline and NURBS surfaces.

G^0 and G^1 connection between two adjacent B-spline surfaces

In this paper, the smooth connection between two B-spline surfaces is discussed. First, a brief proof of some simple sufficient conditions of Go and G1 continuity is given. On this basis, a novel method for Go or G1 connection between two adjacent B-spline surfaces is presented. A reparameterization step is firstly taken for one of the surfaces such that they have the same parameterization in v direction, then, adjust their boundary control vertices to make them Go or Gl connected. The GI connection parameter is determined by an optimization problem. Compared with the existed methods, our method is simple and easy to be used in practice.

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.

G^1 Continuity Conditions of B-spline Surfaces

According to the B-spline theory and Boehm algorithm, this paper presents several necessary and sufficient G1 continuity conditions between two adjacent B-spline surfaces. In order to meet the need of application, a kind of sufficient conditions of G1 continuity are developed, and a kind of sufficient conditions of G1 continuity among N(N>2) patch B-spline surfaces meeting at a common corner are given at the end.

RECONSTRUCTION OF SYMMETRIC B-SPLINE CURVES AND SURFACES

A method to reconstruct symmetric B-spline curves and surfaces is presented. The symmetry property is realized by using symmetric knot vector and symmetric control points. Firstly, data points are divided into two parts based on the symmetry axis or symmetry plane extracted from data points. Then the divided data points are parameterized and a symmetric knot vector is selected in order to get symmetric B-spline basis functions. Constraint equations regarding the control points are deduced to keep the control points of the B-spline curve or surface to be symmetric with respect to the extracted symmetry axis or symmetry plane. Lastly, the constrained least squares fitting problem is solved with the Lagrange multiplier method. Two examples from industry are given to show that the proposed method is efficient, robust and able to meet the general engineering requirements.

Fast B-spline surface extraction algorithm of seismic volume data on GPU

In the process of seismic data interpretation, the extraction of a horizon or a fault is generally needed. In this paper we present a fast extraction method. First select some feature points interactively, then reconstruct the surface according to the selected feature points by using B-spline interpolation curve or surface. In order to solve the error-drawing problem appeared in the process of interactive rendering, which is caused by the change of sampling interval as the view point changes, we combine shear-warp and splatting algorithm to render the surface. The rendering of seismic data and specific surface in our work are achieved on GPU platform using CUDA programming language, which make it able to meet the requirements of real-time rendering.

Modification of B-Spline Surfaces with Optimization

Algorithms of modifying a surface to approximate some scattered points, or pass through some characteristic points/curves are presented. Similar to variational approach, the algorithms are based on optimization. For the deviation between the modified surface and the original one is adopted as the objective functions, the change of the surface shape is as small as possible with the modified surface satisfying the specified requirements.

B-SPLINE SURFACE SMOOTH JOINING

Optimization techniques are being applied to solve the problems of surface interpolation, approximation, smooth joining and fairing, aiming at corresponding objective functions. This paper focuses on the construction of fair surface interpolating the given mesh of curved boundaries with G 2 adjustment at comers and G 1, G 2 smoothness between adjacent patches. Many papers on surface blending have been presented, but almost all of them are restricted to the discussion of Bezier patches, there are no good results for B-spline surface. This paper gives a solution to the B-spline surface, allowing the surface to degenerate at comer in and have different parameterization along the common boundary of two patches.

An Algorithm of B-Spline Surface Interpolation

A surface interpolation algorithm is presented. By using a special kind of knot vector. a B-spline surface can be constructed to interpolate an array of m ×n positions, including parameter u and v tangent vectors and twist vector at each positions. Single surface interpolation approach is easier to ensure the smoothness of the interpolating surface than multi-patches method. This algorithm can be used to solve the approximating problem of B-spline approximation of general parametric surface.

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.

NURBS Parameterization for Medical Surface Reconstruction

InVesalius is an open-source software for reconstruction of computed tomography and magnetic resonance images, which allows the user to make analysis and segmentation of virtual anatomical models. Physical models can be printed with the aid of rapid prototyping, giving the medical community a reliable instrument to help planning surgeries. To offer the user more control over the model, this work describes a methodology and tool developed for NURBS parameterization that provides mechanisms for adjusting the shape or even selecting a particular region of interest of the surface. Furthermore, the tool gives the option to export the final results of the process to a STEP file, which allows further edition in any well-known CAD software.

Image Interpolation Through Surface Reconstruction

Reconstructing an HR （high-resolution） image which preserves the image intrinsic structures from its LR （low-resolution） counterpart is highly challenging. This paper proposes a new surface reconstruction algorithm applied to image interpolation. The interpolation surface for the whole image is generated by putting all the quadratic polynomial patches together. In order to eliminate the jaggies of the edge, a new weight fimction containing edge information is incorporated into the patch reconstruction procedure as a constraint. Extensive experimental results demonstrate that our method produces better results across a wide range of scenes in terms of both quantitative evaluation and subjective visual quality.

Analysis and applications of a frequency selective surface via a random distribution method

A novel frequency selective surface （FSS） for reducing radar cross section （RCS） is proposed in this paper. This FSS is based on the random distribution method, so it can be called random surface. In this paper, the stacked patches serving as periodic elements are employed for RCS reduction. Previous work has demonstrated the efficiency by utilizing the microstrip patches, especially for the reflectarray. First, the relevant theory of the method is described. Then a sample of a three-layer variable-sized stacked patch random surface with a dimension of 260 mm x 260 mm is simulated, fabricated, and measured in order to demonstrate the validity of the proposed design. For the normal incidence, the 8-dB RCS reduction can be achieved both by the simulation and the measurement in 8 GHz-13 GHz. The oblique incidence of 30° is also investigated, in which the 7-dB RCS reduction can be obtained in a frequency range of 8 GHz-14 GHz.

Bounds on partial derivatives of NURBS surfaces

In this paper, we estimate the partial derivative bounds for Non-Uniform Rational B-spline(NURBS) surfaces. Firstly, based on the formula of translating the product into sum of B-spline functions, discrete B-spline theory and Dir function, some derivative bounds on NURBS curves are provided. Then, the derivative bounds on the magnitudes of NURBS surfaces are proposed by regarding a rational surface as the locus of a rational curve. Finally, some numerical examples are provided to elucidate how tight the bounds are.

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.